Vendor dependencies for 0.3.0 release

vendor/libm/CHANGELOG.md

@@ -0,0 +1,229 @@
+# Changelog
+
+All notable changes to this project will be documented in this file.
+
+The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
+and this project adheres to
+[Semantic Versioning](https://semver.org/spec/v2.0.0.html).
+
+## [Unreleased]
+
+## [0.2.15](https://github.com/rust-lang/compiler-builtins/compare/libm-v0.2.14...libm-v0.2.15) - 2025-05-06
+
+### Other
+
+- Require `target_has_atomic = "ptr"` for runtime feature detection
+
+## [0.2.14](https://github.com/rust-lang/compiler-builtins/compare/libm-v0.2.13...libm-v0.2.14) - 2025-05-03
+
+### Other
+
+- Use runtime feature detection for fma routines on x86
+
+## [0.2.13](https://github.com/rust-lang/compiler-builtins/compare/libm-v0.2.12...libm-v0.2.13) - 2025-04-21
+
+### Fixed
+
+- Switch back to workspace resolver v2 to unbreak builds without the 2024 edition
+
+## [0.2.12](https://github.com/rust-lang/compiler-builtins/compare/libm-v0.2.11...libm-v0.2.12) - 2025-04-21
+
+- Mark generic functions `#[inline]`
+- Combine the source files for `fmod`
+- Ensure all public functions are marked `no_panic`
+- Add assembly version of simple operations on aarch64
+- Add `roundeven{,f,f16,f128}`
+- Add `fminimum`, `fmaximum`, `fminimum_num`, and `fmaximum_num`
+- Eliminate the use of `force_eval!` in `ceil`, `floor`, and `trunc`
+- Port the CORE-MATH version of `cbrt`
+- Add `fmaf128`
+- fma: Ensure zero has the correct sign
+- Add `scalbnf16`, `scalbnf128`, `ldexpf16`, and `ldexpf128`
+- Specify license as just MIT
+- Add `fmodf128`
+- Add `fmodf16` using the generic implementation
+- Add `fminf16`, `fmaxf16`, `fminf128`, and `fmaxf128`
+- Add `roundf16` and `roundf128`
+- Add `rintf16` and `rintf128`
+- Add `floorf16` and `floorf128`
+- Add `ceilf16` and `ceilf128`
+- Add `sqrtf16` and `sqrtf128`
+- Simplify and optimize `fdim` ([#442](https://github.com/rust-lang/libm/pull/442))
+- Add `fdimf16` and `fdimf128`
+- Add `truncf16` and `truncf128`
+- Add `fabsf16`, `fabsf128`, `copysignf16`, and `copysignf128`
+- Move some numeric trait logic to default implementations
+- Add some more basic docstrings ([#352](https://github.com/rust-lang/libm/pull/352))
+- Add support for loongarch64-unknown-linux-gnu
+- Add an "arch" Cargo feature that is on by default
+- Rename the `special_case` module to `precision` and move default ULP
+- Move the existing "unstable" feature to "unstable-intrinsics"
+
+There are a number of things that changed internally, see the git log for a full
+list of changes.
+
+## [0.2.11](https://github.com/rust-lang/libm/compare/libm-v0.2.10...libm-v0.2.11) - 2024-10-28
+
+### Fixed
+
+- fix type of constants in ported sincosf ([#331](https://github.com/rust-lang/libm/pull/331))
+
+### Other
+
+- Disable a unit test that is failing on i586
+- Add a procedural macro for expanding all function signatures
+- Introduce `musl-math-sys` for bindings to musl math symbols
+- Add basic docstrings to some functions ([#337](https://github.com/rust-lang/libm/pull/337))
+
+## [0.2.10](https://github.com/rust-lang/libm/compare/libm-v0.2.9...libm-v0.2.10) - 2024-10-28
+
+### Other
+
+- Set the MSRV to 1.63 and test this in CI
+
+## [0.2.9](https://github.com/rust-lang/libm/compare/libm-v0.2.8...libm-v0.2.9) - 2024-10-26
+
+### Fixed
+
+- Update exponent calculations in nextafter to match musl
+
+### Changed
+
+- Update licensing to MIT AND (MIT OR Apache-2.0), as this is derivative from
+  MIT-licensed musl.
+- Set edition to 2021 for all crates
+- Upgrade all dependencies
+
+### Other
+
+- Don't deny warnings in lib.rs
+- Rename the `musl-bitwise-tests` feature to `test-musl-serialized`
+- Rename the `musl-reference-tests` feature to `musl-bitwise-tests`
+- Move `musl-reference-tests` to a new `libm-test` crate
+- Add a `force-soft-floats` feature to prevent using any intrinsics or
+  arch-specific code
+- Deny warnings in CI
+- Fix `clippy::deprecated_cfg_attr` on compiler_builtins
+- Corrected English typos
+- Remove unneeded `extern core` in `tgamma`
+- Allow internal_features lint when building with "unstable"
+
+## [v0.2.1] - 2019-11-22
+
+### Fixed
+
+- sincosf
+
+## [v0.2.0] - 2019-10-18
+
+### Added
+
+- Benchmarks
+- signum
+- remainder
+- remainderf
+- nextafter
+- nextafterf
+
+### Fixed
+
+- Rounding to negative zero
+- Overflows in rem_pio2 and remquo
+- Overflows in fma
+- sincosf
+
+### Removed
+
+- F32Ext and F64Ext traits
+
+## [v0.1.4] - 2019-06-12
+
+### Fixed
+
+- Restored compatibility with Rust 1.31.0
+
+## [v0.1.3] - 2019-05-14
+
+### Added
+
+- minf
+- fmin
+- fmaxf
+- fmax
+
+## [v0.1.2] - 2018-07-18
+
+### Added
+
+- acosf
+- asin
+- asinf
+- atan
+- atan2
+- atan2f
+- atanf
+- cos
+- cosf
+- cosh
+- coshf
+- exp2
+- expm1
+- expm1f
+- expo2
+- fmaf
+- pow
+- sin
+- sinf
+- sinh
+- sinhf
+- tan
+- tanf
+- tanh
+- tanhf
+
+## [v0.1.1] - 2018-07-14
+
+### Added
+
+- acos
+- acosf
+- asin
+- asinf
+- atanf
+- cbrt
+- cbrtf
+- ceil
+- ceilf
+- cosf
+- exp
+- exp2
+- exp2f
+- expm1
+- expm1f
+- fdim
+- fdimf
+- floorf
+- fma
+- fmod
+- log
+- log2
+- log10
+- log10f
+- log1p
+- log1pf
+- log2f
+- roundf
+- sinf
+- tanf
+
+## v0.1.0 - 2018-07-13
+
+- Initial release
+
+[Unreleased]: https://github.com/japaric/libm/compare/v0.2.1...HEAD
+[v0.2.1]: https://github.com/japaric/libm/compare/0.2.0...v0.2.1
+[v0.2.0]: https://github.com/japaric/libm/compare/0.1.4...v0.2.0
+[v0.1.4]: https://github.com/japaric/libm/compare/0.1.3...v0.1.4
+[v0.1.3]: https://github.com/japaric/libm/compare/v0.1.2...0.1.3
+[v0.1.2]: https://github.com/japaric/libm/compare/v0.1.1...v0.1.2
+[v0.1.1]: https://github.com/japaric/libm/compare/v0.1.0...v0.1.1

vendor/libm/Cargo.lock

@@ -0,0 +1,56 @@
+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+version = 3
+
+[[package]]
+name = "libm"
+version = "0.2.15"
+dependencies = [
+ "no-panic",
+]
+
+[[package]]
+name = "no-panic"
+version = "0.1.35"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "113d1abd5bb3dc25a75d9b3a973f40e31eb03e0bae23c172b32cca4bcb9cfad2"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "proc-macro2"
+version = "1.0.95"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "02b3e5e68a3a1a02aad3ec490a98007cbc13c37cbe84a3cd7b8e406d76e7f778"
+dependencies = [
+ "unicode-ident",
+]
+
+[[package]]
+name = "quote"
+version = "1.0.40"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1885c039570dc00dcb4ff087a89e185fd56bae234ddc7f056a945bf36467248d"
+dependencies = [
+ "proc-macro2",
+]
+
+[[package]]
+name = "syn"
+version = "2.0.101"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "8ce2b7fc941b3a24138a0a7cf8e858bfc6a992e7978a068a5c760deb0ed43caf"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "unicode-ident",
+]
+
+[[package]]
+name = "unicode-ident"
+version = "1.0.18"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5a5f39404a5da50712a4c1eecf25e90dd62b613502b7e925fd4e4d19b5c96512"

vendor/libm/Cargo.toml

@@ -0,0 +1,57 @@
+# THIS FILE IS AUTOMATICALLY GENERATED BY CARGO
+#
+# When uploading crates to the registry Cargo will automatically
+# "normalize" Cargo.toml files for maximal compatibility
+# with all versions of Cargo and also rewrite `path` dependencies
+# to registry (e.g., crates.io) dependencies.
+#
+# If you are reading this file be aware that the original Cargo.toml
+# will likely look very different (and much more reasonable).
+# See Cargo.toml.orig for the original contents.
+
+[package]
+edition = "2021"
+rust-version = "1.63"
+name = "libm"
+version = "0.2.15"
+authors = ["Jorge Aparicio <jorge@japaric.io>"]
+build = "build.rs"
+autolib = false
+autobins = false
+autoexamples = false
+autotests = false
+autobenches = false
+description = "libm in pure Rust"
+documentation = "https://docs.rs/libm"
+readme = "README.md"
+keywords = [
+    "libm",
+    "math",
+]
+categories = ["no-std"]
+license = "MIT"
+repository = "https://github.com/rust-lang/compiler-builtins"
+
+[features]
+arch = []
+default = ["arch"]
+force-soft-floats = []
+unstable = [
+    "unstable-intrinsics",
+    "unstable-float",
+]
+unstable-float = []
+unstable-intrinsics = []
+unstable-public-internals = []
+
+[lib]
+name = "libm"
+path = "src/lib.rs"
+
+[dev-dependencies.no-panic]
+version = "0.1.35"
+
+[lints.rust.unexpected_cfgs]
+level = "warn"
+priority = 0
+check-cfg = ['cfg(feature, values("compiler-builtins"))']

vendor/libm/LICENSE.txt

@@ -0,0 +1,258 @@
+rust-lang/libm as a whole is available for use under the MIT license:
+
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+
+This Rust library contains the following copyrights:
+
+    Copyright (c) 2018 Jorge Aparicio
+
+Portions of this software are derived from third-party works licensed under
+terms compatible with the above MIT license:
+
+* musl libc https://www.musl-libc.org/. This library contains the following
+  copyright:
+
+      Copyright © 2005-2020 Rich Felker, et al.
+
+* The CORE-MATH project https://core-math.gitlabpages.inria.fr/. CORE-MATH
+  routines are available under the MIT license on a per-file basis.
+
+The musl libc COPYRIGHT file also includes the following notice relevant to
+math portions of the library:
+
+------------------------------------------------------------------------------
+Much of the math library code (src/math/* and src/complex/*) is
+Copyright © 1993,2004 Sun Microsystems or
+Copyright © 2003-2011 David Schultz or
+Copyright © 2003-2009 Steven G. Kargl or
+Copyright © 2003-2009 Bruce D. Evans or
+Copyright © 2008 Stephen L. Moshier or
+Copyright © 2017-2018 Arm Limited
+and labelled as such in comments in the individual source files. All
+have been licensed under extremely permissive terms.
+------------------------------------------------------------------------------
+
+Copyright notices are retained in src/* files where relevant.

vendor/libm/README.md

@@ -0,0 +1,42 @@
+# `libm`
+
+A Rust implementations of the C math library.
+
+## Usage
+
+`libm` provides fallback implementations for Rust's [float math functions] in
+`core`, and the [`core_float_math`] feature. If what is available suits your
+needs, there is no need to add `libm` as a dependency.
+
+If more functionality is needed, this crate can also be used directly:
+
+```toml
+[dependencies]
+libm = "0.2.11"
+```
+
+[float math functions]: https://doc.rust-lang.org/std/primitive.f32.html
+[`core_float_math`]: https://github.com/rust-lang/rust/issues/137578
+
+## Contributing
+
+Please check [CONTRIBUTING.md](../CONTRIBUTING.md)
+
+## Minimum Rust version policy
+
+This crate supports rustc 1.63 and newer.
+
+## License
+
+Usage is under the MIT license, available at
+<https://opensource.org/license/mit>.
+
+### Contribution
+
+Contributions are licensed under both the MIT license and the Apache License,
+Version 2.0, available at <htps://www.apache.org/licenses/LICENSE-2.0>. Unless
+you explicitly state otherwise, any contribution intentionally submitted for
+inclusion in the work by you, as defined in the Apache-2.0 license, shall be
+dual licensed as mentioned, without any additional terms or conditions.
+
+See [LICENSE.txt](LICENSE.txt) for full details.

vendor/libm/build.rs

@@ -0,0 +1,18 @@
+use std::env;
+
+mod configure;
+
+fn main() {
+    let cfg = configure::Config::from_env();
+
+    println!("cargo:rerun-if-changed=build.rs");
+    println!("cargo:rerun-if-changed=configure.rs");
+    println!("cargo:rustc-check-cfg=cfg(assert_no_panic)");
+
+    // If set, enable `no-panic`. Requires LTO (`release-opt` profile).
+    if env::var("ENSURE_NO_PANIC").is_ok() {
+        println!("cargo:rustc-cfg=assert_no_panic");
+    }
+
+    configure::emit_libm_config(&cfg);
+}

vendor/libm/configure.rs

@@ -0,0 +1,189 @@
+// Configuration shared with both libm and libm-test
+
+use std::env;
+use std::path::PathBuf;
+
+#[allow(dead_code)]
+pub struct Config {
+    pub manifest_dir: PathBuf,
+    pub out_dir: PathBuf,
+    pub opt_level: String,
+    pub cargo_features: Vec<String>,
+    pub target_arch: String,
+    pub target_env: String,
+    pub target_family: Option<String>,
+    pub target_os: String,
+    pub target_string: String,
+    pub target_vendor: String,
+    pub target_features: Vec<String>,
+}
+
+impl Config {
+    pub fn from_env() -> Self {
+        let target_features = env::var("CARGO_CFG_TARGET_FEATURE")
+            .map(|feats| feats.split(',').map(ToOwned::to_owned).collect())
+            .unwrap_or_default();
+        let cargo_features = env::vars()
+            .filter_map(|(name, _value)| name.strip_prefix("CARGO_FEATURE_").map(ToOwned::to_owned))
+            .map(|s| s.to_lowercase().replace("_", "-"))
+            .collect();
+
+        Self {
+            manifest_dir: PathBuf::from(env::var("CARGO_MANIFEST_DIR").unwrap()),
+            out_dir: PathBuf::from(env::var("OUT_DIR").unwrap()),
+            opt_level: env::var("OPT_LEVEL").unwrap(),
+            cargo_features,
+            target_arch: env::var("CARGO_CFG_TARGET_ARCH").unwrap(),
+            target_env: env::var("CARGO_CFG_TARGET_ENV").unwrap(),
+            target_family: env::var("CARGO_CFG_TARGET_FAMILY").ok(),
+            target_os: env::var("CARGO_CFG_TARGET_OS").unwrap(),
+            target_string: env::var("TARGET").unwrap(),
+            target_vendor: env::var("CARGO_CFG_TARGET_VENDOR").unwrap(),
+            target_features,
+        }
+    }
+}
+
+/// Libm gets most config options made available.
+#[allow(dead_code)]
+pub fn emit_libm_config(cfg: &Config) {
+    emit_intrinsics_cfg();
+    emit_arch_cfg();
+    emit_optimization_cfg(cfg);
+    emit_cfg_shorthands(cfg);
+    emit_cfg_env(cfg);
+    emit_f16_f128_cfg(cfg);
+}
+
+/// Tests don't need most feature-related config.
+#[allow(dead_code)]
+pub fn emit_test_config(cfg: &Config) {
+    emit_optimization_cfg(cfg);
+    emit_cfg_shorthands(cfg);
+    emit_cfg_env(cfg);
+    emit_f16_f128_cfg(cfg);
+}
+
+/// Simplify the feature logic for enabling intrinsics so code only needs to use
+/// `cfg(intrinsics_enabled)`.
+fn emit_intrinsics_cfg() {
+    println!("cargo:rustc-check-cfg=cfg(intrinsics_enabled)");
+
+    // Disabled by default; `unstable-intrinsics` enables again; `force-soft-floats` overrides
+    // to disable.
+    if cfg!(feature = "unstable-intrinsics") && !cfg!(feature = "force-soft-floats") {
+        println!("cargo:rustc-cfg=intrinsics_enabled");
+    }
+}
+
+/// Simplify the feature logic for enabling arch-specific features so code only needs to use
+/// `cfg(arch_enabled)`.
+fn emit_arch_cfg() {
+    println!("cargo:rustc-check-cfg=cfg(arch_enabled)");
+
+    // Enabled by default via the "arch" feature, `force-soft-floats` overrides to disable.
+    if cfg!(feature = "arch") && !cfg!(feature = "force-soft-floats") {
+        println!("cargo:rustc-cfg=arch_enabled");
+    }
+}
+
+/// Some tests are extremely slow. Emit a config option based on optimization level.
+fn emit_optimization_cfg(cfg: &Config) {
+    println!("cargo:rustc-check-cfg=cfg(optimizations_enabled)");
+
+    if !matches!(cfg.opt_level.as_str(), "0" | "1") {
+        println!("cargo:rustc-cfg=optimizations_enabled");
+    }
+}
+
+/// Provide an alias for common longer config combinations.
+fn emit_cfg_shorthands(cfg: &Config) {
+    println!("cargo:rustc-check-cfg=cfg(x86_no_sse)");
+    if cfg.target_arch == "x86" && !cfg.target_features.iter().any(|f| f == "sse") {
+        // Shorthand to detect i586 targets
+        println!("cargo:rustc-cfg=x86_no_sse");
+    }
+}
+
+/// Reemit config that we make use of for test logging.
+fn emit_cfg_env(cfg: &Config) {
+    println!(
+        "cargo:rustc-env=CFG_CARGO_FEATURES={:?}",
+        cfg.cargo_features
+    );
+    println!("cargo:rustc-env=CFG_OPT_LEVEL={}", cfg.opt_level);
+    println!(
+        "cargo:rustc-env=CFG_TARGET_FEATURES={:?}",
+        cfg.target_features
+    );
+}
+
+/// Configure whether or not `f16` and `f128` support should be enabled.
+fn emit_f16_f128_cfg(cfg: &Config) {
+    println!("cargo:rustc-check-cfg=cfg(f16_enabled)");
+    println!("cargo:rustc-check-cfg=cfg(f128_enabled)");
+
+    // `unstable-float` enables these features.
+    if !cfg!(feature = "unstable-float") {
+        return;
+    }
+
+    // Set whether or not `f16` and `f128` are supported at a basic level by LLVM. This only means
+    // that the backend will not crash when using these types and generates code that can be called
+    // without crashing (no infinite recursion). This does not mean that the platform doesn't have
+    // ABI or other bugs.
+    //
+    // We do this here rather than in `rust-lang/rust` because configuring via cargo features is
+    // not straightforward.
+    //
+    // Original source of this list:
+    // <https://github.com/rust-lang/compiler-builtins/pull/652#issuecomment-2266151350>
+    let f16_enabled = match cfg.target_arch.as_str() {
+        // Unsupported <https://github.com/llvm/llvm-project/issues/94434>
+        "arm64ec" => false,
+        // Selection failure <https://github.com/llvm/llvm-project/issues/50374>
+        "s390x" => false,
+        // Infinite recursion <https://github.com/llvm/llvm-project/issues/97981>
+        // FIXME(llvm): loongarch fixed by <https://github.com/llvm/llvm-project/pull/107791>
+        "csky" => false,
+        "hexagon" => false,
+        "loongarch64" => false,
+        "mips" | "mips64" | "mips32r6" | "mips64r6" => false,
+        "powerpc" | "powerpc64" => false,
+        "sparc" | "sparc64" => false,
+        "wasm32" | "wasm64" => false,
+        // Most everything else works as of LLVM 19
+        _ => true,
+    };
+
+    let f128_enabled = match cfg.target_arch.as_str() {
+        // Unsupported (libcall is not supported) <https://github.com/llvm/llvm-project/issues/121122>
+        "amdgpu" => false,
+        // Unsupported <https://github.com/llvm/llvm-project/issues/94434>
+        "arm64ec" => false,
+        // Selection failure <https://github.com/llvm/llvm-project/issues/96432>
+        "mips64" | "mips64r6" => false,
+        // Selection failure <https://github.com/llvm/llvm-project/issues/95471>
+        "nvptx64" => false,
+        // Selection failure <https://github.com/llvm/llvm-project/issues/101545>
+        "powerpc64" if &cfg.target_os == "aix" => false,
+        // Selection failure <https://github.com/llvm/llvm-project/issues/41838>
+        "sparc" => false,
+        // Most everything else works as of LLVM 19
+        _ => true,
+    };
+
+    // If the feature is set, disable these types.
+    let disable_both = env::var_os("CARGO_FEATURE_NO_F16_F128").is_some();
+
+    println!("cargo:rustc-check-cfg=cfg(f16_enabled)");
+    println!("cargo:rustc-check-cfg=cfg(f128_enabled)");
+
+    if f16_enabled && !disable_both {
+        println!("cargo:rustc-cfg=f16_enabled");
+    }
+
+    if f128_enabled && !disable_both {
+        println!("cargo:rustc-cfg=f128_enabled");
+    }
+}

vendor/libm/src/lib.rs

@@ -0,0 +1,33 @@
+//! libm in pure Rust
+#![no_std]
+#![cfg_attr(intrinsics_enabled, allow(internal_features))]
+#![cfg_attr(intrinsics_enabled, feature(core_intrinsics))]
+#![cfg_attr(
+    all(intrinsics_enabled, target_family = "wasm"),
+    feature(wasm_numeric_instr)
+)]
+#![cfg_attr(f128_enabled, feature(f128))]
+#![cfg_attr(f16_enabled, feature(f16))]
+#![allow(clippy::assign_op_pattern)]
+#![allow(clippy::deprecated_cfg_attr)]
+#![allow(clippy::eq_op)]
+#![allow(clippy::excessive_precision)]
+#![allow(clippy::float_cmp)]
+#![allow(clippy::int_plus_one)]
+#![allow(clippy::just_underscores_and_digits)]
+#![allow(clippy::many_single_char_names)]
+#![allow(clippy::mixed_case_hex_literals)]
+#![allow(clippy::needless_late_init)]
+#![allow(clippy::needless_return)]
+#![allow(clippy::unreadable_literal)]
+#![allow(clippy::zero_divided_by_zero)]
+#![forbid(unsafe_op_in_unsafe_fn)]
+
+mod libm_helper;
+mod math;
+
+use core::{f32, f64};
+
+pub use libm_helper::*;
+
+pub use self::math::*;

vendor/libm/src/libm_helper.rs

@@ -0,0 +1,244 @@
+use core::marker::PhantomData;
+
+use crate::*;
+
+/// Generic helper for libm functions, abstracting over f32 and f64. <br/>
+/// # Type Parameter:
+/// - `T`: Either `f32` or `f64`
+///
+/// # Examples
+/// ```rust
+/// use libm::{self, Libm};
+///
+/// const PI_F32: f32 = 3.1415927410e+00;
+/// const PI_F64: f64 = 3.1415926535897931160e+00;
+///
+/// assert!(Libm::<f32>::cos(0.0f32) == libm::cosf(0.0));
+/// assert!(Libm::<f32>::sin(PI_F32) == libm::sinf(PI_F32));
+///
+/// assert!(Libm::<f64>::cos(0.0f64) == libm::cos(0.0));
+/// assert!(Libm::<f64>::sin(PI_F64) == libm::sin(PI_F64));
+/// ```
+pub struct Libm<T>(PhantomData<T>);
+
+macro_rules! libm_helper {
+    ($t:ident, funcs: $funcs:tt) => {
+        impl Libm<$t> {
+            #![allow(unused_parens)]
+
+            libm_helper! { $funcs }
+        }
+    };
+
+    ({$($func:tt;)*}) => {
+        $(
+            libm_helper! { $func }
+        )*
+    };
+
+    ((fn $func:ident($($arg:ident: $arg_typ:ty),*) -> ($($ret_typ:ty),*); => $libm_fn:ident)) => {
+        #[inline(always)]
+        pub fn $func($($arg: $arg_typ),*) -> ($($ret_typ),*) {
+            $libm_fn($($arg),*)
+        }
+    };
+}
+
+// verify-apilist-start
+libm_helper! {
+    f32,
+    funcs: {
+        // verify-sorted-start
+        (fn acos(x: f32) -> (f32);                  => acosf);
+        (fn acosh(x: f32) -> (f32);                 => acoshf);
+        (fn asin(x: f32) -> (f32);                  => asinf);
+        (fn asinh(x: f32) -> (f32);                 => asinhf);
+        (fn atan(x: f32) -> (f32);                  => atanf);
+        (fn atan2(y: f32, x: f32) -> (f32);         => atan2f);
+        (fn atanh(x: f32) -> (f32);                 => atanhf);
+        (fn cbrt(x: f32) -> (f32);                  => cbrtf);
+        (fn ceil(x: f32) -> (f32);                  => ceilf);
+        (fn copysign(x: f32, y: f32) -> (f32);      => copysignf);
+        (fn cos(x: f32) -> (f32);                   => cosf);
+        (fn cosh(x: f32) -> (f32);                  => coshf);
+        (fn erf(x: f32) -> (f32);                   => erff);
+        (fn erfc(x: f32) -> (f32);                  => erfcf);
+        (fn exp(x: f32) -> (f32);                   => expf);
+        (fn exp10(x: f32) -> (f32);                 => exp10f);
+        (fn exp2(x: f32) -> (f32);                  => exp2f);
+        (fn expm1(x: f32) -> (f32);                 => expm1f);
+        (fn fabs(x: f32) -> (f32);                  => fabsf);
+        (fn fdim(x: f32, y: f32) -> (f32);          => fdimf);
+        (fn floor(x: f32) -> (f32);                 => floorf);
+        (fn fma(x: f32, y: f32, z: f32) -> (f32);   => fmaf);
+        (fn fmax(x: f32, y: f32) -> (f32);          => fmaxf);
+        (fn fmin(x: f32, y: f32) -> (f32);          => fminf);
+        (fn fmod(x: f32, y: f32) -> (f32);          => fmodf);
+        (fn frexp(x: f32) -> (f32, i32);            => frexpf);
+        (fn hypot(x: f32, y: f32) -> (f32);         => hypotf);
+        (fn ilogb(x: f32) -> (i32);                 => ilogbf);
+        (fn j0(x: f32) -> (f32);                    => j0f);
+        (fn j1(x: f32) -> (f32);                    => j1f);
+        (fn jn(n: i32, x: f32) -> (f32);            => jnf);
+        (fn ldexp(x: f32, n: i32) -> (f32);         => ldexpf);
+        (fn lgamma(x: f32) -> (f32);                => lgammaf);
+        (fn lgamma_r(x: f32) -> (f32, i32);         => lgammaf_r);
+        (fn log(x: f32) -> (f32);                   => logf);
+        (fn log10(x: f32) -> (f32);                 => log10f);
+        (fn log1p(x: f32) -> (f32);                 => log1pf);
+        (fn log2(x: f32) -> (f32);                  => log2f);
+        (fn modf(x: f32) -> (f32, f32);             => modff);
+        (fn nextafter(x: f32, y: f32) -> (f32);     => nextafterf);
+        (fn pow(x: f32, y: f32) -> (f32);           => powf);
+        (fn remainder(x: f32, y: f32) -> (f32);     => remainderf);
+        (fn remquo(x: f32, y: f32) -> (f32, i32);   => remquof);
+        (fn rint(x: f32) -> (f32);                  => rintf);
+        (fn round(x: f32) -> (f32);                 => roundf);
+        (fn roundeven(x: f32) -> (f32);             => roundevenf);
+        (fn scalbn(x: f32, n: i32) -> (f32);        => scalbnf);
+        (fn sin(x: f32) -> (f32);                   => sinf);
+        (fn sincos(x: f32) -> (f32, f32);           => sincosf);
+        (fn sinh(x: f32) -> (f32);                  => sinhf);
+        (fn sqrt(x: f32) -> (f32);                  => sqrtf);
+        (fn tan(x: f32) -> (f32);                   => tanf);
+        (fn tanh(x: f32) -> (f32);                  => tanhf);
+        (fn tgamma(x: f32) -> (f32);                => tgammaf);
+        (fn trunc(x: f32) -> (f32);                 => truncf);
+        (fn y0(x: f32) -> (f32);                    => y0f);
+        (fn y1(x: f32) -> (f32);                    => y1f);
+        (fn yn(n: i32, x: f32) -> (f32);            => ynf);
+        // verify-sorted-end
+    }
+}
+
+libm_helper! {
+    f64,
+    funcs: {
+        // verify-sorted-start
+        (fn acos(x: f64) -> (f64);                  => acos);
+        (fn acosh(x: f64) -> (f64);                 => acosh);
+        (fn asin(x: f64) -> (f64);                  => asin);
+        (fn asinh(x: f64) -> (f64);                 => asinh);
+        (fn atan(x: f64) -> (f64);                  => atan);
+        (fn atan2(y: f64, x: f64) -> (f64);         => atan2);
+        (fn atanh(x: f64) -> (f64);                 => atanh);
+        (fn cbrt(x: f64) -> (f64);                  => cbrt);
+        (fn ceil(x: f64) -> (f64);                  => ceil);
+        (fn copysign(x: f64, y: f64) -> (f64);      => copysign);
+        (fn cos(x: f64) -> (f64);                   => cos);
+        (fn cosh(x: f64) -> (f64);                  => cosh);
+        (fn erf(x: f64) -> (f64);                   => erf);
+        (fn erfc(x: f64) -> (f64);                  => erfc);
+        (fn exp(x: f64) -> (f64);                   => exp);
+        (fn exp10(x: f64) -> (f64);                 => exp10);
+        (fn exp2(x: f64) -> (f64);                  => exp2);
+        (fn expm1(x: f64) -> (f64);                 => expm1);
+        (fn fabs(x: f64) -> (f64);                  => fabs);
+        (fn fdim(x: f64, y: f64) -> (f64);          => fdim);
+        (fn floor(x: f64) -> (f64);                 => floor);
+        (fn fma(x: f64, y: f64, z: f64) -> (f64);   => fma);
+        (fn fmax(x: f64, y: f64) -> (f64);          => fmax);
+        (fn fmaximum(x: f64, y: f64) -> (f64);      => fmaximum);
+        (fn fmaximum_num(x: f64, y: f64) -> (f64);  => fmaximum_num);
+        (fn fmaximum_numf(x: f32, y: f32) -> (f32); => fmaximum_numf);
+        (fn fmaximumf(x: f32, y: f32) -> (f32);     => fmaximumf);
+        (fn fmin(x: f64, y: f64) -> (f64);          => fmin);
+        (fn fminimum(x: f64, y: f64) -> (f64);      => fminimum);
+        (fn fminimum_num(x: f64, y: f64) -> (f64);  => fminimum_num);
+        (fn fminimum_numf(x: f32, y: f32) -> (f32); => fminimum_numf);
+        (fn fminimumf(x: f32, y: f32) -> (f32);     => fminimumf);
+        (fn fmod(x: f64, y: f64) -> (f64);          => fmod);
+        (fn frexp(x: f64) -> (f64, i32);            => frexp);
+        (fn hypot(x: f64, y: f64) -> (f64);         => hypot);
+        (fn ilogb(x: f64) -> (i32);                 => ilogb);
+        (fn j0(x: f64) -> (f64);                    => j0);
+        (fn j1(x: f64) -> (f64);                    => j1);
+        (fn jn(n: i32, x: f64) -> (f64);            => jn);
+        (fn ldexp(x: f64, n: i32) -> (f64);         => ldexp);
+        (fn lgamma(x: f64) -> (f64);                => lgamma);
+        (fn lgamma_r(x: f64) -> (f64, i32);         => lgamma_r);
+        (fn log(x: f64) -> (f64);                   => log);
+        (fn log10(x: f64) -> (f64);                 => log10);
+        (fn log1p(x: f64) -> (f64);                 => log1p);
+        (fn log2(x: f64) -> (f64);                  => log2);
+        (fn modf(x: f64) -> (f64, f64);             => modf);
+        (fn nextafter(x: f64, y: f64) -> (f64);     => nextafter);
+        (fn pow(x: f64, y: f64) -> (f64);           => pow);
+        (fn remainder(x: f64, y: f64) -> (f64);     => remainder);
+        (fn remquo(x: f64, y: f64) -> (f64, i32);   => remquo);
+        (fn rint(x: f64) -> (f64);                  => rint);
+        (fn round(x: f64) -> (f64);                 => round);
+        (fn roundevem(x: f64) -> (f64);             => roundeven);
+        (fn scalbn(x: f64, n: i32) -> (f64);        => scalbn);
+        (fn sin(x: f64) -> (f64);                   => sin);
+        (fn sincos(x: f64) -> (f64, f64);           => sincos);
+        (fn sinh(x: f64) -> (f64);                  => sinh);
+        (fn sqrt(x: f64) -> (f64);                  => sqrt);
+        (fn tan(x: f64) -> (f64);                   => tan);
+        (fn tanh(x: f64) -> (f64);                  => tanh);
+        (fn tgamma(x: f64) -> (f64);                => tgamma);
+        (fn trunc(x: f64) -> (f64);                 => trunc);
+        (fn y0(x: f64) -> (f64);                    => y0);
+        (fn y1(x: f64) -> (f64);                    => y1);
+        (fn yn(n: i32, x: f64) -> (f64);            => yn);
+        // verify-sorted-end
+    }
+}
+
+#[cfg(f16_enabled)]
+libm_helper! {
+    f16,
+    funcs: {
+        // verify-sorted-start
+        (fn ceil(x: f16) -> (f16);                  => ceilf16);
+        (fn copysign(x: f16, y: f16) -> (f16);      => copysignf16);
+        (fn fabs(x: f16) -> (f16);                  => fabsf16);
+        (fn fdim(x: f16, y: f16) -> (f16);          => fdimf16);
+        (fn floor(x: f16) -> (f16);                 => floorf16);
+        (fn fmax(x: f16, y: f16) -> (f16);          => fmaxf16);
+        (fn fmaximum_num(x: f16, y: f16) -> (f16);  => fmaximum_numf16);
+        (fn fmaximumf16(x: f16, y: f16) -> (f16);   => fmaximumf16);
+        (fn fmin(x: f16, y: f16) -> (f16);          => fminf16);
+        (fn fminimum(x: f16, y: f16) -> (f16);      => fminimumf16);
+        (fn fminimum_num(x: f16, y: f16) -> (f16);  => fminimum_numf16);
+        (fn fmod(x: f16, y: f16) -> (f16);          => fmodf16);
+        (fn ldexp(x: f16, n: i32) -> (f16);         => ldexpf16);
+        (fn rint(x: f16) -> (f16);                  => rintf16);
+        (fn round(x: f16) -> (f16);                 => roundf16);
+        (fn roundeven(x: f16) -> (f16);             => roundevenf16);
+        (fn scalbn(x: f16, n: i32) -> (f16);        => scalbnf16);
+        (fn sqrtf(x: f16) -> (f16);                 => sqrtf16);
+        (fn truncf(x: f16) -> (f16);                => truncf16);
+        // verify-sorted-end
+    }
+}
+
+#[cfg(f128_enabled)]
+libm_helper! {
+    f128,
+    funcs: {
+        // verify-sorted-start
+        (fn ceil(x: f128) -> (f128);                => ceilf128);
+        (fn copysign(x: f128, y: f128) -> (f128);   => copysignf128);
+        (fn fabs(x: f128) -> (f128);                => fabsf128);
+        (fn fdim(x: f128, y: f128) -> (f128);       => fdimf128);
+        (fn floor(x: f128) -> (f128);               => floorf128);
+        (fn fma(x: f128, y: f128, z: f128) -> (f128); => fmaf128);
+        (fn fmax(x: f128, y: f128) -> (f128);       => fmaxf128);
+        (fn fmaximum(x: f128, y: f128) -> (f128);      => fmaximumf128);
+        (fn fmaximum_num(x: f128, y: f128) -> (f128);  => fmaximum_numf128);
+        (fn fmin(x: f128, y: f128) -> (f128);       => fminf128);
+        (fn fminimum(x: f128, y: f128) -> (f128);      => fminimumf128);
+        (fn fminimum_num(x: f128, y: f128) -> (f128);  => fminimum_numf128);
+        (fn fmod(x: f128, y: f128) -> (f128);       => fmodf128);
+        (fn ldexp(x: f128, n: i32) -> (f128);       => ldexpf128);
+        (fn rint(x: f128) -> (f128);                => rintf128);
+        (fn round(x: f128) -> (f128);               => roundf128);
+        (fn roundeven(x: f128) -> (f128);           => roundevenf128);
+        (fn scalbn(x: f128, n: i32) -> (f128);      => scalbnf128);
+        (fn sqrt(x: f128) -> (f128);                => sqrtf128);
+        (fn trunc(x: f128) -> (f128);               => truncf128);
+        // verify-sorted-end
+    }
+}
+// verify-apilist-end

vendor/libm/src/math/acos.rs

@@ -0,0 +1,112 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* acos(x)
+ * Method :
+ *      acos(x)  = pi/2 - asin(x)
+ *      acos(-x) = pi/2 + asin(x)
+ * For |x|<=0.5
+ *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
+ * For x>0.5
+ *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
+ *              = 2asin(sqrt((1-x)/2))
+ *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
+ *              = 2f + (2c + 2s*z*R(z))
+ *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
+ *     for f so that f+c ~ sqrt(z).
+ * For x<-0.5
+ *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
+ *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
+ *
+ * Special cases:
+ *      if x is NaN, return x itself;
+ *      if |x|>1, return NaN with invalid signal.
+ *
+ * Function needed: sqrt
+ */
+
+use super::sqrt;
+
+const PIO2_HI: f64 = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
+const PIO2_LO: f64 = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
+const PS0: f64 = 1.66666666666666657415e-01; /* 0x3FC55555, 0x55555555 */
+const PS1: f64 = -3.25565818622400915405e-01; /* 0xBFD4D612, 0x03EB6F7D */
+const PS2: f64 = 2.01212532134862925881e-01; /* 0x3FC9C155, 0x0E884455 */
+const PS3: f64 = -4.00555345006794114027e-02; /* 0xBFA48228, 0xB5688F3B */
+const PS4: f64 = 7.91534994289814532176e-04; /* 0x3F49EFE0, 0x7501B288 */
+const PS5: f64 = 3.47933107596021167570e-05; /* 0x3F023DE1, 0x0DFDF709 */
+const QS1: f64 = -2.40339491173441421878e+00; /* 0xC0033A27, 0x1C8A2D4B */
+const QS2: f64 = 2.02094576023350569471e+00; /* 0x40002AE5, 0x9C598AC8 */
+const QS3: f64 = -6.88283971605453293030e-01; /* 0xBFE6066C, 0x1B8D0159 */
+const QS4: f64 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+fn r(z: f64) -> f64 {
+    let p: f64 = z * (PS0 + z * (PS1 + z * (PS2 + z * (PS3 + z * (PS4 + z * PS5)))));
+    let q: f64 = 1.0 + z * (QS1 + z * (QS2 + z * (QS3 + z * QS4)));
+    p / q
+}
+
+/// Arccosine (f64)
+///
+/// Computes the inverse cosine (arc cosine) of the input value.
+/// Arguments must be in the range -1 to 1.
+/// Returns values in radians, in the range of 0 to pi.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn acos(x: f64) -> f64 {
+    let x1p_120f = f64::from_bits(0x3870000000000000); // 0x1p-120 === 2 ^ -120
+    let z: f64;
+    let w: f64;
+    let s: f64;
+    let c: f64;
+    let df: f64;
+    let hx: u32;
+    let ix: u32;
+
+    hx = (x.to_bits() >> 32) as u32;
+    ix = hx & 0x7fffffff;
+    /* |x| >= 1 or nan */
+    if ix >= 0x3ff00000 {
+        let lx: u32 = x.to_bits() as u32;
+
+        if ((ix - 0x3ff00000) | lx) == 0 {
+            /* acos(1)=0, acos(-1)=pi */
+            if (hx >> 31) != 0 {
+                return 2. * PIO2_HI + x1p_120f;
+            }
+            return 0.;
+        }
+        return 0. / (x - x);
+    }
+    /* |x| < 0.5 */
+    if ix < 0x3fe00000 {
+        if ix <= 0x3c600000 {
+            /* |x| < 2**-57 */
+            return PIO2_HI + x1p_120f;
+        }
+        return PIO2_HI - (x - (PIO2_LO - x * r(x * x)));
+    }
+    /* x < -0.5 */
+    if (hx >> 31) != 0 {
+        z = (1.0 + x) * 0.5;
+        s = sqrt(z);
+        w = r(z) * s - PIO2_LO;
+        return 2. * (PIO2_HI - (s + w));
+    }
+    /* x > 0.5 */
+    z = (1.0 - x) * 0.5;
+    s = sqrt(z);
+    // Set the low 4 bytes to zero
+    df = f64::from_bits(s.to_bits() & 0xff_ff_ff_ff_00_00_00_00);
+
+    c = (z - df * df) / (s + df);
+    w = r(z) * s + c;
+    2. * (df + w)
+}

