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b7449926 XL |
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 | ||
f035d41b | 21 | use crate::common::*; |
b7449926 | 22 | #[cfg(not(feature = "small"))] |
f035d41b XL |
23 | pub use crate::d2s_full_table::*; |
24 | use crate::d2s_intrinsics::*; | |
b7449926 | 25 | #[cfg(feature = "small")] |
f035d41b XL |
26 | pub use crate::d2s_small_table::*; |
27 | #[cfg(not(maybe_uninit))] | |
28 | use core::mem; | |
29 | #[cfg(maybe_uninit)] | |
30 | use core::mem::MaybeUninit; | |
b7449926 XL |
31 | |
32 | pub const DOUBLE_MANTISSA_BITS: u32 = 52; | |
33 | pub const DOUBLE_EXPONENT_BITS: u32 = 11; | |
f035d41b XL |
34 | pub const DOUBLE_BIAS: i32 = 1023; |
35 | pub const DOUBLE_POW5_INV_BITCOUNT: i32 = 125; | |
36 | pub const DOUBLE_POW5_BITCOUNT: i32 = 125; | |
b7449926 XL |
37 | |
38 | #[cfg_attr(feature = "no-panic", inline)] | |
416331ca | 39 | pub fn decimal_length17(v: u64) -> u32 { |
b7449926 XL |
40 | // This is slightly faster than a loop. |
41 | // The average output length is 16.38 digits, so we check high-to-low. | |
42 | // Function precondition: v is not an 18, 19, or 20-digit number. | |
43 | // (17 digits are sufficient for round-tripping.) | |
44 | debug_assert!(v < 100000000000000000); | |
45 | ||
46 | if v >= 10000000000000000 { | |
47 | 17 | |
48 | } else if v >= 1000000000000000 { | |
49 | 16 | |
50 | } else if v >= 100000000000000 { | |
51 | 15 | |
52 | } else if v >= 10000000000000 { | |
53 | 14 | |
54 | } else if v >= 1000000000000 { | |
55 | 13 | |
56 | } else if v >= 100000000000 { | |
57 | 12 | |
58 | } else if v >= 10000000000 { | |
59 | 11 | |
60 | } else if v >= 1000000000 { | |
61 | 10 | |
62 | } else if v >= 100000000 { | |
63 | 9 | |
64 | } else if v >= 10000000 { | |
65 | 8 | |
66 | } else if v >= 1000000 { | |
67 | 7 | |
68 | } else if v >= 100000 { | |
69 | 6 | |
70 | } else if v >= 10000 { | |
71 | 5 | |
72 | } else if v >= 1000 { | |
73 | 4 | |
74 | } else if v >= 100 { | |
75 | 3 | |
76 | } else if v >= 10 { | |
77 | 2 | |
78 | } else { | |
79 | 1 | |
80 | } | |
81 | } | |
82 | ||
83 | // A floating decimal representing m * 10^e. | |
84 | pub struct FloatingDecimal64 { | |
85 | pub mantissa: u64, | |
416331ca XL |
86 | // Decimal exponent's range is -324 to 308 |
87 | // inclusive, and can fit in i16 if needed. | |
b7449926 XL |
88 | pub exponent: i32, |
89 | } | |
90 | ||
91 | #[cfg_attr(feature = "no-panic", inline)] | |
92 | pub fn d2d(ieee_mantissa: u64, ieee_exponent: u32) -> FloatingDecimal64 { | |
b7449926 XL |
93 | let (e2, m2) = if ieee_exponent == 0 { |
94 | ( | |
95 | // We subtract 2 so that the bounds computation has 2 additional bits. | |
416331ca | 96 | 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS as i32 - 2, |
b7449926 XL |
97 | ieee_mantissa, |
98 | ) | |
99 | } else { | |
100 | ( | |
416331ca | 101 | ieee_exponent as i32 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS as i32 - 2, |
b7449926 XL |
102 | (1u64 << DOUBLE_MANTISSA_BITS) | ieee_mantissa, |
103 | ) | |
104 | }; | |
105 | let even = (m2 & 1) == 0; | |
