303 lines
11 KiB
Rust
303 lines
11 KiB
Rust
// Translated from C to Rust. The original C code can be found at
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// https://github.com/ulfjack/ryu and carries the following license:
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//
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// Copyright 2018 Ulf Adams
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//
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// The contents of this file may be used under the terms of the Apache License,
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// Version 2.0.
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//
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// (See accompanying file LICENSE-Apache or copy at
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// http://www.apache.org/licenses/LICENSE-2.0)
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//
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// Alternatively, the contents of this file may be used under the terms of
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// the Boost Software License, Version 1.0.
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// (See accompanying file LICENSE-Boost or copy at
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// https://www.boost.org/LICENSE_1_0.txt)
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//
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// Unless required by applicable law or agreed to in writing, this software
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// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
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// KIND, either express or implied.
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use crate::common::{log10_pow2, log10_pow5, pow5bits};
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#[cfg(not(feature = "small"))]
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pub use crate::d2s_full_table::{DOUBLE_POW5_INV_SPLIT, DOUBLE_POW5_SPLIT};
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use crate::d2s_intrinsics::{
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div10, div100, div5, mul_shift_all_64, multiple_of_power_of_2, multiple_of_power_of_5,
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};
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#[cfg(feature = "small")]
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pub use crate::d2s_small_table::{compute_inv_pow5, compute_pow5};
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use core::mem::MaybeUninit;
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pub const DOUBLE_MANTISSA_BITS: u32 = 52;
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pub const DOUBLE_EXPONENT_BITS: u32 = 11;
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pub const DOUBLE_BIAS: i32 = 1023;
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pub const DOUBLE_POW5_INV_BITCOUNT: i32 = 125;
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pub const DOUBLE_POW5_BITCOUNT: i32 = 125;
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#[cfg_attr(feature = "no-panic", inline)]
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pub fn decimal_length17(v: u64) -> u32 {
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// This is slightly faster than a loop.
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// The average output length is 16.38 digits, so we check high-to-low.
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// Function precondition: v is not an 18, 19, or 20-digit number.
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// (17 digits are sufficient for round-tripping.)
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debug_assert!(v < 100000000000000000);
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if v >= 10000000000000000 {
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17
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} else if v >= 1000000000000000 {
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16
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} else if v >= 100000000000000 {
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15
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} else if v >= 10000000000000 {
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14
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} else if v >= 1000000000000 {
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13
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} else if v >= 100000000000 {
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12
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} else if v >= 10000000000 {
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11
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} else if v >= 1000000000 {
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10
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} else if v >= 100000000 {
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9
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} else if v >= 10000000 {
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8
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} else if v >= 1000000 {
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7
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} else if v >= 100000 {
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6
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} else if v >= 10000 {
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5
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} else if v >= 1000 {
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4
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} else if v >= 100 {
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3
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} else if v >= 10 {
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2
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} else {
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1
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}
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}
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// A floating decimal representing m * 10^e.
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pub struct FloatingDecimal64 {
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pub mantissa: u64,
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// Decimal exponent's range is -324 to 308
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// inclusive, and can fit in i16 if needed.
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pub exponent: i32,
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}
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#[cfg_attr(feature = "no-panic", inline)]
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pub fn d2d(ieee_mantissa: u64, ieee_exponent: u32) -> FloatingDecimal64 {
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let (e2, m2) = if ieee_exponent == 0 {
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(
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// We subtract 2 so that the bounds computation has 2 additional bits.
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1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS as i32 - 2,
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ieee_mantissa,
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)
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} else {
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(
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ieee_exponent as i32 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS as i32 - 2,
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(1u64 << DOUBLE_MANTISSA_BITS) | ieee_mantissa,
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)
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};
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let even = (m2 & 1) == 0;
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let accept_bounds = even;
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// Step 2: Determine the interval of valid decimal representations.
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let mv = 4 * m2;
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// Implicit bool -> int conversion. True is 1, false is 0.