vendor/libm/src/math/acosf.rs

@@ -0,0 +1,79 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_acosf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::sqrt::sqrtf;
+
+const PIO2_HI: f32 = 1.5707962513e+00; /* 0x3fc90fda */
+const PIO2_LO: f32 = 7.5497894159e-08; /* 0x33a22168 */
+const P_S0: f32 = 1.6666586697e-01;
+const P_S1: f32 = -4.2743422091e-02;
+const P_S2: f32 = -8.6563630030e-03;
+const Q_S1: f32 = -7.0662963390e-01;
+
+fn r(z: f32) -> f32 {
+    let p = z * (P_S0 + z * (P_S1 + z * P_S2));
+    let q = 1. + z * Q_S1;
+    p / q
+}
+
+/// Arccosine (f32)
+///
+/// Computes the inverse cosine (arc cosine) of the input value.
+/// Arguments must be in the range -1 to 1.
+/// Returns values in radians, in the range of 0 to pi.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn acosf(x: f32) -> f32 {
+    let x1p_120 = f32::from_bits(0x03800000); // 0x1p-120 === 2 ^ (-120)
+
+    let z: f32;
+    let w: f32;
+    let s: f32;
+
+    let mut hx = x.to_bits();
+    let ix = hx & 0x7fffffff;
+    /* |x| >= 1 or nan */
+    if ix >= 0x3f800000 {
+        if ix == 0x3f800000 {
+            if (hx >> 31) != 0 {
+                return 2. * PIO2_HI + x1p_120;
+            }
+            return 0.;
+        }
+        return 0. / (x - x);
+    }
+    /* |x| < 0.5 */
+    if ix < 0x3f000000 {
+        if ix <= 0x32800000 {
+            /* |x| < 2**-26 */
+            return PIO2_HI + x1p_120;
+        }
+        return PIO2_HI - (x - (PIO2_LO - x * r(x * x)));
+    }
+    /* x < -0.5 */
+    if (hx >> 31) != 0 {
+        z = (1. + x) * 0.5;
+        s = sqrtf(z);
+        w = r(z) * s - PIO2_LO;
+        return 2. * (PIO2_HI - (s + w));
+    }
+    /* x > 0.5 */
+    z = (1. - x) * 0.5;
+    s = sqrtf(z);
+    hx = s.to_bits();
+    let df = f32::from_bits(hx & 0xfffff000);
+    let c = (z - df * df) / (s + df);
+    w = r(z) * s + c;
+    2. * (df + w)
+}

vendor/libm/src/math/acosh.rs

@@ -0,0 +1,27 @@
+use super::{log, log1p, sqrt};
+
+const LN2: f64 = 0.693147180559945309417232121458176568; /* 0x3fe62e42,  0xfefa39ef*/
+
+/// Inverse hyperbolic cosine (f64)
+///
+/// Calculates the inverse hyperbolic cosine of `x`.
+/// Is defined as `log(x + sqrt(x*x-1))`.
+/// `x` must be a number greater than or equal to 1.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn acosh(x: f64) -> f64 {
+    let u = x.to_bits();
+    let e = ((u >> 52) as usize) & 0x7ff;
+
+    /* x < 1 domain error is handled in the called functions */
+
+    if e < 0x3ff + 1 {
+        /* |x| < 2, up to 2ulp error in [1,1.125] */
+        return log1p(x - 1.0 + sqrt((x - 1.0) * (x - 1.0) + 2.0 * (x - 1.0)));
+    }
+    if e < 0x3ff + 26 {
+        /* |x| < 0x1p26 */
+        return log(2.0 * x - 1.0 / (x + sqrt(x * x - 1.0)));
+    }
+    /* |x| >= 0x1p26 or nan */
+    return log(x) + LN2;
+}

vendor/libm/src/math/acoshf.rs

@@ -0,0 +1,26 @@
+use super::{log1pf, logf, sqrtf};
+
+const LN2: f32 = 0.693147180559945309417232121458176568;
+
+/// Inverse hyperbolic cosine (f32)
+///
+/// Calculates the inverse hyperbolic cosine of `x`.
+/// Is defined as `log(x + sqrt(x*x-1))`.
+/// `x` must be a number greater than or equal to 1.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn acoshf(x: f32) -> f32 {
+    let u = x.to_bits();
+    let a = u & 0x7fffffff;
+
+    if a < 0x3f800000 + (1 << 23) {
+        /* |x| < 2, invalid if x < 1 or nan */
+        /* up to 2ulp error in [1,1.125] */
+        return log1pf(x - 1.0 + sqrtf((x - 1.0) * (x - 1.0) + 2.0 * (x - 1.0)));
+    }
+    if a < 0x3f800000 + (12 << 23) {
+        /* |x| < 0x1p12 */
+        return logf(2.0 * x - 1.0 / (x + sqrtf(x * x - 1.0)));
+    }
+    /* x >= 0x1p12 */
+    return logf(x) + LN2;
+}

vendor/libm/src/math/arch/aarch64.rs

@@ -0,0 +1,115 @@
+//! Architecture-specific support for aarch64 with neon.
+
+use core::arch::asm;
+
+pub fn fma(mut x: f64, y: f64, z: f64) -> f64 {
+    // SAFETY: `fmadd` is available with neon and has no side effects.
+    unsafe {
+        asm!(
+            "fmadd {x:d}, {x:d}, {y:d}, {z:d}",
+            x = inout(vreg) x,
+            y = in(vreg) y,
+            z = in(vreg) z,
+            options(nomem, nostack, pure)
+        );
+    }
+    x
+}
+
+pub fn fmaf(mut x: f32, y: f32, z: f32) -> f32 {
+    // SAFETY: `fmadd` is available with neon and has no side effects.
+    unsafe {
+        asm!(
+            "fmadd {x:s}, {x:s}, {y:s}, {z:s}",
+            x = inout(vreg) x,
+            y = in(vreg) y,
+            z = in(vreg) z,
+            options(nomem, nostack, pure)
+        );
+    }
+    x
+}
+
+pub fn rint(mut x: f64) -> f64 {
+    // SAFETY: `frintn` is available with neon and has no side effects.
+    //
+    // `frintn` is always round-to-nearest which does not match the C specification, but Rust does
+    // not support rounding modes.
+    unsafe {
+        asm!(
+            "frintn {x:d}, {x:d}",
+            x = inout(vreg) x,
+            options(nomem, nostack, pure)
+        );
+    }
+    x
+}
+
+pub fn rintf(mut x: f32) -> f32 {
+    // SAFETY: `frintn` is available with neon and has no side effects.
+    //
+    // `frintn` is always round-to-nearest which does not match the C specification, but Rust does
+    // not support rounding modes.
+    unsafe {
+        asm!(
+            "frintn {x:s}, {x:s}",
+            x = inout(vreg) x,
+            options(nomem, nostack, pure)
+        );
+    }
+    x
+}
+
+#[cfg(all(f16_enabled, target_feature = "fp16"))]
+pub fn rintf16(mut x: f16) -> f16 {
+    // SAFETY: `frintn` is available for `f16` with `fp16` (implies `neon`) and has no side effects.
+    //
+    // `frintn` is always round-to-nearest which does not match the C specification, but Rust does
+    // not support rounding modes.
+    unsafe {
+        asm!(
+            "frintn {x:h}, {x:h}",
+            x = inout(vreg) x,
+            options(nomem, nostack, pure)
+        );
+    }
+    x
+}
+
+pub fn sqrt(mut x: f64) -> f64 {
+    // SAFETY: `fsqrt` is available with neon and has no side effects.
+    unsafe {
+        asm!(
+            "fsqrt {x:d}, {x:d}",
+            x = inout(vreg) x,
+            options(nomem, nostack, pure)
+        );
+    }
+    x
+}
+
+pub fn sqrtf(mut x: f32) -> f32 {
+    // SAFETY: `fsqrt` is available with neon and has no side effects.
+    unsafe {
+        asm!(
+            "fsqrt {x:s}, {x:s}",
+            x = inout(vreg) x,
+            options(nomem, nostack, pure)
+        );
+    }
+    x
+}
+
+#[cfg(all(f16_enabled, target_feature = "fp16"))]
+pub fn sqrtf16(mut x: f16) -> f16 {
+    // SAFETY: `fsqrt` is available for `f16` with `fp16` (implies `neon`) and has no
+    // side effects.
+    unsafe {
+        asm!(
+            "fsqrt {x:h}, {x:h}",
+            x = inout(vreg) x,
+            options(nomem, nostack, pure)
+        );
+    }
+    x
+}

vendor/libm/src/math/arch/i586.rs

@@ -0,0 +1,37 @@
+//! Architecture-specific support for x86-32 without SSE2
+
+use super::super::fabs;
+
+/// Use an alternative implementation on x86, because the
+/// main implementation fails with the x87 FPU used by
+/// debian i386, probably due to excess precision issues.
+/// Basic implementation taken from https://github.com/rust-lang/libm/issues/219.
+pub fn ceil(x: f64) -> f64 {
+    if fabs(x).to_bits() < 4503599627370496.0_f64.to_bits() {
+        let truncated = x as i64 as f64;
+        if truncated < x {
+            return truncated + 1.0;
+        } else {
+            return truncated;
+        }
+    } else {
+        return x;
+    }
+}
+
+/// Use an alternative implementation on x86, because the
+/// main implementation fails with the x87 FPU used by
+/// debian i386, probably due to excess precision issues.
+/// Basic implementation taken from https://github.com/rust-lang/libm/issues/219.
+pub fn floor(x: f64) -> f64 {
+    if fabs(x).to_bits() < 4503599627370496.0_f64.to_bits() {
+        let truncated = x as i64 as f64;
+        if truncated > x {
+            return truncated - 1.0;
+        } else {
+            return truncated;
+        }
+    } else {
+        return x;
+    }
+}

vendor/libm/src/math/arch/mod.rs

@@ -0,0 +1,50 @@
+//! Architecture-specific routines and operations.
+//!
+//! LLVM will already optimize calls to some of these in cases that there are hardware
+//! instructions. Providing an implementation here just ensures that the faster implementation
+//! is used when calling the function directly. This helps anyone who uses `libm` directly, as
+//! well as improving things when these routines are called as part of other implementations.
+
+// Most implementations should be defined here, to ensure they are not made available when
+// soft floats are required.
+#[cfg(arch_enabled)]
+cfg_if! {
+    if #[cfg(all(target_arch = "wasm32", intrinsics_enabled))] {
+        mod wasm32;
+        pub use wasm32::{
+            ceil, ceilf, fabs, fabsf, floor, floorf, rint, rintf, sqrt, sqrtf, trunc, truncf,
+        };
+    } else if #[cfg(target_feature = "sse2")] {
+        mod x86;
+        pub use x86::{sqrt, sqrtf, fma, fmaf};
+    } else if #[cfg(all(
+        any(target_arch = "aarch64", target_arch = "arm64ec"),
+        target_feature = "neon"
+    ))] {
+        mod aarch64;
+
+        pub use aarch64::{
+            fma,
+            fmaf,
+            rint,
+            rintf,
+            sqrt,
+            sqrtf,
+        };
+
+        #[cfg(all(f16_enabled, target_feature = "fp16"))]
+        pub use aarch64::{
+            rintf16,
+            sqrtf16,
+        };
+    }
+}
+
+// There are certain architecture-specific implementations that are needed for correctness
+// even with `force-soft-float`. These are configured here.
+cfg_if! {
+    if #[cfg(all(target_arch = "x86", not(target_feature = "sse2")))] {
+        mod i586;
+        pub use i586::{ceil, floor};
+    }
+}

vendor/libm/src/math/arch/wasm32.rs

@@ -0,0 +1,50 @@
+//! Wasm has builtins for simple float operations. Use the unstable `core::arch` intrinsics which
+//! are significantly faster than soft float operations.
+
+pub fn ceil(x: f64) -> f64 {
+    core::arch::wasm32::f64_ceil(x)
+}
+
+pub fn ceilf(x: f32) -> f32 {
+    core::arch::wasm32::f32_ceil(x)
+}
+
+pub fn fabs(x: f64) -> f64 {
+    x.abs()
+}
+
+pub fn fabsf(x: f32) -> f32 {
+    x.abs()
+}
+
+pub fn floor(x: f64) -> f64 {
+    core::arch::wasm32::f64_floor(x)
+}
+
+pub fn floorf(x: f32) -> f32 {
+    core::arch::wasm32::f32_floor(x)
+}
+
+pub fn rint(x: f64) -> f64 {
+    core::arch::wasm32::f64_nearest(x)
+}
+
+pub fn rintf(x: f32) -> f32 {
+    core::arch::wasm32::f32_nearest(x)
+}
+
+pub fn sqrt(x: f64) -> f64 {
+    core::arch::wasm32::f64_sqrt(x)
+}
+
+pub fn sqrtf(x: f32) -> f32 {
+    core::arch::wasm32::f32_sqrt(x)
+}
+
+pub fn trunc(x: f64) -> f64 {
+    core::arch::wasm32::f64_trunc(x)
+}
+
+pub fn truncf(x: f32) -> f32 {
+    core::arch::wasm32::f32_trunc(x)
+}

vendor/libm/src/math/arch/x86.rs

@@ -0,0 +1,32 @@
+//! Architecture-specific support for x86-32 and x86-64 with SSE2
+
+mod detect;
+mod fma;
+
+pub use fma::{fma, fmaf};
+
+pub fn sqrtf(mut x: f32) -> f32 {
+    // SAFETY: `sqrtss` is part of `sse2`, which this module is gated behind. It has no memory
+    // access or side effects.
+    unsafe {
+        core::arch::asm!(
+            "sqrtss {x}, {x}",
+            x = inout(xmm_reg) x,
+            options(nostack, nomem, pure),
+        )
+    };
+    x
+}
+
+pub fn sqrt(mut x: f64) -> f64 {
+    // SAFETY: `sqrtsd` is part of `sse2`, which this module is gated behind. It has no memory
+    // access or side effects.
+    unsafe {
+        core::arch::asm!(
+            "sqrtsd {x}, {x}",
+            x = inout(xmm_reg) x,
+            options(nostack, nomem, pure),
+        )
+    };
+    x
+}

vendor/libm/src/math/arch/x86/detect.rs

@@ -0,0 +1,232 @@
+// Using runtime feature detection requires atomics. Currently there are no x86 targets
+// that support sse but not `AtomicPtr`.
+
+#[cfg(target_arch = "x86")]
+use core::arch::x86::{__cpuid, __cpuid_count, _xgetbv, CpuidResult};
+#[cfg(target_arch = "x86_64")]
+use core::arch::x86_64::{__cpuid, __cpuid_count, _xgetbv, CpuidResult};
+
+use crate::support::feature_detect::{Flags, get_or_init_flags_cache, unique_masks};
+
+/// CPU features that get cached (doesn't correlate to anything on the CPU).
+pub mod cpu_flags {
+    use super::unique_masks;
+
+    unique_masks! {
+        u32,
+        SSE3,
+        F16C,
+        SSE,
+        SSE2,
+        ERMSB,
+        MOVRS,
+        FMA,
+        FMA4,
+        AVX512FP16,
+        AVX512BF16,
+    }
+}
+
+/// Get CPU features, loading from a cache if available.
+pub fn get_cpu_features() -> Flags {
+    use core::sync::atomic::AtomicU32;
+    static CACHE: AtomicU32 = AtomicU32::new(0);
+    get_or_init_flags_cache(&CACHE, load_x86_features)
+}
+
+/// Read from cpuid and translate to a `Flags` instance, using `cpu_flags`.
+///
+/// Implementation is taken from [std-detect][std-detect].
+///
+/// [std-detect]: https://github.com/rust-lang/stdarch/blob/690b3a6334d482874163bd6fcef408e0518febe9/crates/std_detect/src/detect/os/x86.rs#L142
+fn load_x86_features() -> Flags {
+    let mut value = Flags::empty();
+
+    if cfg!(target_env = "sgx") {
+        // doesn't support this because it is untrusted data
+        return Flags::empty();
+    }
+
+    // Calling `__cpuid`/`__cpuid_count` from here on is safe because the CPU
+    // has `cpuid` support.
+
+    // 0. EAX = 0: Basic Information:
+    // - EAX returns the "Highest Function Parameter", that is, the maximum leaf
+    //   value for subsequent calls of `cpuinfo` in range [0, 0x8000_0000].
+    // - The vendor ID is stored in 12 u8 ascii chars, returned in EBX, EDX, and ECX
+    //   (in that order)
+    let mut vendor_id = [0u8; 12];
+    let max_basic_leaf;
+    unsafe {
+        let CpuidResult { eax, ebx, ecx, edx } = __cpuid(0);
+        max_basic_leaf = eax;
+        vendor_id[0..4].copy_from_slice(&ebx.to_ne_bytes());
+        vendor_id[4..8].copy_from_slice(&edx.to_ne_bytes());
+        vendor_id[8..12].copy_from_slice(&ecx.to_ne_bytes());
+    }
+
+    if max_basic_leaf < 1 {
+        // Earlier Intel 486, CPUID not implemented
+        return value;
+    }
+
+    // EAX = 1, ECX = 0: Queries "Processor Info and Feature Bits";
+    // Contains information about most x86 features.
+    let CpuidResult { ecx, edx, .. } = unsafe { __cpuid(0x0000_0001_u32) };
+    let proc_info_ecx = Flags::from_bits(ecx);
+    let proc_info_edx = Flags::from_bits(edx);
+
+    // EAX = 7: Queries "Extended Features";
+    // Contains information about bmi,bmi2, and avx2 support.
+    let mut extended_features_ebx = Flags::empty();
+    let mut extended_features_edx = Flags::empty();
+    let mut extended_features_eax_leaf_1 = Flags::empty();
+    if max_basic_leaf >= 7 {
+        let CpuidResult { ebx, edx, .. } = unsafe { __cpuid(0x0000_0007_u32) };
+        extended_features_ebx = Flags::from_bits(ebx);
+        extended_features_edx = Flags::from_bits(edx);
+
+        let CpuidResult { eax, .. } = unsafe { __cpuid_count(0x0000_0007_u32, 0x0000_0001_u32) };
+        extended_features_eax_leaf_1 = Flags::from_bits(eax)
+    }
+
+    // EAX = 0x8000_0000, ECX = 0: Get Highest Extended Function Supported
+    // - EAX returns the max leaf value for extended information, that is,
+    //   `cpuid` calls in range [0x8000_0000; u32::MAX]:
+    let extended_max_basic_leaf = unsafe { __cpuid(0x8000_0000_u32) }.eax;
+
+    // EAX = 0x8000_0001, ECX=0: Queries "Extended Processor Info and Feature Bits"
+    let mut extended_proc_info_ecx = Flags::empty();
+    if extended_max_basic_leaf >= 1 {
+        let CpuidResult { ecx, .. } = unsafe { __cpuid(0x8000_0001_u32) };
+        extended_proc_info_ecx = Flags::from_bits(ecx);
+    }
+
+    let mut enable = |regflags: Flags, regbit, flag| {
+        if regflags.test_nth(regbit) {
+            value.insert(flag);
+        }
+    };
+
+    enable(proc_info_ecx, 0, cpu_flags::SSE3);
+    enable(proc_info_ecx, 29, cpu_flags::F16C);
+    enable(proc_info_edx, 25, cpu_flags::SSE);
+    enable(proc_info_edx, 26, cpu_flags::SSE2);
+    enable(extended_features_ebx, 9, cpu_flags::ERMSB);
+    enable(extended_features_eax_leaf_1, 31, cpu_flags::MOVRS);
+
+    // `XSAVE` and `AVX` support:
+    let cpu_xsave = proc_info_ecx.test_nth(26);
+    if cpu_xsave {
+        // 0. Here the CPU supports `XSAVE`.
+
+        // 1. Detect `OSXSAVE`, that is, whether the OS is AVX enabled and
+        //    supports saving the state of the AVX/AVX2 vector registers on
+        //    context-switches, see:
+        //
+        // - [intel: is avx enabled?][is_avx_enabled],
+        // - [mozilla: sse.cpp][mozilla_sse_cpp].
+        //
+        // [is_avx_enabled]: https://software.intel.com/en-us/blogs/2011/04/14/is-avx-enabled
+        // [mozilla_sse_cpp]: https://hg.mozilla.org/mozilla-central/file/64bab5cbb9b6/mozglue/build/SSE.cpp#l190
+        let cpu_osxsave = proc_info_ecx.test_nth(27);
+
+        if cpu_osxsave {
+            // 2. The OS must have signaled the CPU that it supports saving and
+            // restoring the:
+            //
+            // * SSE -> `XCR0.SSE[1]`
+            // * AVX -> `XCR0.AVX[2]`
+            // * AVX-512 -> `XCR0.AVX-512[7:5]`.
+            // * AMX -> `XCR0.AMX[18:17]`
+            //
+            // by setting the corresponding bits of `XCR0` to `1`.
+            //
+            // This is safe because the CPU supports `xsave` and the OS has set `osxsave`.
+            let xcr0 = unsafe { _xgetbv(0) };
+            // Test `XCR0.SSE[1]` and `XCR0.AVX[2]` with the mask `0b110 == 6`:
+            let os_avx_support = xcr0 & 6 == 6;
+            // Test `XCR0.AVX-512[7:5]` with the mask `0b1110_0000 == 0xe0`:
+            let os_avx512_support = xcr0 & 0xe0 == 0xe0;
+
+            // Only if the OS and the CPU support saving/restoring the AVX
+            // registers we enable `xsave` support:
+            if os_avx_support {
+                // See "13.3 ENABLING THE XSAVE FEATURE SET AND XSAVE-ENABLED
+                // FEATURES" in the "Intel® 64 and IA-32 Architectures Software
+                // Developer’s Manual, Volume 1: Basic Architecture":
+                //
+                // "Software enables the XSAVE feature set by setting
+                // CR4.OSXSAVE[bit 18] to 1 (e.g., with the MOV to CR4
+                // instruction). If this bit is 0, execution of any of XGETBV,
+                // XRSTOR, XRSTORS, XSAVE, XSAVEC, XSAVEOPT, XSAVES, and XSETBV
+                // causes an invalid-opcode exception (#UD)"
+
+                // FMA (uses 256-bit wide registers):
+                enable(proc_info_ecx, 12, cpu_flags::FMA);
+
+                // For AVX-512 the OS also needs to support saving/restoring
+                // the extended state, only then we enable AVX-512 support:
+                if os_avx512_support {
+                    enable(extended_features_edx, 23, cpu_flags::AVX512FP16);
+                    enable(extended_features_eax_leaf_1, 5, cpu_flags::AVX512BF16);
+                }
+            }
+        }
+    }
+
+    // As Hygon Dhyana originates from AMD technology and shares most of the architecture with
+    // AMD's family 17h, but with different CPU Vendor ID("HygonGenuine")/Family series number
+    // (Family 18h).
+    //
+    // For CPUID feature bits, Hygon Dhyana(family 18h) share the same definition with AMD
+    // family 17h.
+    //
+    // Related AMD CPUID specification is https://www.amd.com/system/files/TechDocs/25481.pdf
+    // (AMD64 Architecture Programmer's Manual, Appendix E).
+    // Related Hygon kernel patch can be found on
+    // http://lkml.kernel.org/r/5ce86123a7b9dad925ac583d88d2f921040e859b.1538583282.git.puwen@hygon.cn
+    if vendor_id == *b"AuthenticAMD" || vendor_id == *b"HygonGenuine" {
+        // These features are available on AMD arch CPUs:
+        enable(extended_proc_info_ecx, 16, cpu_flags::FMA4);
+    }
+
+    value
+}
+
+#[cfg(test)]
+mod tests {
+    extern crate std;
+    use std::is_x86_feature_detected;
+
+    use super::*;
+
+    #[test]
+    fn check_matches_std() {
+        let features = get_cpu_features();
+        for i in 0..cpu_flags::ALL.len() {
+            let flag = cpu_flags::ALL[i];
+            let name = cpu_flags::NAMES[i];
+
+            let std_detected = match flag {
+                cpu_flags::SSE3 => is_x86_feature_detected!("sse3"),
+                cpu_flags::F16C => is_x86_feature_detected!("f16c"),
+                cpu_flags::SSE => is_x86_feature_detected!("sse"),
+                cpu_flags::SSE2 => is_x86_feature_detected!("sse2"),
+                cpu_flags::ERMSB => is_x86_feature_detected!("ermsb"),
+                cpu_flags::MOVRS => continue, // only very recent support in std
+                cpu_flags::FMA => is_x86_feature_detected!("fma"),
+                cpu_flags::FMA4 => continue, // not yet supported in std
+                cpu_flags::AVX512FP16 => is_x86_feature_detected!("avx512fp16"),
+                cpu_flags::AVX512BF16 => is_x86_feature_detected!("avx512bf16"),
+                _ => panic!("untested CPU flag {name}"),
+            };
+
+            assert_eq!(
+                std_detected,
+                features.contains(flag),
+                "different flag {name}. flags: {features:?}"
+            );
+        }
+    }
+}

vendor/libm/src/math/arch/x86/fma.rs

@@ -0,0 +1,135 @@
+//! Use assembly fma if the `fma` or `fma4` feature is detected at runtime.
+
+use core::arch::asm;
+
+use super::super::super::generic;
+use super::detect::{cpu_flags, get_cpu_features};
+use crate::support::Round;
+use crate::support::feature_detect::select_once;
+
+pub fn fma(x: f64, y: f64, z: f64) -> f64 {
+    select_once! {
+        sig: fn(x: f64, y: f64, z: f64) -> f64,
+        init: || {
+            let features = get_cpu_features();
+            if features.contains(cpu_flags::FMA) {
+                fma_with_fma
+            } else if features.contains(cpu_flags::FMA4) {
+               fma_with_fma4
+            } else {
+                fma_fallback as Func
+            }
+        },
+        // SAFETY: `fn_ptr` is the result of `init`, preconditions have been checked.
+        call: |fn_ptr: Func| unsafe { fn_ptr(x, y, z) },
+    }
+}
+
+pub fn fmaf(x: f32, y: f32, z: f32) -> f32 {
+    select_once! {
+        sig: fn(x: f32, y: f32, z: f32) -> f32,
+        init: || {
+            let features = get_cpu_features();
+            if features.contains(cpu_flags::FMA) {
+                fmaf_with_fma
+            } else if features.contains(cpu_flags::FMA4) {
+                fmaf_with_fma4
+            } else {
+                fmaf_fallback as Func
+            }
+        },
+        // SAFETY: `fn_ptr` is the result of `init`, preconditions have been checked.
+        call: |fn_ptr: Func| unsafe { fn_ptr(x, y, z) },
+    }
+}
+
+/// # Safety
+///
+/// Must have +fma available.
+unsafe fn fma_with_fma(mut x: f64, y: f64, z: f64) -> f64 {
+    debug_assert!(get_cpu_features().contains(cpu_flags::FMA));
+
+    // SAFETY: fma is asserted available by precondition, which provides the instruction. No
+    // memory access or side effects.
+    unsafe {
+        asm!(
+            "vfmadd213sd {x}, {y}, {z}",
+            x = inout(xmm_reg) x,
+            y = in(xmm_reg) y,
+            z = in(xmm_reg) z,
+            options(nostack, nomem, pure),
+        );
+    }
+    x
+}
+
+/// # Safety
+///
+/// Must have +fma available.
+unsafe fn fmaf_with_fma(mut x: f32, y: f32, z: f32) -> f32 {
+    debug_assert!(get_cpu_features().contains(cpu_flags::FMA));
+
+    // SAFETY: fma is asserted available by precondition, which provides the instruction. No
+    // memory access or side effects.
+    unsafe {
+        asm!(
+            "vfmadd213ss {x}, {y}, {z}",
+            x = inout(xmm_reg) x,
+            y = in(xmm_reg) y,
+            z = in(xmm_reg) z,
+            options(nostack, nomem, pure),
+        );
+    }
+    x
+}
+
+/// # Safety
+///
+/// Must have +fma4 available.
+unsafe fn fma_with_fma4(mut x: f64, y: f64, z: f64) -> f64 {
+    debug_assert!(get_cpu_features().contains(cpu_flags::FMA4));
+
+    // SAFETY: fma4 is asserted available by precondition, which provides the instruction. No
+    // memory access or side effects.
+    unsafe {
+        asm!(
+            "vfmaddsd {x}, {x}, {y}, {z}",
+            x = inout(xmm_reg) x,
+            y = in(xmm_reg) y,
+            z = in(xmm_reg) z,
+            options(nostack, nomem, pure),
+        );
+    }
+    x
+}
+
+/// # Safety
+///
+/// Must have +fma4 available.
+unsafe fn fmaf_with_fma4(mut x: f32, y: f32, z: f32) -> f32 {
+    debug_assert!(get_cpu_features().contains(cpu_flags::FMA4));
+
+    // SAFETY: fma4 is asserted available by precondition, which provides the instruction. No
+    // memory access or side effects.
+    unsafe {
+        asm!(
+            "vfmaddss {x}, {x}, {y}, {z}",
+            x = inout(xmm_reg) x,
+            y = in(xmm_reg) y,
+            z = in(xmm_reg) z,
+            options(nostack, nomem, pure),
+        );
+    }
+    x
+}
+
+// FIXME: the `select_implementation` macro should handle arch implementations that want
+// to use the fallback, so we don't need to recreate the body.
+
+fn fma_fallback(x: f64, y: f64, z: f64) -> f64 {
+    generic::fma_round(x, y, z, Round::Nearest).val
+}
+
+fn fmaf_fallback(x: f32, y: f32, z: f32) -> f32 {
+    generic::fma_wide_round(x, y, z, Round::Nearest).val
+}

vendor/libm/src/math/asin.rs

@@ -0,0 +1,115 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_asin.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* asin(x)
+ * Method :
+ *      Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
+ *      we approximate asin(x) on [0,0.5] by
+ *              asin(x) = x + x*x^2*R(x^2)
+ *      where
+ *              R(x^2) is a rational approximation of (asin(x)-x)/x^3
+ *      and its remez error is bounded by
+ *              |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
+ *
+ *      For x in [0.5,1]
+ *              asin(x) = pi/2-2*asin(sqrt((1-x)/2))
+ *      Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
+ *      then for x>0.98
+ *              asin(x) = pi/2 - 2*(s+s*z*R(z))
+ *                      = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
+ *      For x<=0.98, let pio4_hi = pio2_hi/2, then
+ *              f = hi part of s;
+ *              c = sqrt(z) - f = (z-f*f)/(s+f)         ...f+c=sqrt(z)
+ *      and
+ *              asin(x) = pi/2 - 2*(s+s*z*R(z))
+ *                      = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
+ *                      = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
+ *
+ * Special cases:
+ *      if x is NaN, return x itself;
+ *      if |x|>1, return NaN with invalid signal.
+ *
+ */
+
+use super::{fabs, get_high_word, get_low_word, sqrt, with_set_low_word};
+
+const PIO2_HI: f64 = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
+const PIO2_LO: f64 = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
+/* coefficients for R(x^2) */
+const P_S0: f64 = 1.66666666666666657415e-01; /* 0x3FC55555, 0x55555555 */
+const P_S1: f64 = -3.25565818622400915405e-01; /* 0xBFD4D612, 0x03EB6F7D */
+const P_S2: f64 = 2.01212532134862925881e-01; /* 0x3FC9C155, 0x0E884455 */
+const P_S3: f64 = -4.00555345006794114027e-02; /* 0xBFA48228, 0xB5688F3B */
+const P_S4: f64 = 7.91534994289814532176e-04; /* 0x3F49EFE0, 0x7501B288 */
+const P_S5: f64 = 3.47933107596021167570e-05; /* 0x3F023DE1, 0x0DFDF709 */
+const Q_S1: f64 = -2.40339491173441421878e+00; /* 0xC0033A27, 0x1C8A2D4B */
+const Q_S2: f64 = 2.02094576023350569471e+00; /* 0x40002AE5, 0x9C598AC8 */
+const Q_S3: f64 = -6.88283971605453293030e-01; /* 0xBFE6066C, 0x1B8D0159 */
+const Q_S4: f64 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+fn comp_r(z: f64) -> f64 {
+    let p = z * (P_S0 + z * (P_S1 + z * (P_S2 + z * (P_S3 + z * (P_S4 + z * P_S5)))));
+    let q = 1.0 + z * (Q_S1 + z * (Q_S2 + z * (Q_S3 + z * Q_S4)));
+    p / q
+}
+
+/// Arcsine (f64)
+///
+/// Computes the inverse sine (arc sine) of the argument `x`.
+/// Arguments to asin must be in the range -1 to 1.
+/// Returns values in radians, in the range of -pi/2 to pi/2.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn asin(mut x: f64) -> f64 {
+    let z: f64;
+    let r: f64;
+    let s: f64;
+    let hx: u32;
+    let ix: u32;
+
+    hx = get_high_word(x);
+    ix = hx & 0x7fffffff;
+    /* |x| >= 1 or nan */
+    if ix >= 0x3ff00000 {
+        let lx: u32;
+        lx = get_low_word(x);
+        if ((ix - 0x3ff00000) | lx) == 0 {
+            /* asin(1) = +-pi/2 with inexact */
+            return x * PIO2_HI + f64::from_bits(0x3870000000000000);
+        } else {
+            return 0.0 / (x - x);
+        }
+    }
+    /* |x| < 0.5 */
+    if ix < 0x3fe00000 {
+        /* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */
+        if (0x00100000..0x3e500000).contains(&ix) {
+            return x;
+        } else {
+            return x + x * comp_r(x * x);
+        }
+    }
+    /* 1 > |x| >= 0.5 */
+    z = (1.0 - fabs(x)) * 0.5;
+    s = sqrt(z);
+    r = comp_r(z);
+    if ix >= 0x3fef3333 {
+        /* if |x| > 0.975 */
+        x = PIO2_HI - (2. * (s + s * r) - PIO2_LO);
+    } else {
+        let f: f64;
+        let c: f64;
+        /* f+c = sqrt(z) */
+        f = with_set_low_word(s, 0);
+        c = (z - f * f) / (s + f);
+        x = 0.5 * PIO2_HI - (2.0 * s * r - (PIO2_LO - 2.0 * c) - (0.5 * PIO2_HI - 2.0 * f));
+    }
+    if hx >> 31 != 0 { -x } else { x }
+}

vendor/libm/src/math/asinf.rs

@@ -0,0 +1,68 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_asinf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::sqrt::sqrt;
+use super::support::Float;
+
+const PIO2: f64 = 1.570796326794896558e+00;
+
+/* coefficients for R(x^2) */
+const P_S0: f32 = 1.6666586697e-01;
+const P_S1: f32 = -4.2743422091e-02;
+const P_S2: f32 = -8.6563630030e-03;
+const Q_S1: f32 = -7.0662963390e-01;
+
+fn r(z: f32) -> f32 {
+    let p = z * (P_S0 + z * (P_S1 + z * P_S2));
+    let q = 1. + z * Q_S1;
+    p / q
+}
+
+/// Arcsine (f32)
+///
+/// Computes the inverse sine (arc sine) of the argument `x`.
+/// Arguments to asin must be in the range -1 to 1.
+/// Returns values in radians, in the range of -pi/2 to pi/2.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn asinf(mut x: f32) -> f32 {
+    let x1p_120 = f64::from_bits(0x3870000000000000); // 0x1p-120 === 2 ^ (-120)
+
+    let hx = x.to_bits();
+    let ix = hx & 0x7fffffff;
+
+    if ix >= 0x3f800000 {
+        /* |x| >= 1 */
+        if ix == 0x3f800000 {
+            /* |x| == 1 */
+            return ((x as f64) * PIO2 + x1p_120) as f32; /* asin(+-1) = +-pi/2 with inexact */
+        }
+        return 0. / (x - x); /* asin(|x|>1) is NaN */
+    }
+
+    if ix < 0x3f000000 {
+        /* |x| < 0.5 */
+        /* if 0x1p-126 <= |x| < 0x1p-12, avoid raising underflow */
+        if (0x00800000..0x39800000).contains(&ix) {
+            return x;
+        }
+        return x + x * r(x * x);
+    }
+
+    /* 1 > |x| >= 0.5 */
+    let z = (1. - Float::abs(x)) * 0.5;
+    let s = sqrt(z as f64);
+    x = (PIO2 - 2. * (s + s * (r(z) as f64))) as f32;
+    if (hx >> 31) != 0 { -x } else { x }
+}

vendor/libm/src/math/asinh.rs

@@ -0,0 +1,36 @@
+use super::{log, log1p, sqrt};
+
+const LN2: f64 = 0.693147180559945309417232121458176568; /* 0x3fe62e42,  0xfefa39ef*/
+
+/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
+/// Inverse hyperbolic sine (f64)
+///
+/// Calculates the inverse hyperbolic sine of `x`.
+/// Is defined as `sgn(x)*log(|x|+sqrt(x*x+1))`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn asinh(mut x: f64) -> f64 {
+    let mut u = x.to_bits();
+    let e = ((u >> 52) as usize) & 0x7ff;
+    let sign = (u >> 63) != 0;
+
+    /* |x| */
+    u &= (!0) >> 1;
+    x = f64::from_bits(u);
+
+    if e >= 0x3ff + 26 {
+        /* |x| >= 0x1p26 or inf or nan */
+        x = log(x) + LN2;
+    } else if e >= 0x3ff + 1 {
+        /* |x| >= 2 */
+        x = log(2.0 * x + 1.0 / (sqrt(x * x + 1.0) + x));
+    } else if e >= 0x3ff - 26 {
+        /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */
+        x = log1p(x + x * x / (sqrt(x * x + 1.0) + 1.0));
+    } else {
+        /* |x| < 0x1p-26, raise inexact if x != 0 */
+        let x1p120 = f64::from_bits(0x4770000000000000);
+        force_eval!(x + x1p120);
+    }
+
+    if sign { -x } else { x }
+}

vendor/libm/src/math/asinhf.rs

@@ -0,0 +1,35 @@
+use super::{log1pf, logf, sqrtf};
+
+const LN2: f32 = 0.693147180559945309417232121458176568;
+
+/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
+/// Inverse hyperbolic sine (f32)
+///
+/// Calculates the inverse hyperbolic sine of `x`.
+/// Is defined as `sgn(x)*log(|x|+sqrt(x*x+1))`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn asinhf(mut x: f32) -> f32 {
+    let u = x.to_bits();
+    let i = u & 0x7fffffff;
+    let sign = (u >> 31) != 0;
+
+    /* |x| */
+    x = f32::from_bits(i);
+
+    if i >= 0x3f800000 + (12 << 23) {
+        /* |x| >= 0x1p12 or inf or nan */
+        x = logf(x) + LN2;
+    } else if i >= 0x3f800000 + (1 << 23) {
+        /* |x| >= 2 */
+        x = logf(2.0 * x + 1.0 / (sqrtf(x * x + 1.0) + x));
+    } else if i >= 0x3f800000 - (12 << 23) {
+        /* |x| >= 0x1p-12, up to 1.6ulp error in [0.125,0.5] */
+        x = log1pf(x + x * x / (sqrtf(x * x + 1.0) + 1.0));
+    } else {
+        /* |x| < 0x1p-12, raise inexact if x!=0 */
+        let x1p120 = f32::from_bits(0x7b800000);
+        force_eval!(x + x1p120);
+    }
+
+    if sign { -x } else { x }
+}