106 | let accept_bounds = even; | |
107 | ||
416331ca | 108 | // Step 2: Determine the interval of valid decimal representations. |
b7449926 XL |
109 | let mv = 4 * m2; |
110 | // Implicit bool -> int conversion. True is 1, false is 0. | |
111 | let mm_shift = (ieee_mantissa != 0 || ieee_exponent <= 1) as u32; | |
112 | // We would compute mp and mm like this: | |
113 | // uint64_t mp = 4 * m2 + 2; | |
114 | // uint64_t mm = mv - 1 - mm_shift; | |
115 | ||
116 | // Step 3: Convert to a decimal power base using 128-bit arithmetic. | |
117 | let mut vr: u64; | |
f035d41b XL |
118 | let mut vp: u64; |
119 | let mut vm: u64; | |
120 | #[cfg(not(maybe_uninit))] | |
121 | { | |
122 | vp = unsafe { mem::uninitialized() }; | |
123 | vm = unsafe { mem::uninitialized() }; | |
124 | } | |
125 | #[cfg(maybe_uninit)] | |
126 | let mut vp_uninit: MaybeUninit<u64> = MaybeUninit::uninit(); | |
127 | #[cfg(maybe_uninit)] | |
128 | let mut vm_uninit: MaybeUninit<u64> = MaybeUninit::uninit(); | |
b7449926 XL |
129 | let e10: i32; |
130 | let mut vm_is_trailing_zeros = false; | |
131 | let mut vr_is_trailing_zeros = false; | |
132 | if e2 >= 0 { | |
133 | // I tried special-casing q == 0, but there was no effect on performance. | |
134 | // This expression is slightly faster than max(0, log10_pow2(e2) - 1). | |
416331ca | 135 | let q = log10_pow2(e2) - (e2 > 3) as u32; |
b7449926 | 136 | e10 = q as i32; |
416331ca | 137 | let k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q as i32) - 1; |
b7449926 | 138 | let i = -e2 + q as i32 + k; |
f035d41b XL |
139 | vr = unsafe { |
140 | mul_shift_all_64( | |
141 | m2, | |
142 | #[cfg(feature = "small")] | |
143 | &compute_inv_pow5(q), | |
144 | #[cfg(not(feature = "small"))] | |
145 | { | |
146 | debug_assert!(q < DOUBLE_POW5_INV_SPLIT.len() as u32); | |
147 | DOUBLE_POW5_INV_SPLIT.get_unchecked(q as usize) | |
148 | }, | |
149 | i as u32, | |
150 | #[cfg(maybe_uninit)] | |
151 | { | |
152 | vp_uninit.as_mut_ptr() | |
153 | }, | |
154 | #[cfg(not(maybe_uninit))] | |
155 | { | |
156 | &mut vp | |
157 | }, | |
158 | #[cfg(maybe_uninit)] | |
159 | { | |
160 | vm_uninit.as_mut_ptr() | |
161 | }, | |
162 | #[cfg(not(maybe_uninit))] | |
163 | { | |
164 | &mut vm | |
165 | }, | |
166 | mm_shift, | |
167 | ) | |
168 | }; | |
169 | #[cfg(maybe_uninit)] | |
170 | { | |
171 | vp = unsafe { vp_uninit.assume_init() }; | |
172 | vm = unsafe { vm_uninit.assume_init() }; | |
173 | } | |
b7449926 XL |
174 | if q <= 21 { |
175 | // This should use q <= 22, but I think 21 is also safe. Smaller values | |
176 | // may still be safe, but it's more difficult to reason about them. | |
177 | // Only one of mp, mv, and mm can be a multiple of 5, if any. | |
416331ca | 178 | let mv_mod5 = (mv as u32).wrapping_sub(5u32.wrapping_mul(div5(mv) as u32)); |
b7449926 XL |
179 | if mv_mod5 == 0 { |
180 | vr_is_trailing_zeros = multiple_of_power_of_5(mv, q); | |
181 | } else if accept_bounds { | |
182 | // Same as min(e2 + (~mm & 1), pow5_factor(mm)) >= q | |
183 | // <=> e2 + (~mm & 1) >= q && pow5_factor(mm) >= q | |
184 | // <=> true && pow5_factor(mm) >= q, since e2 >= q. | |