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let mm_shift = (ieee_mantissa != 0 || ieee_exponent <= 1) as u32;
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// We would compute mp and mm like this:
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// uint64_t mp = 4 * m2 + 2;
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// uint64_t mm = mv - 1 - mm_shift;
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// Step 3: Convert to a decimal power base using 128-bit arithmetic.
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let mut vr: u64;
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let mut vp: u64;
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let mut vm: u64;
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let mut vp_uninit: MaybeUninit<u64> = MaybeUninit::uninit();
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let mut vm_uninit: MaybeUninit<u64> = MaybeUninit::uninit();
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let e10: i32;
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let mut vm_is_trailing_zeros = false;
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let mut vr_is_trailing_zeros = false;
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if e2 >= 0 {
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// I tried special-casing q == 0, but there was no effect on performance.
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// This expression is slightly faster than max(0, log10_pow2(e2) - 1).
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let q = log10_pow2(e2) - (e2 > 3) as u32;
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e10 = q as i32;
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let k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q as i32) - 1;
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let i = -e2 + q as i32 + k;
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vr = unsafe {
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mul_shift_all_64(
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m2,
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#[cfg(feature = "small")]
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&compute_inv_pow5(q),
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#[cfg(not(feature = "small"))]
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{
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debug_assert!(q < DOUBLE_POW5_INV_SPLIT.len() as u32);
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DOUBLE_POW5_INV_SPLIT.get_unchecked(q as usize)
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},
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i as u32,
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vp_uninit.as_mut_ptr(),
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vm_uninit.as_mut_ptr(),
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mm_shift,
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)
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};
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vp = unsafe { vp_uninit.assume_init() };
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vm = unsafe { vm_uninit.assume_init() };
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if q <= 21 {
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// This should use q <= 22, but I think 21 is also safe. Smaller values
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// may still be safe, but it's more difficult to reason about them.
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// Only one of mp, mv, and mm can be a multiple of 5, if any.
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let mv_mod5 = (mv as u32).wrapping_sub(5u32.wrapping_mul(div5(mv) as u32));
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if mv_mod5 == 0 {
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vr_is_trailing_zeros = multiple_of_power_of_5(mv, q);
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} else if accept_bounds {
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// Same as min(e2 + (~mm & 1), pow5_factor(mm)) >= q
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// <=> e2 + (~mm & 1) >= q && pow5_factor(mm) >= q
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// <=> true && pow5_factor(mm) >= q, since e2 >= q.
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vm_is_trailing_zeros = multiple_of_power_of_5(mv - 1 - mm_shift as u64, q);
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} else {
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// Same as min(e2 + 1, pow5_factor(mp)) >= q.
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vp -= multiple_of_power_of_5(mv + 2, q) as u64;
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}
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}
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} else {
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// This expression is slightly faster than max(0, log10_pow5(-e2) - 1).
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let q = log10_pow5(-e2) - (-e2 > 1) as u32;
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e10 = q as i32 + e2;
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let i = -e2 - q as i32;
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let k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
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let j = q as i32 - k;
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vr = unsafe {
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mul_shift_all_64(
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m2,
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#[cfg(feature = "small")]
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&compute_pow5(i as u32),
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#[cfg(not(feature = "small"))]
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{
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debug_assert!(i < DOUBLE_POW5_SPLIT.len() as i32);
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DOUBLE_POW5_SPLIT.get_unchecked(i as usize)
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},
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j as u32,
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vp_uninit.as_mut_ptr(),
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vm_uninit.as_mut_ptr(),
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mm_shift,
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)
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};
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vp = unsafe { vp_uninit.assume_init() };
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vm = unsafe { vm_uninit.assume_init() };
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if q <= 1 {
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// {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
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// mv = 4 * m2, so it always has at least two trailing 0 bits.
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vr_is_trailing_zeros = true;
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if accept_bounds {
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// mm = mv - 1 - mm_shift, so it has 1 trailing 0 bit iff mm_shift == 1.
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vm_is_trailing_zeros = mm_shift == 1;
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} else {
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// mp = mv + 2, so it always has at least one trailing 0 bit.
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vp -= 1;
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}
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} else if q < 63 {
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// TODO(ulfjack): Use a tighter bound here.
