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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300
// 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::*;
#[cfg(not(feature = "small"))]
pub use crate::d2s_full_table::*;
use crate::d2s_intrinsics::*;
#[cfg(feature = "small")]
pub use crate::d2s_small_table::*;
use core::mem::MaybeUninit;
pub const DOUBLE_MANTISSA_BITS: u32 = 52;
pub const DOUBLE_EXPONENT_BITS: u32 = 11;
pub const DOUBLE_BIAS: i32 = 1023;
pub const DOUBLE_POW5_INV_BITCOUNT: i32 = 125;
pub const DOUBLE_POW5_BITCOUNT: i32 = 125;
#[cfg_attr(feature = "no-panic", inline)]
pub fn decimal_length17(v: u64) -> u32 {
// This is slightly faster than a loop.
// The average output length is 16.38 digits, so we check high-to-low.
// Function precondition: v is not an 18, 19, or 20-digit number.
// (17 digits are sufficient for round-tripping.)
debug_assert!(v < 100000000000000000);
if v >= 10000000000000000 {
17
} else if v >= 1000000000000000 {
16
} else if v >= 100000000000000 {
15
} else if v >= 10000000000000 {
14
} else if v >= 1000000000000 {
13
} else if v >= 100000000000 {
12
} else if v >= 10000000000 {
11
} else if v >= 1000000000 {
10
} else if v >= 100000000 {
9
} else if v >= 10000000 {
8
} else if v >= 1000000 {
7
} else if v >= 100000 {
6
} else if v >= 10000 {
5
} else if v >= 1000 {
4
} else if v >= 100 {
3
} else if v >= 10 {
2
} else {
1
}
}
// A floating decimal representing m * 10^e.
pub struct FloatingDecimal64 {
pub mantissa: u64,
// Decimal exponent's range is -324 to 308
// inclusive, and can fit in i16 if needed.
pub exponent: i32,
}
#[cfg_attr(feature = "no-panic", inline)]
pub fn d2d(ieee_mantissa: u64, ieee_exponent: u32) -> FloatingDecimal64 {
let (e2, m2) = if ieee_exponent == 0 {
(
// We subtract 2 so that the bounds computation has 2 additional bits.
1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS as i32 - 2,
ieee_mantissa,
)
} else {
(
ieee_exponent as i32 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS as i32 - 2,
(1u64 << DOUBLE_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;
// Implicit bool -> int conversion. True is 1, false is 0.
let mm_shift = (ieee_mantissa != 0 || ieee_exponent <= 1) as u32;
// We would compute mp and mm like this:
// uint64_t mp = 4 * m2 + 2;
// uint64_t mm = mv - 1 - mm_shift;
// Step 3: Convert to a decimal power base using 128-bit arithmetic.
let mut vr: u64;
let mut vp: u64;
let mut vm: u64;
let mut vp_uninit: MaybeUninit<u64> = MaybeUninit::uninit();
let mut vm_uninit: MaybeUninit<u64> = MaybeUninit::uninit();
let e10: i32;
let mut vm_is_trailing_zeros = false;
let mut vr_is_trailing_zeros = false;
if e2 >= 0 {
// I tried special-casing q == 0, but there was no effect on performance.
// This expression is slightly faster than max(0, log10_pow2(e2) - 1).
let q = log10_pow2(e2) - (e2 > 3) as u32;
e10 = q as i32;
let k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q as i32) - 1;
let i = -e2 + q as i32 + k;
vr = unsafe {
mul_shift_all_64(
m2,
#[cfg(feature = "small")]
&compute_inv_pow5(q),
#[cfg(not(feature = "small"))]
{
debug_assert!(q < DOUBLE_POW5_INV_SPLIT.len() as u32);
DOUBLE_POW5_INV_SPLIT.get_unchecked(q as usize)
},
i as u32,
vp_uninit.as_mut_ptr(),
vm_uninit.as_mut_ptr(),
mm_shift,
)
};
vp = unsafe { vp_uninit.assume_init() };
vm = unsafe { vm_uninit.assume_init() };
if q <= 21 {
// This should use q <= 22, but I think 21 is also safe. Smaller values
// may still be safe, but it's more difficult to reason about them.
