177 lines
6.8 KiB
Rust
177 lines
6.8 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::*;
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use crate::f2s_intrinsics::*;
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pub const FLOAT_MANTISSA_BITS: u32 = 23;
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pub const FLOAT_EXPONENT_BITS: u32 = 8;
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const FLOAT_BIAS: i32 = 127;
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pub use crate::f2s_intrinsics::{FLOAT_POW5_BITCOUNT, FLOAT_POW5_INV_BITCOUNT};
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// A floating decimal representing m * 10^e.
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pub struct FloatingDecimal32 {
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pub mantissa: u32,
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// Decimal exponent's range is -45 to 38
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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 f2d(ieee_mantissa: u32, ieee_exponent: u32) -> FloatingDecimal32 {
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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 - FLOAT_BIAS - FLOAT_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 - FLOAT_BIAS - FLOAT_MANTISSA_BITS as i32 - 2,
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(1u32 << FLOAT_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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let mp = 4 * m2 + 2;
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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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let mm = 4 * m2 - 1 - mm_shift;
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// Step 3: Convert to a decimal power base using 64-bit arithmetic.
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let mut vr: u32;
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let mut vp: u32;
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let mut vm: u32;
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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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let mut last_removed_digit = 0u8;
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if e2 >= 0 {
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let q = log10_pow2(e2);
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e10 = q as i32;
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let k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q as i32) - 1;
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let i = -e2 + q as i32 + k;
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vr = mul_pow5_inv_div_pow2(mv, q, i);
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vp = mul_pow5_inv_div_pow2(mp, q, i);
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vm = mul_pow5_inv_div_pow2(mm, q, i);
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if q != 0 && (vp - 1) / 10 <= vm / 10 {
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// We need to know one removed digit even if we are not going to loop below. We could use
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// q = X - 1 above, except that would require 33 bits for the result, and we've found that
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// 32-bit arithmetic is faster even on 64-bit machines.
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let l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q as i32 - 1) - 1;
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last_removed_digit =
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(mul_pow5_inv_div_pow2(mv, q - 1, -e2 + q as i32 - 1 + l) % 10) as u8;
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}
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if q <= 9 {
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// The largest power of 5 that fits in 24 bits is 5^10, but q <= 9 seems to be safe as well.
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// Only one of mp, mv, and mm can be a multiple of 5, if any.
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if mv % 5 == 0 {
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vr_is_trailing_zeros = multiple_of_power_of_5_32(mv, q);
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} else if accept_bounds {
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vm_is_trailing_zeros = multiple_of_power_of_5_32(mm, q);
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} else {
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vp -= multiple_of_power_of_5_32(mp, q) as u32;
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}
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}
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} else {
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let q = log10_pow5(-e2);
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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) - FLOAT_POW5_BITCOUNT;
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let mut j = q as i32 - k;
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vr = mul_pow5_div_pow2(mv, i as u32, j);
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vp = mul_pow5_div_pow2(mp, i as u32, j);
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vm = mul_pow5_div_pow2(mm, i as u32, j);
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if q != 0 && (vp - 1) / 10 <= vm / 10 {
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j = q as i32 - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
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last_removed_digit = (mul_pow5_div_pow2(mv, (i + 1) as u32, j) % 10) as u8;
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}
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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 < 31 {
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// TODO(ulfjack): Use a tighter bound here.
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vr_is_trailing_zeros = multiple_of_power_of_2_32(mv, q - 1);
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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 output = if vm_is_trailing_zeros || vr_is_trailing_zeros {
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// General case, which happens rarely (~4.0%).
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while vp / 10 > vm / 10 {
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vm_is_trailing_zeros &= vm - (vm / 10) * 10 == 0;
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vr_is_trailing_zeros &= last_removed_digit == 0;
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last_removed_digit = (vr % 10) as u8;
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vr /= 10;
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vp /= 10;
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vm /= 10;
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removed += 1;
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}
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if vm_is_trailing_zeros {
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while vm % 10 == 0 {
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vr_is_trailing_zeros &= last_removed_digit == 0;
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last_removed_digit = (vr % 10) as u8;
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vr /= 10;
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vp /= 10;
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vm /= 10;
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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 u32
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} else {
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// Specialized for the common case (~96.0%). Percentages below are relative to this.
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// Loop iterations below (approximately):
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// 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
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while vp / 10 > vm / 10 {
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last_removed_digit = (vr % 10) as u8;
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vr /= 10;
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vp /= 10;
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vm /= 10;
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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 || last_removed_digit >= 5) as u32
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};
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let exp = e10 + removed;
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FloatingDecimal32 {
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exponent: exp,
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mantissa: output,
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}
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}
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