vendor/libm/src/math/atan.rs

@@ -0,0 +1,182 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_atan.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* atan(x)
+ * Method
+ *   1. Reduce x to positive by atan(x) = -atan(-x).
+ *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
+ *      is further reduced to one of the following intervals and the
+ *      arctangent of t is evaluated by the corresponding formula:
+ *
+ *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
+ *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
+ *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
+ *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
+ *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+use core::f64;
+
+use super::fabs;
+
+const ATANHI: [f64; 4] = [
+    4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
+    7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
+    9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
+    1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
+];
+
+const ATANLO: [f64; 4] = [
+    2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
+    3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
+    1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
+    6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
+];
+
+const AT: [f64; 11] = [
+    3.33333333333329318027e-01,  /* 0x3FD55555, 0x5555550D */
+    -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
+    1.42857142725034663711e-01,  /* 0x3FC24924, 0x920083FF */
+    -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
+    9.09088713343650656196e-02,  /* 0x3FB745CD, 0xC54C206E */
+    -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
+    6.66107313738753120669e-02,  /* 0x3FB10D66, 0xA0D03D51 */
+    -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
+    4.97687799461593236017e-02,  /* 0x3FA97B4B, 0x24760DEB */
+    -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
+    1.62858201153657823623e-02,  /* 0x3F90AD3A, 0xE322DA11 */
+];
+
+/// Arctangent (f64)
+///
+/// Computes the inverse tangent (arc tangent) of the input value.
+/// Returns a value in radians, in the range of -pi/2 to pi/2.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn atan(x: f64) -> f64 {
+    let mut x = x;
+    let mut ix = (x.to_bits() >> 32) as u32;
+    let sign = ix >> 31;
+    ix &= 0x7fff_ffff;
+    if ix >= 0x4410_0000 {
+        if x.is_nan() {
+            return x;
+        }
+
+        let z = ATANHI[3] + f64::from_bits(0x0380_0000); // 0x1p-120f
+        return if sign != 0 { -z } else { z };
+    }
+
+    let id = if ix < 0x3fdc_0000 {
+        /* |x| < 0.4375 */
+        if ix < 0x3e40_0000 {
+            /* |x| < 2^-27 */
+            if ix < 0x0010_0000 {
+                /* raise underflow for subnormal x */
+                force_eval!(x as f32);
+            }
+
+            return x;
+        }
+
+        -1
+    } else {
+        x = fabs(x);
+        if ix < 0x3ff30000 {
+            /* |x| < 1.1875 */
+            if ix < 0x3fe60000 {
+                /* 7/16 <= |x| < 11/16 */
+                x = (2. * x - 1.) / (2. + x);
+                0
+            } else {
+                /* 11/16 <= |x| < 19/16 */
+                x = (x - 1.) / (x + 1.);
+                1
+            }
+        } else if ix < 0x40038000 {
+            /* |x| < 2.4375 */
+            x = (x - 1.5) / (1. + 1.5 * x);
+            2
+        } else {
+            /* 2.4375 <= |x| < 2^66 */
+            x = -1. / x;
+            3
+        }
+    };
+
+    let z = x * x;
+    let w = z * z;
+    /* break sum from i=0 to 10 AT[i]z**(i+1) into odd and even poly */
+    let s1 = z * (AT[0] + w * (AT[2] + w * (AT[4] + w * (AT[6] + w * (AT[8] + w * AT[10])))));
+    let s2 = w * (AT[1] + w * (AT[3] + w * (AT[5] + w * (AT[7] + w * AT[9]))));
+
+    if id < 0 {
+        return x - x * (s1 + s2);
+    }
+
+    let z = i!(ATANHI, id as usize) - (x * (s1 + s2) - i!(ATANLO, id as usize) - x);
+
+    if sign != 0 { -z } else { z }
+}
+
+#[cfg(test)]
+mod tests {
+    use core::f64;
+
+    use super::atan;
+
+    #[test]
+    fn sanity_check() {
+        for (input, answer) in [
+            (3.0_f64.sqrt() / 3.0, f64::consts::FRAC_PI_6),
+            (1.0, f64::consts::FRAC_PI_4),
+            (3.0_f64.sqrt(), f64::consts::FRAC_PI_3),
+            (-3.0_f64.sqrt() / 3.0, -f64::consts::FRAC_PI_6),
+            (-1.0, -f64::consts::FRAC_PI_4),
+            (-3.0_f64.sqrt(), -f64::consts::FRAC_PI_3),
+        ]
+        .iter()
+        {
+            assert!(
+                (atan(*input) - answer) / answer < 1e-5,
+                "\natan({:.4}/16) = {:.4}, actual: {}",
+                input * 16.0,
+                answer,
+                atan(*input)
+            );
+        }
+    }
+
+    #[test]
+    fn zero() {
+        assert_eq!(atan(0.0), 0.0);
+    }
+
+    #[test]
+    fn infinity() {
+        assert_eq!(atan(f64::INFINITY), f64::consts::FRAC_PI_2);
+    }
+
+    #[test]
+    fn minus_infinity() {
+        assert_eq!(atan(f64::NEG_INFINITY), -f64::consts::FRAC_PI_2);
+    }
+
+    #[test]
+    fn nan() {
+        assert!(atan(f64::NAN).is_nan());
+    }
+}

vendor/libm/src/math/atan2.rs

@@ -0,0 +1,131 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ *
+ */
+/* atan2(y,x)
+ * Method :
+ *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
+ *      2. Reduce x to positive by (if x and y are unexceptional):
+ *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
+ *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
+ *
+ * Special cases:
+ *
+ *      ATAN2((anything), NaN ) is NaN;
+ *      ATAN2(NAN , (anything) ) is NaN;
+ *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
+ *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
+ *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
+ *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
+ *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
+ *      ATAN2(+-INF,+INF ) is +-pi/4 ;
+ *      ATAN2(+-INF,-INF ) is +-3pi/4;
+ *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+use super::{atan, fabs};
+
+const PI: f64 = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
+const PI_LO: f64 = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
+
+/// Arctangent of y/x (f64)
+///
+/// Computes the inverse tangent (arc tangent) of `y/x`.
+/// Produces the correct result even for angles near pi/2 or -pi/2 (that is, when `x` is near 0).
+/// Returns a value in radians, in the range of -pi to pi.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn atan2(y: f64, x: f64) -> f64 {
+    if x.is_nan() || y.is_nan() {
+        return x + y;
+    }
+    let mut ix = (x.to_bits() >> 32) as u32;
+    let lx = x.to_bits() as u32;
+    let mut iy = (y.to_bits() >> 32) as u32;
+    let ly = y.to_bits() as u32;
+    if ((ix.wrapping_sub(0x3ff00000)) | lx) == 0 {
+        /* x = 1.0 */
+        return atan(y);
+    }
+    let m = ((iy >> 31) & 1) | ((ix >> 30) & 2); /* 2*sign(x)+sign(y) */
+    ix &= 0x7fffffff;
+    iy &= 0x7fffffff;
+
+    /* when y = 0 */
+    if (iy | ly) == 0 {
+        return match m {
+            0 | 1 => y, /* atan(+-0,+anything)=+-0 */
+            2 => PI,    /* atan(+0,-anything) = PI */
+            _ => -PI,   /* atan(-0,-anything) =-PI */
+        };
+    }
+    /* when x = 0 */
+    if (ix | lx) == 0 {
+        return if m & 1 != 0 { -PI / 2.0 } else { PI / 2.0 };
+    }
+    /* when x is INF */
+    if ix == 0x7ff00000 {
+        if iy == 0x7ff00000 {
+            return match m {
+                0 => PI / 4.0,        /* atan(+INF,+INF) */
+                1 => -PI / 4.0,       /* atan(-INF,+INF) */
+                2 => 3.0 * PI / 4.0,  /* atan(+INF,-INF) */
+                _ => -3.0 * PI / 4.0, /* atan(-INF,-INF) */
+            };
+        } else {
+            return match m {
+                0 => 0.0,  /* atan(+...,+INF) */
+                1 => -0.0, /* atan(-...,+INF) */
+                2 => PI,   /* atan(+...,-INF) */
+                _ => -PI,  /* atan(-...,-INF) */
+            };
+        }
+    }
+    /* |y/x| > 0x1p64 */
+    if ix.wrapping_add(64 << 20) < iy || iy == 0x7ff00000 {
+        return if m & 1 != 0 { -PI / 2.0 } else { PI / 2.0 };
+    }
+
+    /* z = atan(|y/x|) without spurious underflow */
+    let z = if (m & 2 != 0) && iy.wrapping_add(64 << 20) < ix {
+        /* |y/x| < 0x1p-64, x<0 */
+        0.0
+    } else {
+        atan(fabs(y / x))
+    };
+    match m {
+        0 => z,                /* atan(+,+) */
+        1 => -z,               /* atan(-,+) */
+        2 => PI - (z - PI_LO), /* atan(+,-) */
+        _ => (z - PI_LO) - PI, /* atan(-,-) */
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    #[cfg_attr(x86_no_sse, ignore = "FIXME(i586): possible incorrect rounding")]
+    fn sanity_check() {
+        assert_eq!(atan2(0.0, 1.0), 0.0);
+        assert_eq!(atan2(0.0, -1.0), PI);
+        assert_eq!(atan2(-0.0, -1.0), -PI);
+        assert_eq!(atan2(3.0, 2.0), atan(3.0 / 2.0));
+        assert_eq!(atan2(2.0, -1.0), atan(2.0 / -1.0) + PI);
+        assert_eq!(atan2(-2.0, -1.0), atan(-2.0 / -1.0) - PI);
+    }
+}

vendor/libm/src/math/atan2f.rs

@@ -0,0 +1,90 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2f.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{atanf, fabsf};
+
+const PI: f32 = 3.1415927410e+00; /* 0x40490fdb */
+const PI_LO: f32 = -8.7422776573e-08; /* 0xb3bbbd2e */
+
+/// Arctangent of y/x (f32)
+///
+/// Computes the inverse tangent (arc tangent) of `y/x`.
+/// Produces the correct result even for angles near pi/2 or -pi/2 (that is, when `x` is near 0).
+/// Returns a value in radians, in the range of -pi to pi.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn atan2f(y: f32, x: f32) -> f32 {
+    if x.is_nan() || y.is_nan() {
+        return x + y;
+    }
+    let mut ix = x.to_bits();
+    let mut iy = y.to_bits();
+
+    if ix == 0x3f800000 {
+        /* x=1.0 */
+        return atanf(y);
+    }
+    let m = ((iy >> 31) & 1) | ((ix >> 30) & 2); /* 2*sign(x)+sign(y) */
+    ix &= 0x7fffffff;
+    iy &= 0x7fffffff;
+
+    /* when y = 0 */
+    if iy == 0 {
+        return match m {
+            0 | 1 => y, /* atan(+-0,+anything)=+-0 */
+            2 => PI,    /* atan(+0,-anything) = pi */
+            _ => -PI,   /* atan(-0,-anything) =-pi */
+        };
+    }
+    /* when x = 0 */
+    if ix == 0 {
+        return if m & 1 != 0 { -PI / 2. } else { PI / 2. };
+    }
+    /* when x is INF */
+    if ix == 0x7f800000 {
+        return if iy == 0x7f800000 {
+            match m {
+                0 => PI / 4.,       /* atan(+INF,+INF) */
+                1 => -PI / 4.,      /* atan(-INF,+INF) */
+                2 => 3. * PI / 4.,  /* atan(+INF,-INF)*/
+                _ => -3. * PI / 4., /* atan(-INF,-INF)*/
+            }
+        } else {
+            match m {
+                0 => 0.,  /* atan(+...,+INF) */
+                1 => -0., /* atan(-...,+INF) */
+                2 => PI,  /* atan(+...,-INF) */
+                _ => -PI, /* atan(-...,-INF) */
+            }
+        };
+    }
+    /* |y/x| > 0x1p26 */
+    if (ix + (26 << 23) < iy) || (iy == 0x7f800000) {
+        return if m & 1 != 0 { -PI / 2. } else { PI / 2. };
+    }
+
+    /* z = atan(|y/x|) with correct underflow */
+    let z = if (m & 2 != 0) && (iy + (26 << 23) < ix) {
+        /*|y/x| < 0x1p-26, x < 0 */
+        0.
+    } else {
+        atanf(fabsf(y / x))
+    };
+    match m {
+        0 => z,                /* atan(+,+) */
+        1 => -z,               /* atan(-,+) */
+        2 => PI - (z - PI_LO), /* atan(+,-) */
+        _ => (z - PI_LO) - PI, /* case 3 */ /* atan(-,-) */
+    }
+}

vendor/libm/src/math/atanf.rs

@@ -0,0 +1,108 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::fabsf;
+
+const ATAN_HI: [f32; 4] = [
+    4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
+    7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
+    9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
+    1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
+];
+
+const ATAN_LO: [f32; 4] = [
+    5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
+    3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
+    3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
+    7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
+];
+
+const A_T: [f32; 5] = [
+    3.3333328366e-01,
+    -1.9999158382e-01,
+    1.4253635705e-01,
+    -1.0648017377e-01,
+    6.1687607318e-02,
+];
+
+/// Arctangent (f32)
+///
+/// Computes the inverse tangent (arc tangent) of the input value.
+/// Returns a value in radians, in the range of -pi/2 to pi/2.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn atanf(mut x: f32) -> f32 {
+    let x1p_120 = f32::from_bits(0x03800000); // 0x1p-120 === 2 ^ (-120)
+
+    let z: f32;
+
+    let mut ix = x.to_bits();
+    let sign = (ix >> 31) != 0;
+    ix &= 0x7fffffff;
+
+    if ix >= 0x4c800000 {
+        /* if |x| >= 2**26 */
+        if x.is_nan() {
+            return x;
+        }
+        z = i!(ATAN_HI, 3) + x1p_120;
+        return if sign { -z } else { z };
+    }
+    let id = if ix < 0x3ee00000 {
+        /* |x| < 0.4375 */
+        if ix < 0x39800000 {
+            /* |x| < 2**-12 */
+            if ix < 0x00800000 {
+                /* raise underflow for subnormal x */
+                force_eval!(x * x);
+            }
+            return x;
+        }
+        -1
+    } else {
+        x = fabsf(x);
+        if ix < 0x3f980000 {
+            /* |x| < 1.1875 */
+            if ix < 0x3f300000 {
+                /*  7/16 <= |x| < 11/16 */
+                x = (2. * x - 1.) / (2. + x);
+                0
+            } else {
+                /* 11/16 <= |x| < 19/16 */
+                x = (x - 1.) / (x + 1.);
+                1
+            }
+        } else if ix < 0x401c0000 {
+            /* |x| < 2.4375 */
+            x = (x - 1.5) / (1. + 1.5 * x);
+            2
+        } else {
+            /* 2.4375 <= |x| < 2**26 */
+            x = -1. / x;
+            3
+        }
+    };
+    /* end of argument reduction */
+    z = x * x;
+    let w = z * z;
+    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
+    let s1 = z * (i!(A_T, 0) + w * (i!(A_T, 2) + w * i!(A_T, 4)));
+    let s2 = w * (i!(A_T, 1) + w * i!(A_T, 3));
+    if id < 0 {
+        return x - x * (s1 + s2);
+    }
+    let id = id as usize;
+    let z = i!(ATAN_HI, id) - ((x * (s1 + s2) - i!(ATAN_LO, id)) - x);
+    if sign { -z } else { z }
+}

vendor/libm/src/math/atanh.rs

@@ -0,0 +1,33 @@
+use super::log1p;
+
+/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
+/// Inverse hyperbolic tangent (f64)
+///
+/// Calculates the inverse hyperbolic tangent of `x`.
+/// Is defined as `log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn atanh(x: f64) -> f64 {
+    let u = x.to_bits();
+    let e = ((u >> 52) as usize) & 0x7ff;
+    let sign = (u >> 63) != 0;
+
+    /* |x| */
+    let mut y = f64::from_bits(u & 0x7fff_ffff_ffff_ffff);
+
+    if e < 0x3ff - 1 {
+        if e < 0x3ff - 32 {
+            /* handle underflow */
+            if e == 0 {
+                force_eval!(y as f32);
+            }
+        } else {
+            /* |x| < 0.5, up to 1.7ulp error */
+            y = 0.5 * log1p(2.0 * y + 2.0 * y * y / (1.0 - y));
+        }
+    } else {
+        /* avoid overflow */
+        y = 0.5 * log1p(2.0 * (y / (1.0 - y)));
+    }
+
+    if sign { -y } else { y }
+}

vendor/libm/src/math/atanhf.rs

@@ -0,0 +1,33 @@
+use super::log1pf;
+
+/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
+/// Inverse hyperbolic tangent (f32)
+///
+/// Calculates the inverse hyperbolic tangent of `x`.
+/// Is defined as `log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn atanhf(mut x: f32) -> f32 {
+    let mut u = x.to_bits();
+    let sign = (u >> 31) != 0;
+
+    /* |x| */
+    u &= 0x7fffffff;
+    x = f32::from_bits(u);
+
+    if u < 0x3f800000 - (1 << 23) {
+        if u < 0x3f800000 - (32 << 23) {
+            /* handle underflow */
+            if u < (1 << 23) {
+                force_eval!(x * x);
+            }
+        } else {
+            /* |x| < 0.5, up to 1.7ulp error */
+            x = 0.5 * log1pf(2.0 * x + 2.0 * x * x / (1.0 - x));
+        }
+    } else {
+        /* avoid overflow */
+        x = 0.5 * log1pf(2.0 * (x / (1.0 - x)));
+    }
+
+    if sign { -x } else { x }
+}

vendor/libm/src/math/cbrt.rs

@@ -0,0 +1,219 @@
+/* SPDX-License-Identifier: MIT */
+/* origin: core-math/src/binary64/cbrt/cbrt.c
+ * Copyright (c) 2021-2022 Alexei Sibidanov.
+ * Ported to Rust in 2025 by Trevor Gross.
+ */
+
+use super::Float;
+use super::support::{FpResult, Round, cold_path};
+
+/// Compute the cube root of the argument.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn cbrt(x: f64) -> f64 {
+    cbrt_round(x, Round::Nearest).val
+}
+
+pub fn cbrt_round(x: f64, round: Round) -> FpResult<f64> {
+    const ESCALE: [f64; 3] = [
+        1.0,
+        hf64!("0x1.428a2f98d728bp+0"), /* 2^(1/3) */
+        hf64!("0x1.965fea53d6e3dp+0"), /* 2^(2/3) */
+    ];
+
+    /* the polynomial c0+c1*x+c2*x^2+c3*x^3 approximates x^(1/3) on [1,2]
+    with maximal error < 9.2e-5 (attained at x=2) */
+    const C: [f64; 4] = [
+        hf64!("0x1.1b0babccfef9cp-1"),
+        hf64!("0x1.2c9a3e94d1da5p-1"),
+        hf64!("-0x1.4dc30b1a1ddbap-3"),
+        hf64!("0x1.7a8d3e4ec9b07p-6"),
+    ];
+
+    let u0: f64 = hf64!("0x1.5555555555555p-2");
+    let u1: f64 = hf64!("0x1.c71c71c71c71cp-3");
+
+    let rsc = [1.0, -1.0, 0.5, -0.5, 0.25, -0.25];
+
+    let off = [hf64!("0x1p-53"), 0.0, 0.0, 0.0];
+
+    /* rm=0 for rounding to nearest, and other values for directed roundings */
+    let hx: u64 = x.to_bits();
+    let mut mant: u64 = hx & f64::SIG_MASK;
+    let sign: u64 = hx >> 63;
+
+    let mut e: u32 = (hx >> f64::SIG_BITS) as u32 & f64::EXP_SAT;
+
+    if ((e + 1) & f64::EXP_SAT) < 2 {
+        cold_path();
+
+        let ix: u64 = hx & !f64::SIGN_MASK;
+
+        /* 0, inf, nan: we return x + x instead of simply x,
+        to that for x a signaling NaN, it correctly triggers
+        the invalid exception. */
+        if e == f64::EXP_SAT || ix == 0 {
+            return FpResult::ok(x + x);
+        }
+
+        let nz = ix.leading_zeros() - 11; /* subnormal */
+        mant <<= nz;
+        mant &= f64::SIG_MASK;
+        e = e.wrapping_sub(nz - 1);
+    }
+
+    e = e.wrapping_add(3072);
+    let cvt1: u64 = mant | (0x3ffu64 << 52);
+    let mut cvt5: u64 = cvt1;
+
+    let et: u32 = e / 3;
+    let it: u32 = e % 3;
+
+    /* 2^(3k+it) <= x < 2^(3k+it+1), with 0 <= it <= 3 */
+    cvt5 += u64::from(it) << f64::SIG_BITS;
+    cvt5 |= sign << 63;
+    let zz: f64 = f64::from_bits(cvt5);
+
+    /* cbrt(x) = cbrt(zz)*2^(et-1365) where 1 <= zz < 8 */
+    let mut isc: u64 = ESCALE[it as usize].to_bits(); // todo: index
+    isc |= sign << 63;
+    let cvt2: u64 = isc;
+    let z: f64 = f64::from_bits(cvt1);
+
+    /* cbrt(zz) = cbrt(z)*isc, where isc encodes 1, 2^(1/3) or 2^(2/3),
+    and 1 <= z < 2 */
+    let r: f64 = 1.0 / z;
+    let rr: f64 = r * rsc[((it as usize) << 1) | sign as usize];
+    let z2: f64 = z * z;
+    let c0: f64 = C[0] + z * C[1];
+    let c2: f64 = C[2] + z * C[3];
+    let mut y: f64 = c0 + z2 * c2;
+    let mut y2: f64 = y * y;
+
+    /* y is an approximation of z^(1/3) */
+    let mut h: f64 = y2 * (y * r) - 1.0;
+
+    /* h determines the error between y and z^(1/3) */
+    y -= (h * y) * (u0 - u1 * h);
+
+    /* The correction y -= (h*y)*(u0 - u1*h) corresponds to a cubic variant
+    of Newton's method, with the function f(y) = 1-z/y^3. */
+    y *= f64::from_bits(cvt2);
+
+    /* Now y is an approximation of zz^(1/3),
+     * and rr an approximation of 1/zz. We now perform another iteration of
+     * Newton-Raphson, this time with a linear approximation only. */
+    y2 = y * y;
+    let mut y2l: f64 = y.fma(y, -y2);
+
+    /* y2 + y2l = y^2 exactly */
+    let mut y3: f64 = y2 * y;
+    let mut y3l: f64 = y.fma(y2, -y3) + y * y2l;
+
+    /* y3 + y3l approximates y^3 with about 106 bits of accuracy */
+    h = ((y3 - zz) + y3l) * rr;
+    let mut dy: f64 = h * (y * u0);
+
+    /* the approximation of zz^(1/3) is y - dy */
+    let mut y1: f64 = y - dy;
+    dy = (y - y1) - dy;
+
+    /* the approximation of zz^(1/3) is now y1 + dy, where |dy| < 1/2 ulp(y)
+     * (for rounding to nearest) */
+    let mut ady: f64 = dy.abs();
+
+    /* For directed roundings, ady0 is tiny when dy is tiny, or ady0 is near
+     * from ulp(1);
+     * for rounding to nearest, ady0 is tiny when dy is near from 1/2 ulp(1),
+     * or from 3/2 ulp(1). */
+    let mut ady0: f64 = (ady - off[round as usize]).abs();
+    let mut ady1: f64 = (ady - (hf64!("0x1p-52") + off[round as usize])).abs();
+
+    if ady0 < hf64!("0x1p-75") || ady1 < hf64!("0x1p-75") {
+        cold_path();
+
+        y2 = y1 * y1;
+        y2l = y1.fma(y1, -y2);
+        y3 = y2 * y1;
+        y3l = y1.fma(y2, -y3) + y1 * y2l;
+        h = ((y3 - zz) + y3l) * rr;
+        dy = h * (y1 * u0);
+        y = y1 - dy;
+        dy = (y1 - y) - dy;
+        y1 = y;
+        ady = dy.abs();
+        ady0 = (ady - off[round as usize]).abs();
+        ady1 = (ady - (hf64!("0x1p-52") + off[round as usize])).abs();
+
+        if ady0 < hf64!("0x1p-98") || ady1 < hf64!("0x1p-98") {
+            cold_path();
+            let azz: f64 = zz.abs();
+
+            // ~ 0x1.79d15d0e8d59b80000000000000ffc3dp+0
+            if azz == hf64!("0x1.9b78223aa307cp+1") {
+                y1 = hf64!("0x1.79d15d0e8d59cp+0").copysign(zz);
+            }
+
+            // ~ 0x1.de87aa837820e80000000000001c0f08p+0
+            if azz == hf64!("0x1.a202bfc89ddffp+2") {
+                y1 = hf64!("0x1.de87aa837820fp+0").copysign(zz);
+            }
+
+            if round != Round::Nearest {
+                let wlist = [
+                    (hf64!("0x1.3a9ccd7f022dbp+0"), hf64!("0x1.1236160ba9b93p+0")), // ~ 0x1.1236160ba9b930000000000001e7e8fap+0
+                    (hf64!("0x1.7845d2faac6fep+0"), hf64!("0x1.23115e657e49cp+0")), // ~ 0x1.23115e657e49c0000000000001d7a799p+0
+                    (hf64!("0x1.d1ef81cbbbe71p+0"), hf64!("0x1.388fb44cdcf5ap+0")), // ~ 0x1.388fb44cdcf5a0000000000002202c55p+0
+                    (hf64!("0x1.0a2014f62987cp+1"), hf64!("0x1.46bcbf47dc1e8p+0")), // ~ 0x1.46bcbf47dc1e8000000000000303aa2dp+0
+                    (hf64!("0x1.fe18a044a5501p+1"), hf64!("0x1.95decfec9c904p+0")), // ~ 0x1.95decfec9c9040000000000000159e8ep+0
+                    (hf64!("0x1.a6bb8c803147bp+2"), hf64!("0x1.e05335a6401dep+0")), // ~ 0x1.e05335a6401de00000000000027ca017p+0
+                    (hf64!("0x1.ac8538a031cbdp+2"), hf64!("0x1.e281d87098de8p+0")), // ~ 0x1.e281d87098de80000000000000ee9314p+0
+                ];
+
+                for (a, b) in wlist {
+                    if azz == a {
+                        let tmp = if round as u64 + sign == 2 {
+                            hf64!("0x1p-52")
+                        } else {
+                            0.0
+                        };
+                        y1 = (b + tmp).copysign(zz);
+                    }
+                }
+            }
+        }
+    }
+
+    let mut cvt3: u64 = y1.to_bits();
+    cvt3 = cvt3.wrapping_add(((et.wrapping_sub(342).wrapping_sub(1023)) as u64) << 52);
+    let m0: u64 = cvt3 << 30;
+    let m1 = m0 >> 63;
+
+    if (m0 ^ m1) <= (1u64 << 30) {
+        cold_path();
+
+        let mut cvt4: u64 = y1.to_bits();
+        cvt4 = (cvt4 + (164 << 15)) & 0xffffffffffff0000u64;
+
+        if ((f64::from_bits(cvt4) - y1) - dy).abs() < hf64!("0x1p-60") || (zz).abs() == 1.0 {
+            cvt3 = (cvt3 + (1u64 << 15)) & 0xffffffffffff0000u64;
+        }
+    }
+
+    FpResult::ok(f64::from_bits(cvt3))
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn spot_checks() {
+        if !cfg!(x86_no_sse) {
+            // Exposes a rounding mode problem. Ignored on i586 because of inaccurate FMA.
+            assert_biteq!(
+                cbrt(f64::from_bits(0xf7f792b28f600000)),
+                f64::from_bits(0xd29ce68655d962f3)
+            );
+        }
+    }
+}

vendor/libm/src/math/cbrtf.rs

@@ -0,0 +1,75 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Debugged and optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* cbrtf(x)
+ * Return cube root of x
+ */
+
+use core::f32;
+
+const B1: u32 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */
+const B2: u32 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
+
+/// Cube root (f32)
+///
+/// Computes the cube root of the argument.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn cbrtf(x: f32) -> f32 {
+    let x1p24 = f32::from_bits(0x4b800000); // 0x1p24f === 2 ^ 24
+
+    let mut r: f64;
+    let mut t: f64;
+    let mut ui: u32 = x.to_bits();
+    let mut hx: u32 = ui & 0x7fffffff;
+
+    if hx >= 0x7f800000 {
+        /* cbrt(NaN,INF) is itself */
+        return x + x;
+    }
+
+    /* rough cbrt to 5 bits */
+    if hx < 0x00800000 {
+        /* zero or subnormal? */
+        if hx == 0 {
+            return x; /* cbrt(+-0) is itself */
+        }
+        ui = (x * x1p24).to_bits();
+        hx = ui & 0x7fffffff;
+        hx = hx / 3 + B2;
+    } else {
+        hx = hx / 3 + B1;
+    }
+    ui &= 0x80000000;
+    ui |= hx;
+
+    /*
+     * First step Newton iteration (solving t*t-x/t == 0) to 16 bits.  In
+     * double precision so that its terms can be arranged for efficiency
+     * without causing overflow or underflow.
+     */
+    t = f32::from_bits(ui) as f64;
+    r = t * t * t;
+    t = t * (x as f64 + x as f64 + r) / (x as f64 + r + r);
+
+    /*
+     * Second step Newton iteration to 47 bits.  In double precision for
+     * efficiency and accuracy.
+     */
+    r = t * t * t;
+    t = t * (x as f64 + x as f64 + r) / (x as f64 + r + r);
+
+    /* rounding to 24 bits is perfect in round-to-nearest mode */
+    t as f32
+}

vendor/libm/src/math/ceil.rs

@@ -0,0 +1,46 @@
+/// Ceil (f16)
+///
+/// Finds the nearest integer greater than or equal to `x`.
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn ceilf16(x: f16) -> f16 {
+    super::generic::ceil(x)
+}
+
+/// Ceil (f32)
+///
+/// Finds the nearest integer greater than or equal to `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn ceilf(x: f32) -> f32 {
+    select_implementation! {
+        name: ceilf,
+        use_arch: all(target_arch = "wasm32", intrinsics_enabled),
+        args: x,
+    }
+
+    super::generic::ceil(x)
+}
+
+/// Ceil (f64)
+///
+/// Finds the nearest integer greater than or equal to `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn ceil(x: f64) -> f64 {
+    select_implementation! {
+        name: ceil,
+        use_arch: all(target_arch = "wasm32", intrinsics_enabled),
+        use_arch_required: all(target_arch = "x86", not(target_feature = "sse2")),
+        args: x,
+    }
+
+    super::generic::ceil(x)
+}
+
+/// Ceil (f128)
+///
+/// Finds the nearest integer greater than or equal to `x`.
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn ceilf128(x: f128) -> f128 {
+    super::generic::ceil(x)
+}

vendor/libm/src/math/copysign.rs

@@ -0,0 +1,88 @@
+/// Sign of Y, magnitude of X (f16)
+///
+/// Constructs a number with the magnitude (absolute value) of its
+/// first argument, `x`, and the sign of its second argument, `y`.
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn copysignf16(x: f16, y: f16) -> f16 {
+    super::generic::copysign(x, y)
+}
+
+/// Sign of Y, magnitude of X (f32)
+///
+/// Constructs a number with the magnitude (absolute value) of its
+/// first argument, `x`, and the sign of its second argument, `y`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn copysignf(x: f32, y: f32) -> f32 {
+    super::generic::copysign(x, y)
+}
+
+/// Sign of Y, magnitude of X (f64)
+///
+/// Constructs a number with the magnitude (absolute value) of its
+/// first argument, `x`, and the sign of its second argument, `y`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn copysign(x: f64, y: f64) -> f64 {
+    super::generic::copysign(x, y)
+}
+
+/// Sign of Y, magnitude of X (f128)
+///
+/// Constructs a number with the magnitude (absolute value) of its
+/// first argument, `x`, and the sign of its second argument, `y`.
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn copysignf128(x: f128, y: f128) -> f128 {
+    super::generic::copysign(x, y)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::support::Float;
+
+    fn spec_test<F: Float>(f: impl Fn(F, F) -> F) {
+        assert_biteq!(f(F::ZERO, F::ZERO), F::ZERO);
+        assert_biteq!(f(F::NEG_ZERO, F::ZERO), F::ZERO);
+        assert_biteq!(f(F::ZERO, F::NEG_ZERO), F::NEG_ZERO);
+        assert_biteq!(f(F::NEG_ZERO, F::NEG_ZERO), F::NEG_ZERO);
+
+        assert_biteq!(f(F::ONE, F::ONE), F::ONE);
+        assert_biteq!(f(F::NEG_ONE, F::ONE), F::ONE);
+        assert_biteq!(f(F::ONE, F::NEG_ONE), F::NEG_ONE);
+        assert_biteq!(f(F::NEG_ONE, F::NEG_ONE), F::NEG_ONE);
+
+        assert_biteq!(f(F::INFINITY, F::INFINITY), F::INFINITY);
+        assert_biteq!(f(F::NEG_INFINITY, F::INFINITY), F::INFINITY);
+        assert_biteq!(f(F::INFINITY, F::NEG_INFINITY), F::NEG_INFINITY);
+        assert_biteq!(f(F::NEG_INFINITY, F::NEG_INFINITY), F::NEG_INFINITY);
+
+        // Not required but we expect it
+        assert_biteq!(f(F::NAN, F::NAN), F::NAN);
+        assert_biteq!(f(F::NEG_NAN, F::NAN), F::NAN);
+        assert_biteq!(f(F::NAN, F::NEG_NAN), F::NEG_NAN);
+        assert_biteq!(f(F::NEG_NAN, F::NEG_NAN), F::NEG_NAN);
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn spec_tests_f16() {
+        spec_test::<f16>(copysignf16);
+    }
+
+    #[test]
+    fn spec_tests_f32() {
+        spec_test::<f32>(copysignf);
+    }
+
+    #[test]
+    fn spec_tests_f64() {
+        spec_test::<f64>(copysign);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn spec_tests_f128() {
+        spec_test::<f128>(copysignf128);
+    }
+}

vendor/libm/src/math/copysignf.rs

@@ -0,0 +1,8 @@
+/// Sign of Y, magnitude of X (f32)
+///
+/// Constructs a number with the magnitude (absolute value) of its
+/// first argument, `x`, and the sign of its second argument, `y`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn copysignf(x: f32, y: f32) -> f32 {
+    super::generic::copysign(x, y)
+}

vendor/libm/src/math/copysignf128.rs

@@ -0,0 +1,8 @@
+/// Sign of Y, magnitude of X (f128)
+///
+/// Constructs a number with the magnitude (absolute value) of its
+/// first argument, `x`, and the sign of its second argument, `y`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn copysignf128(x: f128, y: f128) -> f128 {
+    super::generic::copysign(x, y)
+}

vendor/libm/src/math/copysignf16.rs

@@ -0,0 +1,8 @@
+/// Sign of Y, magnitude of X (f16)
+///
+/// Constructs a number with the magnitude (absolute value) of its
+/// first argument, `x`, and the sign of its second argument, `y`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn copysignf16(x: f16, y: f16) -> f16 {
+    super::generic::copysign(x, y)
+}

vendor/libm/src/math/cos.rs

@@ -0,0 +1,77 @@
+// origin: FreeBSD /usr/src/lib/msun/src/s_cos.c */
+//
+// ====================================================
+// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+//
+// Developed at SunPro, a Sun Microsystems, Inc. business.
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+
+use super::{k_cos, k_sin, rem_pio2};
+
+// cos(x)
+// Return cosine function of x.
+//
+// kernel function:
+//      k_sin           ... sine function on [-pi/4,pi/4]
+//      k_cos           ... cosine function on [-pi/4,pi/4]
+//      rem_pio2        ... argument reduction routine
+//
+// Method.
+//      Let S,C and T denote the sin, cos and tan respectively on
+//      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+//      in [-pi/4 , +pi/4], and let n = k mod 4.
+//      We have
+//
+//          n        sin(x)      cos(x)        tan(x)
+//     ----------------------------------------------------------
+//          0          S           C             T
+//          1          C          -S            -1/T
+//          2         -S          -C             T
+//          3         -C           S            -1/T
+//     ----------------------------------------------------------
+//
+// Special cases:
+//      Let trig be any of sin, cos, or tan.
+//      trig(+-INF)  is NaN, with signals;
+//      trig(NaN)    is that NaN;
+//
+// Accuracy:
+//      TRIG(x) returns trig(x) nearly rounded
+//
+
+/// The cosine of `x` (f64).
+///
+/// `x` is specified in radians.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn cos(x: f64) -> f64 {
+    let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
+
+    /* |x| ~< pi/4 */
+    if ix <= 0x3fe921fb {
+        if ix < 0x3e46a09e {
+            /* if x < 2**-27 * sqrt(2) */
+            /* raise inexact if x != 0 */
+            if x as i32 == 0 {
+                return 1.0;
+            }
+        }
+        return k_cos(x, 0.0);
+    }
+
+    /* cos(Inf or NaN) is NaN */
+    if ix >= 0x7ff00000 {
+        return x - x;
+    }
+
+    /* argument reduction needed */
+    let (n, y0, y1) = rem_pio2(x);
+    match n & 3 {
+        0 => k_cos(y0, y1),
+        1 => -k_sin(y0, y1, 1),
+        2 => -k_cos(y0, y1),
+        _ => k_sin(y0, y1, 1),
+    }
+}

vendor/libm/src/math/cosf.rs

@@ -0,0 +1,86 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_cosf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use core::f64::consts::FRAC_PI_2;
+
+use super::{k_cosf, k_sinf, rem_pio2f};
+
+/* Small multiples of pi/2 rounded to double precision. */
+const C1_PIO2: f64 = 1. * FRAC_PI_2; /* 0x3FF921FB, 0x54442D18 */
+const C2_PIO2: f64 = 2. * FRAC_PI_2; /* 0x400921FB, 0x54442D18 */
+const C3_PIO2: f64 = 3. * FRAC_PI_2; /* 0x4012D97C, 0x7F3321D2 */
+const C4_PIO2: f64 = 4. * FRAC_PI_2; /* 0x401921FB, 0x54442D18 */
+
+/// The cosine of `x` (f32).
+///
+/// `x` is specified in radians.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn cosf(x: f32) -> f32 {
+    let x64 = x as f64;
+
+    let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120
+
+    let mut ix = x.to_bits();
+    let sign = (ix >> 31) != 0;
+    ix &= 0x7fffffff;
+
+    if ix <= 0x3f490fda {
+        /* |x| ~<= pi/4 */
+        if ix < 0x39800000 {
+            /* |x| < 2**-12 */
+            /* raise inexact if x != 0 */
+            force_eval!(x + x1p120);
+            return 1.;
+        }
+        return k_cosf(x64);
+    }
+    if ix <= 0x407b53d1 {
+        /* |x| ~<= 5*pi/4 */
+        if ix > 0x4016cbe3 {
+            /* |x|  ~> 3*pi/4 */
+            return -k_cosf(if sign { x64 + C2_PIO2 } else { x64 - C2_PIO2 });
+        } else if sign {
+            return k_sinf(x64 + C1_PIO2);
+        } else {
+            return k_sinf(C1_PIO2 - x64);
+        }
+    }
+    if ix <= 0x40e231d5 {
+        /* |x| ~<= 9*pi/4 */
+        if ix > 0x40afeddf {
+            /* |x| ~> 7*pi/4 */
+            return k_cosf(if sign { x64 + C4_PIO2 } else { x64 - C4_PIO2 });
+        } else if sign {
+            return k_sinf(-x64 - C3_PIO2);
+        } else {
+            return k_sinf(x64 - C3_PIO2);
+        }
+    }
+
+    /* cos(Inf or NaN) is NaN */
+    if ix >= 0x7f800000 {
+        return x - x;
+    }
+
+    /* general argument reduction needed */
+    let (n, y) = rem_pio2f(x);
+    match n & 3 {
+        0 => k_cosf(y),
+        1 => k_sinf(-y),
+        2 => -k_cosf(y),
+        _ => k_sinf(y),
+    }
+}

vendor/libm/src/math/cosh.rs

@@ -0,0 +1,36 @@
+use super::{exp, expm1, k_expo2};
+
+/// Hyperbolic cosine (f64)
+///
+/// Computes the hyperbolic cosine of the argument x.
+/// Is defined as `(exp(x) + exp(-x))/2`
+/// Angles are specified in radians.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn cosh(mut x: f64) -> f64 {
+    /* |x| */
+    let mut ix = x.to_bits();
+    ix &= 0x7fffffffffffffff;
+    x = f64::from_bits(ix);
+    let w = ix >> 32;
+
+    /* |x| < log(2) */
+    if w < 0x3fe62e42 {
+        if w < 0x3ff00000 - (26 << 20) {
+            let x1p120 = f64::from_bits(0x4770000000000000);
+            force_eval!(x + x1p120);
+            return 1.;
+        }
+        let t = expm1(x); // exponential minus 1
+        return 1. + t * t / (2. * (1. + t));
+    }
+
+    /* |x| < log(DBL_MAX) */
+    if w < 0x40862e42 {
+        let t = exp(x);
+        /* note: if x>log(0x1p26) then the 1/t is not needed */
+        return 0.5 * (t + 1. / t);
+    }
+
+    /* |x| > log(DBL_MAX) or nan */
+    k_expo2(x)
+}

vendor/libm/src/math/coshf.rs

@@ -0,0 +1,36 @@
+use super::{expf, expm1f, k_expo2f};
+
+/// Hyperbolic cosine (f64)
+///
+/// Computes the hyperbolic cosine of the argument x.
+/// Is defined as `(exp(x) + exp(-x))/2`
+/// Angles are specified in radians.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn coshf(mut x: f32) -> f32 {
+    let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120
+
+    /* |x| */
+    let mut ix = x.to_bits();
+    ix &= 0x7fffffff;
+    x = f32::from_bits(ix);
+    let w = ix;
+
+    /* |x| < log(2) */
+    if w < 0x3f317217 {
+        if w < (0x3f800000 - (12 << 23)) {
+            force_eval!(x + x1p120);
+            return 1.;
+        }
+        let t = expm1f(x);
+        return 1. + t * t / (2. * (1. + t));
+    }
+
+    /* |x| < log(FLT_MAX) */
+    if w < 0x42b17217 {
+        let t = expf(x);
+        return 0.5 * (t + 1. / t);
+    }
+
+    /* |x| > log(FLT_MAX) or nan */
+    k_expo2f(x)
+}