185 | vm_is_trailing_zeros = multiple_of_power_of_5(mv - 1 - mm_shift as u64, q); | |
186 | } else { | |
187 | // Same as min(e2 + 1, pow5_factor(mp)) >= q. | |
188 | vp -= multiple_of_power_of_5(mv + 2, q) as u64; | |
189 | } | |
190 | } | |
191 | } else { | |
192 | // This expression is slightly faster than max(0, log10_pow5(-e2) - 1). | |
416331ca | 193 | let q = log10_pow5(-e2) - (-e2 > 1) as u32; |
b7449926 XL |
194 | e10 = q as i32 + e2; |
195 | let i = -e2 - q as i32; | |
416331ca | 196 | let k = pow5bits(i) - DOUBLE_POW5_BITCOUNT; |
b7449926 | 197 | let j = q as i32 - k; |
f035d41b XL |
198 | vr = unsafe { |
199 | mul_shift_all_64( | |
200 | m2, | |
201 | #[cfg(feature = "small")] | |
202 | &compute_pow5(i as u32), | |
203 | #[cfg(not(feature = "small"))] | |
204 | { | |
205 | debug_assert!(i < DOUBLE_POW5_SPLIT.len() as i32); | |
206 | DOUBLE_POW5_SPLIT.get_unchecked(i as usize) | |
207 | }, | |
208 | j as u32, | |
209 | #[cfg(maybe_uninit)] | |
210 | { | |
211 | vp_uninit.as_mut_ptr() | |
212 | }, | |
213 | #[cfg(not(maybe_uninit))] | |
214 | { | |
215 | &mut vp | |
216 | }, | |
217 | #[cfg(maybe_uninit)] | |
218 | { | |
219 | vm_uninit.as_mut_ptr() | |
220 | }, | |
221 | #[cfg(not(maybe_uninit))] | |
222 | { | |
223 | &mut vm | |
224 | }, | |
225 | mm_shift, | |
226 | ) | |
227 | }; | |
228 | #[cfg(maybe_uninit)] | |
229 | { | |
230 | vp = unsafe { vp_uninit.assume_init() }; | |
231 | vm = unsafe { vm_uninit.assume_init() }; | |
232 | } | |
b7449926 XL |
233 | if q <= 1 { |
234 | // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits. | |
235 | // mv = 4 * m2, so it always has at least two trailing 0 bits. | |
236 | vr_is_trailing_zeros = true; | |
237 | if accept_bounds { | |
238 | // mm = mv - 1 - mm_shift, so it has 1 trailing 0 bit iff mm_shift == 1. | |
239 | vm_is_trailing_zeros = mm_shift == 1; | |
240 | } else { | |
241 | // mp = mv + 2, so it always has at least one trailing 0 bit. | |
242 | vp -= 1; | |
243 | } | |
244 | } else if q < 63 { | |
245 | // TODO(ulfjack): Use a tighter bound here. | |
416331ca XL |
246 | // We want to know if the full product has at least q trailing zeros. |
247 | // We need to compute min(p2(mv), p5(mv) - e2) >= q | |
248 | // <=> p2(mv) >= q && p5(mv) - e2 >= q | |
249 | // <=> p2(mv) >= q (because -e2 >= q) | |
250 | vr_is_trailing_zeros = multiple_of_power_of_2(mv, q); | |
b7449926 XL |
251 | } |
252 | } | |
253 | ||
416331ca XL |
254 | // Step 4: Find the shortest decimal representation in the interval of valid representations. |
255 | let mut removed = 0i32; | |
b7449926 XL |
256 | let mut last_removed_digit = 0u8; |
257 | // On average, we remove ~2 digits. | |
258 | let output = if vm_is_trailing_zeros || vr_is_trailing_zeros { | |
259 | // General case, which happens rarely (~0.7%). | |
260 | loop { | |
261 | let vp_div10 = div10(vp); | |
262 | let vm_div10 = div10(vm); | |
263 | if vp_div10 <= vm_div10 { | |
264 | break; | |
265 | } | |
416331ca | 266 | let vm_mod10 = (vm as u32).wrapping_sub(10u32.wrapping_mul(vm_div10 as u32)); |
b7449926 | 267 | let vr_div10 = div10(vr); |
