encoder_ryu/
f2s.rs

1// Translated from C to Rust. The original C code can be found at
2// https://github.com/ulfjack/ryu and carries the following license:
3//
4// Copyright 2018 Ulf Adams
5//
6// The contents of this file may be used under the terms of the Apache License,
7// Version 2.0.
8//
9//    (See accompanying file LICENSE-Apache or copy at
10//     http://www.apache.org/licenses/LICENSE-2.0)
11//
12// Alternatively, the contents of this file may be used under the terms of
13// the Boost Software License, Version 1.0.
14//    (See accompanying file LICENSE-Boost or copy at
15//     https://www.boost.org/LICENSE_1_0.txt)
16//
17// Unless required by applicable law or agreed to in writing, this software
18// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
19// KIND, either express or implied.
20
21use crate::common::*;
22use crate::f2s_intrinsics::*;
23
24pub const FLOAT_MANTISSA_BITS: u32 = 23;
25pub const FLOAT_EXPONENT_BITS: u32 = 8;
26const FLOAT_BIAS: i32 = 127;
27pub use crate::f2s_intrinsics::{FLOAT_POW5_BITCOUNT, FLOAT_POW5_INV_BITCOUNT};
28
29// A floating decimal representing m * 10^e.
30pub struct FloatingDecimal32 {
31    pub mantissa: u32,
32    // Decimal exponent's range is -45 to 38
33    // inclusive, and can fit in i16 if needed.
34    pub exponent: i32,
35}
36
37#[cfg_attr(feature = "no-panic", inline)]
38pub fn f2d(ieee_mantissa: u32, ieee_exponent: u32) -> FloatingDecimal32 {
39    let (e2, m2) = if ieee_exponent == 0 {
40        (
41            // We subtract 2 so that the bounds computation has 2 additional bits.
42            1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS as i32 - 2,
43            ieee_mantissa,
44        )
45    } else {
46        (
47            ieee_exponent as i32 - FLOAT_BIAS - FLOAT_MANTISSA_BITS as i32 - 2,
48            (1u32 << FLOAT_MANTISSA_BITS) | ieee_mantissa,
49        )
50    };
51    let even = (m2 & 1) == 0;
52    let accept_bounds = even;
53
54    // Step 2: Determine the interval of valid decimal representations.
55    let mv = 4 * m2;
56    let mp = 4 * m2 + 2;
57    // Implicit bool -> int conversion. True is 1, false is 0.
58    let mm_shift = (ieee_mantissa != 0 || ieee_exponent <= 1) as u32;
59    let mm = 4 * m2 - 1 - mm_shift;
60
61    // Step 3: Convert to a decimal power base using 64-bit arithmetic.
62    let mut vr: u32;
63    let mut vp: u32;
64    let mut vm: u32;
65    let e10: i32;
66    let mut vm_is_trailing_zeros = false;
67    let mut vr_is_trailing_zeros = false;
68    let mut last_removed_digit = 0u8;
69    if e2 >= 0 {
70        let q = log10_pow2(e2);
71        e10 = q as i32;
72        let k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q as i32) - 1;
73        let i = -e2 + q as i32 + k;
74        vr = mul_pow5_inv_div_pow2(mv, q, i);
75        vp = mul_pow5_inv_div_pow2(mp, q, i);
76        vm = mul_pow5_inv_div_pow2(mm, q, i);
77        if q != 0 && (vp - 1) / 10 <= vm / 10 {
78            // We need to know one removed digit even if we are not going to loop below. We could use
79            // q = X - 1 above, except that would require 33 bits for the result, and we've found that
80            // 32-bit arithmetic is faster even on 64-bit machines.
81            let l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q as i32 - 1) - 1;
82            last_removed_digit =
83                (mul_pow5_inv_div_pow2(mv, q - 1, -e2 + q as i32 - 1 + l) % 10) as u8;
84        }
85        if q <= 9 {
86            // The largest power of 5 that fits in 24 bits is 5^10, but q <= 9 seems to be safe as well.
