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