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