416331ca | 268 | let vr_mod10 = (vr as u32).wrapping_sub(10u32.wrapping_mul(vr_div10 as u32)); |
b7449926 XL |
269 | vm_is_trailing_zeros &= vm_mod10 == 0; |
270 | vr_is_trailing_zeros &= last_removed_digit == 0; | |
271 | last_removed_digit = vr_mod10 as u8; | |
272 | vr = vr_div10; | |
273 | vp = vp_div10; | |
274 | vm = vm_div10; | |
275 | removed += 1; | |
276 | } | |
277 | if vm_is_trailing_zeros { | |
278 | loop { | |
279 | let vm_div10 = div10(vm); | |
416331ca | 280 | let vm_mod10 = (vm as u32).wrapping_sub(10u32.wrapping_mul(vm_div10 as u32)); |
b7449926 XL |
281 | if vm_mod10 != 0 { |
282 | break; | |
283 | } | |
284 | let vp_div10 = div10(vp); | |
285 | let vr_div10 = div10(vr); | |
416331ca | 286 | let vr_mod10 = (vr as u32).wrapping_sub(10u32.wrapping_mul(vr_div10 as u32)); |
b7449926 XL |
287 | vr_is_trailing_zeros &= last_removed_digit == 0; |
288 | last_removed_digit = vr_mod10 as u8; | |
289 | vr = vr_div10; | |
290 | vp = vp_div10; | |
291 | vm = vm_div10; | |
292 | removed += 1; | |
293 | } | |
294 | } | |
295 | if vr_is_trailing_zeros && last_removed_digit == 5 && vr % 2 == 0 { | |
296 | // Round even if the exact number is .....50..0. | |
297 | last_removed_digit = 4; | |
298 | } | |
299 | // We need to take vr + 1 if vr is outside bounds or we need to round up. | |
300 | vr + ((vr == vm && (!accept_bounds || !vm_is_trailing_zeros)) || last_removed_digit >= 5) | |
301 | as u64 | |
302 | } else { | |
303 | // Specialized for the common case (~99.3%). Percentages below are relative to this. | |
304 | let mut round_up = false; | |
305 | let vp_div100 = div100(vp); | |
306 | let vm_div100 = div100(vm); | |
307 | // Optimization: remove two digits at a time (~86.2%). | |
308 | if vp_div100 > vm_div100 { | |
309 | let vr_div100 = div100(vr); | |
416331ca | 310 | let vr_mod100 = (vr as u32).wrapping_sub(100u32.wrapping_mul(vr_div100 as u32)); |
b7449926 XL |
311 | round_up = vr_mod100 >= 50; |
312 | vr = vr_div100; | |
313 | vp = vp_div100; | |
314 | vm = vm_div100; | |
315 | removed += 2; | |
316 | } | |
317 | // Loop iterations below (approximately), without optimization above: | |
318 | // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02% | |
319 | // Loop iterations below (approximately), with optimization above: | |
320 | // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02% | |
321 | loop { | |
322 | let vp_div10 = div10(vp); | |
323 | let vm_div10 = div10(vm); | |
324 | if vp_div10 <= vm_div10 { | |
325 | break; | |
326 | } | |
327 | let vr_div10 = div10(vr); | |
416331ca | 328 | let vr_mod10 = (vr as u32).wrapping_sub(10u32.wrapping_mul(vr_div10 as u32)); |
b7449926 XL |
329 | round_up = vr_mod10 >= 5; |
330 | vr = vr_div10; | |
331 | vp = vp_div10; | |
332 | vm = vm_div10; | |
333 | removed += 1; | |
334 | } | |
335 | // We need to take vr + 1 if vr is outside bounds or we need to round up. | |
336 | vr + (vr == vm || round_up) as u64 | |
337 | }; | |
416331ca | 338 | let exp = e10 + removed; |
b7449926 XL |
339 | |
340 | FloatingDecimal64 { | |
341 | exponent: exp, | |
342 | mantissa: output, | |
343 | } | |
344 | } |