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
21 use crate::common::*;
22 use crate::f2s_intrinsics::*;
23
24 pub const FLOAT_MANTISSA_BITS: u32 = 23;
25 pub const FLOAT_EXPONENT_BITS: u32 = 8;
26 const FLOAT_BIAS: i32 = 127;
27 pub use crate::f2s_intrinsics::{FLOAT_POW5_BITCOUNT, FLOAT_POW5_INV_BITCOUNT};
28
29 // A floating decimal representing m * 10^e.
30 pub 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)]
f2d(ieee_mantissa: u32, ieee_exponent: u32) -> FloatingDecimal3238 pub 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 }
177