87            // Only one of mp, mv, and mm can be a multiple of 5, if any.
88            if mv % 5 == 0 {
89                vr_is_trailing_zeros = multiple_of_power_of_5_32(mv, q);
90            } else if accept_bounds {
91                vm_is_trailing_zeros = multiple_of_power_of_5_32(mm, q);
92            } else {
93                vp -= multiple_of_power_of_5_32(mp, q) as u32;
94            }
95        }
96    } else {
97        let q = log10_pow5(-e2);
98        e10 = q as i32 + e2;
99        let i = -e2 - q as i32;
100        let k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
101        let mut j = q as i32 - k;
102        vr = mul_pow5_div_pow2(mv, i as u32, j);
103        vp = mul_pow5_div_pow2(mp, i as u32, j);
104        vm = mul_pow5_div_pow2(mm, i as u32, j);
105        if q != 0 && (vp - 1) / 10 <= vm / 10 {
106            j = q as i32 - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
107            last_removed_digit = (mul_pow5_div_pow2(mv, (i + 1) as u32, j) % 10) as u8;
108        }
109        if q <= 1 {
110            // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
111            // mv = 4 * m2, so it always has at least two trailing 0 bits.
112            vr_is_trailing_zeros = true;
113            if accept_bounds {
114                // mm = mv - 1 - mm_shift, so it has 1 trailing 0 bit iff mm_shift == 1.
115                vm_is_trailing_zeros = mm_shift == 1;
116            } else {
117                // mp = mv + 2, so it always has at least one trailing 0 bit.
118                vp -= 1;
119            }
120        } else if q < 31 {
121            // TODO(ulfjack): Use a tighter bound here.
122            vr_is_trailing_zeros = multiple_of_power_of_2_32(mv, q - 1);
123        }
124    }
125
126    // Step 4: Find the shortest decimal representation in the interval of valid representations.
127    let mut removed = 0i32;
128    let output = if vm_is_trailing_zeros || vr_is_trailing_zeros {
129        // General case, which happens rarely (~4.0%).
130        while vp / 10 > vm / 10 {
131            vm_is_trailing_zeros &= vm - (vm / 10) * 10 == 0;
132            vr_is_trailing_zeros &= last_removed_digit == 0;
133            last_removed_digit = (vr % 10) as u8;
134            vr /= 10;
135            vp /= 10;
136            vm /= 10;
137            removed += 1;
138        }
139        if vm_is_trailing_zeros {
140            while vm % 10 == 0 {
141                vr_is_trailing_zeros &= last_removed_digit == 0;
142                last_removed_digit = (vr % 10) as u8;
143                vr /= 10;
144                vp /= 10;
145                vm /= 10;
146                removed += 1;
147            }
148        }
149        if vr_is_trailing_zeros && last_removed_digit == 5 && vr % 2 == 0 {
150            // Round even if the exact number is .....50..0.
151            last_removed_digit = 4;
152        }
153        // We need to take vr + 1 if vr is outside bounds or we need to round up.
154        vr + ((vr == vm && (!accept_bounds || !vm_is_trailing_zeros)) || last_removed_digit >= 5)
155            as u32
156    } else {
157        // Specialized for the common case (~96.0%). Percentages below are relative to this.
158        // Loop iterations below (approximately):
159        // 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
160        while vp / 10 > vm / 10 {
161            last_removed_digit = (vr % 10) as u8;
162            vr /= 10;
163            vp /= 10;
164            vm /= 10;
165            removed += 1;
166        }
167        // We need to take vr + 1 if vr is outside bounds or we need to round up.
168        vr + (vr == vm || last_removed_digit >= 5) as u32
169    };
170    let exp = e10 + removed;
171
172    FloatingDecimal32 {
173        exponent: exp,
174        mantissa: output,
175    }
176}
encoder_ryu/f2s.rs

encoder_ryu/
f2s.rs