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// We want to know if the full product has at least q trailing zeros.
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// We need to compute min(p2(mv), p5(mv) - e2) >= q
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// <=> p2(mv) >= q && p5(mv) - e2 >= q
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// <=> p2(mv) >= q (because -e2 >= q)
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vr_is_trailing_zeros = multiple_of_power_of_2(mv, q);
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}
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}
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// Step 4: Find the shortest decimal representation in the interval of valid representations.
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let mut removed = 0i32;
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let mut last_removed_digit = 0u8;
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// On average, we remove ~2 digits.
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let output = if vm_is_trailing_zeros || vr_is_trailing_zeros {
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// General case, which happens rarely (~0.7%).
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loop {
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let vp_div10 = div10(vp);
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let vm_div10 = div10(vm);
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if vp_div10 <= vm_div10 {
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break;
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}
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let vm_mod10 = (vm as u32).wrapping_sub(10u32.wrapping_mul(vm_div10 as u32));
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let vr_div10 = div10(vr);
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let vr_mod10 = (vr as u32).wrapping_sub(10u32.wrapping_mul(vr_div10 as u32));
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vm_is_trailing_zeros &= vm_mod10 == 0;
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vr_is_trailing_zeros &= last_removed_digit == 0;
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last_removed_digit = vr_mod10 as u8;
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vr = vr_div10;
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vp = vp_div10;
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vm = vm_div10;
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removed += 1;
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}
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if vm_is_trailing_zeros {
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loop {
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let vm_div10 = div10(vm);
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let vm_mod10 = (vm as u32).wrapping_sub(10u32.wrapping_mul(vm_div10 as u32));
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if vm_mod10 != 0 {
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break;
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}
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let vp_div10 = div10(vp);
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let vr_div10 = div10(vr);
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let vr_mod10 = (vr as u32).wrapping_sub(10u32.wrapping_mul(vr_div10 as u32));
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vr_is_trailing_zeros &= last_removed_digit == 0;
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last_removed_digit = vr_mod10 as u8;
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vr = vr_div10;
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vp = vp_div10;
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vm = vm_div10;
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removed += 1;
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}
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}
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if vr_is_trailing_zeros && last_removed_digit == 5 && vr % 2 == 0 {
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// Round even if the exact number is .....50..0.
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last_removed_digit = 4;
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}
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// We need to take vr + 1 if vr is outside bounds or we need to round up.
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vr + ((vr == vm && (!accept_bounds || !vm_is_trailing_zeros)) || last_removed_digit >= 5)
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as u64
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} else {
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// Specialized for the common case (~99.3%). Percentages below are relative to this.
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let mut round_up = false;
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let vp_div100 = div100(vp);
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let vm_div100 = div100(vm);
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// Optimization: remove two digits at a time (~86.2%).
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if vp_div100 > vm_div100 {
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let vr_div100 = div100(vr);
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let vr_mod100 = (vr as u32).wrapping_sub(100u32.wrapping_mul(vr_div100 as u32));
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round_up = vr_mod100 >= 50;
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vr = vr_div100;
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vp = vp_div100;
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vm = vm_div100;
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removed += 2;
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}
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// Loop iterations below (approximately), without optimization above:
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// 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
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// Loop iterations below (approximately), with optimization above:
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// 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
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loop {
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let vp_div10 = div10(vp);
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let vm_div10 = div10(vm);
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if vp_div10 <= vm_div10 {
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break;
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}
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let vr_div10 = div10(vr);
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let vr_mod10 = (vr as u32).wrapping_sub(10u32.wrapping_mul(vr_div10 as u32));
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round_up = vr_mod10 >= 5;
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vr = vr_div10;
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vp = vp_div10;
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vm = vm_div10;
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removed += 1;
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}
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// We need to take vr + 1 if vr is outside bounds or we need to round up.
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vr + (vr == vm || round_up) as u64
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};
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let exp = e10 + removed;
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FloatingDecimal64 {
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exponent: exp,
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mantissa: output,
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}
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}
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