vendor/libm/src/math/erf.rs

@@ -0,0 +1,314 @@
+use super::{exp, fabs, get_high_word, with_set_low_word};
+/* origin: FreeBSD /usr/src/lib/msun/src/s_erf.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* double erf(double x)
+ * double erfc(double x)
+ *                           x
+ *                    2      |\
+ *     erf(x)  =  ---------  | exp(-t*t)dt
+ *                 sqrt(pi) \|
+ *                           0
+ *
+ *     erfc(x) =  1-erf(x)
+ *  Note that
+ *              erf(-x) = -erf(x)
+ *              erfc(-x) = 2 - erfc(x)
+ *
+ * Method:
+ *      1. For |x| in [0, 0.84375]
+ *          erf(x)  = x + x*R(x^2)
+ *          erfc(x) = 1 - erf(x)           if x in [-.84375,0.25]
+ *                  = 0.5 + ((0.5-x)-x*R)  if x in [0.25,0.84375]
+ *         where R = P/Q where P is an odd poly of degree 8 and
+ *         Q is an odd poly of degree 10.
+ *                                               -57.90
+ *                      | R - (erf(x)-x)/x | <= 2
+ *
+ *
+ *         Remark. The formula is derived by noting
+ *          erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
+ *         and that
+ *          2/sqrt(pi) = 1.128379167095512573896158903121545171688
+ *         is close to one. The interval is chosen because the fix
+ *         point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
+ *         near 0.6174), and by some experiment, 0.84375 is chosen to
+ *         guarantee the error is less than one ulp for erf.
+ *
+ *      2. For |x| in [0.84375,1.25], let s = |x| - 1, and
+ *         c = 0.84506291151 rounded to single (24 bits)
+ *              erf(x)  = sign(x) * (c  + P1(s)/Q1(s))
+ *              erfc(x) = (1-c)  - P1(s)/Q1(s) if x > 0
+ *                        1+(c+P1(s)/Q1(s))    if x < 0
+ *              |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
+ *         Remark: here we use the taylor series expansion at x=1.
+ *              erf(1+s) = erf(1) + s*Poly(s)
+ *                       = 0.845.. + P1(s)/Q1(s)
+ *         That is, we use rational approximation to approximate
+ *                      erf(1+s) - (c = (single)0.84506291151)
+ *         Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
+ *         where
+ *              P1(s) = degree 6 poly in s
+ *              Q1(s) = degree 6 poly in s
+ *
+ *      3. For x in [1.25,1/0.35(~2.857143)],
+ *              erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
+ *              erf(x)  = 1 - erfc(x)
+ *         where
+ *              R1(z) = degree 7 poly in z, (z=1/x^2)
+ *              S1(z) = degree 8 poly in z
+ *
+ *      4. For x in [1/0.35,28]
+ *              erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
+ *                      = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0
+ *                      = 2.0 - tiny            (if x <= -6)
+ *              erf(x)  = sign(x)*(1.0 - erfc(x)) if x < 6, else
+ *              erf(x)  = sign(x)*(1.0 - tiny)
+ *         where
+ *              R2(z) = degree 6 poly in z, (z=1/x^2)
+ *              S2(z) = degree 7 poly in z
+ *
+ *      Note1:
+ *         To compute exp(-x*x-0.5625+R/S), let s be a single
+ *         precision number and s := x; then
+ *              -x*x = -s*s + (s-x)*(s+x)
+ *              exp(-x*x-0.5626+R/S) =
+ *                      exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
+ *      Note2:
+ *         Here 4 and 5 make use of the asymptotic series
+ *                        exp(-x*x)
+ *              erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
+ *                        x*sqrt(pi)
+ *         We use rational approximation to approximate
+ *              g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
+ *         Here is the error bound for R1/S1 and R2/S2
+ *              |R1/S1 - f(x)|  < 2**(-62.57)
+ *              |R2/S2 - f(x)|  < 2**(-61.52)
+ *
+ *      5. For inf > x >= 28
+ *              erf(x)  = sign(x) *(1 - tiny)  (raise inexact)
+ *              erfc(x) = tiny*tiny (raise underflow) if x > 0
+ *                      = 2 - tiny if x<0
+ *
+ *      7. Special case:
+ *              erf(0)  = 0, erf(inf)  = 1, erf(-inf) = -1,
+ *              erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
+ *              erfc/erf(NaN) is NaN
+ */
+
+const ERX: f64 = 8.45062911510467529297e-01; /* 0x3FEB0AC1, 0x60000000 */
+/*
+ * Coefficients for approximation to  erf on [0,0.84375]
+ */
+const EFX8: f64 = 1.02703333676410069053e+00; /* 0x3FF06EBA, 0x8214DB69 */
+const PP0: f64 = 1.28379167095512558561e-01; /* 0x3FC06EBA, 0x8214DB68 */
+const PP1: f64 = -3.25042107247001499370e-01; /* 0xBFD4CD7D, 0x691CB913 */
+const PP2: f64 = -2.84817495755985104766e-02; /* 0xBF9D2A51, 0xDBD7194F */
+const PP3: f64 = -5.77027029648944159157e-03; /* 0xBF77A291, 0x236668E4 */
+const PP4: f64 = -2.37630166566501626084e-05; /* 0xBEF8EAD6, 0x120016AC */
+const QQ1: f64 = 3.97917223959155352819e-01; /* 0x3FD97779, 0xCDDADC09 */
+const QQ2: f64 = 6.50222499887672944485e-02; /* 0x3FB0A54C, 0x5536CEBA */
+const QQ3: f64 = 5.08130628187576562776e-03; /* 0x3F74D022, 0xC4D36B0F */
+const QQ4: f64 = 1.32494738004321644526e-04; /* 0x3F215DC9, 0x221C1A10 */
+const QQ5: f64 = -3.96022827877536812320e-06; /* 0xBED09C43, 0x42A26120 */
+/*
+ * Coefficients for approximation to  erf  in [0.84375,1.25]
+ */
+const PA0: f64 = -2.36211856075265944077e-03; /* 0xBF6359B8, 0xBEF77538 */
+const PA1: f64 = 4.14856118683748331666e-01; /* 0x3FDA8D00, 0xAD92B34D */
+const PA2: f64 = -3.72207876035701323847e-01; /* 0xBFD7D240, 0xFBB8C3F1 */
+const PA3: f64 = 3.18346619901161753674e-01; /* 0x3FD45FCA, 0x805120E4 */
+const PA4: f64 = -1.10894694282396677476e-01; /* 0xBFBC6398, 0x3D3E28EC */
+const PA5: f64 = 3.54783043256182359371e-02; /* 0x3FA22A36, 0x599795EB */
+const PA6: f64 = -2.16637559486879084300e-03; /* 0xBF61BF38, 0x0A96073F */
+const QA1: f64 = 1.06420880400844228286e-01; /* 0x3FBB3E66, 0x18EEE323 */
+const QA2: f64 = 5.40397917702171048937e-01; /* 0x3FE14AF0, 0x92EB6F33 */
+const QA3: f64 = 7.18286544141962662868e-02; /* 0x3FB2635C, 0xD99FE9A7 */
+const QA4: f64 = 1.26171219808761642112e-01; /* 0x3FC02660, 0xE763351F */
+const QA5: f64 = 1.36370839120290507362e-02; /* 0x3F8BEDC2, 0x6B51DD1C */
+const QA6: f64 = 1.19844998467991074170e-02; /* 0x3F888B54, 0x5735151D */
+/*
+ * Coefficients for approximation to  erfc in [1.25,1/0.35]
+ */
+const RA0: f64 = -9.86494403484714822705e-03; /* 0xBF843412, 0x600D6435 */
+const RA1: f64 = -6.93858572707181764372e-01; /* 0xBFE63416, 0xE4BA7360 */
+const RA2: f64 = -1.05586262253232909814e+01; /* 0xC0251E04, 0x41B0E726 */
+const RA3: f64 = -6.23753324503260060396e+01; /* 0xC04F300A, 0xE4CBA38D */
+const RA4: f64 = -1.62396669462573470355e+02; /* 0xC0644CB1, 0x84282266 */
+const RA5: f64 = -1.84605092906711035994e+02; /* 0xC067135C, 0xEBCCABB2 */
+const RA6: f64 = -8.12874355063065934246e+01; /* 0xC0545265, 0x57E4D2F2 */
+const RA7: f64 = -9.81432934416914548592e+00; /* 0xC023A0EF, 0xC69AC25C */
+const SA1: f64 = 1.96512716674392571292e+01; /* 0x4033A6B9, 0xBD707687 */
+const SA2: f64 = 1.37657754143519042600e+02; /* 0x4061350C, 0x526AE721 */
+const SA3: f64 = 4.34565877475229228821e+02; /* 0x407B290D, 0xD58A1A71 */
+const SA4: f64 = 6.45387271733267880336e+02; /* 0x40842B19, 0x21EC2868 */
+const SA5: f64 = 4.29008140027567833386e+02; /* 0x407AD021, 0x57700314 */
+const SA6: f64 = 1.08635005541779435134e+02; /* 0x405B28A3, 0xEE48AE2C */
+const SA7: f64 = 6.57024977031928170135e+00; /* 0x401A47EF, 0x8E484A93 */
+const SA8: f64 = -6.04244152148580987438e-02; /* 0xBFAEEFF2, 0xEE749A62 */
+/*
+ * Coefficients for approximation to  erfc in [1/.35,28]
+ */
+const RB0: f64 = -9.86494292470009928597e-03; /* 0xBF843412, 0x39E86F4A */
+const RB1: f64 = -7.99283237680523006574e-01; /* 0xBFE993BA, 0x70C285DE */
+const RB2: f64 = -1.77579549177547519889e+01; /* 0xC031C209, 0x555F995A */
+const RB3: f64 = -1.60636384855821916062e+02; /* 0xC064145D, 0x43C5ED98 */
+const RB4: f64 = -6.37566443368389627722e+02; /* 0xC083EC88, 0x1375F228 */
+const RB5: f64 = -1.02509513161107724954e+03; /* 0xC0900461, 0x6A2E5992 */
+const RB6: f64 = -4.83519191608651397019e+02; /* 0xC07E384E, 0x9BDC383F */
+const SB1: f64 = 3.03380607434824582924e+01; /* 0x403E568B, 0x261D5190 */
+const SB2: f64 = 3.25792512996573918826e+02; /* 0x40745CAE, 0x221B9F0A */
+const SB3: f64 = 1.53672958608443695994e+03; /* 0x409802EB, 0x189D5118 */
+const SB4: f64 = 3.19985821950859553908e+03; /* 0x40A8FFB7, 0x688C246A */
+const SB5: f64 = 2.55305040643316442583e+03; /* 0x40A3F219, 0xCEDF3BE6 */
+const SB6: f64 = 4.74528541206955367215e+02; /* 0x407DA874, 0xE79FE763 */
+const SB7: f64 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
+
+fn erfc1(x: f64) -> f64 {
+    let s: f64;
+    let p: f64;
+    let q: f64;
+
+    s = fabs(x) - 1.0;
+    p = PA0 + s * (PA1 + s * (PA2 + s * (PA3 + s * (PA4 + s * (PA5 + s * PA6)))));
+    q = 1.0 + s * (QA1 + s * (QA2 + s * (QA3 + s * (QA4 + s * (QA5 + s * QA6)))));
+
+    1.0 - ERX - p / q
+}
+
+fn erfc2(ix: u32, mut x: f64) -> f64 {
+    let s: f64;
+    let r: f64;
+    let big_s: f64;
+    let z: f64;
+
+    if ix < 0x3ff40000 {
+        /* |x| < 1.25 */
+        return erfc1(x);
+    }
+
+    x = fabs(x);
+    s = 1.0 / (x * x);
+    if ix < 0x4006db6d {
+        /* |x| < 1/.35 ~ 2.85714 */
+        r = RA0 + s * (RA1 + s * (RA2 + s * (RA3 + s * (RA4 + s * (RA5 + s * (RA6 + s * RA7))))));
+        big_s = 1.0
+            + s * (SA1
+                + s * (SA2 + s * (SA3 + s * (SA4 + s * (SA5 + s * (SA6 + s * (SA7 + s * SA8)))))));
+    } else {
+        /* |x| > 1/.35 */
+        r = RB0 + s * (RB1 + s * (RB2 + s * (RB3 + s * (RB4 + s * (RB5 + s * RB6)))));
+        big_s =
+            1.0 + s * (SB1 + s * (SB2 + s * (SB3 + s * (SB4 + s * (SB5 + s * (SB6 + s * SB7))))));
+    }
+    z = with_set_low_word(x, 0);
+
+    exp(-z * z - 0.5625) * exp((z - x) * (z + x) + r / big_s) / x
+}
+
+/// Error function (f64)
+///
+/// Calculates an approximation to the “error function”, which estimates
+/// the probability that an observation will fall within x standard
+/// deviations of the mean (assuming a normal distribution).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn erf(x: f64) -> f64 {
+    let r: f64;
+    let s: f64;
+    let z: f64;
+    let y: f64;
+    let mut ix: u32;
+    let sign: usize;
+
+    ix = get_high_word(x);
+    sign = (ix >> 31) as usize;
+    ix &= 0x7fffffff;
+    if ix >= 0x7ff00000 {
+        /* erf(nan)=nan, erf(+-inf)=+-1 */
+        return 1.0 - 2.0 * (sign as f64) + 1.0 / x;
+    }
+    if ix < 0x3feb0000 {
+        /* |x| < 0.84375 */
+        if ix < 0x3e300000 {
+            /* |x| < 2**-28 */
+            /* avoid underflow */
+            return 0.125 * (8.0 * x + EFX8 * x);
+        }
+        z = x * x;
+        r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4)));
+        s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5))));
+        y = r / s;
+        return x + x * y;
+    }
+    if ix < 0x40180000 {
+        /* 0.84375 <= |x| < 6 */
+        y = 1.0 - erfc2(ix, x);
+    } else {
+        let x1p_1022 = f64::from_bits(0x0010000000000000);
+        y = 1.0 - x1p_1022;
+    }
+
+    if sign != 0 { -y } else { y }
+}
+
+/// Complementary error function (f64)
+///
+/// Calculates the complementary probability.
+/// Is `1 - erf(x)`. Is computed directly, so that you can use it to avoid
+/// the loss of precision that would result from subtracting
+/// large probabilities (on large `x`) from 1.
+pub fn erfc(x: f64) -> f64 {
+    let r: f64;
+    let s: f64;
+    let z: f64;
+    let y: f64;
+    let mut ix: u32;
+    let sign: usize;
+
+    ix = get_high_word(x);
+    sign = (ix >> 31) as usize;
+    ix &= 0x7fffffff;
+    if ix >= 0x7ff00000 {
+        /* erfc(nan)=nan, erfc(+-inf)=0,2 */
+        return 2.0 * (sign as f64) + 1.0 / x;
+    }
+    if ix < 0x3feb0000 {
+        /* |x| < 0.84375 */
+        if ix < 0x3c700000 {
+            /* |x| < 2**-56 */
+            return 1.0 - x;
+        }
+        z = x * x;
+        r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4)));
+        s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5))));
+        y = r / s;
+        if sign != 0 || ix < 0x3fd00000 {
+            /* x < 1/4 */
+            return 1.0 - (x + x * y);
+        }
+        return 0.5 - (x - 0.5 + x * y);
+    }
+    if ix < 0x403c0000 {
+        /* 0.84375 <= |x| < 28 */
+        if sign != 0 {
+            return 2.0 - erfc2(ix, x);
+        } else {
+            return erfc2(ix, x);
+        }
+    }
+
+    let x1p_1022 = f64::from_bits(0x0010000000000000);
+    if sign != 0 {
+        2.0 - x1p_1022
+    } else {
+        x1p_1022 * x1p_1022
+    }
+}

vendor/libm/src/math/erff.rs

@@ -0,0 +1,226 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_erff.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{expf, fabsf};
+
+const ERX: f32 = 8.4506291151e-01; /* 0x3f58560b */
+/*
+ * Coefficients for approximation to  erf on [0,0.84375]
+ */
+const EFX8: f32 = 1.0270333290e+00; /* 0x3f8375d4 */
+const PP0: f32 = 1.2837916613e-01; /* 0x3e0375d4 */
+const PP1: f32 = -3.2504209876e-01; /* 0xbea66beb */
+const PP2: f32 = -2.8481749818e-02; /* 0xbce9528f */
+const PP3: f32 = -5.7702702470e-03; /* 0xbbbd1489 */
+const PP4: f32 = -2.3763017452e-05; /* 0xb7c756b1 */
+const QQ1: f32 = 3.9791721106e-01; /* 0x3ecbbbce */
+const QQ2: f32 = 6.5022252500e-02; /* 0x3d852a63 */
+const QQ3: f32 = 5.0813062117e-03; /* 0x3ba68116 */
+const QQ4: f32 = 1.3249473704e-04; /* 0x390aee49 */
+const QQ5: f32 = -3.9602282413e-06; /* 0xb684e21a */
+/*
+ * Coefficients for approximation to  erf  in [0.84375,1.25]
+ */
+const PA0: f32 = -2.3621185683e-03; /* 0xbb1acdc6 */
+const PA1: f32 = 4.1485610604e-01; /* 0x3ed46805 */
+const PA2: f32 = -3.7220788002e-01; /* 0xbebe9208 */
+const PA3: f32 = 3.1834661961e-01; /* 0x3ea2fe54 */
+const PA4: f32 = -1.1089469492e-01; /* 0xbde31cc2 */
+const PA5: f32 = 3.5478305072e-02; /* 0x3d1151b3 */
+const PA6: f32 = -2.1663755178e-03; /* 0xbb0df9c0 */
+const QA1: f32 = 1.0642088205e-01; /* 0x3dd9f331 */
+const QA2: f32 = 5.4039794207e-01; /* 0x3f0a5785 */
+const QA3: f32 = 7.1828655899e-02; /* 0x3d931ae7 */
+const QA4: f32 = 1.2617121637e-01; /* 0x3e013307 */
+const QA5: f32 = 1.3637083583e-02; /* 0x3c5f6e13 */
+const QA6: f32 = 1.1984500103e-02; /* 0x3c445aa3 */
+/*
+ * Coefficients for approximation to  erfc in [1.25,1/0.35]
+ */
+const RA0: f32 = -9.8649440333e-03; /* 0xbc21a093 */
+const RA1: f32 = -6.9385856390e-01; /* 0xbf31a0b7 */
+const RA2: f32 = -1.0558626175e+01; /* 0xc128f022 */
+const RA3: f32 = -6.2375331879e+01; /* 0xc2798057 */
+const RA4: f32 = -1.6239666748e+02; /* 0xc322658c */
+const RA5: f32 = -1.8460508728e+02; /* 0xc3389ae7 */
+const RA6: f32 = -8.1287437439e+01; /* 0xc2a2932b */
+const RA7: f32 = -9.8143291473e+00; /* 0xc11d077e */
+const SA1: f32 = 1.9651271820e+01; /* 0x419d35ce */
+const SA2: f32 = 1.3765776062e+02; /* 0x4309a863 */
+const SA3: f32 = 4.3456588745e+02; /* 0x43d9486f */
+const SA4: f32 = 6.4538726807e+02; /* 0x442158c9 */
+const SA5: f32 = 4.2900814819e+02; /* 0x43d6810b */
+const SA6: f32 = 1.0863500214e+02; /* 0x42d9451f */
+const SA7: f32 = 6.5702495575e+00; /* 0x40d23f7c */
+const SA8: f32 = -6.0424413532e-02; /* 0xbd777f97 */
+/*
+ * Coefficients for approximation to  erfc in [1/.35,28]
+ */
+const RB0: f32 = -9.8649431020e-03; /* 0xbc21a092 */
+const RB1: f32 = -7.9928326607e-01; /* 0xbf4c9dd4 */
+const RB2: f32 = -1.7757955551e+01; /* 0xc18e104b */
+const RB3: f32 = -1.6063638306e+02; /* 0xc320a2ea */
+const RB4: f32 = -6.3756646729e+02; /* 0xc41f6441 */
+const RB5: f32 = -1.0250950928e+03; /* 0xc480230b */
+const RB6: f32 = -4.8351919556e+02; /* 0xc3f1c275 */
+const SB1: f32 = 3.0338060379e+01; /* 0x41f2b459 */
+const SB2: f32 = 3.2579251099e+02; /* 0x43a2e571 */
+const SB3: f32 = 1.5367296143e+03; /* 0x44c01759 */
+const SB4: f32 = 3.1998581543e+03; /* 0x4547fdbb */
+const SB5: f32 = 2.5530502930e+03; /* 0x451f90ce */
+const SB6: f32 = 4.7452853394e+02; /* 0x43ed43a7 */
+const SB7: f32 = -2.2440952301e+01; /* 0xc1b38712 */
+
+fn erfc1(x: f32) -> f32 {
+    let s: f32;
+    let p: f32;
+    let q: f32;
+
+    s = fabsf(x) - 1.0;
+    p = PA0 + s * (PA1 + s * (PA2 + s * (PA3 + s * (PA4 + s * (PA5 + s * PA6)))));
+    q = 1.0 + s * (QA1 + s * (QA2 + s * (QA3 + s * (QA4 + s * (QA5 + s * QA6)))));
+    return 1.0 - ERX - p / q;
+}
+
+fn erfc2(mut ix: u32, mut x: f32) -> f32 {
+    let s: f32;
+    let r: f32;
+    let big_s: f32;
+    let z: f32;
+
+    if ix < 0x3fa00000 {
+        /* |x| < 1.25 */
+        return erfc1(x);
+    }
+
+    x = fabsf(x);
+    s = 1.0 / (x * x);
+    if ix < 0x4036db6d {
+        /* |x| < 1/0.35 */
+        r = RA0 + s * (RA1 + s * (RA2 + s * (RA3 + s * (RA4 + s * (RA5 + s * (RA6 + s * RA7))))));
+        big_s = 1.0
+            + s * (SA1
+                + s * (SA2 + s * (SA3 + s * (SA4 + s * (SA5 + s * (SA6 + s * (SA7 + s * SA8)))))));
+    } else {
+        /* |x| >= 1/0.35 */
+        r = RB0 + s * (RB1 + s * (RB2 + s * (RB3 + s * (RB4 + s * (RB5 + s * RB6)))));
+        big_s =
+            1.0 + s * (SB1 + s * (SB2 + s * (SB3 + s * (SB4 + s * (SB5 + s * (SB6 + s * SB7))))));
+    }
+    ix = x.to_bits();
+    z = f32::from_bits(ix & 0xffffe000);
+
+    expf(-z * z - 0.5625) * expf((z - x) * (z + x) + r / big_s) / x
+}
+
+/// Error function (f32)
+///
+/// Calculates an approximation to the “error function”, which estimates
+/// the probability that an observation will fall within x standard
+/// deviations of the mean (assuming a normal distribution).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn erff(x: f32) -> f32 {
+    let r: f32;
+    let s: f32;
+    let z: f32;
+    let y: f32;
+    let mut ix: u32;
+    let sign: usize;
+
+    ix = x.to_bits();
+    sign = (ix >> 31) as usize;
+    ix &= 0x7fffffff;
+    if ix >= 0x7f800000 {
+        /* erf(nan)=nan, erf(+-inf)=+-1 */
+        return 1.0 - 2.0 * (sign as f32) + 1.0 / x;
+    }
+    if ix < 0x3f580000 {
+        /* |x| < 0.84375 */
+        if ix < 0x31800000 {
+            /* |x| < 2**-28 */
+            /*avoid underflow */
+            return 0.125 * (8.0 * x + EFX8 * x);
+        }
+        z = x * x;
+        r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4)));
+        s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5))));
+        y = r / s;
+        return x + x * y;
+    }
+    if ix < 0x40c00000 {
+        /* |x| < 6 */
+        y = 1.0 - erfc2(ix, x);
+    } else {
+        let x1p_120 = f32::from_bits(0x03800000);
+        y = 1.0 - x1p_120;
+    }
+
+    if sign != 0 { -y } else { y }
+}
+
+/// Complementary error function (f32)
+///
+/// Calculates the complementary probability.
+/// Is `1 - erf(x)`. Is computed directly, so that you can use it to avoid
+/// the loss of precision that would result from subtracting
+/// large probabilities (on large `x`) from 1.
+pub fn erfcf(x: f32) -> f32 {
+    let r: f32;
+    let s: f32;
+    let z: f32;
+    let y: f32;
+    let mut ix: u32;
+    let sign: usize;
+
+    ix = x.to_bits();
+    sign = (ix >> 31) as usize;
+    ix &= 0x7fffffff;
+    if ix >= 0x7f800000 {
+        /* erfc(nan)=nan, erfc(+-inf)=0,2 */
+        return 2.0 * (sign as f32) + 1.0 / x;
+    }
+
+    if ix < 0x3f580000 {
+        /* |x| < 0.84375 */
+        if ix < 0x23800000 {
+            /* |x| < 2**-56 */
+            return 1.0 - x;
+        }
+        z = x * x;
+        r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4)));
+        s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5))));
+        y = r / s;
+        if sign != 0 || ix < 0x3e800000 {
+            /* x < 1/4 */
+            return 1.0 - (x + x * y);
+        }
+        return 0.5 - (x - 0.5 + x * y);
+    }
+    if ix < 0x41e00000 {
+        /* |x| < 28 */
+        if sign != 0 {
+            return 2.0 - erfc2(ix, x);
+        } else {
+            return erfc2(ix, x);
+        }
+    }
+
+    let x1p_120 = f32::from_bits(0x03800000);
+    if sign != 0 {
+        2.0 - x1p_120
+    } else {
+        x1p_120 * x1p_120
+    }
+}

vendor/libm/src/math/exp.rs

@@ -0,0 +1,150 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_exp.c */
+/*
+ * ====================================================
+ * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* exp(x)
+ * Returns the exponential of x.
+ *
+ * Method
+ *   1. Argument reduction:
+ *      Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
+ *      Given x, find r and integer k such that
+ *
+ *               x = k*ln2 + r,  |r| <= 0.5*ln2.
+ *
+ *      Here r will be represented as r = hi-lo for better
+ *      accuracy.
+ *
+ *   2. Approximation of exp(r) by a special rational function on
+ *      the interval [0,0.34658]:
+ *      Write
+ *          R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
+ *      We use a special Remez algorithm on [0,0.34658] to generate
+ *      a polynomial of degree 5 to approximate R. The maximum error
+ *      of this polynomial approximation is bounded by 2**-59. In
+ *      other words,
+ *          R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
+ *      (where z=r*r, and the values of P1 to P5 are listed below)
+ *      and
+ *          |                  5          |     -59
+ *          | 2.0+P1*z+...+P5*z   -  R(z) | <= 2
+ *          |                             |
+ *      The computation of exp(r) thus becomes
+ *                              2*r
+ *              exp(r) = 1 + ----------
+ *                            R(r) - r
+ *                                 r*c(r)
+ *                     = 1 + r + ----------- (for better accuracy)
+ *                                2 - c(r)
+ *      where
+ *                              2       4             10
+ *              c(r) = r - (P1*r  + P2*r  + ... + P5*r   ).
+ *
+ *   3. Scale back to obtain exp(x):
+ *      From step 1, we have
+ *         exp(x) = 2^k * exp(r)
+ *
+ * Special cases:
+ *      exp(INF) is INF, exp(NaN) is NaN;
+ *      exp(-INF) is 0, and
+ *      for finite argument, only exp(0)=1 is exact.
+ *
+ * Accuracy:
+ *      according to an error analysis, the error is always less than
+ *      1 ulp (unit in the last place).
+ *
+ * Misc. info.
+ *      For IEEE double
+ *          if x >  709.782712893383973096 then exp(x) overflows
+ *          if x < -745.133219101941108420 then exp(x) underflows
+ */
+
+use super::scalbn;
+
+const HALF: [f64; 2] = [0.5, -0.5];
+const LN2HI: f64 = 6.93147180369123816490e-01; /* 0x3fe62e42, 0xfee00000 */
+const LN2LO: f64 = 1.90821492927058770002e-10; /* 0x3dea39ef, 0x35793c76 */
+const INVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */
+const P1: f64 = 1.66666666666666019037e-01; /* 0x3FC55555, 0x5555553E */
+const P2: f64 = -2.77777777770155933842e-03; /* 0xBF66C16C, 0x16BEBD93 */
+const P3: f64 = 6.61375632143793436117e-05; /* 0x3F11566A, 0xAF25DE2C */
+const P4: f64 = -1.65339022054652515390e-06; /* 0xBEBBBD41, 0xC5D26BF1 */
+const P5: f64 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
+
+/// Exponential, base *e* (f64)
+///
+/// Calculate the exponential of `x`, that is, *e* raised to the power `x`
+/// (where *e* is the base of the natural system of logarithms, approximately 2.71828).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn exp(mut x: f64) -> f64 {
+    let x1p1023 = f64::from_bits(0x7fe0000000000000); // 0x1p1023 === 2 ^ 1023
+    let x1p_149 = f64::from_bits(0x36a0000000000000); // 0x1p-149 === 2 ^ -149
+
+    let hi: f64;
+    let lo: f64;
+    let c: f64;
+    let xx: f64;
+    let y: f64;
+    let k: i32;
+    let sign: i32;
+    let mut hx: u32;
+
+    hx = (x.to_bits() >> 32) as u32;
+    sign = (hx >> 31) as i32;
+    hx &= 0x7fffffff; /* high word of |x| */
+
+    /* special cases */
+    if hx >= 0x4086232b {
+        /* if |x| >= 708.39... */
+        if x.is_nan() {
+            return x;
+        }
+        if x > 709.782712893383973096 {
+            /* overflow if x!=inf */
+            x *= x1p1023;
+            return x;
+        }
+        if x < -708.39641853226410622 {
+            /* underflow if x!=-inf */
+            force_eval!((-x1p_149 / x) as f32);
+            if x < -745.13321910194110842 {
+                return 0.;
+            }
+        }
+    }
+
+    /* argument reduction */
+    if hx > 0x3fd62e42 {
+        /* if |x| > 0.5 ln2 */
+        if hx >= 0x3ff0a2b2 {
+            /* if |x| >= 1.5 ln2 */
+            k = (INVLN2 * x + i!(HALF, sign as usize)) as i32;
+        } else {
+            k = 1 - sign - sign;
+        }
+        hi = x - k as f64 * LN2HI; /* k*ln2hi is exact here */
+        lo = k as f64 * LN2LO;
+        x = hi - lo;
+    } else if hx > 0x3e300000 {
+        /* if |x| > 2**-28 */
+        k = 0;
+        hi = x;
+        lo = 0.;
+    } else {
+        /* inexact if x!=0 */
+        force_eval!(x1p1023 + x);
+        return 1. + x;
+    }
+
+    /* x is now in primary range */
+    xx = x * x;
+    c = x - xx * (P1 + xx * (P2 + xx * (P3 + xx * (P4 + xx * P5))));
+    y = 1. + (x * c / (2. - c) - lo + hi);
+    if k == 0 { y } else { scalbn(y, k) }
+}

vendor/libm/src/math/exp10.rs

@@ -0,0 +1,23 @@
+use super::{exp2, modf, pow};
+
+const LN10: f64 = 3.32192809488736234787031942948939;
+const P10: &[f64] = &[
+    1e-15, 1e-14, 1e-13, 1e-12, 1e-11, 1e-10, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1,
+    1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15,
+];
+
+/// Calculates 10 raised to the power of `x` (f64).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn exp10(x: f64) -> f64 {
+    let (mut y, n) = modf(x);
+    let u: u64 = n.to_bits();
+    /* fabs(n) < 16 without raising invalid on nan */
+    if ((u >> 52) & 0x7ff) < 0x3ff + 4 {
+        if y == 0.0 {
+            return i!(P10, ((n as isize) + 15) as usize);
+        }
+        y = exp2(LN10 * y);
+        return y * i!(P10, ((n as isize) + 15) as usize);
+    }
+    return pow(10.0, x);
+}

vendor/libm/src/math/exp10f.rs

@@ -0,0 +1,23 @@
+use super::{exp2, exp2f, modff};
+
+const LN10_F32: f32 = 3.32192809488736234787031942948939;
+const LN10_F64: f64 = 3.32192809488736234787031942948939;
+const P10: &[f32] = &[
+    1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1, 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7,
+];
+
+/// Calculates 10 raised to the power of `x` (f32).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn exp10f(x: f32) -> f32 {
+    let (mut y, n) = modff(x);
+    let u = n.to_bits();
+    /* fabsf(n) < 8 without raising invalid on nan */
+    if ((u >> 23) & 0xff) < 0x7f + 3 {
+        if y == 0.0 {
+            return i!(P10, ((n as isize) + 7) as usize);
+        }
+        y = exp2f(LN10_F32 * y);
+        return y * i!(P10, ((n as isize) + 7) as usize);
+    }
+    return exp2(LN10_F64 * (x as f64)) as f32;
+}