// Only one of mp, mv, and mm can be a multiple of 5, if any.
let mv_mod5 = (mv as u32).wrapping_sub(5u32.wrapping_mul(div5(mv) as u32));
if mv_mod5 == 0 {
vr_is_trailing_zeros = multiple_of_power_of_5(mv, q);
} else if accept_bounds {
// Same as min(e2 + (~mm & 1), pow5_factor(mm)) >= q
// <=> e2 + (~mm & 1) >= q && pow5_factor(mm) >= q
// <=> true && pow5_factor(mm) >= q, since e2 >= q.
vm_is_trailing_zeros = multiple_of_power_of_5(mv - 1 - mm_shift as u64, q);
} else {
// Same as min(e2 + 1, pow5_factor(mp)) >= q.
vp -= multiple_of_power_of_5(mv + 2, q) as u64;
}
}
} else {
// This expression is slightly faster than max(0, log10_pow5(-e2) - 1).
let q = log10_pow5(-e2) - (-e2 > 1) as u32;
e10 = q as i32 + e2;
let i = -e2 - q as i32;
let k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
let j = q as i32 - k;
vr = unsafe {
mul_shift_all_64(
m2,
#[cfg(feature = "small")]
&compute_pow5(i as u32),
#[cfg(not(feature = "small"))]
{
debug_assert!(i < DOUBLE_POW5_SPLIT.len() as i32);
DOUBLE_POW5_SPLIT.get_unchecked(i as usize)
},
j as u32,
vp_uninit.as_mut_ptr(),
vm_uninit.as_mut_ptr(),
mm_shift,
)
};
vp = unsafe { vp_uninit.assume_init() };
vm = unsafe { vm_uninit.assume_init() };
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 < 63 {
// TODO(ulfjack): Use a tighter bound here.
// We want to know if the full product has at least q trailing zeros.
// We need to compute min(p2(mv), p5(mv) - e2) >= q
// <=> p2(mv) >= q && p5(mv) - e2 >= q
// <=> p2(mv) >= q (because -e2 >= q)
vr_is_trailing_zeros = multiple_of_power_of_2(mv, q);
}
}
// Step 4: Find the shortest decimal representation in the interval of valid representations.
let mut removed = 0i32;
let mut last_removed_digit = 0u8;
// On average, we remove ~2 digits.
let output = if vm_is_trailing_zeros || vr_is_trailing_zeros {
// General case, which happens rarely (~0.7%).
loop {
let vp_div10 = div10(vp);
let vm_div10 = div10(vm);
if vp_div10 <= vm_div10 {
break;
}
let vm_mod10 = (vm as u32).wrapping_sub(10u32.wrapping_mul(vm_div10 as u32));
let vr_div10 = div10(vr);
let vr_mod10 = (vr as u32).wrapping_sub(10u32.wrapping_mul(vr_div10 as u32));
vm_is_trailing_zeros &= vm_mod10 == 0;
vr_is_trailing_zeros &= last_removed_digit == 0;
last_removed_digit = vr_mod10 as u8;
vr = vr_div10;
vp = vp_div10;
vm = vm_div10;
removed += 1;
}
if vm_is_trailing_zeros {
loop {
let vm_div10 = div10(vm);
let vm_mod10 = (vm as u32).wrapping_sub(10u32.wrapping_mul(vm_div10 as u32));
if vm_mod10 != 0 {
break;
}
let vp_div10 = div10(vp);
let vr_div10 = div10(vr);
let vr_mod10 = (vr as u32).wrapping_sub(10u32.wrapping_mul(vr_div10 as u32));
vr_is_trailing_zeros &= last_removed_digit == 0;
last_removed_digit = vr_mod10 as u8;
vr = vr_div10;
vp = vp_div10;
vm = vm_div10;
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 u64
} else {
// Specialized for the common case (~99.3%). Percentages below are relative to this.
let mut round_up = false;
let vp_div100 = div100(vp);
let vm_div100 = div100(vm);
// Optimization: remove two digits at a time (~86.2%).
if vp_div100 > vm_div100 {
let vr_div100 = div100(vr);
let vr_mod100 = (vr as u32).wrapping_sub(100u32.wrapping_mul(vr_div100 as u32));
round_up = vr_mod100 >= 50;
vr = vr_div100;
vp = vp_div100;
vm = vm_div100;
removed += 2;
}
// Loop iterations below (approximately), without optimization above:
// 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
// Loop iterations below (approximately), with optimization above:
// 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
loop {
let vp_div10 = div10(vp);
let vm_div10 = div10(vm);
if vp_div10 <= vm_div10 {
break;
}
let vr_div10 = div10(vr);
let vr_mod10 = (vr as u32).wrapping_sub(10u32.wrapping_mul(vr_div10 as u32));
round_up = vr_mod10 >= 5;
vr = vr_div10;
vp = vp_div10;
vm = vm_div10;
removed += 1;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up.
vr + (vr == vm || round_up) as u64
};
let exp = e10 + removed;
FloatingDecimal64 {
exponent: exp,
mantissa: output,
}
}