vendor/libm/src/math/exp2.rs

@@ -0,0 +1,394 @@
+// origin: FreeBSD /usr/src/lib/msun/src/s_exp2.c */
+//-
+// Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
+// All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions
+// are met:
+// 1. Redistributions of source code must retain the above copyright
+//    notice, this list of conditions and the following disclaimer.
+// 2. Redistributions in binary form must reproduce the above copyright
+//    notice, this list of conditions and the following disclaimer in the
+//    documentation and/or other materials provided with the distribution.
+//
+// THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+// OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+// OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+// SUCH DAMAGE.
+
+use super::scalbn;
+
+const TBLSIZE: usize = 256;
+
+#[rustfmt::skip]
+static TBL: [u64; TBLSIZE * 2] = [
+    //  exp2(z + eps)          eps
+    0x3fe6a09e667f3d5d, 0x3d39880000000000,
+    0x3fe6b052fa751744, 0x3cd8000000000000,
+    0x3fe6c012750bd9fe, 0xbd28780000000000,
+    0x3fe6cfdcddd476bf, 0x3d1ec00000000000,
+    0x3fe6dfb23c651a29, 0xbcd8000000000000,
+    0x3fe6ef9298593ae3, 0xbcbc000000000000,
+    0x3fe6ff7df9519386, 0xbd2fd80000000000,
+    0x3fe70f7466f42da3, 0xbd2c880000000000,
+    0x3fe71f75e8ec5fc3, 0x3d13c00000000000,
+    0x3fe72f8286eacf05, 0xbd38300000000000,
+    0x3fe73f9a48a58152, 0xbd00c00000000000,
+    0x3fe74fbd35d7ccfc, 0x3d2f880000000000,
+    0x3fe75feb564267f1, 0x3d03e00000000000,
+    0x3fe77024b1ab6d48, 0xbd27d00000000000,
+    0x3fe780694fde5d38, 0xbcdd000000000000,
+    0x3fe790b938ac1d00, 0x3ce3000000000000,
+    0x3fe7a11473eb0178, 0xbced000000000000,
+    0x3fe7b17b0976d060, 0x3d20400000000000,
+    0x3fe7c1ed0130c133, 0x3ca0000000000000,
+    0x3fe7d26a62ff8636, 0xbd26900000000000,
+    0x3fe7e2f336cf4e3b, 0xbd02e00000000000,
+    0x3fe7f3878491c3e8, 0xbd24580000000000,
+    0x3fe80427543e1b4e, 0x3d33000000000000,
+    0x3fe814d2add1071a, 0x3d0f000000000000,
+    0x3fe82589994ccd7e, 0xbd21c00000000000,
+    0x3fe8364c1eb942d0, 0x3d29d00000000000,
+    0x3fe8471a4623cab5, 0x3d47100000000000,
+    0x3fe857f4179f5bbc, 0x3d22600000000000,
+    0x3fe868d99b4491af, 0xbd32c40000000000,
+    0x3fe879cad931a395, 0xbd23000000000000,
+    0x3fe88ac7d98a65b8, 0xbd2a800000000000,
+    0x3fe89bd0a4785800, 0xbced000000000000,
+    0x3fe8ace5422aa223, 0x3d33280000000000,
+    0x3fe8be05bad619fa, 0x3d42b40000000000,
+    0x3fe8cf3216b54383, 0xbd2ed00000000000,
+    0x3fe8e06a5e08664c, 0xbd20500000000000,
+    0x3fe8f1ae99157807, 0x3d28280000000000,
+    0x3fe902fed0282c0e, 0xbd1cb00000000000,
+    0x3fe9145b0b91ff96, 0xbd05e00000000000,
+    0x3fe925c353aa2ff9, 0x3cf5400000000000,
+    0x3fe93737b0cdc64a, 0x3d17200000000000,
+    0x3fe948b82b5f98ae, 0xbd09000000000000,
+    0x3fe95a44cbc852cb, 0x3d25680000000000,
+    0x3fe96bdd9a766f21, 0xbd36d00000000000,
+    0x3fe97d829fde4e2a, 0xbd01000000000000,
+    0x3fe98f33e47a23a3, 0x3d2d000000000000,
+    0x3fe9a0f170ca0604, 0xbd38a40000000000,
+    0x3fe9b2bb4d53ff89, 0x3d355c0000000000,
+    0x3fe9c49182a3f15b, 0x3d26b80000000000,
+    0x3fe9d674194bb8c5, 0xbcec000000000000,
+    0x3fe9e86319e3238e, 0x3d17d00000000000,
+    0x3fe9fa5e8d07f302, 0x3d16400000000000,
+    0x3fea0c667b5de54d, 0xbcf5000000000000,
+    0x3fea1e7aed8eb8f6, 0x3d09e00000000000,
+    0x3fea309bec4a2e27, 0x3d2ad80000000000,
+    0x3fea42c980460a5d, 0xbd1af00000000000,
+    0x3fea5503b23e259b, 0x3d0b600000000000,
+    0x3fea674a8af46213, 0x3d38880000000000,
+    0x3fea799e1330b3a7, 0x3d11200000000000,
+    0x3fea8bfe53c12e8d, 0x3d06c00000000000,
+    0x3fea9e6b5579fcd2, 0xbd29b80000000000,
+    0x3feab0e521356fb8, 0x3d2b700000000000,
+    0x3feac36bbfd3f381, 0x3cd9000000000000,
+    0x3fead5ff3a3c2780, 0x3ce4000000000000,
+    0x3feae89f995ad2a3, 0xbd2c900000000000,
+    0x3feafb4ce622f367, 0x3d16500000000000,
+    0x3feb0e07298db790, 0x3d2fd40000000000,
+    0x3feb20ce6c9a89a9, 0x3d12700000000000,
+    0x3feb33a2b84f1a4b, 0x3d4d470000000000,
+    0x3feb468415b747e7, 0xbd38380000000000,
+    0x3feb59728de5593a, 0x3c98000000000000,
+    0x3feb6c6e29f1c56a, 0x3d0ad00000000000,
+    0x3feb7f76f2fb5e50, 0x3cde800000000000,
+    0x3feb928cf22749b2, 0xbd04c00000000000,
+    0x3feba5b030a10603, 0xbd0d700000000000,
+    0x3febb8e0b79a6f66, 0x3d0d900000000000,
+    0x3febcc1e904bc1ff, 0x3d02a00000000000,
+    0x3febdf69c3f3a16f, 0xbd1f780000000000,
+    0x3febf2c25bd71db8, 0xbd10a00000000000,
+    0x3fec06286141b2e9, 0xbd11400000000000,
+    0x3fec199bdd8552e0, 0x3d0be00000000000,
+    0x3fec2d1cd9fa64ee, 0xbd09400000000000,
+    0x3fec40ab5fffd02f, 0xbd0ed00000000000,
+    0x3fec544778fafd15, 0x3d39660000000000,
+    0x3fec67f12e57d0cb, 0xbd1a100000000000,
+    0x3fec7ba88988c1b6, 0xbd58458000000000,
+    0x3fec8f6d9406e733, 0xbd1a480000000000,
+    0x3feca3405751c4df, 0x3ccb000000000000,
+    0x3fecb720dcef9094, 0x3d01400000000000,
+    0x3feccb0f2e6d1689, 0x3cf0200000000000,
+    0x3fecdf0b555dc412, 0x3cf3600000000000,
+    0x3fecf3155b5bab3b, 0xbd06900000000000,
+    0x3fed072d4a0789bc, 0x3d09a00000000000,
+    0x3fed1b532b08c8fa, 0xbd15e00000000000,
+    0x3fed2f87080d8a85, 0x3d1d280000000000,
+    0x3fed43c8eacaa203, 0x3d01a00000000000,
+    0x3fed5818dcfba491, 0x3cdf000000000000,
+    0x3fed6c76e862e6a1, 0xbd03a00000000000,
+    0x3fed80e316c9834e, 0xbd0cd80000000000,
+    0x3fed955d71ff6090, 0x3cf4c00000000000,
+    0x3feda9e603db32ae, 0x3cff900000000000,
+    0x3fedbe7cd63a8325, 0x3ce9800000000000,
+    0x3fedd321f301b445, 0xbcf5200000000000,
+    0x3fede7d5641c05bf, 0xbd1d700000000000,
+    0x3fedfc97337b9aec, 0xbd16140000000000,
+    0x3fee11676b197d5e, 0x3d0b480000000000,
+    0x3fee264614f5a3e7, 0x3d40ce0000000000,
+    0x3fee3b333b16ee5c, 0x3d0c680000000000,
+    0x3fee502ee78b3fb4, 0xbd09300000000000,
+    0x3fee653924676d68, 0xbce5000000000000,
+    0x3fee7a51fbc74c44, 0xbd07f80000000000,
+    0x3fee8f7977cdb726, 0xbcf3700000000000,
+    0x3feea4afa2a490e8, 0x3ce5d00000000000,
+    0x3feeb9f4867ccae4, 0x3d161a0000000000,
+    0x3feecf482d8e680d, 0x3cf5500000000000,
+    0x3feee4aaa2188514, 0x3cc6400000000000,
+    0x3feefa1bee615a13, 0xbcee800000000000,
+    0x3fef0f9c1cb64106, 0xbcfa880000000000,
+    0x3fef252b376bb963, 0xbd2c900000000000,
+    0x3fef3ac948dd7275, 0x3caa000000000000,
+    0x3fef50765b6e4524, 0xbcf4f00000000000,
+    0x3fef6632798844fd, 0x3cca800000000000,
+    0x3fef7bfdad9cbe38, 0x3cfabc0000000000,
+    0x3fef91d802243c82, 0xbcd4600000000000,
+    0x3fefa7c1819e908e, 0xbd0b0c0000000000,
+    0x3fefbdba3692d511, 0xbcc0e00000000000,
+    0x3fefd3c22b8f7194, 0xbd10de8000000000,
+    0x3fefe9d96b2a23ee, 0x3cee430000000000,
+    0x3ff0000000000000, 0x0,
+    0x3ff00b1afa5abcbe, 0xbcb3400000000000,
+    0x3ff0163da9fb3303, 0xbd12170000000000,
+    0x3ff02168143b0282, 0x3cba400000000000,
+    0x3ff02c9a3e77806c, 0x3cef980000000000,
+    0x3ff037d42e11bbca, 0xbcc7400000000000,
+    0x3ff04315e86e7f89, 0x3cd8300000000000,
+    0x3ff04e5f72f65467, 0xbd1a3f0000000000,
+    0x3ff059b0d315855a, 0xbd02840000000000,
+    0x3ff0650a0e3c1f95, 0x3cf1600000000000,
+    0x3ff0706b29ddf71a, 0x3d15240000000000,
+    0x3ff07bd42b72a82d, 0xbce9a00000000000,
+    0x3ff0874518759bd0, 0x3ce6400000000000,
+    0x3ff092bdf66607c8, 0xbd00780000000000,
+    0x3ff09e3ecac6f383, 0xbc98000000000000,
+    0x3ff0a9c79b1f3930, 0x3cffa00000000000,
+    0x3ff0b5586cf988fc, 0xbcfac80000000000,
+    0x3ff0c0f145e46c8a, 0x3cd9c00000000000,
+    0x3ff0cc922b724816, 0x3d05200000000000,
+    0x3ff0d83b23395dd8, 0xbcfad00000000000,
+    0x3ff0e3ec32d3d1f3, 0x3d1bac0000000000,
+    0x3ff0efa55fdfa9a6, 0xbd04e80000000000,
+    0x3ff0fb66affed2f0, 0xbd0d300000000000,
+    0x3ff1073028d7234b, 0x3cf1500000000000,
+    0x3ff11301d0125b5b, 0x3cec000000000000,
+    0x3ff11edbab5e2af9, 0x3d16bc0000000000,
+    0x3ff12abdc06c31d5, 0x3ce8400000000000,
+    0x3ff136a814f2047d, 0xbd0ed00000000000,
+    0x3ff1429aaea92de9, 0x3ce8e00000000000,
+    0x3ff14e95934f3138, 0x3ceb400000000000,
+    0x3ff15a98c8a58e71, 0x3d05300000000000,
+    0x3ff166a45471c3df, 0x3d03380000000000,
+    0x3ff172b83c7d5211, 0x3d28d40000000000,
+    0x3ff17ed48695bb9f, 0xbd05d00000000000,
+    0x3ff18af9388c8d93, 0xbd1c880000000000,
+    0x3ff1972658375d66, 0x3d11f00000000000,
+    0x3ff1a35beb6fcba7, 0x3d10480000000000,
+    0x3ff1af99f81387e3, 0xbd47390000000000,
+    0x3ff1bbe084045d54, 0x3d24e40000000000,
+    0x3ff1c82f95281c43, 0xbd0a200000000000,
+    0x3ff1d4873168b9b2, 0x3ce3800000000000,
+    0x3ff1e0e75eb44031, 0x3ceac00000000000,
+    0x3ff1ed5022fcd938, 0x3d01900000000000,
+    0x3ff1f9c18438cdf7, 0xbd1b780000000000,
+    0x3ff2063b88628d8f, 0x3d2d940000000000,
+    0x3ff212be3578a81e, 0x3cd8000000000000,
+    0x3ff21f49917ddd41, 0x3d2b340000000000,
+    0x3ff22bdda2791323, 0x3d19f80000000000,
+    0x3ff2387a6e7561e7, 0xbd19c80000000000,
+    0x3ff2451ffb821427, 0x3d02300000000000,
+    0x3ff251ce4fb2a602, 0xbd13480000000000,
+    0x3ff25e85711eceb0, 0x3d12700000000000,
+    0x3ff26b4565e27d16, 0x3d11d00000000000,
+    0x3ff2780e341de00f, 0x3d31ee0000000000,
+    0x3ff284dfe1f5633e, 0xbd14c00000000000,
+    0x3ff291ba7591bb30, 0xbd13d80000000000,
+    0x3ff29e9df51fdf09, 0x3d08b00000000000,
+    0x3ff2ab8a66d10e9b, 0xbd227c0000000000,
+    0x3ff2b87fd0dada3a, 0x3d2a340000000000,
+    0x3ff2c57e39771af9, 0xbd10800000000000,
+    0x3ff2d285a6e402d9, 0xbd0ed00000000000,
+    0x3ff2df961f641579, 0xbcf4200000000000,
+    0x3ff2ecafa93e2ecf, 0xbd24980000000000,
+    0x3ff2f9d24abd8822, 0xbd16300000000000,
+    0x3ff306fe0a31b625, 0xbd32360000000000,
+    0x3ff31432edeea50b, 0xbd70df8000000000,
+    0x3ff32170fc4cd7b8, 0xbd22480000000000,
+    0x3ff32eb83ba8e9a2, 0xbd25980000000000,
+    0x3ff33c08b2641766, 0x3d1ed00000000000,
+    0x3ff3496266e3fa27, 0xbcdc000000000000,
+    0x3ff356c55f929f0f, 0xbd30d80000000000,
+    0x3ff36431a2de88b9, 0x3d22c80000000000,
+    0x3ff371a7373aaa39, 0x3d20600000000000,
+    0x3ff37f26231e74fe, 0xbd16600000000000,
+    0x3ff38cae6d05d838, 0xbd0ae00000000000,
+    0x3ff39a401b713ec3, 0xbd44720000000000,
+    0x3ff3a7db34e5a020, 0x3d08200000000000,
+    0x3ff3b57fbfec6e95, 0x3d3e800000000000,
+    0x3ff3c32dc313a8f2, 0x3cef800000000000,
+    0x3ff3d0e544ede122, 0xbd17a00000000000,
+    0x3ff3dea64c1234bb, 0x3d26300000000000,
+    0x3ff3ec70df1c4ecc, 0xbd48a60000000000,
+    0x3ff3fa4504ac7e8c, 0xbd3cdc0000000000,
+    0x3ff40822c367a0bb, 0x3d25b80000000000,
+    0x3ff4160a21f72e95, 0x3d1ec00000000000,
+    0x3ff423fb27094646, 0xbd13600000000000,
+    0x3ff431f5d950a920, 0x3d23980000000000,
+    0x3ff43ffa3f84b9eb, 0x3cfa000000000000,
+    0x3ff44e0860618919, 0xbcf6c00000000000,
+    0x3ff45c2042a7d201, 0xbd0bc00000000000,
+    0x3ff46a41ed1d0016, 0xbd12800000000000,
+    0x3ff4786d668b3326, 0x3d30e00000000000,
+    0x3ff486a2b5c13c00, 0xbd2d400000000000,
+    0x3ff494e1e192af04, 0x3d0c200000000000,
+    0x3ff4a32af0d7d372, 0xbd1e500000000000,
+    0x3ff4b17dea6db801, 0x3d07800000000000,
+    0x3ff4bfdad53629e1, 0xbd13800000000000,
+    0x3ff4ce41b817c132, 0x3d00800000000000,
+    0x3ff4dcb299fddddb, 0x3d2c700000000000,
+    0x3ff4eb2d81d8ab96, 0xbd1ce00000000000,
+    0x3ff4f9b2769d2d02, 0x3d19200000000000,
+    0x3ff508417f4531c1, 0xbd08c00000000000,
+    0x3ff516daa2cf662a, 0xbcfa000000000000,
+    0x3ff5257de83f51ea, 0x3d4a080000000000,
+    0x3ff5342b569d4eda, 0xbd26d80000000000,
+    0x3ff542e2f4f6ac1a, 0xbd32440000000000,
+    0x3ff551a4ca5d94db, 0x3d483c0000000000,
+    0x3ff56070dde9116b, 0x3d24b00000000000,
+    0x3ff56f4736b529de, 0x3d415a0000000000,
+    0x3ff57e27dbe2c40e, 0xbd29e00000000000,
+    0x3ff58d12d497c76f, 0xbd23080000000000,
+    0x3ff59c0827ff0b4c, 0x3d4dec0000000000,
+    0x3ff5ab07dd485427, 0xbcc4000000000000,
+    0x3ff5ba11fba87af4, 0x3d30080000000000,
+    0x3ff5c9268a59460b, 0xbd26c80000000000,
+    0x3ff5d84590998e3f, 0x3d469a0000000000,
+    0x3ff5e76f15ad20e1, 0xbd1b400000000000,
+    0x3ff5f6a320dcebca, 0x3d17700000000000,
+    0x3ff605e1b976dcb8, 0x3d26f80000000000,
+    0x3ff6152ae6cdf715, 0x3d01000000000000,
+    0x3ff6247eb03a5531, 0xbd15d00000000000,
+    0x3ff633dd1d1929b5, 0xbd12d00000000000,
+    0x3ff6434634ccc313, 0xbcea800000000000,
+    0x3ff652b9febc8efa, 0xbd28600000000000,
+    0x3ff6623882553397, 0x3d71fe0000000000,
+    0x3ff671c1c708328e, 0xbd37200000000000,
+    0x3ff68155d44ca97e, 0x3ce6800000000000,
+    0x3ff690f4b19e9471, 0xbd29780000000000,
+];
+
+// exp2(x): compute the base 2 exponential of x
+//
+// Accuracy: Peak error < 0.503 ulp for normalized results.
+//
+// Method: (accurate tables)
+//
+//   Reduce x:
+//     x = k + y, for integer k and |y| <= 1/2.
+//     Thus we have exp2(x) = 2**k * exp2(y).
+//
+//   Reduce y:
+//     y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE.
+//     Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]),
+//     with |z - eps[i]| <= 2**-9 + 2**-39 for the table used.
+//
+//   We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via
+//   a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61.
+//   The values in exp2t[] and eps[] are chosen such that
+//   exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such
+//   that exp2t[i] is accurate to 2**-64.
+//
+//   Note that the range of i is +-TBLSIZE/2, so we actually index the tables
+//   by i0 = i + TBLSIZE/2.  For cache efficiency, exp2t[] and eps[] are
+//   virtual tables, interleaved in the real table tbl[].
+//
+//   This method is due to Gal, with many details due to Gal and Bachelis:
+//
+//      Gal, S. and Bachelis, B.  An Accurate Elementary Mathematical Library
+//      for the IEEE Floating Point Standard.  TOMS 17(1), 26-46 (1991).
+
+/// Exponential, base 2 (f64)
+///
+/// Calculate `2^x`, that is, 2 raised to the power `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn exp2(mut x: f64) -> f64 {
+    let redux = f64::from_bits(0x4338000000000000) / TBLSIZE as f64;
+    let p1 = f64::from_bits(0x3fe62e42fefa39ef);
+    let p2 = f64::from_bits(0x3fcebfbdff82c575);
+    let p3 = f64::from_bits(0x3fac6b08d704a0a6);
+    let p4 = f64::from_bits(0x3f83b2ab88f70400);
+    let p5 = f64::from_bits(0x3f55d88003875c74);
+
+    // double_t r, t, z;
+    // uint32_t ix, i0;
+    // union {double f; uint64_t i;} u = {x};
+    // union {uint32_t u; int32_t i;} k;
+    let x1p1023 = f64::from_bits(0x7fe0000000000000);
+    let x1p52 = f64::from_bits(0x4330000000000000);
+    let _0x1p_149 = f64::from_bits(0xb6a0000000000000);
+
+    /* Filter out exceptional cases. */
+    let ui = f64::to_bits(x);
+    let ix = (ui >> 32) & 0x7fffffff;
+    if ix >= 0x408ff000 {
+        /* |x| >= 1022 or nan */
+        if ix >= 0x40900000 && ui >> 63 == 0 {
+            /* x >= 1024 or nan */
+            /* overflow */
+            x *= x1p1023;
+            return x;
+        }
+        if ix >= 0x7ff00000 {
+            /* -inf or -nan */
+            return -1.0 / x;
+        }
+        if ui >> 63 != 0 {
+            /* x <= -1022 */
+            /* underflow */
+            if x <= -1075.0 || x - x1p52 + x1p52 != x {
+                force_eval!((_0x1p_149 / x) as f32);
+            }
+            if x <= -1075.0 {
+                return 0.0;
+            }
+        }
+    } else if ix < 0x3c900000 {
+        /* |x| < 0x1p-54 */
+        return 1.0 + x;
+    }
+
+    /* Reduce x, computing z, i0, and k. */
+    let ui = f64::to_bits(x + redux);
+    let mut i0 = ui as u32;
+    i0 = i0.wrapping_add(TBLSIZE as u32 / 2);
+    let ku = i0 / TBLSIZE as u32 * TBLSIZE as u32;
+    let ki = div!(ku as i32, TBLSIZE as i32);
+    i0 %= TBLSIZE as u32;
+    let uf = f64::from_bits(ui) - redux;
+    let mut z = x - uf;
+
+    /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */
+    let t = f64::from_bits(i!(TBL, 2 * i0 as usize)); /* exp2t[i0] */
+    z -= f64::from_bits(i!(TBL, 2 * i0 as usize + 1)); /* eps[i0]   */
+    let r = t + t * z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * p5))));
+
+    scalbn(r, ki)
+}
+
+#[test]
+fn i0_wrap_test() {
+    let x = -3.0 / 256.0;
+    assert_eq!(exp2(x), f64::from_bits(0x3fefbdba3692d514));
+}

vendor/libm/src/math/exp2f.rs

@@ -0,0 +1,135 @@
+// origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c
+//-
+// Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
+// All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions
+// are met:
+// 1. Redistributions of source code must retain the above copyright
+//    notice, this list of conditions and the following disclaimer.
+// 2. Redistributions in binary form must reproduce the above copyright
+//    notice, this list of conditions and the following disclaimer in the
+//    documentation and/or other materials provided with the distribution.
+//
+// THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+// OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+// OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+// SUCH DAMAGE.
+
+const TBLSIZE: usize = 16;
+
+static EXP2FT: [u64; TBLSIZE] = [
+    0x3fe6a09e667f3bcd,
+    0x3fe7a11473eb0187,
+    0x3fe8ace5422aa0db,
+    0x3fe9c49182a3f090,
+    0x3feae89f995ad3ad,
+    0x3fec199bdd85529c,
+    0x3fed5818dcfba487,
+    0x3feea4afa2a490da,
+    0x3ff0000000000000,
+    0x3ff0b5586cf9890f,
+    0x3ff172b83c7d517b,
+    0x3ff2387a6e756238,
+    0x3ff306fe0a31b715,
+    0x3ff3dea64c123422,
+    0x3ff4bfdad5362a27,
+    0x3ff5ab07dd485429,
+];
+
+// exp2f(x): compute the base 2 exponential of x
+//
+// Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
+//
+// Method: (equally-spaced tables)
+//
+//   Reduce x:
+//     x = k + y, for integer k and |y| <= 1/2.
+//     Thus we have exp2f(x) = 2**k * exp2(y).
+//
+//   Reduce y:
+//     y = i/TBLSIZE + z for integer i near y * TBLSIZE.
+//     Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
+//     with |z| <= 2**-(TBLSIZE+1).
+//
+//   We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
+//   degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
+//   Using double precision for everything except the reduction makes
+//   roundoff error insignificant and simplifies the scaling step.
+//
+//   This method is due to Tang, but I do not use his suggested parameters:
+//
+//      Tang, P.  Table-driven Implementation of the Exponential Function
+//      in IEEE Floating-Point Arithmetic.  TOMS 15(2), 144-157 (1989).
+
+/// Exponential, base 2 (f32)
+///
+/// Calculate `2^x`, that is, 2 raised to the power `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn exp2f(mut x: f32) -> f32 {
+    let redux = f32::from_bits(0x4b400000) / TBLSIZE as f32;
+    let p1 = f32::from_bits(0x3f317218);
+    let p2 = f32::from_bits(0x3e75fdf0);
+    let p3 = f32::from_bits(0x3d6359a4);
+    let p4 = f32::from_bits(0x3c1d964e);
+
+    // double_t t, r, z;
+    // uint32_t ix, i0, k;
+
+    let x1p127 = f32::from_bits(0x7f000000);
+
+    /* Filter out exceptional cases. */
+    let ui = f32::to_bits(x);
+    let ix = ui & 0x7fffffff;
+    if ix > 0x42fc0000 {
+        /* |x| > 126 */
+        if ix > 0x7f800000 {
+            /* NaN */
+            return x;
+        }
+        if (0x43000000..0x80000000).contains(&ui) {
+            /* x >= 128 */
+            x *= x1p127;
+            return x;
+        }
+        if ui >= 0x80000000 {
+            /* x < -126 */
+            if ui >= 0xc3160000 || (ui & 0x0000ffff != 0) {
+                force_eval!(f32::from_bits(0x80000001) / x);
+            }
+            if ui >= 0xc3160000 {
+                /* x <= -150 */
+                return 0.0;
+            }
+        }
+    } else if ix <= 0x33000000 {
+        /* |x| <= 0x1p-25 */
+        return 1.0 + x;
+    }
+
+    /* Reduce x, computing z, i0, and k. */
+    let ui = f32::to_bits(x + redux);
+    let mut i0 = ui;
+    i0 += TBLSIZE as u32 / 2;
+    let k = i0 / TBLSIZE as u32;
+    let ukf = f64::from_bits(((0x3ff + k) as u64) << 52);
+    i0 &= TBLSIZE as u32 - 1;
+    let mut uf = f32::from_bits(ui);
+    uf -= redux;
+    let z: f64 = (x - uf) as f64;
+    /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
+    let r: f64 = f64::from_bits(i!(EXP2FT, i0 as usize));
+    let t: f64 = r * z;
+    let r: f64 = r + t * (p1 as f64 + z * p2 as f64) + t * (z * z) * (p3 as f64 + z * p4 as f64);
+
+    /* Scale by 2**k */
+    (r * ukf) as f32
+}

vendor/libm/src/math/expf.rs

@@ -0,0 +1,97 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_expf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::scalbnf;
+
+const HALF: [f32; 2] = [0.5, -0.5];
+const LN2_HI: f32 = 6.9314575195e-01; /* 0x3f317200 */
+const LN2_LO: f32 = 1.4286067653e-06; /* 0x35bfbe8e */
+const INV_LN2: f32 = 1.4426950216e+00; /* 0x3fb8aa3b */
+/*
+ * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
+ * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
+ */
+const P1: f32 = 1.6666625440e-1; /*  0xaaaa8f.0p-26 */
+const P2: f32 = -2.7667332906e-3; /* -0xb55215.0p-32 */
+
+/// Exponential, base *e* (f32)
+///
+/// Calculate the exponential of `x`, that is, *e* raised to the power `x`
+/// (where *e* is the base of the natural system of logarithms, approximately 2.71828).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn expf(mut x: f32) -> f32 {
+    let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
+    let x1p_126 = f32::from_bits(0x800000); // 0x1p-126f === 2 ^ -126  /*original 0x1p-149f    ??????????? */
+    let mut hx = x.to_bits();
+    let sign = (hx >> 31) as i32; /* sign bit of x */
+    let signb: bool = sign != 0;
+    hx &= 0x7fffffff; /* high word of |x| */
+
+    /* special cases */
+    if hx >= 0x42aeac50 {
+        /* if |x| >= -87.33655f or NaN */
+        if hx > 0x7f800000 {
+            /* NaN */
+            return x;
+        }
+        if (hx >= 0x42b17218) && (!signb) {
+            /* x >= 88.722839f */
+            /* overflow */
+            x *= x1p127;
+            return x;
+        }
+        if signb {
+            /* underflow */
+            force_eval!(-x1p_126 / x);
+            if hx >= 0x42cff1b5 {
+                /* x <= -103.972084f */
+                return 0.;
+            }
+        }
+    }
+
+    /* argument reduction */
+    let k: i32;
+    let hi: f32;
+    let lo: f32;
+    if hx > 0x3eb17218 {
+        /* if |x| > 0.5 ln2 */
+        if hx > 0x3f851592 {
+            /* if |x| > 1.5 ln2 */
+            k = (INV_LN2 * x + i!(HALF, sign as usize)) as i32;
+        } else {
+            k = 1 - sign - sign;
+        }
+        let kf = k as f32;
+        hi = x - kf * LN2_HI; /* k*ln2hi is exact here */
+        lo = kf * LN2_LO;
+        x = hi - lo;
+    } else if hx > 0x39000000 {
+        /* |x| > 2**-14 */
+        k = 0;
+        hi = x;
+        lo = 0.;
+    } else {
+        /* raise inexact */
+        force_eval!(x1p127 + x);
+        return 1. + x;
+    }
+
+    /* x is now in primary range */
+    let xx = x * x;
+    let c = x - xx * (P1 + xx * P2);
+    let y = 1. + (x * c / (2. - c) - lo + hi);
+    if k == 0 { y } else { scalbnf(y, k) }
+}

vendor/libm/src/math/expm1.rs

@@ -0,0 +1,144 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use core::f64;
+
+const O_THRESHOLD: f64 = 7.09782712893383973096e+02; /* 0x40862E42, 0xFEFA39EF */
+const LN2_HI: f64 = 6.93147180369123816490e-01; /* 0x3fe62e42, 0xfee00000 */
+const LN2_LO: f64 = 1.90821492927058770002e-10; /* 0x3dea39ef, 0x35793c76 */
+const INVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */
+/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */
+const Q1: f64 = -3.33333333333331316428e-02; /* BFA11111 111110F4 */
+const Q2: f64 = 1.58730158725481460165e-03; /* 3F5A01A0 19FE5585 */
+const Q3: f64 = -7.93650757867487942473e-05; /* BF14CE19 9EAADBB7 */
+const Q4: f64 = 4.00821782732936239552e-06; /* 3ED0CFCA 86E65239 */
+const Q5: f64 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
+
+/// Exponential, base *e*, of x-1 (f64)
+///
+/// Calculates the exponential of `x` and subtract 1, that is, *e* raised
+/// to the power `x` minus 1 (where *e* is the base of the natural
+/// system of logarithms, approximately 2.71828).
+/// The result is accurate even for small values of `x`,
+/// where using `exp(x)-1` would lose many significant digits.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn expm1(mut x: f64) -> f64 {
+    let hi: f64;
+    let lo: f64;
+    let k: i32;
+    let c: f64;
+    let mut t: f64;
+    let mut y: f64;
+
+    let mut ui = x.to_bits();
+    let hx = ((ui >> 32) & 0x7fffffff) as u32;
+    let sign = (ui >> 63) as i32;
+
+    /* filter out huge and non-finite argument */
+    if hx >= 0x4043687A {
+        /* if |x|>=56*ln2 */
+        if x.is_nan() {
+            return x;
+        }
+        if sign != 0 {
+            return -1.0;
+        }
+        if x > O_THRESHOLD {
+            x *= f64::from_bits(0x7fe0000000000000);
+            return x;
+        }
+    }
+
+    /* argument reduction */
+    if hx > 0x3fd62e42 {
+        /* if  |x| > 0.5 ln2 */
+        if hx < 0x3FF0A2B2 {
+            /* and |x| < 1.5 ln2 */
+            if sign == 0 {
+                hi = x - LN2_HI;
+                lo = LN2_LO;
+                k = 1;
+            } else {
+                hi = x + LN2_HI;
+                lo = -LN2_LO;
+                k = -1;
+            }
+        } else {
+            k = (INVLN2 * x + if sign != 0 { -0.5 } else { 0.5 }) as i32;
+            t = k as f64;
+            hi = x - t * LN2_HI; /* t*ln2_hi is exact here */
+            lo = t * LN2_LO;
+        }
+        x = hi - lo;
+        c = (hi - x) - lo;
+    } else if hx < 0x3c900000 {
+        /* |x| < 2**-54, return x */
+        if hx < 0x00100000 {
+            force_eval!(x);
+        }
+        return x;
+    } else {
+        c = 0.0;
+        k = 0;
+    }
+
+    /* x is now in primary range */
+    let hfx = 0.5 * x;
+    let hxs = x * hfx;
+    let r1 = 1.0 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
+    t = 3.0 - r1 * hfx;
+    let mut e = hxs * ((r1 - t) / (6.0 - x * t));
+    if k == 0 {
+        /* c is 0 */
+        return x - (x * e - hxs);
+    }
+    e = x * (e - c) - c;
+    e -= hxs;
+    /* exp(x) ~ 2^k (x_reduced - e + 1) */
+    if k == -1 {
+        return 0.5 * (x - e) - 0.5;
+    }
+    if k == 1 {
+        if x < -0.25 {
+            return -2.0 * (e - (x + 0.5));
+        }
+        return 1.0 + 2.0 * (x - e);
+    }
+    ui = ((0x3ff + k) as u64) << 52; /* 2^k */
+    let twopk = f64::from_bits(ui);
+    if !(0..=56).contains(&k) {
+        /* suffice to return exp(x)-1 */
+        y = x - e + 1.0;
+        if k == 1024 {
+            y = y * 2.0 * f64::from_bits(0x7fe0000000000000);
+        } else {
+            y = y * twopk;
+        }
+        return y - 1.0;
+    }
+    ui = ((0x3ff - k) as u64) << 52; /* 2^-k */
+    let uf = f64::from_bits(ui);
+    if k < 20 {
+        y = (x - e + (1.0 - uf)) * twopk;
+    } else {
+        y = (x - (e + uf) + 1.0) * twopk;
+    }
+    y
+}
+
+#[cfg(test)]
+mod tests {
+    #[test]
+    fn sanity_check() {
+        assert_eq!(super::expm1(1.1), 2.0041660239464334);
+    }
+}

vendor/libm/src/math/expm1f.rs

@@ -0,0 +1,134 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+const O_THRESHOLD: f32 = 8.8721679688e+01; /* 0x42b17180 */
+const LN2_HI: f32 = 6.9313812256e-01; /* 0x3f317180 */
+const LN2_LO: f32 = 9.0580006145e-06; /* 0x3717f7d1 */
+const INV_LN2: f32 = 1.4426950216e+00; /* 0x3fb8aa3b */
+/*
+ * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
+ * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
+ * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
+ */
+const Q1: f32 = -3.3333212137e-2; /* -0x888868.0p-28 */
+const Q2: f32 = 1.5807170421e-3; /*  0xcf3010.0p-33 */
+
+/// Exponential, base *e*, of x-1 (f32)
+///
+/// Calculates the exponential of `x` and subtract 1, that is, *e* raised
+/// to the power `x` minus 1 (where *e* is the base of the natural
+/// system of logarithms, approximately 2.71828).
+/// The result is accurate even for small values of `x`,
+/// where using `exp(x)-1` would lose many significant digits.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn expm1f(mut x: f32) -> f32 {
+    let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
+
+    let mut hx = x.to_bits();
+    let sign = (hx >> 31) != 0;
+    hx &= 0x7fffffff;
+
+    /* filter out huge and non-finite argument */
+    if hx >= 0x4195b844 {
+        /* if |x|>=27*ln2 */
+        if hx > 0x7f800000 {
+            /* NaN */
+            return x;
+        }
+        if sign {
+            return -1.;
+        }
+        if x > O_THRESHOLD {
+            x *= x1p127;
+            return x;
+        }
+    }
+
+    let k: i32;
+    let hi: f32;
+    let lo: f32;
+    let mut c = 0f32;
+    /* argument reduction */
+    if hx > 0x3eb17218 {
+        /* if  |x| > 0.5 ln2 */
+        if hx < 0x3F851592 {
+            /* and |x| < 1.5 ln2 */
+            if !sign {
+                hi = x - LN2_HI;
+                lo = LN2_LO;
+                k = 1;
+            } else {
+                hi = x + LN2_HI;
+                lo = -LN2_LO;
+                k = -1;
+            }
+        } else {
+            k = (INV_LN2 * x + (if sign { -0.5 } else { 0.5 })) as i32;
+            let t = k as f32;
+            hi = x - t * LN2_HI; /* t*ln2_hi is exact here */
+            lo = t * LN2_LO;
+        }
+        x = hi - lo;
+        c = (hi - x) - lo;
+    } else if hx < 0x33000000 {
+        /* when |x|<2**-25, return x */
+        if hx < 0x00800000 {
+            force_eval!(x * x);
+        }
+        return x;
+    } else {
+        k = 0;
+    }
+
+    /* x is now in primary range */
+    let hfx = 0.5 * x;
+    let hxs = x * hfx;
+    let r1 = 1. + hxs * (Q1 + hxs * Q2);
+    let t = 3. - r1 * hfx;
+    let mut e = hxs * ((r1 - t) / (6. - x * t));
+    if k == 0 {
+        /* c is 0 */
+        return x - (x * e - hxs);
+    }
+    e = x * (e - c) - c;
+    e -= hxs;
+    /* exp(x) ~ 2^k (x_reduced - e + 1) */
+    if k == -1 {
+        return 0.5 * (x - e) - 0.5;
+    }
+    if k == 1 {
+        if x < -0.25 {
+            return -2. * (e - (x + 0.5));
+        }
+        return 1. + 2. * (x - e);
+    }
+    let twopk = f32::from_bits(((0x7f + k) << 23) as u32); /* 2^k */
+    if !(0..=56).contains(&k) {
+        /* suffice to return exp(x)-1 */
+        let mut y = x - e + 1.;
+        if k == 128 {
+            y = y * 2. * x1p127;
+        } else {
+            y = y * twopk;
+        }
+        return y - 1.;
+    }
+    let uf = f32::from_bits(((0x7f - k) << 23) as u32); /* 2^-k */
+    if k < 23 {
+        (x - e + (1. - uf)) * twopk
+    } else {
+        (x - (e + uf) + 1.) * twopk
+    }
+}

vendor/libm/src/math/expo2.rs

@@ -0,0 +1,14 @@
+use super::{combine_words, exp};
+
+/* exp(x)/2 for x >= log(DBL_MAX), slightly better than 0.5*exp(x/2)*exp(x/2) */
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn expo2(x: f64) -> f64 {
+    /* k is such that k*ln2 has minimal relative error and x - kln2 > log(DBL_MIN) */
+    const K: i32 = 2043;
+    let kln2 = f64::from_bits(0x40962066151add8b);
+
+    /* note that k is odd and scale*scale overflows */
+    let scale = combine_words(((0x3ff + K / 2) as u32) << 20, 0);
+    /* exp(x - k ln2) * 2**(k-1) */
+    exp(x - kln2) * scale * scale
+}

vendor/libm/src/math/fabs.rs

@@ -0,0 +1,116 @@
+/// Absolute value (magnitude) (f16)
+///
+/// Calculates the absolute value (magnitude) of the argument `x`,
+/// by direct manipulation of the bit representation of `x`.
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fabsf16(x: f16) -> f16 {
+    super::generic::fabs(x)
+}
+
+/// Absolute value (magnitude) (f32)
+///
+/// Calculates the absolute value (magnitude) of the argument `x`,
+/// by direct manipulation of the bit representation of `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fabsf(x: f32) -> f32 {
+    select_implementation! {
+        name: fabsf,
+        use_arch: all(target_arch = "wasm32", intrinsics_enabled),
+        args: x,
+    }
+
+    super::generic::fabs(x)
+}
+
+/// Absolute value (magnitude) (f64)
+///
+/// Calculates the absolute value (magnitude) of the argument `x`,
+/// by direct manipulation of the bit representation of `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fabs(x: f64) -> f64 {
+    select_implementation! {
+        name: fabs,
+        use_arch: all(target_arch = "wasm32", intrinsics_enabled),
+        args: x,
+    }
+
+    super::generic::fabs(x)
+}
+
+/// Absolute value (magnitude) (f128)
+///
+/// Calculates the absolute value (magnitude) of the argument `x`,
+/// by direct manipulation of the bit representation of `x`.
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fabsf128(x: f128) -> f128 {
+    super::generic::fabs(x)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::support::Float;
+
+    /// Based on https://en.cppreference.com/w/cpp/numeric/math/fabs
+    fn spec_test<F: Float>(f: impl Fn(F) -> F) {
+        assert_biteq!(f(F::ZERO), F::ZERO);
+        assert_biteq!(f(F::NEG_ZERO), F::ZERO);
+        assert_biteq!(f(F::INFINITY), F::INFINITY);
+        assert_biteq!(f(F::NEG_INFINITY), F::INFINITY);
+        assert!(f(F::NAN).is_nan());
+
+        // Not spec rewquired but we expect it
+        assert!(f(F::NAN).is_sign_positive());
+        assert!(f(F::from_bits(F::NAN.to_bits() | F::SIGN_MASK)).is_sign_positive());
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn sanity_check_f16() {
+        assert_eq!(fabsf16(-1.0f16), 1.0);
+        assert_eq!(fabsf16(2.8f16), 2.8);
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn spec_tests_f16() {
+        spec_test::<f16>(fabsf16);
+    }
+
+    #[test]
+    fn sanity_check_f32() {
+        assert_eq!(fabsf(-1.0f32), 1.0);
+        assert_eq!(fabsf(2.8f32), 2.8);
+    }
+
+    #[test]
+    fn spec_tests_f32() {
+        spec_test::<f32>(fabsf);
+    }
+
+    #[test]
+    fn sanity_check_f64() {
+        assert_eq!(fabs(-1.0f64), 1.0);
+        assert_eq!(fabs(2.8f64), 2.8);
+    }
+
+    #[test]
+    fn spec_tests_f64() {
+        spec_test::<f64>(fabs);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn sanity_check_f128() {
+        assert_eq!(fabsf128(-1.0f128), 1.0);
+        assert_eq!(fabsf128(2.8f128), 2.8);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn spec_tests_f128() {
+        spec_test::<f128>(fabsf128);
+    }
+}

vendor/libm/src/math/fabsf.rs

@@ -0,0 +1,39 @@
+/// Absolute value (magnitude) (f32)
+///
+/// Calculates the absolute value (magnitude) of the argument `x`,
+/// by direct manipulation of the bit representation of `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fabsf(x: f32) -> f32 {
+    select_implementation! {
+        name: fabsf,
+        use_arch: all(target_arch = "wasm32", intrinsics_enabled),
+        args: x,
+    }
+
+    super::generic::fabs(x)
+}
+
+// PowerPC tests are failing on LLVM 13: https://github.com/rust-lang/rust/issues/88520
+#[cfg(not(target_arch = "powerpc64"))]
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn sanity_check() {
+        assert_eq!(fabsf(-1.0), 1.0);
+        assert_eq!(fabsf(2.8), 2.8);
+    }
+
+    /// The spec: https://en.cppreference.com/w/cpp/numeric/math/fabs
+    #[test]
+    fn spec_tests() {
+        assert!(fabsf(f32::NAN).is_nan());
+        for f in [0.0, -0.0].iter().copied() {
+            assert_eq!(fabsf(f), 0.0);
+        }
+        for f in [f32::INFINITY, f32::NEG_INFINITY].iter().copied() {
+            assert_eq!(fabsf(f), f32::INFINITY);
+        }
+    }
+}

vendor/libm/src/math/fabsf128.rs

@@ -0,0 +1,31 @@
+/// Absolute value (magnitude) (f128)
+///
+/// Calculates the absolute value (magnitude) of the argument `x`,
+/// by direct manipulation of the bit representation of `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fabsf128(x: f128) -> f128 {
+    super::generic::fabs(x)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn sanity_check() {
+        assert_eq!(fabsf128(-1.0), 1.0);
+        assert_eq!(fabsf128(2.8), 2.8);
+    }
+
+    /// The spec: https://en.cppreference.com/w/cpp/numeric/math/fabs
+    #[test]
+    fn spec_tests() {
+        assert!(fabsf128(f128::NAN).is_nan());
+        for f in [0.0, -0.0].iter().copied() {
+            assert_eq!(fabsf128(f), 0.0);
+        }
+        for f in [f128::INFINITY, f128::NEG_INFINITY].iter().copied() {
+            assert_eq!(fabsf128(f), f128::INFINITY);
+        }
+    }
+}

vendor/libm/src/math/fabsf16.rs

@@ -0,0 +1,31 @@
+/// Absolute value (magnitude) (f16)
+///
+/// Calculates the absolute value (magnitude) of the argument `x`,
+/// by direct manipulation of the bit representation of `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fabsf16(x: f16) -> f16 {
+    super::generic::fabs(x)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn sanity_check() {
+        assert_eq!(fabsf16(-1.0), 1.0);
+        assert_eq!(fabsf16(2.8), 2.8);
+    }
+
+    /// The spec: https://en.cppreference.com/w/cpp/numeric/math/fabs
+    #[test]
+    fn spec_tests() {
+        assert!(fabsf16(f16::NAN).is_nan());
+        for f in [0.0, -0.0].iter().copied() {
+            assert_eq!(fabsf16(f), 0.0);
+        }
+        for f in [f16::INFINITY, f16::NEG_INFINITY].iter().copied() {
+            assert_eq!(fabsf16(f), f16::INFINITY);
+        }
+    }
+}

vendor/libm/src/math/fdim.rs

@@ -0,0 +1,53 @@
+/// Positive difference (f16)
+///
+/// Determines the positive difference between arguments, returning:
+/// * x - y if x > y, or
+/// * +0    if x <= y, or
+/// * NAN   if either argument is NAN.
+///
+/// A range error may occur.
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fdimf16(x: f16, y: f16) -> f16 {
+    super::generic::fdim(x, y)
+}
+
+/// Positive difference (f32)
+///
+/// Determines the positive difference between arguments, returning:
+/// * x - y if x > y, or
+/// * +0    if x <= y, or
+/// * NAN   if either argument is NAN.
+///
+/// A range error may occur.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fdimf(x: f32, y: f32) -> f32 {
+    super::generic::fdim(x, y)
+}
+
+/// Positive difference (f64)
+///
+/// Determines the positive difference between arguments, returning:
+/// * x - y if x > y, or
+/// * +0    if x <= y, or
+/// * NAN   if either argument is NAN.
+///
+/// A range error may occur.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fdim(x: f64, y: f64) -> f64 {
+    super::generic::fdim(x, y)
+}
+
+/// Positive difference (f128)
+///
+/// Determines the positive difference between arguments, returning:
+/// * x - y if x > y, or
+/// * +0    if x <= y, or
+/// * NAN   if either argument is NAN.
+///
+/// A range error may occur.
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fdimf128(x: f128, y: f128) -> f128 {
+    super::generic::fdim(x, y)
+}

vendor/libm/src/math/fdimf.rs

@@ -0,0 +1,12 @@
+/// Positive difference (f32)
+///
+/// Determines the positive difference between arguments, returning:
+/// * x - y if x > y, or
+/// * +0    if x <= y, or
+/// * NAN   if either argument is NAN.
+///
+/// A range error may occur.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fdimf(x: f32, y: f32) -> f32 {
+    super::generic::fdim(x, y)
+}

vendor/libm/src/math/fdimf128.rs

@@ -0,0 +1,12 @@
+/// Positive difference (f128)
+///
+/// Determines the positive difference between arguments, returning:
+/// * x - y if x > y, or
+/// * +0    if x <= y, or
+/// * NAN   if either argument is NAN.
+///
+/// A range error may occur.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fdimf128(x: f128, y: f128) -> f128 {
+    super::generic::fdim(x, y)
+}

vendor/libm/src/math/fdimf16.rs

@@ -0,0 +1,12 @@
+/// Positive difference (f16)
+///
+/// Determines the positive difference between arguments, returning:
+/// * x - y if x > y, or
+/// * +0    if x <= y, or
+/// * NAN   if either argument is NAN.
+///
+/// A range error may occur.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fdimf16(x: f16, y: f16) -> f16 {
+    super::generic::fdim(x, y)
+}

vendor/libm/src/math/floor.rs

@@ -0,0 +1,46 @@
+/// Floor (f16)
+///
+/// Finds the nearest integer less than or equal to `x`.
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn floorf16(x: f16) -> f16 {
+    return super::generic::floor(x);
+}
+
+/// Floor (f64)
+///
+/// Finds the nearest integer less than or equal to `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn floor(x: f64) -> f64 {
+    select_implementation! {
+        name: floor,
+        use_arch: all(target_arch = "wasm32", intrinsics_enabled),
+        use_arch_required: all(target_arch = "x86", not(target_feature = "sse2")),
+        args: x,
+    }
+
+    return super::generic::floor(x);
+}
+
+/// Floor (f32)
+///
+/// Finds the nearest integer less than or equal to `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn floorf(x: f32) -> f32 {
+    select_implementation! {
+        name: floorf,
+        use_arch: all(target_arch = "wasm32", intrinsics_enabled),
+        args: x,
+    }
+
+    return super::generic::floor(x);
+}
+
+/// Floor (f128)
+///
+/// Finds the nearest integer less than or equal to `x`.
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn floorf128(x: f128) -> f128 {
+    return super::generic::floor(x);
+}

vendor/libm/src/math/floorf.rs

@@ -0,0 +1,13 @@
+/// Floor (f32)
+///
+/// Finds the nearest integer less than or equal to `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn floorf(x: f32) -> f32 {
+    select_implementation! {
+        name: floorf,
+        use_arch: all(target_arch = "wasm32", intrinsics_enabled),
+        args: x,
+    }
+
+    return super::generic::floor(x);
+}

vendor/libm/src/math/floorf128.rs

@@ -0,0 +1,7 @@
+/// Floor (f128)
+///
+/// Finds the nearest integer less than or equal to `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn floorf128(x: f128) -> f128 {
+    return super::generic::floor(x);
+}

vendor/libm/src/math/floorf16.rs

@@ -0,0 +1,7 @@
+/// Floor (f16)
+///
+/// Finds the nearest integer less than or equal to `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn floorf16(x: f16) -> f16 {
+    return super::generic::floor(x);
+}

vendor/libm/src/math/fma.rs

@@ -0,0 +1,171 @@
+/* SPDX-License-Identifier: MIT */
+/* origin: musl src/math/fma.c, fmaf.c Ported to generic Rust algorithm in 2025, TG. */
+
+use super::generic;
+use crate::support::Round;
+
+// Placeholder so we can have `fmaf16` in the `Float` trait.
+#[allow(unused)]
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn fmaf16(_x: f16, _y: f16, _z: f16) -> f16 {
+    unimplemented!()
+}
+
+/// Floating multiply add (f32)
+///
+/// Computes `(x*y)+z`, rounded as one ternary operation (i.e. calculated with infinite precision).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaf(x: f32, y: f32, z: f32) -> f32 {
+    select_implementation! {
+        name: fmaf,
+        use_arch: any(
+            all(target_arch = "aarch64", target_feature = "neon"),
+            target_feature = "sse2",
+        ),
+        args: x, y, z,
+    }
+
+    generic::fma_wide_round(x, y, z, Round::Nearest).val
+}
+
+/// Fused multiply add (f64)
+///
+/// Computes `(x*y)+z`, rounded as one ternary operation (i.e. calculated with infinite precision).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fma(x: f64, y: f64, z: f64) -> f64 {
+    select_implementation! {
+        name: fma,
+        use_arch: any(
+            all(target_arch = "aarch64", target_feature = "neon"),
+            target_feature = "sse2",
+        ),
+        args: x, y, z,
+    }
+
+    generic::fma_round(x, y, z, Round::Nearest).val
+}
+
+/// Fused multiply add (f128)
+///
+/// Computes `(x*y)+z`, rounded as one ternary operation (i.e. calculated with infinite precision).
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaf128(x: f128, y: f128, z: f128) -> f128 {
+    generic::fma_round(x, y, z, Round::Nearest).val
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::support::{CastFrom, CastInto, Float, FpResult, HInt, MinInt, Round, Status};
+
+    /// Test the generic `fma_round` algorithm for a given float.
+    fn spec_test<F>(f: impl Fn(F, F, F) -> F)
+    where
+        F: Float,
+        F: CastFrom<F::SignedInt>,
+        F: CastFrom<i8>,
+        F::Int: HInt,
+        u32: CastInto<F::Int>,
+    {
+        let x = F::from_bits(F::Int::ONE);
+        let y = F::from_bits(F::Int::ONE);
+        let z = F::ZERO;
+
+        // 754-2020 says "When the exact result of (a × b) + c is non-zero yet the result of
+        // fusedMultiplyAdd is zero because of rounding, the zero result takes the sign of the
+        // exact result"
+        assert_biteq!(f(x, y, z), F::ZERO);
+        assert_biteq!(f(x, -y, z), F::NEG_ZERO);
+        assert_biteq!(f(-x, y, z), F::NEG_ZERO);
+        assert_biteq!(f(-x, -y, z), F::ZERO);
+    }
+
+    #[test]
+    fn spec_test_f32() {
+        spec_test::<f32>(fmaf);
+
+        // Also do a small check that the non-widening version works for f32 (this should ideally
+        // get tested some more).
+        spec_test::<f32>(|x, y, z| generic::fma_round(x, y, z, Round::Nearest).val);
+    }
+
+    #[test]
+    fn spec_test_f64() {
+        spec_test::<f64>(fma);
+
+        let expect_underflow = [
+            (
+                hf64!("0x1.0p-1070"),
+                hf64!("0x1.0p-1070"),
+                hf64!("0x1.ffffffffffffp-1023"),
+                hf64!("0x0.ffffffffffff8p-1022"),
+            ),
+            (
+                // FIXME: we raise underflow but this should only be inexact (based on C and
+                // `rustc_apfloat`).
+                hf64!("0x1.0p-1070"),
+                hf64!("0x1.0p-1070"),
+                hf64!("-0x1.0p-1022"),
+                hf64!("-0x1.0p-1022"),
+            ),
+        ];
+
+        for (x, y, z, res) in expect_underflow {
+            let FpResult { val, status } = generic::fma_round(x, y, z, Round::Nearest);
+            assert_biteq!(val, res);
+            assert_eq!(status, Status::UNDERFLOW);
+        }
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn spec_test_f128() {
+        spec_test::<f128>(fmaf128);
+    }
+
+    #[test]
+    fn issue_263() {
+        let a = f32::from_bits(1266679807);
+        let b = f32::from_bits(1300234242);
+        let c = f32::from_bits(1115553792);
+        let expected = f32::from_bits(1501560833);
+        assert_eq!(fmaf(a, b, c), expected);
+    }
+
+    #[test]
+    fn fma_segfault() {
+        // These two inputs cause fma to segfault on release due to overflow:
+        assert_eq!(
+            fma(
+                -0.0000000000000002220446049250313,
+                -0.0000000000000002220446049250313,
+                -0.0000000000000002220446049250313
+            ),
+            -0.00000000000000022204460492503126,
+        );
+
+        let result = fma(-0.992, -0.992, -0.992);
+        //force rounding to storage format on x87 to prevent superious errors.
+        #[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
+        let result = force_eval!(result);
+        assert_eq!(result, -0.007936000000000007,);
+    }
+
+    #[test]
+    fn fma_sbb() {
+        assert_eq!(
+            fma(-(1.0 - f64::EPSILON), f64::MIN, f64::MIN),
+            -3991680619069439e277
+        );
+    }
+
+    #[test]
+    fn fma_underflow() {
+        assert_eq!(
+            fma(1.1102230246251565e-16, -9.812526705433188e-305, 1.0894e-320),
+            0.0,
+        );
+    }
+}

vendor/libm/src/math/fmin_fmax.rs

@@ -0,0 +1,167 @@
+/// Return the lesser of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2011 `minNum`. The result disregards signed zero (meaning if
+/// the inputs are -0.0 and +0.0, either may be returned).
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fminf16(x: f16, y: f16) -> f16 {
+    super::generic::fmin(x, y)
+}
+
+/// Return the lesser of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2011 `minNum`. The result disregards signed zero (meaning if
+/// the inputs are -0.0 and +0.0, either may be returned).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fminf(x: f32, y: f32) -> f32 {
+    super::generic::fmin(x, y)
+}
+
+/// Return the lesser of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2011 `minNum`. The result disregards signed zero (meaning if
+/// the inputs are -0.0 and +0.0, either may be returned).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmin(x: f64, y: f64) -> f64 {
+    super::generic::fmin(x, y)
+}
+
+/// Return the lesser of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2011 `minNum`. The result disregards signed zero (meaning if
+/// the inputs are -0.0 and +0.0, either may be returned).
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fminf128(x: f128, y: f128) -> f128 {
+    super::generic::fmin(x, y)
+}
+
+/// Return the greater of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2011 `maxNum`. The result disregards signed zero (meaning if
+/// the inputs are -0.0 and +0.0, either may be returned).
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaxf16(x: f16, y: f16) -> f16 {
+    super::generic::fmax(x, y)
+}
+
+/// Return the greater of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2011 `maxNum`. The result disregards signed zero (meaning if
+/// the inputs are -0.0 and +0.0, either may be returned).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaxf(x: f32, y: f32) -> f32 {
+    super::generic::fmax(x, y)
+}
+
+/// Return the greater of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2011 `maxNum`. The result disregards signed zero (meaning if
+/// the inputs are -0.0 and +0.0, either may be returned).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmax(x: f64, y: f64) -> f64 {
+    super::generic::fmax(x, y)
+}
+
+/// Return the greater of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2011 `maxNum`. The result disregards signed zero (meaning if
+/// the inputs are -0.0 and +0.0, either may be returned).
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaxf128(x: f128, y: f128) -> f128 {
+    super::generic::fmax(x, y)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::support::{Float, Hexf};
+
+    fn fmin_spec_test<F: Float>(f: impl Fn(F, F) -> F) {
+        let cases = [
+            (F::ZERO, F::ZERO, F::ZERO),
+            (F::ONE, F::ONE, F::ONE),
+            (F::ZERO, F::ONE, F::ZERO),
+            (F::ONE, F::ZERO, F::ZERO),
+            (F::ZERO, F::NEG_ONE, F::NEG_ONE),
+            (F::NEG_ONE, F::ZERO, F::NEG_ONE),
+            (F::INFINITY, F::ZERO, F::ZERO),
+            (F::NEG_INFINITY, F::ZERO, F::NEG_INFINITY),
+            (F::NAN, F::ZERO, F::ZERO),
+            (F::ZERO, F::NAN, F::ZERO),
+            (F::NAN, F::NAN, F::NAN),
+        ];
+
+        for (x, y, res) in cases {
+            let val = f(x, y);
+            assert_biteq!(val, res, "fmin({}, {})", Hexf(x), Hexf(y));
+        }
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn fmin_spec_tests_f16() {
+        fmin_spec_test::<f16>(fminf16);
+    }
+
+    #[test]
+    fn fmin_spec_tests_f32() {
+        fmin_spec_test::<f32>(fminf);
+    }
+
+    #[test]
+    fn fmin_spec_tests_f64() {
+        fmin_spec_test::<f64>(fmin);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn fmin_spec_tests_f128() {
+        fmin_spec_test::<f128>(fminf128);
+    }
+
+    fn fmax_spec_test<F: Float>(f: impl Fn(F, F) -> F) {
+        let cases = [
+            (F::ZERO, F::ZERO, F::ZERO),
+            (F::ONE, F::ONE, F::ONE),
+            (F::ZERO, F::ONE, F::ONE),
+            (F::ONE, F::ZERO, F::ONE),
+            (F::ZERO, F::NEG_ONE, F::ZERO),
+            (F::NEG_ONE, F::ZERO, F::ZERO),
+            (F::INFINITY, F::ZERO, F::INFINITY),
+            (F::NEG_INFINITY, F::ZERO, F::ZERO),
+            (F::NAN, F::ZERO, F::ZERO),
+            (F::ZERO, F::NAN, F::ZERO),
+            (F::NAN, F::NAN, F::NAN),
+        ];
+
+        for (x, y, res) in cases {
+            let val = f(x, y);
+            assert_biteq!(val, res, "fmax({}, {})", Hexf(x), Hexf(y));
+        }
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn fmax_spec_tests_f16() {
+        fmax_spec_test::<f16>(fmaxf16);
+    }
+
+    #[test]
+    fn fmax_spec_tests_f32() {
+        fmax_spec_test::<f32>(fmaxf);
+    }
+
+    #[test]
+    fn fmax_spec_tests_f64() {
+        fmax_spec_test::<f64>(fmax);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn fmax_spec_tests_f128() {
+        fmax_spec_test::<f128>(fmaxf128);
+    }
+}

vendor/libm/src/math/fminimum_fmaximum.rs

@@ -0,0 +1,163 @@
+/// Return the lesser of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2019 `minimum`. The result orders -0.0 < 0.0.
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fminimumf16(x: f16, y: f16) -> f16 {
+    super::generic::fminimum(x, y)
+}
+
+/// Return the lesser of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2019 `minimum`. The result orders -0.0 < 0.0.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fminimum(x: f64, y: f64) -> f64 {
+    super::generic::fminimum(x, y)
+}
+
+/// Return the lesser of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2019 `minimum`. The result orders -0.0 < 0.0.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fminimumf(x: f32, y: f32) -> f32 {
+    super::generic::fminimum(x, y)
+}
+
+/// Return the lesser of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2019 `minimum`. The result orders -0.0 < 0.0.
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fminimumf128(x: f128, y: f128) -> f128 {
+    super::generic::fminimum(x, y)
+}
+
+/// Return the greater of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2019 `maximum`. The result orders -0.0 < 0.0.
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaximumf16(x: f16, y: f16) -> f16 {
+    super::generic::fmaximum(x, y)
+}
+
+/// Return the greater of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2019 `maximum`. The result orders -0.0 < 0.0.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaximumf(x: f32, y: f32) -> f32 {
+    super::generic::fmaximum(x, y)
+}
+
+/// Return the greater of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2019 `maximum`. The result orders -0.0 < 0.0.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaximum(x: f64, y: f64) -> f64 {
+    super::generic::fmaximum(x, y)
+}
+
+/// Return the greater of two arguments or, if either argument is NaN, the other argument.
+///
+/// This coincides with IEEE 754-2019 `maximum`. The result orders -0.0 < 0.0.
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaximumf128(x: f128, y: f128) -> f128 {
+    super::generic::fmaximum(x, y)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::support::{Float, Hexf};
+
+    fn fminimum_spec_test<F: Float>(f: impl Fn(F, F) -> F) {
+        let cases = [
+            (F::ZERO, F::ZERO, F::ZERO),
+            (F::ONE, F::ONE, F::ONE),
+            (F::ZERO, F::ONE, F::ZERO),
+            (F::ONE, F::ZERO, F::ZERO),
+            (F::ZERO, F::NEG_ONE, F::NEG_ONE),
+            (F::NEG_ONE, F::ZERO, F::NEG_ONE),
+            (F::INFINITY, F::ZERO, F::ZERO),
+            (F::NEG_INFINITY, F::ZERO, F::NEG_INFINITY),
+            (F::NAN, F::ZERO, F::NAN),
+            (F::ZERO, F::NAN, F::NAN),
+            (F::NAN, F::NAN, F::NAN),
+            (F::ZERO, F::NEG_ZERO, F::NEG_ZERO),
+            (F::NEG_ZERO, F::ZERO, F::NEG_ZERO),
+        ];
+
+        for (x, y, res) in cases {
+            let val = f(x, y);
+            assert_biteq!(val, res, "fminimum({}, {})", Hexf(x), Hexf(y));
+        }
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn fminimum_spec_tests_f16() {
+        fminimum_spec_test::<f16>(fminimumf16);
+    }
+
+    #[test]
+    fn fminimum_spec_tests_f32() {
+        fminimum_spec_test::<f32>(fminimumf);
+    }
+
+    #[test]
+    fn fminimum_spec_tests_f64() {
+        fminimum_spec_test::<f64>(fminimum);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn fminimum_spec_tests_f128() {
+        fminimum_spec_test::<f128>(fminimumf128);
+    }
+
+    fn fmaximum_spec_test<F: Float>(f: impl Fn(F, F) -> F) {
+        let cases = [
+            (F::ZERO, F::ZERO, F::ZERO),
+            (F::ONE, F::ONE, F::ONE),
+            (F::ZERO, F::ONE, F::ONE),
+            (F::ONE, F::ZERO, F::ONE),
+            (F::ZERO, F::NEG_ONE, F::ZERO),
+            (F::NEG_ONE, F::ZERO, F::ZERO),
+            (F::INFINITY, F::ZERO, F::INFINITY),
+            (F::NEG_INFINITY, F::ZERO, F::ZERO),
+            (F::NAN, F::ZERO, F::NAN),
+            (F::ZERO, F::NAN, F::NAN),
+            (F::NAN, F::NAN, F::NAN),
+            (F::ZERO, F::NEG_ZERO, F::ZERO),
+            (F::NEG_ZERO, F::ZERO, F::ZERO),
+        ];
+
+        for (x, y, res) in cases {
+            let val = f(x, y);
+            assert_biteq!(val, res, "fmaximum({}, {})", Hexf(x), Hexf(y));
+        }
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn fmaximum_spec_tests_f16() {
+        fmaximum_spec_test::<f16>(fmaximumf16);
+    }
+
+    #[test]
+    fn fmaximum_spec_tests_f32() {
+        fmaximum_spec_test::<f32>(fmaximumf);
+    }
+
+    #[test]
+    fn fmaximum_spec_tests_f64() {
+        fmaximum_spec_test::<f64>(fmaximum);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn fmaximum_spec_tests_f128() {
+        fmaximum_spec_test::<f128>(fmaximumf128);
+    }
+}

vendor/libm/src/math/fminimum_fmaximum_num.rs

@@ -0,0 +1,163 @@
+/// Return the lesser of two arguments or, if either argument is NaN, NaN.
+///
+/// This coincides with IEEE 754-2019 `minimumNumber`. The result orders -0.0 < 0.0.
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fminimum_numf16(x: f16, y: f16) -> f16 {
+    super::generic::fminimum_num(x, y)
+}
+
+/// Return the lesser of two arguments or, if either argument is NaN, NaN.
+///
+/// This coincides with IEEE 754-2019 `minimumNumber`. The result orders -0.0 < 0.0.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fminimum_numf(x: f32, y: f32) -> f32 {
+    super::generic::fminimum_num(x, y)
+}
+
+/// Return the lesser of two arguments or, if either argument is NaN, NaN.
+///
+/// This coincides with IEEE 754-2019 `minimumNumber`. The result orders -0.0 < 0.0.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fminimum_num(x: f64, y: f64) -> f64 {
+    super::generic::fminimum_num(x, y)
+}
+
+/// Return the lesser of two arguments or, if either argument is NaN, NaN.
+///
+/// This coincides with IEEE 754-2019 `minimumNumber`. The result orders -0.0 < 0.0.
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fminimum_numf128(x: f128, y: f128) -> f128 {
+    super::generic::fminimum_num(x, y)
+}
+
+/// Return the greater of two arguments or, if either argument is NaN, NaN.
+///
+/// This coincides with IEEE 754-2019 `maximumNumber`. The result orders -0.0 < 0.0.
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaximum_numf16(x: f16, y: f16) -> f16 {
+    super::generic::fmaximum_num(x, y)
+}
+
+/// Return the greater of two arguments or, if either argument is NaN, NaN.
+///
+/// This coincides with IEEE 754-2019 `maximumNumber`. The result orders -0.0 < 0.0.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaximum_numf(x: f32, y: f32) -> f32 {
+    super::generic::fmaximum_num(x, y)
+}
+
+/// Return the greater of two arguments or, if either argument is NaN, NaN.
+///
+/// This coincides with IEEE 754-2019 `maximumNumber`. The result orders -0.0 < 0.0.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaximum_num(x: f64, y: f64) -> f64 {
+    super::generic::fmaximum_num(x, y)
+}
+
+/// Return the greater of two arguments or, if either argument is NaN, NaN.
+///
+/// This coincides with IEEE 754-2019 `maximumNumber`. The result orders -0.0 < 0.0.
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaximum_numf128(x: f128, y: f128) -> f128 {
+    super::generic::fmaximum_num(x, y)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::support::{Float, Hexf};
+
+    fn fminimum_num_spec_test<F: Float>(f: impl Fn(F, F) -> F) {
+        let cases = [
+            (F::ZERO, F::ZERO, F::ZERO),
+            (F::ONE, F::ONE, F::ONE),
+            (F::ZERO, F::ONE, F::ZERO),
+            (F::ONE, F::ZERO, F::ZERO),
+            (F::ZERO, F::NEG_ONE, F::NEG_ONE),
+            (F::NEG_ONE, F::ZERO, F::NEG_ONE),
+            (F::INFINITY, F::ZERO, F::ZERO),
+            (F::NEG_INFINITY, F::ZERO, F::NEG_INFINITY),
+            (F::NAN, F::ZERO, F::ZERO),
+            (F::ZERO, F::NAN, F::ZERO),
+            (F::NAN, F::NAN, F::NAN),
+            (F::ZERO, F::NEG_ZERO, F::NEG_ZERO),
+            (F::NEG_ZERO, F::ZERO, F::NEG_ZERO),
+        ];
+
+        for (x, y, res) in cases {
+            let val = f(x, y);
+            assert_biteq!(val, res, "fminimum_num({}, {})", Hexf(x), Hexf(y));
+        }
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn fminimum_num_spec_tests_f16() {
+        fminimum_num_spec_test::<f16>(fminimum_numf16);
+    }
+
+    #[test]
+    fn fminimum_num_spec_tests_f32() {
+        fminimum_num_spec_test::<f32>(fminimum_numf);
+    }
+
+    #[test]
+    fn fminimum_num_spec_tests_f64() {
+        fminimum_num_spec_test::<f64>(fminimum_num);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn fminimum_num_spec_tests_f128() {
+        fminimum_num_spec_test::<f128>(fminimum_numf128);
+    }
+
+    fn fmaximum_num_spec_test<F: Float>(f: impl Fn(F, F) -> F) {
+        let cases = [
+            (F::ZERO, F::ZERO, F::ZERO),
+            (F::ONE, F::ONE, F::ONE),
+            (F::ZERO, F::ONE, F::ONE),
+            (F::ONE, F::ZERO, F::ONE),
+            (F::ZERO, F::NEG_ONE, F::ZERO),
+            (F::NEG_ONE, F::ZERO, F::ZERO),
+            (F::INFINITY, F::ZERO, F::INFINITY),
+            (F::NEG_INFINITY, F::ZERO, F::ZERO),
+            (F::NAN, F::ZERO, F::ZERO),
+            (F::ZERO, F::NAN, F::ZERO),
+            (F::NAN, F::NAN, F::NAN),
+            (F::ZERO, F::NEG_ZERO, F::ZERO),
+            (F::NEG_ZERO, F::ZERO, F::ZERO),
+        ];
+
+        for (x, y, res) in cases {
+            let val = f(x, y);
+            assert_biteq!(val, res, "fmaximum_num({}, {})", Hexf(x), Hexf(y));
+        }
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn fmaximum_num_spec_tests_f16() {
+        fmaximum_num_spec_test::<f16>(fmaximum_numf16);
+    }
+
+    #[test]
+    fn fmaximum_num_spec_tests_f32() {
+        fmaximum_num_spec_test::<f32>(fmaximum_numf);
+    }
+
+    #[test]
+    fn fmaximum_num_spec_tests_f64() {
+        fmaximum_num_spec_test::<f64>(fmaximum_num);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn fmaximum_num_spec_tests_f128() {
+        fmaximum_num_spec_test::<f128>(fmaximum_numf128);
+    }
+}

vendor/libm/src/math/fmod.rs

@@ -0,0 +1,25 @@
+/// Calculate the remainder of `x / y`, the precise result of `x - trunc(x / y) * y`.
+#[cfg(f16_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmodf16(x: f16, y: f16) -> f16 {
+    super::generic::fmod(x, y)
+}
+
+/// Calculate the remainder of `x / y`, the precise result of `x - trunc(x / y) * y`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmodf(x: f32, y: f32) -> f32 {
+    super::generic::fmod(x, y)
+}
+
+/// Calculate the remainder of `x / y`, the precise result of `x - trunc(x / y) * y`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmod(x: f64, y: f64) -> f64 {
+    super::generic::fmod(x, y)
+}
+
+/// Calculate the remainder of `x / y`, the precise result of `x - trunc(x / y) * y`.
+#[cfg(f128_enabled)]
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmodf128(x: f128, y: f128) -> f128 {
+    super::generic::fmod(x, y)
+}

vendor/libm/src/math/fmodf.rs

@@ -0,0 +1,5 @@
+/// Calculate the remainder of `x / y`, the precise result of `x - trunc(x / y) * y`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmodf(x: f32, y: f32) -> f32 {
+    super::generic::fmod(x, y)
+}

vendor/libm/src/math/fmodf128.rs

@@ -0,0 +1,5 @@
+/// Calculate the remainder of `x / y`, the precise result of `x - trunc(x / y) * y`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmodf128(x: f128, y: f128) -> f128 {
+    super::generic::fmod(x, y)
+}

vendor/libm/src/math/fmodf16.rs

@@ -0,0 +1,5 @@
+/// Calculate the remainder of `x / y`, the precise result of `x - trunc(x / y) * y`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmodf16(x: f16, y: f16) -> f16 {
+    super::generic::fmod(x, y)
+}

vendor/libm/src/math/frexp.rs

@@ -0,0 +1,21 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn frexp(x: f64) -> (f64, i32) {
+    let mut y = x.to_bits();
+    let ee = ((y >> 52) & 0x7ff) as i32;
+
+    if ee == 0 {
+        if x != 0.0 {
+            let x1p64 = f64::from_bits(0x43f0000000000000);
+            let (x, e) = frexp(x * x1p64);
+            return (x, e - 64);
+        }
+        return (x, 0);
+    } else if ee == 0x7ff {
+        return (x, 0);
+    }
+
+    let e = ee - 0x3fe;
+    y &= 0x800fffffffffffff;
+    y |= 0x3fe0000000000000;
+    return (f64::from_bits(y), e);
+}

vendor/libm/src/math/frexpf.rs

@@ -0,0 +1,22 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn frexpf(x: f32) -> (f32, i32) {
+    let mut y = x.to_bits();
+    let ee: i32 = ((y >> 23) & 0xff) as i32;
+
+    if ee == 0 {
+        if x != 0.0 {
+            let x1p64 = f32::from_bits(0x5f800000);
+            let (x, e) = frexpf(x * x1p64);
+            return (x, e - 64);
+        } else {
+            return (x, 0);
+        }
+    } else if ee == 0xff {
+        return (x, 0);
+    }
+
+    let e = ee - 0x7e;
+    y &= 0x807fffff;
+    y |= 0x3f000000;
+    (f32::from_bits(y), e)
+}

vendor/libm/src/math/generic/ceil.rs

@@ -0,0 +1,174 @@
+/* SPDX-License-Identifier: MIT */
+/* origin: musl src/math/ceilf.c */
+
+//! Generic `ceil` algorithm.
+//!
+//! Note that this uses the algorithm from musl's `ceilf` rather than `ceil` or `ceill` because
+//! performance seems to be better (based on icount) and it does not seem to experience rounding
+//! errors on i386.
+
+use crate::support::{Float, FpResult, Int, IntTy, MinInt, Status};
+
+#[inline]
+pub fn ceil<F: Float>(x: F) -> F {
+    ceil_status(x).val
+}
+
+#[inline]
+pub fn ceil_status<F: Float>(x: F) -> FpResult<F> {
+    let zero = IntTy::<F>::ZERO;
+
+    let mut ix = x.to_bits();
+    let e = x.exp_unbiased();
+
+    // If the represented value has no fractional part, no truncation is needed.
+    if e >= F::SIG_BITS as i32 {
+        return FpResult::ok(x);
+    }
+
+    let status;
+    let res = if e >= 0 {
+        // |x| >= 1.0
+        let m = F::SIG_MASK >> e.unsigned();
+        if (ix & m) == zero {
+            // Portion to be masked is already zero; no adjustment needed.
+            return FpResult::ok(x);
+        }
+
+        // Otherwise, raise an inexact exception.
+        status = Status::INEXACT;
+
+        if x.is_sign_positive() {
+            ix += m;
+        }
+
+        ix &= !m;
+        F::from_bits(ix)
+    } else {
+        // |x| < 1.0, raise an inexact exception since truncation will happen (unless x == 0).
+        if ix & F::SIG_MASK == F::Int::ZERO {
+            status = Status::OK;
+        } else {
+            status = Status::INEXACT;
+        }
+
+        if x.is_sign_negative() {
+            // -1.0 < x <= -0.0; rounding up goes toward -0.0.
+            F::NEG_ZERO
+        } else if ix << 1 != zero {
+            // 0.0 < x < 1.0; rounding up goes toward +1.0.
+            F::ONE
+        } else {
+            // +0.0 remains unchanged
+            x
+        }
+    };
+
+    FpResult::new(res, status)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::support::Hexf;
+
+    /// Test against https://en.cppreference.com/w/cpp/numeric/math/ceil
+    fn spec_test<F: Float>(cases: &[(F, F, Status)]) {
+        let roundtrip = [
+            F::ZERO,
+            F::ONE,
+            F::NEG_ONE,
+            F::NEG_ZERO,
+            F::INFINITY,
+            F::NEG_INFINITY,
+        ];
+
+        for x in roundtrip {
+            let FpResult { val, status } = ceil_status(x);
+            assert_biteq!(val, x, "{}", Hexf(x));
+            assert_eq!(status, Status::OK, "{}", Hexf(x));
+        }
+
+        for &(x, res, res_stat) in cases {
+            let FpResult { val, status } = ceil_status(x);
+            assert_biteq!(val, res, "{}", Hexf(x));
+            assert_eq!(status, res_stat, "{}", Hexf(x));
+        }
+    }
+
+    /* Skipping f16 / f128 "sanity_check"s due to rejected literal lexing at MSRV */
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn spec_tests_f16() {
+        let cases = [
+            (0.1, 1.0, Status::INEXACT),
+            (-0.1, -0.0, Status::INEXACT),
+            (0.9, 1.0, Status::INEXACT),
+            (-0.9, -0.0, Status::INEXACT),
+            (1.1, 2.0, Status::INEXACT),
+            (-1.1, -1.0, Status::INEXACT),
+            (1.9, 2.0, Status::INEXACT),
+            (-1.9, -1.0, Status::INEXACT),
+        ];
+        spec_test::<f16>(&cases);
+    }
+
+    #[test]
+    fn sanity_check_f32() {
+        assert_eq!(ceil(1.1f32), 2.0);
+        assert_eq!(ceil(2.9f32), 3.0);
+    }
+
+    #[test]
+    fn spec_tests_f32() {
+        let cases = [
+            (0.1, 1.0, Status::INEXACT),
+            (-0.1, -0.0, Status::INEXACT),
+            (0.9, 1.0, Status::INEXACT),
+            (-0.9, -0.0, Status::INEXACT),
+            (1.1, 2.0, Status::INEXACT),
+            (-1.1, -1.0, Status::INEXACT),
+            (1.9, 2.0, Status::INEXACT),
+            (-1.9, -1.0, Status::INEXACT),
+        ];
+        spec_test::<f32>(&cases);
+    }
+
+    #[test]
+    fn sanity_check_f64() {
+        assert_eq!(ceil(1.1f64), 2.0);
+        assert_eq!(ceil(2.9f64), 3.0);
+    }
+
+    #[test]
+    fn spec_tests_f64() {
+        let cases = [
+            (0.1, 1.0, Status::INEXACT),
+            (-0.1, -0.0, Status::INEXACT),
+            (0.9, 1.0, Status::INEXACT),
+            (-0.9, -0.0, Status::INEXACT),
+            (1.1, 2.0, Status::INEXACT),
+            (-1.1, -1.0, Status::INEXACT),
+            (1.9, 2.0, Status::INEXACT),
+            (-1.9, -1.0, Status::INEXACT),
+        ];
+        spec_test::<f64>(&cases);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn spec_tests_f128() {
+        let cases = [
+            (0.1, 1.0, Status::INEXACT),
+            (-0.1, -0.0, Status::INEXACT),
+            (0.9, 1.0, Status::INEXACT),
+            (-0.9, -0.0, Status::INEXACT),
+            (1.1, 2.0, Status::INEXACT),
+            (-1.1, -1.0, Status::INEXACT),
+            (1.9, 2.0, Status::INEXACT),
+            (-1.9, -1.0, Status::INEXACT),
+        ];
+        spec_test::<f128>(&cases);
+    }
+}

vendor/libm/src/math/generic/copysign.rs

@@ -0,0 +1,11 @@
+use crate::support::Float;
+
+/// Copy the sign of `y` to `x`.
+#[inline]
+pub fn copysign<F: Float>(x: F, y: F) -> F {
+    let mut ux = x.to_bits();
+    let uy = y.to_bits();
+    ux &= !F::SIGN_MASK;
+    ux |= uy & F::SIGN_MASK;
+    F::from_bits(ux)
+}

vendor/libm/src/math/generic/fabs.rs

@@ -0,0 +1,8 @@
+use crate::support::Float;
+
+/// Absolute value.
+#[inline]
+pub fn fabs<F: Float>(x: F) -> F {
+    let abs_mask = !F::SIGN_MASK;
+    F::from_bits(x.to_bits() & abs_mask)
+}

vendor/libm/src/math/generic/fdim.rs

@@ -0,0 +1,6 @@
+use crate::support::Float;
+
+#[inline]
+pub fn fdim<F: Float>(x: F, y: F) -> F {
+    if x <= y { F::ZERO } else { x - y }
+}

vendor/libm/src/math/generic/floor.rs

@@ -0,0 +1,157 @@
+/* SPDX-License-Identifier: MIT
+ * origin: musl src/math/floor.c */
+
+//! Generic `floor` algorithm.
+//!
+//! Note that this uses the algorithm from musl's `floorf` rather than `floor` or `floorl` because
+//! performance seems to be better (based on icount) and it does not seem to experience rounding
+//! errors on i386.
+
+use crate::support::{Float, FpResult, Int, IntTy, MinInt, Status};
+
+#[inline]
+pub fn floor<F: Float>(x: F) -> F {
+    floor_status(x).val
+}
+
+#[inline]
+pub fn floor_status<F: Float>(x: F) -> FpResult<F> {
+    let zero = IntTy::<F>::ZERO;
+
+    let mut ix = x.to_bits();
+    let e = x.exp_unbiased();
+
+    // If the represented value has no fractional part, no truncation is needed.
+    if e >= F::SIG_BITS as i32 {
+        return FpResult::ok(x);
+    }
+
+    let status;
+    let res = if e >= 0 {
+        // |x| >= 1.0
+        let m = F::SIG_MASK >> e.unsigned();
+        if ix & m == zero {
+            // Portion to be masked is already zero; no adjustment needed.
+            return FpResult::ok(x);
+        }
+
+        // Otherwise, raise an inexact exception.
+        status = Status::INEXACT;
+
+        if x.is_sign_negative() {
+            ix += m;
+        }
+
+        ix &= !m;
+        F::from_bits(ix)
+    } else {
+        // |x| < 1.0, raise an inexact exception since truncation will happen.
+        if ix & F::SIG_MASK == F::Int::ZERO {
+            status = Status::OK;
+        } else {
+            status = Status::INEXACT;
+        }
+
+        if x.is_sign_positive() {
+            // 0.0 <= x < 1.0; rounding down goes toward +0.0.
+            F::ZERO
+        } else if ix << 1 != zero {
+            // -1.0 < x < 0.0; rounding down goes toward -1.0.
+            F::NEG_ONE
+        } else {
+            // -0.0 remains unchanged
+            x
+        }
+    };
+
+    FpResult::new(res, status)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::support::Hexf;
+
+    /// Test against https://en.cppreference.com/w/cpp/numeric/math/floor
+    fn spec_test<F: Float>(cases: &[(F, F, Status)]) {
+        let roundtrip = [
+            F::ZERO,
+            F::ONE,
+            F::NEG_ONE,
+            F::NEG_ZERO,
+            F::INFINITY,
+            F::NEG_INFINITY,
+        ];
+
+        for x in roundtrip {
+            let FpResult { val, status } = floor_status(x);
+            assert_biteq!(val, x, "{}", Hexf(x));
+            assert_eq!(status, Status::OK, "{}", Hexf(x));
+        }
+
+        for &(x, res, res_stat) in cases {
+            let FpResult { val, status } = floor_status(x);
+            assert_biteq!(val, res, "{}", Hexf(x));
+            assert_eq!(status, res_stat, "{}", Hexf(x));
+        }
+    }
+
+    /* Skipping f16 / f128 "sanity_check"s and spec cases due to rejected literal lexing at MSRV */
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn spec_tests_f16() {
+        let cases = [];
+        spec_test::<f16>(&cases);
+    }
+
+    #[test]
+    fn sanity_check_f32() {
+        assert_eq!(floor(0.5f32), 0.0);
+        assert_eq!(floor(1.1f32), 1.0);
+        assert_eq!(floor(2.9f32), 2.0);
+    }
+
+    #[test]
+    fn spec_tests_f32() {
+        let cases = [
+            (0.1, 0.0, Status::INEXACT),
+            (-0.1, -1.0, Status::INEXACT),
+            (0.9, 0.0, Status::INEXACT),
+            (-0.9, -1.0, Status::INEXACT),
+            (1.1, 1.0, Status::INEXACT),
+            (-1.1, -2.0, Status::INEXACT),
+            (1.9, 1.0, Status::INEXACT),
+            (-1.9, -2.0, Status::INEXACT),
+        ];
+        spec_test::<f32>(&cases);
+    }
+
+    #[test]
+    fn sanity_check_f64() {
+        assert_eq!(floor(1.1f64), 1.0);
+        assert_eq!(floor(2.9f64), 2.0);
+    }
+
+    #[test]
+    fn spec_tests_f64() {
+        let cases = [
+            (0.1, 0.0, Status::INEXACT),
+            (-0.1, -1.0, Status::INEXACT),
+            (0.9, 0.0, Status::INEXACT),
+            (-0.9, -1.0, Status::INEXACT),
+            (1.1, 1.0, Status::INEXACT),
+            (-1.1, -2.0, Status::INEXACT),
+            (1.9, 1.0, Status::INEXACT),
+            (-1.9, -2.0, Status::INEXACT),
+        ];
+        spec_test::<f64>(&cases);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn spec_tests_f128() {
+        let cases = [];
+        spec_test::<f128>(&cases);
+    }
+}

vendor/libm/src/math/generic/fma.rs

@@ -0,0 +1,278 @@
+/* SPDX-License-Identifier: MIT */
+/* origin: musl src/math/fma.c. Ported to generic Rust algorithm in 2025, TG. */
+
+use crate::support::{
+    CastFrom, CastInto, DInt, Float, FpResult, HInt, Int, IntTy, MinInt, Round, Status,
+};
+
+/// Fused multiply-add that works when there is not a larger float size available. Computes
+/// `(x * y) + z`.
+#[inline]
+pub fn fma_round<F>(x: F, y: F, z: F, _round: Round) -> FpResult<F>
+where
+    F: Float,
+    F: CastFrom<F::SignedInt>,
+    F: CastFrom<i8>,
+    F::Int: HInt,
+    u32: CastInto<F::Int>,
+{
+    let one = IntTy::<F>::ONE;
+    let zero = IntTy::<F>::ZERO;
+
+    // Normalize such that the top of the mantissa is zero and we have a guard bit.
+    let nx = Norm::from_float(x);
+    let ny = Norm::from_float(y);
+    let nz = Norm::from_float(z);
+
+    if nx.is_zero_nan_inf() || ny.is_zero_nan_inf() {
+        // Value will overflow, defer to non-fused operations.
+        return FpResult::ok(x * y + z);
+    }
+
+    if nz.is_zero_nan_inf() {
+        if nz.is_zero() {
+            // Empty add component means we only need to multiply.
+            return FpResult::ok(x * y);
+        }
+        // `z` is NaN or infinity, which sets the result.
+        return FpResult::ok(z);
+    }
+
+    // multiply: r = x * y
+    let zhi: F::Int;
+    let zlo: F::Int;
+    let (mut rlo, mut rhi) = nx.m.widen_mul(ny.m).lo_hi();
+
+    // Exponent result of multiplication
+    let mut e: i32 = nx.e + ny.e;
+    // Needed shift to align `z` to the multiplication result
+    let mut d: i32 = nz.e - e;
+    let sbits = F::BITS as i32;
+
+    // Scale `z`. Shift `z <<= kz`, `r >>= kr`, so `kz+kr == d`, set `e = e+kr` (== ez-kz)
+    if d > 0 {
+        // The magnitude of `z` is larger than `x * y`
+        if d < sbits {
+            // Maximum shift of one `F::BITS` means shifted `z` will fit into `2 * F::BITS`. Shift
+            // it into `(zhi, zlo)`. No exponent adjustment necessary.
+            zlo = nz.m << d;
+            zhi = nz.m >> (sbits - d);
+        } else {
+            // Shift larger than `sbits`, `z` only needs the top half `zhi`. Place it there (acts
+            // as a shift by `sbits`).
+            zlo = zero;
+            zhi = nz.m;
+            d -= sbits;
+
+            // `z`'s exponent is large enough that it now needs to be taken into account.
+            e = nz.e - sbits;
+
+            if d == 0 {
+                // Exactly `sbits`, nothing to do
+            } else if d < sbits {
+                // Remaining shift fits within `sbits`. Leave `z` in place, shift `x * y`
+                rlo = (rhi << (sbits - d)) | (rlo >> d);
+                // Set the sticky bit
+                rlo |= IntTy::<F>::from((rlo << (sbits - d)) != zero);
+                rhi = rhi >> d;
+            } else {
+                // `z`'s magnitude is enough that `x * y` is irrelevant. It was nonzero, so set
+                // the sticky bit.
+                rlo = one;
+                rhi = zero;
+            }
+        }
+    } else {
+        // `z`'s magnitude once shifted fits entirely within `zlo`
+        zhi = zero;
+        d = -d;
+        if d == 0 {
+            // No shift needed
+            zlo = nz.m;
+        } else if d < sbits {
+            // Shift s.t. `nz.m` fits into `zlo`
+            let sticky = IntTy::<F>::from((nz.m << (sbits - d)) != zero);
+            zlo = (nz.m >> d) | sticky;
+        } else {
+            // Would be entirely shifted out, only set the sticky bit
+            zlo = one;
+        }
+    }
+
+    /* addition */
+
+    let mut neg = nx.neg ^ ny.neg;
+    let samesign: bool = !neg ^ nz.neg;
+    let mut rhi_nonzero = true;
+
+    if samesign {
+        // r += z
+        rlo = rlo.wrapping_add(zlo);
+        rhi += zhi + IntTy::<F>::from(rlo < zlo);
+    } else {
+        // r -= z
+        let (res, borrow) = rlo.overflowing_sub(zlo);
+        rlo = res;
+        rhi = rhi.wrapping_sub(zhi.wrapping_add(IntTy::<F>::from(borrow)));
+        if (rhi >> (F::BITS - 1)) != zero {
+            rlo = rlo.signed().wrapping_neg().unsigned();
+            rhi = rhi.signed().wrapping_neg().unsigned() - IntTy::<F>::from(rlo != zero);
+            neg = !neg;
+        }
+        rhi_nonzero = rhi != zero;
+    }
+
+    /* Construct result */
+
+    // Shift result into `rhi`, left-aligned. Last bit is sticky
+    if rhi_nonzero {
+        // `d` > 0, need to shift both `rhi` and `rlo` into result
+        e += sbits;
+        d = rhi.leading_zeros() as i32 - 1;
+        rhi = (rhi << d) | (rlo >> (sbits - d));
+        // Update sticky
+        rhi |= IntTy::<F>::from((rlo << d) != zero);
+    } else if rlo != zero {
+        // `rhi` is zero, `rlo` is the entire result and needs to be shifted
+        d = rlo.leading_zeros() as i32 - 1;
+        if d < 0 {
+            // Shift and set sticky
+            rhi = (rlo >> 1) | (rlo & one);
+        } else {
+            rhi = rlo << d;
+        }
+    } else {
+        // exact +/- 0.0
+        return FpResult::ok(x * y + z);
+    }
+
+    e -= d;
+
+    // Use int->float conversion to populate the significand.
+    // i is in [1 << (BITS - 2), (1 << (BITS - 1)) - 1]
+    let mut i: F::SignedInt = rhi.signed();
+
+    if neg {
+        i = -i;
+    }
+
+    // `|r|` is in `[0x1p62,0x1p63]` for `f64`
+    let mut r: F = F::cast_from_lossy(i);
+
+    /* Account for subnormal and rounding */
+
+    // Unbiased exponent for the maximum value of `r`
+    let max_pow = F::BITS - 1 + F::EXP_BIAS;
+
+    let mut status = Status::OK;
+
+    if e < -(max_pow as i32 - 2) {
+        // Result is subnormal before rounding
+        if e == -(max_pow as i32 - 1) {
+            let mut c = F::from_parts(false, max_pow, zero);
+            if neg {
+                c = -c;
+            }
+
+            if r == c {
+                // Min normal after rounding,
+                status.set_underflow(true);
+                r = F::MIN_POSITIVE_NORMAL.copysign(r);
+                return FpResult::new(r, status);
+            }
+
+            if (rhi << (F::SIG_BITS + 1)) != zero {
+                // Account for truncated bits. One bit will be lost in the `scalbn` call, add
+                // another top bit to avoid double rounding if inexact.
+                let iu: F::Int = (rhi >> 1) | (rhi & one) | (one << (F::BITS - 2));
+                i = iu.signed();
+
+                if neg {
+                    i = -i;
+                }
+
+                r = F::cast_from_lossy(i);
+
+                // Remove the top bit
+                r = F::cast_from(2i8) * r - c;
+                status.set_underflow(true);
+            }
+        } else {
+            // Only round once when scaled
+            d = F::EXP_BITS as i32 - 1;
+            let sticky = IntTy::<F>::from(rhi << (F::BITS as i32 - d) != zero);
+            i = (((rhi >> d) | sticky) << d).signed();
+
+            if neg {
+                i = -i;
+            }
+
+            r = F::cast_from_lossy(i);
+        }
+    }
+
+    // Use our exponent to scale the final value.
+    FpResult::new(super::scalbn(r, e), status)
+}
+
+/// Representation of `F` that has handled subnormals.
+#[derive(Clone, Copy, Debug)]
+struct Norm<F: Float> {
+    /// Normalized significand with one guard bit, unsigned.
+    m: F::Int,
+    /// Exponent of the mantissa such that `m * 2^e = x`. Accounts for the shift in the mantissa
+    /// and the guard bit; that is, 1.0 will normalize as `m = 1 << 53` and `e = -53`.
+    e: i32,
+    neg: bool,
+}
+
+impl<F: Float> Norm<F> {
+    /// Unbias the exponent and account for the mantissa's precision, including the guard bit.
+    const EXP_UNBIAS: u32 = F::EXP_BIAS + F::SIG_BITS + 1;
+
+    /// Values greater than this had a saturated exponent (infinity or NaN), OR were zero and we
+    /// adjusted the exponent such that it exceeds this threashold.
+    const ZERO_INF_NAN: u32 = F::EXP_SAT - Self::EXP_UNBIAS;
+
+    fn from_float(x: F) -> Self {
+        let mut ix = x.to_bits();
+        let mut e = x.ex() as i32;
+        let neg = x.is_sign_negative();
+        if e == 0 {
+            // Normalize subnormals by multiplication
+            let scale_i = F::BITS - 1;
+            let scale_f = F::from_parts(false, scale_i + F::EXP_BIAS, F::Int::ZERO);
+            let scaled = x * scale_f;
+            ix = scaled.to_bits();
+            e = scaled.ex() as i32;
+            e = if e == 0 {
+                // If the exponent is still zero, the input was zero. Artifically set this value
+                // such that the final `e` will exceed `ZERO_INF_NAN`.
+                1 << F::EXP_BITS
+            } else {
+                // Otherwise, account for the scaling we just did.
+                e - scale_i as i32
+            };
+        }
+
+        e -= Self::EXP_UNBIAS as i32;
+
+        // Absolute  value, set the implicit bit, and shift to create a guard bit
+        ix &= F::SIG_MASK;
+        ix |= F::IMPLICIT_BIT;
+        ix <<= 1;
+
+        Self { m: ix, e, neg }
+    }
+
+    /// True if the value was zero, infinity, or NaN.
+    fn is_zero_nan_inf(self) -> bool {
+        self.e >= Self::ZERO_INF_NAN as i32
+    }
+
+    /// The only value we have
+    fn is_zero(self) -> bool {
+        // The only exponent that strictly exceeds this value is our sentinel value for zero.
+        self.e > Self::ZERO_INF_NAN as i32
+    }
+}

vendor/libm/src/math/generic/fma_wide.rs

@@ -0,0 +1,73 @@
+use crate::support::{
+    CastFrom, CastInto, DFloat, Float, FpResult, HFloat, IntTy, MinInt, Round, Status,
+};
+
+/// Fma implementation when a hardware-backed larger float type is available. For `f32` and `f64`,
+/// `f64` has enough precision to represent the `f32` in its entirety, except for double rounding.
+#[inline]
+pub fn fma_wide_round<F, B>(x: F, y: F, z: F, round: Round) -> FpResult<F>
+where
+    F: Float + HFloat<D = B>,
+    B: Float + DFloat<H = F>,
+    B::Int: CastInto<i32>,
+    i32: CastFrom<i32>,
+{
+    let one = IntTy::<B>::ONE;
+
+    let xy: B = x.widen() * y.widen();
+    let mut result: B = xy + z.widen();
+    let mut ui: B::Int = result.to_bits();
+    let re = result.ex();
+    let zb: B = z.widen();
+
+    let prec_diff = B::SIG_BITS - F::SIG_BITS;
+    let excess_prec = ui & ((one << prec_diff) - one);
+    let halfway = one << (prec_diff - 1);
+
+    // Common case: the larger precision is fine if...
+    // This is not a halfway case
+    if excess_prec != halfway
+        // Or the result is NaN
+        || re == B::EXP_SAT
+        // Or the result is exact
+        || (result - xy == zb && result - zb == xy)
+        // Or the mode is something other than round to nearest
+        || round != Round::Nearest
+    {
+        let min_inexact_exp = (B::EXP_BIAS as i32 + F::EXP_MIN_SUBNORM) as u32;
+        let max_inexact_exp = (B::EXP_BIAS as i32 + F::EXP_MIN) as u32;
+
+        let mut status = Status::OK;
+
+        if (min_inexact_exp..max_inexact_exp).contains(&re) && status.inexact() {
+            // This branch is never hit; requires previous operations to set a status
+            status.set_inexact(false);
+
+            result = xy + z.widen();
+            if status.inexact() {
+                status.set_underflow(true);
+            } else {
+                status.set_inexact(true);
+            }
+        }
+
+        return FpResult {
+            val: result.narrow(),
+            status,
+        };
+    }
+
+    let neg = ui >> (B::BITS - 1) != IntTy::<B>::ZERO;
+    let err = if neg == (zb > xy) {
+        xy - result + zb
+    } else {
+        zb - result + xy
+    };
+    if neg == (err < B::ZERO) {
+        ui += one;
+    } else {
+        ui -= one;
+    }
+
+    FpResult::ok(B::from_bits(ui).narrow())
+}

vendor/libm/src/math/generic/fmax.rs

@@ -0,0 +1,24 @@
+/* SPDX-License-Identifier: MIT OR Apache-2.0 */
+//! IEEE 754-2011 `maxNum`. This has been superseded by IEEE 754-2019 `maximumNumber`.
+//!
+//! Per the spec, returns the canonicalized result of:
+//! - `x` if `x > y`
+//! - `y` if `y > x`
+//! - The other number if one is NaN
+//! - Otherwise, either `x` or `y`, canonicalized
+//! - -0.0 and +0.0 may be disregarded (unlike newer operations)
+//!
+//! Excluded from our implementation is sNaN handling.
+//!
+//! More on the differences: [link].
+//!
+//! [link]: https://grouper.ieee.org/groups/msc/ANSI_IEEE-Std-754-2019/background/minNum_maxNum_Removal_Demotion_v3.pdf
+
+use crate::support::Float;
+
+#[inline]
+pub fn fmax<F: Float>(x: F, y: F) -> F {
+    let res = if x.is_nan() || x < y { y } else { x };
+    // Canonicalize
+    res * F::ONE
+}

vendor/libm/src/math/generic/fmaximum.rs

@@ -0,0 +1,28 @@
+/* SPDX-License-Identifier: MIT OR Apache-2.0 */
+//! IEEE 754-2019 `maximum`.
+//!
+//! Per the spec, returns the canonicalized result of:
+//! - `x` if `x > y`
+//! - `y` if `y > x`
+//! - qNaN if either operation is NaN
+//! - Logic following +0.0 > -0.0
+//!
+//! Excluded from our implementation is sNaN handling.
+
+use crate::support::Float;
+
+#[inline]
+pub fn fmaximum<F: Float>(x: F, y: F) -> F {
+    let res = if x.is_nan() {
+        x
+    } else if y.is_nan() {
+        y
+    } else if x > y || (y.to_bits() == F::NEG_ZERO.to_bits() && x.is_sign_positive()) {
+        x
+    } else {
+        y
+    };
+
+    // Canonicalize
+    res * F::ONE
+}

vendor/libm/src/math/generic/fmaximum_num.rs

@@ -0,0 +1,27 @@
+/* SPDX-License-Identifier: MIT OR Apache-2.0 */
+//! IEEE 754-2019 `maximumNumber`.
+//!
+//! Per the spec, returns:
+//! - `x` if `x > y`
+//! - `y` if `y > x`
+//! - Non-NaN if one operand is NaN
+//! - Logic following +0.0 > -0.0
+//! - Either `x` or `y` if `x == y` and the signs are the same
+//! - qNaN if either operand is a NaN
+//!
+//! Excluded from our implementation is sNaN handling.
+
+use crate::support::Float;
+
+#[inline]
+pub fn fmaximum_num<F: Float>(x: F, y: F) -> F {
+    let res =
+        if x.is_nan() || x < y || (x.to_bits() == F::NEG_ZERO.to_bits() && y.is_sign_positive()) {
+            y
+        } else {
+            x
+        };
+
+    // Canonicalize
+    res * F::ONE
+}

vendor/libm/src/math/generic/fmin.rs

@@ -0,0 +1,24 @@
+/* SPDX-License-Identifier: MIT OR Apache-2.0 */
+//! IEEE 754-2008 `minNum`. This has been superseded by IEEE 754-2019 `minimumNumber`.
+//!
+//! Per the spec, returns the canonicalized result of:
+//! - `x` if `x < y`
+//! - `y` if `y < x`
+//! - The other number if one is NaN
+//! - Otherwise, either `x` or `y`, canonicalized
+//! - -0.0 and +0.0 may be disregarded (unlike newer operations)
+//!
+//! Excluded from our implementation is sNaN handling.
+//!
+//! More on the differences: [link].
+//!
+//! [link]: https://grouper.ieee.org/groups/msc/ANSI_IEEE-Std-754-2019/background/minNum_maxNum_Removal_Demotion_v3.pdf
+
+use crate::support::Float;
+
+#[inline]
+pub fn fmin<F: Float>(x: F, y: F) -> F {
+    let res = if y.is_nan() || x < y { x } else { y };
+    // Canonicalize
+    res * F::ONE
+}

vendor/libm/src/math/generic/fminimum.rs

@@ -0,0 +1,28 @@
+/* SPDX-License-Identifier: MIT OR Apache-2.0 */
+//! IEEE 754-2019 `minimum`.
+//!
+//! Per the spec, returns the canonicalized result of:
+//! - `x` if `x < y`
+//! - `y` if `y < x`
+//! - qNaN if either operation is NaN
+//! - Logic following +0.0 > -0.0
+//!
+//! Excluded from our implementation is sNaN handling.
+
+use crate::support::Float;
+
+#[inline]
+pub fn fminimum<F: Float>(x: F, y: F) -> F {
+    let res = if x.is_nan() {
+        x
+    } else if y.is_nan() {
+        y
+    } else if x < y || (x.to_bits() == F::NEG_ZERO.to_bits() && y.is_sign_positive()) {
+        x
+    } else {
+        y
+    };
+
+    // Canonicalize
+    res * F::ONE
+}

vendor/libm/src/math/generic/fminimum_num.rs

@@ -0,0 +1,27 @@
+/* SPDX-License-Identifier: MIT OR Apache-2.0 */
+//! IEEE 754-2019 `minimum`.
+//!
+//! Per the spec, returns:
+//! - `x` if `x < y`
+//! - `y` if `y < x`
+//! - Non-NaN if one operand is NaN
+//! - Logic following +0.0 > -0.0
+//! - Either `x` or `y` if `x == y` and the signs are the same
+//! - qNaN if either operand is a NaN
+//!
+//! Excluded from our implementation is sNaN handling.
+
+use crate::support::Float;
+
+#[inline]
+pub fn fminimum_num<F: Float>(x: F, y: F) -> F {
+    let res =
+        if y.is_nan() || x < y || (x.to_bits() == F::NEG_ZERO.to_bits() && y.is_sign_positive()) {
+            x
+        } else {
+            y
+        };
+
+    // Canonicalize
+    res * F::ONE
+}

vendor/libm/src/math/generic/fmod.rs

@@ -0,0 +1,68 @@
+/* SPDX-License-Identifier: MIT OR Apache-2.0 */
+use crate::support::{CastFrom, Float, Int, MinInt};
+
+#[inline]
+pub fn fmod<F: Float>(x: F, y: F) -> F {
+    let _1 = F::Int::ONE;
+    let sx = x.to_bits() & F::SIGN_MASK;
+    let ux = x.to_bits() & !F::SIGN_MASK;
+    let uy = y.to_bits() & !F::SIGN_MASK;
+
+    // Cases that return NaN:
+    //   NaN % _
+    //   Inf % _
+    //     _ % NaN
+    //     _ % 0
+    let x_nan_or_inf = ux & F::EXP_MASK == F::EXP_MASK;
+    let y_nan_or_zero = uy.wrapping_sub(_1) & F::EXP_MASK == F::EXP_MASK;
+    if x_nan_or_inf | y_nan_or_zero {
+        return (x * y) / (x * y);
+    }
+
+    if ux < uy {
+        // |x| < |y|
+        return x;
+    }
+
+    let (num, ex) = into_sig_exp::<F>(ux);
+    let (div, ey) = into_sig_exp::<F>(uy);
+
+    // To compute `(num << ex) % (div << ey)`, first
+    // evaluate `rem = (num << (ex - ey)) % div` ...
+    let rem = reduction(num, ex - ey, div);
+    // ... so the result will be `rem << ey`
+
+    if rem.is_zero() {
+        // Return zero with the sign of `x`
+        return F::from_bits(sx);
+    };
+
+    // We would shift `rem` up by `ey`, but have to stop at `F::SIG_BITS`
+    let shift = ey.min(F::SIG_BITS - rem.ilog2());
+    // Anything past that is added to the exponent field
+    let bits = (rem << shift) + (F::Int::cast_from(ey - shift) << F::SIG_BITS);
+    F::from_bits(sx + bits)
+}
+
+/// Given the bits of a finite float, return a tuple of
+///  - the mantissa with the implicit bit (0 if subnormal, 1 otherwise)
+///  - the additional exponent past 1, (0 for subnormal, 0 or more otherwise)
+fn into_sig_exp<F: Float>(mut bits: F::Int) -> (F::Int, u32) {
+    bits &= !F::SIGN_MASK;
+    // Subtract 1 from the exponent, clamping at 0
+    let sat = bits.checked_sub(F::IMPLICIT_BIT).unwrap_or(F::Int::ZERO);
+    (
+        bits - (sat & F::EXP_MASK),
+        u32::cast_from(sat >> F::SIG_BITS),
+    )
+}
+
+/// Compute the remainder `(x * 2.pow(e)) % y` without overflow.
+fn reduction<I: Int>(mut x: I, e: u32, y: I) -> I {
+    x %= y;
+    for _ in 0..e {
+        x <<= 1;
+        x = x.checked_sub(y).unwrap_or(x);
+    }
+    x
+}

vendor/libm/src/math/generic/mod.rs

@@ -0,0 +1,42 @@
+// Note: generic functions are marked `#[inline]` because, even though generic functions are
+// typically inlined, this does not seem to always be the case.
+
+mod ceil;
+mod copysign;
+mod fabs;
+mod fdim;
+mod floor;
+mod fma;
+mod fma_wide;
+mod fmax;
+mod fmaximum;
+mod fmaximum_num;
+mod fmin;
+mod fminimum;
+mod fminimum_num;
+mod fmod;
+mod rint;
+mod round;
+mod scalbn;
+mod sqrt;
+mod trunc;
+
+pub use ceil::ceil;
+pub use copysign::copysign;
+pub use fabs::fabs;
+pub use fdim::fdim;
+pub use floor::floor;
+pub use fma::fma_round;
+pub use fma_wide::fma_wide_round;
+pub use fmax::fmax;
+pub use fmaximum::fmaximum;
+pub use fmaximum_num::fmaximum_num;
+pub use fmin::fmin;
+pub use fminimum::fminimum;
+pub use fminimum_num::fminimum_num;
+pub use fmod::fmod;
+pub use rint::rint_round;
+pub use round::round;
+pub use scalbn::scalbn;
+pub use sqrt::sqrt;
+pub use trunc::trunc;

vendor/libm/src/math/generic/rint.rs

@@ -0,0 +1,130 @@
+/* SPDX-License-Identifier: MIT */
+/* origin: musl src/math/rint.c */
+
+use crate::support::{Float, FpResult, Round};
+
+/// IEEE 754-2019 `roundToIntegralExact`, which respects rounding mode and raises inexact if
+/// applicable.
+#[inline]
+pub fn rint_round<F: Float>(x: F, _round: Round) -> FpResult<F> {
+    let toint = F::ONE / F::EPSILON;
+    let e = x.ex();
+    let positive = x.is_sign_positive();
+
+    // On i386 `force_eval!` must be used to force rounding via storage to memory. Otherwise,
+    // the excess precission from x87 would cause an incorrect final result.
+    let force = |x| {
+        if cfg!(x86_no_sse) && (F::BITS == 32 || F::BITS == 64) {
+            force_eval!(x)
+        } else {
+            x
+        }
+    };
+
+    let res = if e >= F::EXP_BIAS + F::SIG_BITS {
+        // No fractional part; exact result can be returned.
+        x
+    } else {
+        // Apply a net-zero adjustment that nudges `y` in the direction of the rounding mode. For
+        // Rust this is always nearest, but ideally it would take `round` into account.
+        let y = if positive {
+            force(force(x) + toint) - toint
+        } else {
+            force(force(x) - toint) + toint
+        };
+
+        if y == F::ZERO {
+            // A zero result takes the sign of the input.
+            if positive { F::ZERO } else { F::NEG_ZERO }
+        } else {
+            y
+        }
+    };
+
+    FpResult::ok(res)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::support::{Hexf, Status};
+
+    fn spec_test<F: Float>(cases: &[(F, F, Status)]) {
+        let roundtrip = [
+            F::ZERO,
+            F::ONE,
+            F::NEG_ONE,
+            F::NEG_ZERO,
+            F::INFINITY,
+            F::NEG_INFINITY,
+        ];
+
+        for x in roundtrip {
+            let FpResult { val, status } = rint_round(x, Round::Nearest);
+            assert_biteq!(val, x, "rint_round({})", Hexf(x));
+            assert_eq!(status, Status::OK, "{}", Hexf(x));
+        }
+
+        for &(x, res, res_stat) in cases {
+            let FpResult { val, status } = rint_round(x, Round::Nearest);
+            assert_biteq!(val, res, "rint_round({})", Hexf(x));
+            assert_eq!(status, res_stat, "{}", Hexf(x));
+        }
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn spec_tests_f16() {
+        let cases = [];
+        spec_test::<f16>(&cases);
+    }
+
+    #[test]
+    fn spec_tests_f32() {
+        let cases = [
+            (0.1, 0.0, Status::OK),
+            (-0.1, -0.0, Status::OK),
+            (0.5, 0.0, Status::OK),
+            (-0.5, -0.0, Status::OK),
+            (0.9, 1.0, Status::OK),
+            (-0.9, -1.0, Status::OK),
+            (1.1, 1.0, Status::OK),
+            (-1.1, -1.0, Status::OK),
+            (1.5, 2.0, Status::OK),
+            (-1.5, -2.0, Status::OK),
+            (1.9, 2.0, Status::OK),
+            (-1.9, -2.0, Status::OK),
+            (2.8, 3.0, Status::OK),
+            (-2.8, -3.0, Status::OK),
+        ];
+        spec_test::<f32>(&cases);
+    }
+
+    #[test]
+    fn spec_tests_f64() {
+        let cases = [
+            (0.1, 0.0, Status::OK),
+            (-0.1, -0.0, Status::OK),
+            (0.5, 0.0, Status::OK),
+            (-0.5, -0.0, Status::OK),
+            (0.9, 1.0, Status::OK),
+            (-0.9, -1.0, Status::OK),
+            (1.1, 1.0, Status::OK),
+            (-1.1, -1.0, Status::OK),
+            (1.5, 2.0, Status::OK),
+            (-1.5, -2.0, Status::OK),
+            (1.9, 2.0, Status::OK),
+            (-1.9, -2.0, Status::OK),
+            (2.8, 3.0, Status::OK),
+            (-2.8, -3.0, Status::OK),
+        ];
+        spec_test::<f64>(&cases);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn spec_tests_f128() {
+        let cases = [];
+        spec_test::<f128>(&cases);
+    }
+}

vendor/libm/src/math/generic/round.rs

@@ -0,0 +1,83 @@
+use super::{copysign, trunc};
+use crate::support::{Float, MinInt};
+
+#[inline]
+pub fn round<F: Float>(x: F) -> F {
+    let f0p5 = F::from_parts(false, F::EXP_BIAS - 1, F::Int::ZERO); // 0.5
+    let f0p25 = F::from_parts(false, F::EXP_BIAS - 2, F::Int::ZERO); // 0.25
+
+    trunc(x + copysign(f0p5 - f0p25 * F::EPSILON, x))
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn zeroes_f16() {
+        assert_biteq!(round(0.0_f16), 0.0_f16);
+        assert_biteq!(round(-0.0_f16), -0.0_f16);
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn sanity_check_f16() {
+        assert_eq!(round(-1.0_f16), -1.0);
+        assert_eq!(round(2.8_f16), 3.0);
+        assert_eq!(round(-0.5_f16), -1.0);
+        assert_eq!(round(0.5_f16), 1.0);
+        assert_eq!(round(-1.5_f16), -2.0);
+        assert_eq!(round(1.5_f16), 2.0);
+    }
+
+    #[test]
+    fn zeroes_f32() {
+        assert_biteq!(round(0.0_f32), 0.0_f32);
+        assert_biteq!(round(-0.0_f32), -0.0_f32);
+    }
+
+    #[test]
+    fn sanity_check_f32() {
+        assert_eq!(round(-1.0_f32), -1.0);
+        assert_eq!(round(2.8_f32), 3.0);
+        assert_eq!(round(-0.5_f32), -1.0);
+        assert_eq!(round(0.5_f32), 1.0);
+        assert_eq!(round(-1.5_f32), -2.0);
+        assert_eq!(round(1.5_f32), 2.0);
+    }
+
+    #[test]
+    fn zeroes_f64() {
+        assert_biteq!(round(0.0_f64), 0.0_f64);
+        assert_biteq!(round(-0.0_f64), -0.0_f64);
+    }
+
+    #[test]
+    fn sanity_check_f64() {
+        assert_eq!(round(-1.0_f64), -1.0);
+        assert_eq!(round(2.8_f64), 3.0);
+        assert_eq!(round(-0.5_f64), -1.0);
+        assert_eq!(round(0.5_f64), 1.0);
+        assert_eq!(round(-1.5_f64), -2.0);
+        assert_eq!(round(1.5_f64), 2.0);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn zeroes_f128() {
+        assert_biteq!(round(0.0_f128), 0.0_f128);
+        assert_biteq!(round(-0.0_f128), -0.0_f128);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn sanity_check_f128() {
+        assert_eq!(round(-1.0_f128), -1.0);
+        assert_eq!(round(2.8_f128), 3.0);
+        assert_eq!(round(-0.5_f128), -1.0);
+        assert_eq!(round(0.5_f128), 1.0);
+        assert_eq!(round(-1.5_f128), -2.0);
+        assert_eq!(round(1.5_f128), 2.0);
+    }
+}

vendor/libm/src/math/generic/scalbn.rs

@@ -0,0 +1,121 @@
+use crate::support::{CastFrom, CastInto, Float, IntTy, MinInt};
+
+/// Scale the exponent.
+///
+/// From N3220:
+///
+/// > The scalbn and scalbln functions compute `x * b^n`, where `b = FLT_RADIX` if the return type
+/// > of the function is a standard floating type, or `b = 10` if the return type of the function
+/// > is a decimal floating type. A range error occurs for some finite x, depending on n.
+/// >
+/// > [...]
+/// >
+/// > * `scalbn(±0, n)` returns `±0`.
+/// > * `scalbn(x, 0)` returns `x`.
+/// > * `scalbn(±∞, n)` returns `±∞`.
+/// >
+/// > If the calculation does not overflow or underflow, the returned value is exact and
+/// > independent of the current rounding direction mode.
+#[inline]
+pub fn scalbn<F: Float>(mut x: F, mut n: i32) -> F
+where
+    u32: CastInto<F::Int>,
+    F::Int: CastFrom<i32>,
+    F::Int: CastFrom<u32>,
+{
+    let zero = IntTy::<F>::ZERO;
+
+    // Bits including the implicit bit
+    let sig_total_bits = F::SIG_BITS + 1;
+
+    // Maximum and minimum values when biased
+    let exp_max = F::EXP_MAX;
+    let exp_min = F::EXP_MIN;
+
+    // 2 ^ Emax, maximum positive with null significand (0x1p1023 for f64)
+    let f_exp_max = F::from_parts(false, F::EXP_BIAS << 1, zero);
+
+    // 2 ^ Emin, minimum positive normal with null significand (0x1p-1022 for f64)
+    let f_exp_min = F::from_parts(false, 1, zero);
+
+    // 2 ^ sig_total_bits, moltiplier to normalize subnormals (0x1p53 for f64)
+    let f_pow_subnorm = F::from_parts(false, sig_total_bits + F::EXP_BIAS, zero);
+
+    /*
+     * The goal is to multiply `x` by a scale factor that applies `n`. However, there are cases
+     * where `2^n` is not representable by `F` but the result should be, e.g. `x = 2^Emin` with
+     * `n = -EMin + 2` (one out of range of 2^Emax). To get around this, reduce the magnitude of
+     * the final scale operation by prescaling by the max/min power representable by `F`.
+     */
+
+    if n > exp_max {
+        // Worse case positive `n`: `x`  is the minimum subnormal value, the result is `F::MAX`.
+        // This can be reached by three scaling multiplications (two here and one final).
+        debug_assert!(-exp_min + F::SIG_BITS as i32 + exp_max <= exp_max * 3);
+
+        x *= f_exp_max;
+        n -= exp_max;
+        if n > exp_max {
+            x *= f_exp_max;
+            n -= exp_max;
+            if n > exp_max {
+                n = exp_max;
+            }
+        }
+    } else if n < exp_min {
+        // When scaling toward 0, the prescaling is limited to a value that does not allow `x` to
+        // go subnormal. This avoids double rounding.
+        if F::BITS > 16 {
+            // `mul` s.t. `!(x * mul).is_subnormal() ∀ x`
+            let mul = f_exp_min * f_pow_subnorm;
+            let add = -exp_min - sig_total_bits as i32;
+
+            // Worse case negative `n`: `x`  is the maximum positive value, the result is `F::MIN`.
+            // This must be reachable by three scaling multiplications (two here and one final).
+            debug_assert!(-exp_min + F::SIG_BITS as i32 + exp_max <= add * 2 + -exp_min);
+
+            x *= mul;
+            n += add;
+
+            if n < exp_min {
+                x *= mul;
+                n += add;
+
+                if n < exp_min {
+                    n = exp_min;
+                }
+            }
+        } else {
+            // `f16` is unique compared to other float types in that the difference between the
+            // minimum exponent and the significand bits (`add = -exp_min - sig_total_bits`) is
+            // small, only three. The above method depend on decrementing `n` by `add` two times;
+            // for other float types this works out because `add` is a substantial fraction of
+            // the exponent range. For `f16`, however, 3 is relatively small compared to the
+            // exponent range (which is 39), so that requires ~10 prescale rounds rather than two.
+            //
+            // Work aroudn this by using a different algorithm that calculates the prescale
+            // dynamically based on the maximum possible value. This adds more operations per round
+            // since it needs to construct the scale, but works better in the general case.
+            let add = -(n + sig_total_bits as i32).clamp(exp_min, sig_total_bits as i32);
+            let mul = F::from_parts(false, (F::EXP_BIAS as i32 - add) as u32, zero);
+
+            x *= mul;
+            n += add;
+
+            if n < exp_min {
+                let add = -(n + sig_total_bits as i32).clamp(exp_min, sig_total_bits as i32);
+                let mul = F::from_parts(false, (F::EXP_BIAS as i32 - add) as u32, zero);
+
+                x *= mul;
+                n += add;
+
+                if n < exp_min {
+                    n = exp_min;
+                }
+            }
+        }
+    }
+
+    let scale = F::from_parts(false, (F::EXP_BIAS as i32 + n) as u32, zero);
+    x * scale
+}

vendor/libm/src/math/generic/sqrt.rs

@@ -0,0 +1,541 @@
+/* SPDX-License-Identifier: MIT */
+/* origin: musl src/math/sqrt.c. Ported to generic Rust algorithm in 2025, TG. */
+
+//! Generic square root algorithm.
+//!
+//! This routine operates around `m_u2`, a U.2 (fixed point with two integral bits) mantissa
+//! within the range [1, 4). A table lookup provides an initial estimate, then goldschmidt
+//! iterations at various widths are used to approach the real values.
+//!
+//! For the iterations, `r` is a U0 number that approaches `1/sqrt(m_u2)`, and `s` is a U2 number
+//! that approaches `sqrt(m_u2)`. Recall that m_u2 ∈ [1, 4).
+//!
+//! With Newton-Raphson iterations, this would be:
+//!
+//! - `w = r * r           w ~ 1 / m`
+//! - `u = 3 - m * w       u ~ 3 - m * w = 3 - m / m = 2`
+//! - `r = r * u / 2       r ~ r`
+//!
+//! (Note that the righthand column does not show anything analytically meaningful (i.e. r ~ r),
+//! since the value of performing one iteration is in reducing the error representable by `~`).
+//!
+//! Instead of Newton-Raphson iterations, Goldschmidt iterations are used to calculate
+//! `s = m * r`:
+//!
+//! - `s = m * r           s ~ m / sqrt(m)`
+//! - `u = 3 - s * r       u ~ 3 - (m / sqrt(m)) * (1 / sqrt(m)) = 3 - m / m = 2`
+//! - `r = r * u / 2       r ~ r`
+//! - `s = s * u / 2       s ~ s`
+//!
+//! The above is precise because it uses the original value `m`. There is also a faster version
+//! that performs fewer steps but does not use `m`:
+//!
+//! - `u = 3 - s * r       u ~ 3 - 1`
+//! - `r = r * u / 2       r ~ r`
+//! - `s = s * u / 2       s ~ s`
+//!
+//! Rounding errors accumulate faster with the second version, so it is only used for subsequent
+//! iterations within the same width integer. The first version is always used for the first
+//! iteration at a new width in order to avoid this accumulation.
+//!
+//! Goldschmidt has the advantage over Newton-Raphson that `sqrt(x)` and `1/sqrt(x)` are
+//! computed at the same time, i.e. there is no need to calculate `1/sqrt(x)` and invert it.
+
+use crate::support::{
+    CastFrom, CastInto, DInt, Float, FpResult, HInt, Int, IntTy, MinInt, Round, Status, cold_path,
+};
+
+#[inline]
+pub fn sqrt<F>(x: F) -> F
+where
+    F: Float + SqrtHelper,
+    F::Int: HInt,
+    F::Int: From<u8>,
+    F::Int: From<F::ISet2>,
+    F::Int: CastInto<F::ISet1>,
+    F::Int: CastInto<F::ISet2>,
+    u32: CastInto<F::Int>,
+{
+    sqrt_round(x, Round::Nearest).val
+}
+
+#[inline]
+pub fn sqrt_round<F>(x: F, _round: Round) -> FpResult<F>
+where
+    F: Float + SqrtHelper,
+    F::Int: HInt,
+    F::Int: From<u8>,
+    F::Int: From<F::ISet2>,
+    F::Int: CastInto<F::ISet1>,
+    F::Int: CastInto<F::ISet2>,
+    u32: CastInto<F::Int>,
+{
+    let zero = IntTy::<F>::ZERO;
+    let one = IntTy::<F>::ONE;
+
+    let mut ix = x.to_bits();
+
+    // Top is the exponent and sign, which may or may not be shifted. If the float fits into a
+    // `u32`, we can get by without paying shifting costs.
+    let noshift = F::BITS <= u32::BITS;
+    let (mut top, special_case) = if noshift {
+        let exp_lsb = one << F::SIG_BITS;
+        let special_case = ix.wrapping_sub(exp_lsb) >= F::EXP_MASK - exp_lsb;
+        (Exp::NoShift(()), special_case)
+    } else {
+        let top = u32::cast_from(ix >> F::SIG_BITS);
+        let special_case = top.wrapping_sub(1) >= F::EXP_SAT - 1;
+        (Exp::Shifted(top), special_case)
+    };
+
+    // Handle NaN, zero, and out of domain (<= 0)
+    if special_case {
+        cold_path();
+
+        // +/-0
+        if ix << 1 == zero {
+            return FpResult::ok(x);
+        }
+
+        // Positive infinity
+        if ix == F::EXP_MASK {
+            return FpResult::ok(x);
+        }
+
+        // NaN or negative
+        if ix > F::EXP_MASK {
+            return FpResult::new(F::NAN, Status::INVALID);
+        }
+
+        // Normalize subnormals by multiplying by 1.0 << SIG_BITS (e.g. 0x1p52 for doubles).
+        let scaled = x * F::from_parts(false, F::SIG_BITS + F::EXP_BIAS, zero);
+        ix = scaled.to_bits();
+        match top {
+            Exp::Shifted(ref mut v) => {
+                *v = scaled.ex();
+                *v = (*v).wrapping_sub(F::SIG_BITS);
+            }
+            Exp::NoShift(()) => {
+                ix = ix.wrapping_sub((F::SIG_BITS << F::SIG_BITS).cast());
+            }
+        }
+    }
+
+    // Reduce arguments such that `x = 4^e * m`:
+    //
+    // - m_u2 ∈ [1, 4), a fixed point U2.BITS number
+    // - 2^e is the exponent part of the result
+    let (m_u2, exp) = match top {
+        Exp::Shifted(top) => {
+            // We now know `x` is positive, so `top` is just its (biased) exponent
+            let mut e = top;
+            // Construct a fixed point representation of the mantissa.
+            let mut m_u2 = (ix | F::IMPLICIT_BIT) << F::EXP_BITS;
+            let even = (e & 1) != 0;
+            if even {
+                m_u2 >>= 1;
+            }
+            e = (e.wrapping_add(F::EXP_SAT >> 1)) >> 1;
+            (m_u2, Exp::Shifted(e))
+        }
+        Exp::NoShift(()) => {
+            let even = ix & (one << F::SIG_BITS) != zero;
+
+            // Exponent part of the return value
+            let mut e_noshift = ix >> 1;
+            // ey &= (F::EXP_MASK << 2) >> 2; // clear the top exponent bit (result = 1.0)
+            e_noshift += (F::EXP_MASK ^ (F::SIGN_MASK >> 1)) >> 1;
+            e_noshift &= F::EXP_MASK;
+
+            let m1 = (ix << F::EXP_BITS) | F::SIGN_MASK;
+            let m0 = (ix << (F::EXP_BITS - 1)) & !F::SIGN_MASK;
+            let m_u2 = if even { m0 } else { m1 };
+
+            (m_u2, Exp::NoShift(e_noshift))
+        }
+    };
+
+    // Extract the top 6 bits of the significand with the lowest bit of the exponent.
+    let i = usize::cast_from(ix >> (F::SIG_BITS - 6)) & 0b1111111;
+
+    // Start with an initial guess for `r = 1 / sqrt(m)` from the table, and shift `m` as an
+    // initial value for `s = sqrt(m)`. See the module documentation for details.
+    let r1_u0: F::ISet1 = F::ISet1::cast_from(RSQRT_TAB[i]) << (F::ISet1::BITS - 16);
+    let s1_u2: F::ISet1 = ((m_u2) >> (F::BITS - F::ISet1::BITS)).cast();
+
+    // Perform iterations, if any, at quarter width (used for `f128`).
+    let (r1_u0, _s1_u2) = goldschmidt::<F, F::ISet1>(r1_u0, s1_u2, F::SET1_ROUNDS, false);
+
+    // Widen values and perform iterations at half width (used for `f64` and `f128`).
+    let r2_u0: F::ISet2 = F::ISet2::from(r1_u0) << (F::ISet2::BITS - F::ISet1::BITS);
+    let s2_u2: F::ISet2 = ((m_u2) >> (F::BITS - F::ISet2::BITS)).cast();
+    let (r2_u0, _s2_u2) = goldschmidt::<F, F::ISet2>(r2_u0, s2_u2, F::SET2_ROUNDS, false);
+
+    // Perform final iterations at full width (used for all float types).
+    let r_u0: F::Int = F::Int::from(r2_u0) << (F::BITS - F::ISet2::BITS);
+    let s_u2: F::Int = m_u2;
+    let (_r_u0, s_u2) = goldschmidt::<F, F::Int>(r_u0, s_u2, F::FINAL_ROUNDS, true);
+
+    // Shift back to mantissa position.
+    let mut m = s_u2 >> (F::EXP_BITS - 2);
+
+    // The musl source includes the following comment (with literals replaced):
+    //
+    // > s < sqrt(m) < s + 0x1.09p-SIG_BITS
+    // > compute nearest rounded result: the nearest result to SIG_BITS bits is either s or
+    // > s+0x1p-SIG_BITS, we can decide by comparing (2^SIG_BITS s + 0.5)^2 to 2^(2*SIG_BITS) m.
+    //
+    // Expanding this with , with `SIG_BITS = p` and adjusting based on the operations done to
+    // `d0` and `d1`:
+    //
+    // - `2^(2p)m ≟ ((2^p)m + 0.5)^2`
+    // - `2^(2p)m ≟ 2^(2p)m^2 + (2^p)m + 0.25`
+    // - `2^(2p)m - m^2 ≟ (2^(2p) - 1)m^2 + (2^p)m + 0.25`
+    // - `(1 - 2^(2p))m + m^2 ≟ (1 - 2^(2p))m^2 + (1 - 2^p)m + 0.25` (?)
+    //
+    // I do not follow how the rounding bit is extracted from this comparison with the below
+    // operations. In any case, the algorithm is well tested.
+
+    // The value needed to shift `m_u2` by to create `m*2^(2p)`. `2p = 2 * F::SIG_BITS`,
+    // `F::BITS - 2` accounts for the offset that `m_u2` already has.
+    let shift = 2 * F::SIG_BITS - (F::BITS - 2);
+
+    // `2^(2p)m - m^2`
+    let d0 = (m_u2 << shift).wrapping_sub(m.wrapping_mul(m));
+    // `m - 2^(2p)m + m^2`
+    let d1 = m.wrapping_sub(d0);
+    m += d1 >> (F::BITS - 1);
+    m &= F::SIG_MASK;
+
+    match exp {
+        Exp::Shifted(e) => m |= IntTy::<F>::cast_from(e) << F::SIG_BITS,
+        Exp::NoShift(e) => m |= e,
+    };
+
+    let mut y = F::from_bits(m);
+
+    // FIXME(f16): the fenv math does not work for `f16`
+    if F::BITS > 16 {
+        // Handle rounding and inexact. `(m + 1)^2 == 2^shift m` is exact; for all other cases, add
+        // a tiny value to cause fenv effects.
+        let d2 = d1.wrapping_add(m).wrapping_add(one);
+        let mut tiny = if d2 == zero {
+            cold_path();
+            zero
+        } else {
+            F::IMPLICIT_BIT
+        };
+
+        tiny |= (d1 ^ d2) & F::SIGN_MASK;
+        let t = F::from_bits(tiny);
+        y = y + t;
+    }
+
+    FpResult::ok(y)
+}
+
+/// Multiply at the wider integer size, returning the high half.
+fn wmulh<I: HInt>(a: I, b: I) -> I {
+    a.widen_mul(b).hi()
+}
+
+/// Perform `count` goldschmidt iterations, returning `(r_u0, s_u?)`.
+///
+/// - `r_u0` is the reciprocal `r ~ 1 / sqrt(m)`, as U0.
+/// - `s_u2` is the square root, `s ~ sqrt(m)`, as U2.
+/// - `count` is the number of iterations to perform.
+/// - `final_set` should be true if this is the last round (same-sized integer). If so, the
+///   returned `s` will be U3, for later shifting. Otherwise, the returned `s` is U2.
+///
+/// Note that performance relies on the optimizer being able to unroll these loops (reasonably
+/// trivial, `count` is a constant when called).
+#[inline]
+fn goldschmidt<F, I>(mut r_u0: I, mut s_u2: I, count: u32, final_set: bool) -> (I, I)
+where
+    F: SqrtHelper,
+    I: HInt + From<u8>,
+{
+    let three_u2 = I::from(0b11u8) << (I::BITS - 2);
+    let mut u_u0 = r_u0;
+
+    for i in 0..count {
+        // First iteration: `s = m*r` (`u_u0 = r_u0` set above)
+        // Subsequent iterations: `s=s*u/2`
+        s_u2 = wmulh(s_u2, u_u0);
+
+        // Perform `s /= 2` if:
+        //
+        // 1. This is not the first iteration (the first iteration is `s = m*r`)...
+        // 2. ... and this is not the last set of iterations
+        // 3. ... or, if this is the last set, it is not the last iteration
+        //
+        // This step is not performed for the final iteration because the shift is combined with
+        // a later shift (moving `s` into the mantissa).
+        if i > 0 && (!final_set || i + 1 < count) {
+            s_u2 <<= 1;
+        }
+
+        // u = 3 - s*r
+        let d_u2 = wmulh(s_u2, r_u0);
+        u_u0 = three_u2.wrapping_sub(d_u2);
+
+        // r = r*u/2
+        r_u0 = wmulh(r_u0, u_u0) << 1;
+    }
+
+    (r_u0, s_u2)
+}
+
+/// Representation of whether we shift the exponent into a `u32`, or modify it in place to save
+/// the shift operations.
+enum Exp<T> {
+    /// The exponent has been shifted to a `u32` and is LSB-aligned.
+    Shifted(u32),
+    /// The exponent is in its natural position in integer repr.
+    NoShift(T),
+}
+
+/// Size-specific constants related to the square root routine.
+pub trait SqrtHelper: Float {
+    /// Integer for the first set of rounds. If unused, set to the same type as the next set.
+    type ISet1: HInt + Into<Self::ISet2> + CastFrom<Self::Int> + From<u8>;
+    /// Integer for the second set of rounds. If unused, set to the same type as the next set.
+    type ISet2: HInt + From<Self::ISet1> + From<u8>;
+
+    /// Number of rounds at `ISet1`.
+    const SET1_ROUNDS: u32 = 0;
+    /// Number of rounds at `ISet2`.
+    const SET2_ROUNDS: u32 = 0;
+    /// Number of rounds at `Self::Int`.
+    const FINAL_ROUNDS: u32;
+}
+
+#[cfg(f16_enabled)]
+impl SqrtHelper for f16 {
+    type ISet1 = u16; // unused
+    type ISet2 = u16; // unused
+
+    const FINAL_ROUNDS: u32 = 2;
+}
+
+impl SqrtHelper for f32 {
+    type ISet1 = u32; // unused
+    type ISet2 = u32; // unused
+
+    const FINAL_ROUNDS: u32 = 3;
+}
+
+impl SqrtHelper for f64 {
+    type ISet1 = u32; // unused
+    type ISet2 = u32;
+
+    const SET2_ROUNDS: u32 = 2;
+    const FINAL_ROUNDS: u32 = 2;
+}
+
+#[cfg(f128_enabled)]
+impl SqrtHelper for f128 {
+    type ISet1 = u32;
+    type ISet2 = u64;
+
+    const SET1_ROUNDS: u32 = 1;
+    const SET2_ROUNDS: u32 = 2;
+    const FINAL_ROUNDS: u32 = 2;
+}
+
+/// A U0.16 representation of `1/sqrt(x)`.
+///
+/// The index is a 7-bit number consisting of a single exponent bit and 6 bits of significand.
+#[rustfmt::skip]
+static RSQRT_TAB: [u16; 128] = [
+    0xb451, 0xb2f0, 0xb196, 0xb044, 0xaef9, 0xadb6, 0xac79, 0xab43,
+    0xaa14, 0xa8eb, 0xa7c8, 0xa6aa, 0xa592, 0xa480, 0xa373, 0xa26b,
+    0xa168, 0xa06a, 0x9f70, 0x9e7b, 0x9d8a, 0x9c9d, 0x9bb5, 0x9ad1,
+    0x99f0, 0x9913, 0x983a, 0x9765, 0x9693, 0x95c4, 0x94f8, 0x9430,
+    0x936b, 0x92a9, 0x91ea, 0x912e, 0x9075, 0x8fbe, 0x8f0a, 0x8e59,
+    0x8daa, 0x8cfe, 0x8c54, 0x8bac, 0x8b07, 0x8a64, 0x89c4, 0x8925,
+    0x8889, 0x87ee, 0x8756, 0x86c0, 0x862b, 0x8599, 0x8508, 0x8479,
+    0x83ec, 0x8361, 0x82d8, 0x8250, 0x81c9, 0x8145, 0x80c2, 0x8040,
+    0xff02, 0xfd0e, 0xfb25, 0xf947, 0xf773, 0xf5aa, 0xf3ea, 0xf234,
+    0xf087, 0xeee3, 0xed47, 0xebb3, 0xea27, 0xe8a3, 0xe727, 0xe5b2,
+    0xe443, 0xe2dc, 0xe17a, 0xe020, 0xdecb, 0xdd7d, 0xdc34, 0xdaf1,
+    0xd9b3, 0xd87b, 0xd748, 0xd61a, 0xd4f1, 0xd3cd, 0xd2ad, 0xd192,
+    0xd07b, 0xcf69, 0xce5b, 0xcd51, 0xcc4a, 0xcb48, 0xca4a, 0xc94f,
+    0xc858, 0xc764, 0xc674, 0xc587, 0xc49d, 0xc3b7, 0xc2d4, 0xc1f4,
+    0xc116, 0xc03c, 0xbf65, 0xbe90, 0xbdbe, 0xbcef, 0xbc23, 0xbb59,
+    0xba91, 0xb9cc, 0xb90a, 0xb84a, 0xb78c, 0xb6d0, 0xb617, 0xb560,
+];
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    /// Test behavior specified in IEEE 754 `squareRoot`.
+    fn spec_test<F>()
+    where
+        F: Float + SqrtHelper,
+        F::Int: HInt,
+        F::Int: From<u8>,
+        F::Int: From<F::ISet2>,
+        F::Int: CastInto<F::ISet1>,
+        F::Int: CastInto<F::ISet2>,
+        u32: CastInto<F::Int>,
+    {
+        // Values that should return a NaN and raise invalid
+        let nan = [F::NEG_INFINITY, F::NEG_ONE, F::NAN, F::MIN];
+
+        // Values that return unaltered
+        let roundtrip = [F::ZERO, F::NEG_ZERO, F::INFINITY];
+
+        for x in nan {
+            let FpResult { val, status } = sqrt_round(x, Round::Nearest);
+            assert!(val.is_nan());
+            assert!(status == Status::INVALID);
+        }
+
+        for x in roundtrip {
+            let FpResult { val, status } = sqrt_round(x, Round::Nearest);
+            assert_biteq!(val, x);
+            assert!(status == Status::OK);
+        }
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn sanity_check_f16() {
+        assert_biteq!(sqrt(100.0f16), 10.0);
+        assert_biteq!(sqrt(4.0f16), 2.0);
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn spec_tests_f16() {
+        spec_test::<f16>();
+    }
+
+    #[test]
+    #[cfg(f16_enabled)]
+    #[allow(clippy::approx_constant)]
+    fn conformance_tests_f16() {
+        let cases = [
+            (f16::PI, 0x3f17_u16),
+            // 10_000.0, using a hex literal for MSRV hack (Rust < 1.67 checks literal widths as
+            // part of the AST, so the `cfg` is irrelevant here).
+            (f16::from_bits(0x70e2), 0x5640_u16),
+            (f16::from_bits(0x0000000f), 0x13bf_u16),
+            (f16::INFINITY, f16::INFINITY.to_bits()),
+        ];
+
+        for (input, output) in cases {
+            assert_biteq!(
+                sqrt(input),
+                f16::from_bits(output),
+                "input: {input:?} ({:#018x})",
+                input.to_bits()
+            );
+        }
+    }
+
+    #[test]
+    fn sanity_check_f32() {
+        assert_biteq!(sqrt(100.0f32), 10.0);
+        assert_biteq!(sqrt(4.0f32), 2.0);
+    }
+
+    #[test]
+    fn spec_tests_f32() {
+        spec_test::<f32>();
+    }
+
+    #[test]
+    #[allow(clippy::approx_constant)]
+    fn conformance_tests_f32() {
+        let cases = [
+            (f32::PI, 0x3fe2dfc5_u32),
+            (10000.0f32, 0x42c80000_u32),
+            (f32::from_bits(0x0000000f), 0x1b2f456f_u32),
+            (f32::INFINITY, f32::INFINITY.to_bits()),
+        ];
+
+        for (input, output) in cases {
+            assert_biteq!(
+                sqrt(input),
+                f32::from_bits(output),
+                "input: {input:?} ({:#018x})",
+                input.to_bits()
+            );
+        }
+    }
+
+    #[test]
+    fn sanity_check_f64() {
+        assert_biteq!(sqrt(100.0f64), 10.0);
+        assert_biteq!(sqrt(4.0f64), 2.0);
+    }
+
+    #[test]
+    fn spec_tests_f64() {
+        spec_test::<f64>();
+    }
+
+    #[test]
+    #[allow(clippy::approx_constant)]
+    fn conformance_tests_f64() {
+        let cases = [
+            (f64::PI, 0x3ffc5bf891b4ef6a_u64),
+            (10000.0, 0x4059000000000000_u64),
+            (f64::from_bits(0x0000000f), 0x1e7efbdeb14f4eda_u64),
+            (f64::INFINITY, f64::INFINITY.to_bits()),
+        ];
+
+        for (input, output) in cases {
+            assert_biteq!(
+                sqrt(input),
+                f64::from_bits(output),
+                "input: {input:?} ({:#018x})",
+                input.to_bits()
+            );
+        }
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn sanity_check_f128() {
+        assert_biteq!(sqrt(100.0f128), 10.0);
+        assert_biteq!(sqrt(4.0f128), 2.0);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn spec_tests_f128() {
+        spec_test::<f128>();
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    #[allow(clippy::approx_constant)]
+    fn conformance_tests_f128() {
+        let cases = [
+            (f128::PI, 0x3fffc5bf891b4ef6aa79c3b0520d5db9_u128),
+            // 10_000.0, see `f16` for reasoning.
+            (
+                f128::from_bits(0x400c3880000000000000000000000000),
+                0x40059000000000000000000000000000_u128,
+            ),
+            (
+                f128::from_bits(0x0000000f),
+                0x1fc9efbdeb14f4ed9b17ae807907e1e9_u128,
+            ),
+            (f128::INFINITY, f128::INFINITY.to_bits()),
+        ];
+
+        for (input, output) in cases {
+            assert_biteq!(
+                sqrt(input),
+                f128::from_bits(output),
+                "input: {input:?} ({:#018x})",
+                input.to_bits()
+            );
+        }
+    }
+}

vendor/libm/src/math/generic/trunc.rs

@@ -0,0 +1,148 @@
+/* SPDX-License-Identifier: MIT
+ * origin: musl src/math/trunc.c */
+
+use crate::support::{Float, FpResult, Int, IntTy, MinInt, Status};
+
+#[inline]
+pub fn trunc<F: Float>(x: F) -> F {
+    trunc_status(x).val
+}
+
+#[inline]
+pub fn trunc_status<F: Float>(x: F) -> FpResult<F> {
+    let mut xi: F::Int = x.to_bits();
+    let e: i32 = x.exp_unbiased();
+
+    // C1: The represented value has no fractional part, so no truncation is needed
+    if e >= F::SIG_BITS as i32 {
+        return FpResult::ok(x);
+    }
+
+    let mask = if e < 0 {
+        // C2: If the exponent is negative, the result will be zero so we mask out everything
+        // except the sign.
+        F::SIGN_MASK
+    } else {
+        // C3: Otherwise, we mask out the last `e` bits of the significand.
+        !(F::SIG_MASK >> e.unsigned())
+    };
+
+    // C4: If the to-be-masked-out portion is already zero, we have an exact result
+    if (xi & !mask) == IntTy::<F>::ZERO {
+        return FpResult::ok(x);
+    }
+
+    // C5: Otherwise the result is inexact and we will truncate. Raise `FE_INEXACT`, mask the
+    // result, and return.
+
+    let status = if xi & F::SIG_MASK == F::Int::ZERO {
+        Status::OK
+    } else {
+        Status::INEXACT
+    };
+    xi &= mask;
+    FpResult::new(F::from_bits(xi), status)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::support::Hexf;
+
+    fn spec_test<F: Float>(cases: &[(F, F, Status)]) {
+        let roundtrip = [
+            F::ZERO,
+            F::ONE,
+            F::NEG_ONE,
+            F::NEG_ZERO,
+            F::INFINITY,
+            F::NEG_INFINITY,
+        ];
+
+        for x in roundtrip {
+            let FpResult { val, status } = trunc_status(x);
+            assert_biteq!(val, x, "{}", Hexf(x));
+            assert_eq!(status, Status::OK, "{}", Hexf(x));
+        }
+
+        for &(x, res, res_stat) in cases {
+            let FpResult { val, status } = trunc_status(x);
+            assert_biteq!(val, res, "{}", Hexf(x));
+            assert_eq!(status, res_stat, "{}", Hexf(x));
+        }
+    }
+
+    /* Skipping f16 / f128 "sanity_check"s and spec cases due to rejected literal lexing at MSRV */
+
+    #[test]
+    #[cfg(f16_enabled)]
+    fn spec_tests_f16() {
+        let cases = [];
+        spec_test::<f16>(&cases);
+    }
+
+    #[test]
+    fn sanity_check_f32() {
+        assert_eq!(trunc(0.5f32), 0.0);
+        assert_eq!(trunc(1.1f32), 1.0);
+        assert_eq!(trunc(2.9f32), 2.0);
+    }
+
+    #[test]
+    fn spec_tests_f32() {
+        let cases = [
+            (0.1, 0.0, Status::INEXACT),
+            (-0.1, -0.0, Status::INEXACT),
+            (0.9, 0.0, Status::INEXACT),
+            (-0.9, -0.0, Status::INEXACT),
+            (1.1, 1.0, Status::INEXACT),
+            (-1.1, -1.0, Status::INEXACT),
+            (1.9, 1.0, Status::INEXACT),
+            (-1.9, -1.0, Status::INEXACT),
+        ];
+        spec_test::<f32>(&cases);
+
+        assert_biteq!(trunc(1.1f32), 1.0);
+        assert_biteq!(trunc(1.1f64), 1.0);
+
+        // C1
+        assert_biteq!(trunc(hf32!("0x1p23")), hf32!("0x1p23"));
+        assert_biteq!(trunc(hf64!("0x1p52")), hf64!("0x1p52"));
+        assert_biteq!(trunc(hf32!("-0x1p23")), hf32!("-0x1p23"));
+        assert_biteq!(trunc(hf64!("-0x1p52")), hf64!("-0x1p52"));
+
+        // C2
+        assert_biteq!(trunc(hf32!("0x1p-1")), 0.0);
+        assert_biteq!(trunc(hf64!("0x1p-1")), 0.0);
+        assert_biteq!(trunc(hf32!("-0x1p-1")), -0.0);
+        assert_biteq!(trunc(hf64!("-0x1p-1")), -0.0);
+    }
+
+    #[test]
+    fn sanity_check_f64() {
+        assert_eq!(trunc(1.1f64), 1.0);
+        assert_eq!(trunc(2.9f64), 2.0);
+    }
+
+    #[test]
+    fn spec_tests_f64() {
+        let cases = [
+            (0.1, 0.0, Status::INEXACT),
+            (-0.1, -0.0, Status::INEXACT),
+            (0.9, 0.0, Status::INEXACT),
+            (-0.9, -0.0, Status::INEXACT),
+            (1.1, 1.0, Status::INEXACT),
+            (-1.1, -1.0, Status::INEXACT),
+            (1.9, 1.0, Status::INEXACT),
+            (-1.9, -1.0, Status::INEXACT),
+        ];
+        spec_test::<f64>(&cases);
+    }
+
+    #[test]
+    #[cfg(f128_enabled)]
+    fn spec_tests_f128() {
+        let cases = [];
+        spec_test::<f128>(&cases);
+    }
+}

vendor/libm/src/math/hypot.rs

@@ -0,0 +1,74 @@
+use core::f64;
+
+use super::sqrt;
+
+const SPLIT: f64 = 134217728. + 1.; // 0x1p27 + 1 === (2 ^ 27) + 1
+
+fn sq(x: f64) -> (f64, f64) {
+    let xh: f64;
+    let xl: f64;
+    let xc: f64;
+
+    xc = x * SPLIT;
+    xh = x - xc + xc;
+    xl = x - xh;
+    let hi = x * x;
+    let lo = xh * xh - hi + 2. * xh * xl + xl * xl;
+    (hi, lo)
+}
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn hypot(mut x: f64, mut y: f64) -> f64 {
+    let x1p700 = f64::from_bits(0x6bb0000000000000); // 0x1p700 === 2 ^ 700
+    let x1p_700 = f64::from_bits(0x1430000000000000); // 0x1p-700 === 2 ^ -700
+
+    let mut uxi = x.to_bits();
+    let mut uyi = y.to_bits();
+    let uti;
+    let ex: i64;
+    let ey: i64;
+    let mut z: f64;
+
+    /* arrange |x| >= |y| */
+    uxi &= -1i64 as u64 >> 1;
+    uyi &= -1i64 as u64 >> 1;
+    if uxi < uyi {
+        uti = uxi;
+        uxi = uyi;
+        uyi = uti;
+    }
+
+    /* special cases */
+    ex = (uxi >> 52) as i64;
+    ey = (uyi >> 52) as i64;
+    x = f64::from_bits(uxi);
+    y = f64::from_bits(uyi);
+    /* note: hypot(inf,nan) == inf */
+    if ey == 0x7ff {
+        return y;
+    }
+    if ex == 0x7ff || uyi == 0 {
+        return x;
+    }
+    /* note: hypot(x,y) ~= x + y*y/x/2 with inexact for small y/x */
+    /* 64 difference is enough for ld80 double_t */
+    if ex - ey > 64 {
+        return x + y;
+    }
+
+    /* precise sqrt argument in nearest rounding mode without overflow */
+    /* xh*xh must not overflow and xl*xl must not underflow in sq */
+    z = 1.;
+    if ex > 0x3ff + 510 {
+        z = x1p700;
+        x *= x1p_700;
+        y *= x1p_700;
+    } else if ey < 0x3ff - 450 {
+        z = x1p_700;
+        x *= x1p700;
+        y *= x1p700;
+    }
+    let (hx, lx) = sq(x);
+    let (hy, ly) = sq(y);
+    z * sqrt(ly + lx + hy + hx)
+}

vendor/libm/src/math/hypotf.rs

@@ -0,0 +1,43 @@
+use core::f32;
+
+use super::sqrtf;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn hypotf(mut x: f32, mut y: f32) -> f32 {
+    let x1p90 = f32::from_bits(0x6c800000); // 0x1p90f === 2 ^ 90
+    let x1p_90 = f32::from_bits(0x12800000); // 0x1p-90f === 2 ^ -90
+
+    let mut uxi = x.to_bits();
+    let mut uyi = y.to_bits();
+    let uti;
+    let mut z: f32;
+
+    uxi &= -1i32 as u32 >> 1;
+    uyi &= -1i32 as u32 >> 1;
+    if uxi < uyi {
+        uti = uxi;
+        uxi = uyi;
+        uyi = uti;
+    }
+
+    x = f32::from_bits(uxi);
+    y = f32::from_bits(uyi);
+    if uyi == 0xff << 23 {
+        return y;
+    }
+    if uxi >= 0xff << 23 || uyi == 0 || uxi - uyi >= 25 << 23 {
+        return x + y;
+    }
+
+    z = 1.;
+    if uxi >= (0x7f + 60) << 23 {
+        z = x1p90;
+        x *= x1p_90;
+        y *= x1p_90;
+    } else if uyi < (0x7f - 60) << 23 {
+        z = x1p_90;
+        x *= x1p90;
+        y *= x1p90;
+    }
+    z * sqrtf((x as f64 * x as f64 + y as f64 * y as f64) as f32)
+}

vendor/libm/src/math/ilogb.rs

@@ -0,0 +1,32 @@
+const FP_ILOGBNAN: i32 = -1 - 0x7fffffff;
+const FP_ILOGB0: i32 = FP_ILOGBNAN;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn ilogb(x: f64) -> i32 {
+    let mut i: u64 = x.to_bits();
+    let e = ((i >> 52) & 0x7ff) as i32;
+
+    if e == 0 {
+        i <<= 12;
+        if i == 0 {
+            force_eval!(0.0 / 0.0);
+            return FP_ILOGB0;
+        }
+        /* subnormal x */
+        let mut e = -0x3ff;
+        while (i >> 63) == 0 {
+            e -= 1;
+            i <<= 1;
+        }
+        e
+    } else if e == 0x7ff {
+        force_eval!(0.0 / 0.0);
+        if (i << 12) != 0 {
+            FP_ILOGBNAN
+        } else {
+            i32::MAX
+        }
+    } else {
+        e - 0x3ff
+    }
+}

vendor/libm/src/math/ilogbf.rs

@@ -0,0 +1,28 @@
+const FP_ILOGBNAN: i32 = -1 - 0x7fffffff;
+const FP_ILOGB0: i32 = FP_ILOGBNAN;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn ilogbf(x: f32) -> i32 {
+    let mut i = x.to_bits();
+    let e = ((i >> 23) & 0xff) as i32;
+
+    if e == 0 {
+        i <<= 9;
+        if i == 0 {
+            force_eval!(0.0 / 0.0);
+            return FP_ILOGB0;
+        }
+        /* subnormal x */
+        let mut e = -0x7f;
+        while (i >> 31) == 0 {
+            e -= 1;
+            i <<= 1;
+        }
+        e
+    } else if e == 0xff {
+        force_eval!(0.0 / 0.0);
+        if (i << 9) != 0 { FP_ILOGBNAN } else { i32::MAX }
+    } else {
+        e - 0x7f
+    }
+}

vendor/libm/src/math/j0.rs

@@ -0,0 +1,426 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_j0.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* j0(x), y0(x)
+ * Bessel function of the first and second kinds of order zero.
+ * Method -- j0(x):
+ *      1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
+ *      2. Reduce x to |x| since j0(x)=j0(-x),  and
+ *         for x in (0,2)
+ *              j0(x) = 1-z/4+ z^2*R0/S0,  where z = x*x;
+ *         (precision:  |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
+ *         for x in (2,inf)
+ *              j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
+ *         where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
+ *         as follow:
+ *              cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
+ *                      = 1/sqrt(2) * (cos(x) + sin(x))
+ *              sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
+ *                      = 1/sqrt(2) * (sin(x) - cos(x))
+ *         (To avoid cancellation, use
+ *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+ *          to compute the worse one.)
+ *
+ *      3 Special cases
+ *              j0(nan)= nan
+ *              j0(0) = 1
+ *              j0(inf) = 0
+ *
+ * Method -- y0(x):
+ *      1. For x<2.
+ *         Since
+ *              y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
+ *         therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
+ *         We use the following function to approximate y0,
+ *              y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
+ *         where
+ *              U(z) = u00 + u01*z + ... + u06*z^6
+ *              V(z) = 1  + v01*z + ... + v04*z^4
+ *         with absolute approximation error bounded by 2**-72.
+ *         Note: For tiny x, U/V = u0 and j0(x)~1, hence
+ *              y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
+ *      2. For x>=2.
+ *              y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
+ *         where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
+ *         by the method mentioned above.
+ *      3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
+ */
+
+use super::{cos, fabs, get_high_word, get_low_word, log, sin, sqrt};
+const INVSQRTPI: f64 = 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */
+const TPI: f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
+
+/* common method when |x|>=2 */
+fn common(ix: u32, x: f64, y0: bool) -> f64 {
+    let s: f64;
+    let mut c: f64;
+    let mut ss: f64;
+    let mut cc: f64;
+    let z: f64;
+
+    /*
+     * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x-pi/4)-q0(x)*sin(x-pi/4))
+     * y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x-pi/4)+q0(x)*cos(x-pi/4))
+     *
+     * sin(x-pi/4) = (sin(x) - cos(x))/sqrt(2)
+     * cos(x-pi/4) = (sin(x) + cos(x))/sqrt(2)
+     * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+     */
+    s = sin(x);
+    c = cos(x);
+    if y0 {
+        c = -c;
+    }
+    cc = s + c;
+    /* avoid overflow in 2*x, big ulp error when x>=0x1p1023 */
+    if ix < 0x7fe00000 {
+        ss = s - c;
+        z = -cos(2.0 * x);
+        if s * c < 0.0 {
+            cc = z / ss;
+        } else {
+            ss = z / cc;
+        }
+        if ix < 0x48000000 {
+            if y0 {
+                ss = -ss;
+            }
+            cc = pzero(x) * cc - qzero(x) * ss;
+        }
+    }
+    return INVSQRTPI * cc / sqrt(x);
+}
+
+/* R0/S0 on [0, 2.00] */
+const R02: f64 = 1.56249999999999947958e-02; /* 0x3F8FFFFF, 0xFFFFFFFD */
+const R03: f64 = -1.89979294238854721751e-04; /* 0xBF28E6A5, 0xB61AC6E9 */
+const R04: f64 = 1.82954049532700665670e-06; /* 0x3EBEB1D1, 0x0C503919 */
+const R05: f64 = -4.61832688532103189199e-09; /* 0xBE33D5E7, 0x73D63FCE */
+const S01: f64 = 1.56191029464890010492e-02; /* 0x3F8FFCE8, 0x82C8C2A4 */
+const S02: f64 = 1.16926784663337450260e-04; /* 0x3F1EA6D2, 0xDD57DBF4 */
+const S03: f64 = 5.13546550207318111446e-07; /* 0x3EA13B54, 0xCE84D5A9 */
+const S04: f64 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
+
+/// Zeroth order of the [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the first kind (f64).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn j0(mut x: f64) -> f64 {
+    let z: f64;
+    let r: f64;
+    let s: f64;
+    let mut ix: u32;
+
+    ix = get_high_word(x);
+    ix &= 0x7fffffff;
+
+    /* j0(+-inf)=0, j0(nan)=nan */
+    if ix >= 0x7ff00000 {
+        return 1.0 / (x * x);
+    }
+    x = fabs(x);
+
+    if ix >= 0x40000000 {
+        /* |x| >= 2 */
+        /* large ulp error near zeros: 2.4, 5.52, 8.6537,.. */
+        return common(ix, x, false);
+    }
+
+    /* 1 - x*x/4 + x*x*R(x^2)/S(x^2) */
+    if ix >= 0x3f200000 {
+        /* |x| >= 2**-13 */
+        /* up to 4ulp error close to 2 */
+        z = x * x;
+        r = z * (R02 + z * (R03 + z * (R04 + z * R05)));
+        s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * S04)));
+        return (1.0 + x / 2.0) * (1.0 - x / 2.0) + z * (r / s);
+    }
+
+    /* 1 - x*x/4 */
+    /* prevent underflow */
+    /* inexact should be raised when x!=0, this is not done correctly */
+    if ix >= 0x38000000 {
+        /* |x| >= 2**-127 */
+        x = 0.25 * x * x;
+    }
+    return 1.0 - x;
+}
+
+const U00: f64 = -7.38042951086872317523e-02; /* 0xBFB2E4D6, 0x99CBD01F */
+const U01: f64 = 1.76666452509181115538e-01; /* 0x3FC69D01, 0x9DE9E3FC */
+const U02: f64 = -1.38185671945596898896e-02; /* 0xBF8C4CE8, 0xB16CFA97 */
+const U03: f64 = 3.47453432093683650238e-04; /* 0x3F36C54D, 0x20B29B6B */
+const U04: f64 = -3.81407053724364161125e-06; /* 0xBECFFEA7, 0x73D25CAD */
+const U05: f64 = 1.95590137035022920206e-08; /* 0x3E550057, 0x3B4EABD4 */
+const U06: f64 = -3.98205194132103398453e-11; /* 0xBDC5E43D, 0x693FB3C8 */
+const V01: f64 = 1.27304834834123699328e-02; /* 0x3F8A1270, 0x91C9C71A */
+const V02: f64 = 7.60068627350353253702e-05; /* 0x3F13ECBB, 0xF578C6C1 */
+const V03: f64 = 2.59150851840457805467e-07; /* 0x3E91642D, 0x7FF202FD */
+const V04: f64 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
+
+/// Zeroth order of the [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the second kind (f64).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn y0(x: f64) -> f64 {
+    let z: f64;
+    let u: f64;
+    let v: f64;
+    let ix: u32;
+    let lx: u32;
+
+    ix = get_high_word(x);
+    lx = get_low_word(x);
+
+    /* y0(nan)=nan, y0(<0)=nan, y0(0)=-inf, y0(inf)=0 */
+    if ((ix << 1) | lx) == 0 {
+        return -1.0 / 0.0;
+    }
+    if (ix >> 31) != 0 {
+        return 0.0 / 0.0;
+    }
+    if ix >= 0x7ff00000 {
+        return 1.0 / x;
+    }
+
+    if ix >= 0x40000000 {
+        /* x >= 2 */
+        /* large ulp errors near zeros: 3.958, 7.086,.. */
+        return common(ix, x, true);
+    }
+
+    /* U(x^2)/V(x^2) + (2/pi)*j0(x)*log(x) */
+    if ix >= 0x3e400000 {
+        /* x >= 2**-27 */
+        /* large ulp error near the first zero, x ~= 0.89 */
+        z = x * x;
+        u = U00 + z * (U01 + z * (U02 + z * (U03 + z * (U04 + z * (U05 + z * U06)))));
+        v = 1.0 + z * (V01 + z * (V02 + z * (V03 + z * V04)));
+        return u / v + TPI * (j0(x) * log(x));
+    }
+    return U00 + TPI * log(x);
+}
+
+/* The asymptotic expansions of pzero is
+ *      1 - 9/128 s^2 + 11025/98304 s^4 - ...,  where s = 1/x.
+ * For x >= 2, We approximate pzero by
+ *      pzero(x) = 1 + (R/S)
+ * where  R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
+ *        S = 1 + pS0*s^2 + ... + pS4*s^10
+ * and
+ *      | pzero(x)-1-R/S | <= 2  ** ( -60.26)
+ */
+const PR8: [f64; 6] = [
+    /* for x in [inf, 8]=1/[0,0.125] */
+    0.00000000000000000000e+00,  /* 0x00000000, 0x00000000 */
+    -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
+    -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
+    -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
+    -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
+    -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
+];
+const PS8: [f64; 5] = [
+    1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
+    3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
+    4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
+    1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
+    4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
+];
+
+const PR5: [f64; 6] = [
+    /* for x in [8,4.5454]=1/[0.125,0.22001] */
+    -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
+    -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
+    -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
+    -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
+    -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
+    -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
+];
+const PS5: [f64; 5] = [
+    6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
+    1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
+    5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
+    9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
+    2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
+];
+
+const PR3: [f64; 6] = [
+    /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+    -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
+    -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
+    -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
+    -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
+    -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
+    -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
+];
+const PS3: [f64; 5] = [
+    3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
+    3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
+    1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
+    1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
+    1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
+];
+
+const PR2: [f64; 6] = [
+    /* for x in [2.8570,2]=1/[0.3499,0.5] */
+    -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
+    -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
+    -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
+    -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
+    -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
+    -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
+];
+const PS2: [f64; 5] = [
+    2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
+    1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
+    2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
+    1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
+    1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
+];
+
+fn pzero(x: f64) -> f64 {
+    let p: &[f64; 6];
+    let q: &[f64; 5];
+    let z: f64;
+    let r: f64;
+    let s: f64;
+    let mut ix: u32;
+
+    ix = get_high_word(x);
+    ix &= 0x7fffffff;
+    if ix >= 0x40200000 {
+        p = &PR8;
+        q = &PS8;
+    } else if ix >= 0x40122E8B {
+        p = &PR5;
+        q = &PS5;
+    } else if ix >= 0x4006DB6D {
+        p = &PR3;
+        q = &PS3;
+    } else
+    /*ix >= 0x40000000*/
+    {
+        p = &PR2;
+        q = &PS2;
+    }
+    z = 1.0 / (x * x);
+    r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
+    s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
+    return 1.0 + r / s;
+}
+
+/* For x >= 8, the asymptotic expansions of qzero is
+ *      -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
+ * We approximate pzero by
+ *      qzero(x) = s*(-1.25 + (R/S))
+ * where  R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
+ *        S = 1 + qS0*s^2 + ... + qS5*s^12
+ * and
+ *      | qzero(x)/s +1.25-R/S | <= 2  ** ( -61.22)
+ */
+const QR8: [f64; 6] = [
+    /* for x in [inf, 8]=1/[0,0.125] */
+    0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+    7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
+    1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
+    5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
+    8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
+    3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
+];
+const QS8: [f64; 6] = [
+    1.63776026895689824414e+02,  /* 0x406478D5, 0x365B39BC */
+    8.09834494656449805916e+03,  /* 0x40BFA258, 0x4E6B0563 */
+    1.42538291419120476348e+05,  /* 0x41016652, 0x54D38C3F */
+    8.03309257119514397345e+05,  /* 0x412883DA, 0x83A52B43 */
+    8.40501579819060512818e+05,  /* 0x4129A66B, 0x28DE0B3D */
+    -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
+];
+
+const QR5: [f64; 6] = [
+    /* for x in [8,4.5454]=1/[0.125,0.22001] */
+    1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
+    7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
+    5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
+    1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
+    1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
+    1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
+];
+const QS5: [f64; 6] = [
+    8.27766102236537761883e+01,  /* 0x4054B1B3, 0xFB5E1543 */
+    2.07781416421392987104e+03,  /* 0x40A03BA0, 0xDA21C0CE */
+    1.88472887785718085070e+04,  /* 0x40D267D2, 0x7B591E6D */
+    5.67511122894947329769e+04,  /* 0x40EBB5E3, 0x97E02372 */
+    3.59767538425114471465e+04,  /* 0x40E19118, 0x1F7A54A0 */
+    -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
+];
+
+const QR3: [f64; 6] = [
+    /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+    4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
+    7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
+    3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
+    4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
+    1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
+    1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
+];
+const QS3: [f64; 6] = [
+    4.87588729724587182091e+01,  /* 0x40486122, 0xBFE343A6 */
+    7.09689221056606015736e+02,  /* 0x40862D83, 0x86544EB3 */
+    3.70414822620111362994e+03,  /* 0x40ACF04B, 0xE44DFC63 */
+    6.46042516752568917582e+03,  /* 0x40B93C6C, 0xD7C76A28 */
+    2.51633368920368957333e+03,  /* 0x40A3A8AA, 0xD94FB1C0 */
+    -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
+];
+
+const QR2: [f64; 6] = [
+    /* for x in [2.8570,2]=1/[0.3499,0.5] */
+    1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
+    7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
+    1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
+    1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
+    3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
+    1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
+];
+const QS2: [f64; 6] = [
+    3.03655848355219184498e+01,  /* 0x403E5D96, 0xF7C07AED */
+    2.69348118608049844624e+02,  /* 0x4070D591, 0xE4D14B40 */
+    8.44783757595320139444e+02,  /* 0x408A6645, 0x22B3BF22 */
+    8.82935845112488550512e+02,  /* 0x408B977C, 0x9C5CC214 */
+    2.12666388511798828631e+02,  /* 0x406A9553, 0x0E001365 */
+    -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
+];
+
+fn qzero(x: f64) -> f64 {
+    let p: &[f64; 6];
+    let q: &[f64; 6];
+    let s: f64;
+    let r: f64;
+    let z: f64;
+    let mut ix: u32;
+
+    ix = get_high_word(x);
+    ix &= 0x7fffffff;
+    if ix >= 0x40200000 {
+        p = &QR8;
+        q = &QS8;
+    } else if ix >= 0x40122E8B {
+        p = &QR5;
+        q = &QS5;
+    } else if ix >= 0x4006DB6D {
+        p = &QR3;
+        q = &QS3;
+    } else
+    /*ix >= 0x40000000*/
+    {
+        p = &QR2;
+        q = &QS2;
+    }
+    z = 1.0 / (x * x);
+    r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
+    s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
+    return (-0.125 + r / s) / x;
+}