/rust/registry/src/index.crates.io-1949cf8c6b5b557f/lexical-parse-float-1.0.6/src/limits.rs
Line | Count | Source |
1 | | //! Determine the limits of exact exponent and mantissas for floats. |
2 | | |
3 | | #![doc(hidden)] |
4 | | |
5 | | use lexical_util::assert::debug_assert_radix; |
6 | | #[cfg(feature = "f16")] |
7 | | use lexical_util::bf16::bf16; |
8 | | #[cfg(feature = "f16")] |
9 | | use lexical_util::f16::f16; |
10 | | |
11 | | // EXACT EXPONENT |
12 | | // -------------- |
13 | | |
14 | | // Calculating the exponent limit requires determining the largest exponent |
15 | | // we can calculate for a radix that can be **exactly** store in the |
16 | | // float type. If the value is a power-of-two, then we simply |
17 | | // need to scale the minimum, denormal exp and maximum exp to the type |
18 | | // size. Otherwise, we need to calculate the number of digits |
19 | | // that can fit into the type's precision, after removing a power-of-two |
20 | | // (since these values can be represented exactly). |
21 | | // |
22 | | // The mantissa limit is the number of digits we can remove from |
23 | | // the exponent into the mantissa, and is therefore is the |
24 | | // `⌊ precision / log2(radix) ⌋`, where precision does not include |
25 | | // the hidden bit. |
26 | | // |
27 | | // The algorithm for calculating both `exponent_limit` and `mantissa_limit`, |
28 | | // in Python, can be done as follows: |
29 | | // |
30 | | // DO NOT MODIFY: Generated by `src/etc/limits.py` |
31 | | |
32 | | // EXACT FLOAT |
33 | | // ----------- |
34 | | |
35 | | /// Get exact exponent limit for radix. |
36 | | #[doc(hidden)] |
37 | | pub trait ExactFloat { |
38 | | /// Get min and max exponent limits (exact) from radix. |
39 | | fn exponent_limit(radix: u32) -> (i64, i64); |
40 | | |
41 | | /// Get the number of digits that can be shifted from exponent to mantissa. |
42 | | fn mantissa_limit(radix: u32) -> i64; |
43 | | } |
44 | | |
45 | | impl ExactFloat for f32 { |
46 | | #[inline(always)] |
47 | 0 | fn exponent_limit(radix: u32) -> (i64, i64) { |
48 | 0 | debug_assert_radix(radix); |
49 | 0 | f32_exponent_limit(radix) |
50 | 0 | } |
51 | | |
52 | | #[inline(always)] |
53 | 0 | fn mantissa_limit(radix: u32) -> i64 { |
54 | 0 | debug_assert_radix(radix); |
55 | 0 | f32_mantissa_limit(radix) |
56 | 0 | } |
57 | | } |
58 | | |
59 | | impl ExactFloat for f64 { |
60 | | #[inline(always)] |
61 | 734 | fn exponent_limit(radix: u32) -> (i64, i64) { |
62 | 734 | debug_assert_radix(radix); |
63 | 734 | f64_exponent_limit(radix) |
64 | 734 | } |
65 | | |
66 | | #[inline(always)] |
67 | 281 | fn mantissa_limit(radix: u32) -> i64 { |
68 | 281 | debug_assert_radix(radix); |
69 | 281 | f64_mantissa_limit(radix) |
70 | 281 | } |
71 | | } |
72 | | |
73 | | #[cfg(feature = "f16")] |
74 | | impl ExactFloat for f16 { |
75 | | #[inline(always)] |
76 | | fn exponent_limit(_: u32) -> (i64, i64) { |
77 | | unimplemented!() |
78 | | } |
79 | | |
80 | | #[inline(always)] |
81 | | fn mantissa_limit(_: u32) -> i64 { |
82 | | unimplemented!() |
83 | | } |
84 | | } |
85 | | |
86 | | #[cfg(feature = "f16")] |
87 | | impl ExactFloat for bf16 { |
88 | | #[inline(always)] |
89 | | fn exponent_limit(_: u32) -> (i64, i64) { |
90 | | unimplemented!() |
91 | | } |
92 | | |
93 | | #[inline(always)] |
94 | | fn mantissa_limit(_: u32) -> i64 { |
95 | | unimplemented!() |
96 | | } |
97 | | } |
98 | | |
99 | | //#[cfg(feature = "f128")] |
100 | | //impl ExactFloat for f128 { |
101 | | // #[inline(always)] |
102 | | // fn exponent_limit(radix: u32) -> (i64, i64) { |
103 | | // debug_assert_radix(radix); |
104 | | // f128_exponent_limit(radix) |
105 | | // } |
106 | | // } |
107 | | // |
108 | | // #[inline(always)] |
109 | | // fn mantissa_limit(radix: u32) -> i64 { |
110 | | // debug_assert_radix(radix); |
111 | | // f128_mantissa_limit(radix) |
112 | | // } |
113 | | //} |
114 | | |
115 | | // CONST FN |
116 | | // -------- |
117 | | |
118 | | /// Get the exponent limit as a const fn. |
119 | | #[must_use] |
120 | | #[inline(always)] |
121 | | #[cfg(feature = "radix")] |
122 | | pub const fn f32_exponent_limit(radix: u32) -> (i64, i64) { |
123 | | match radix { |
124 | | 2 => (-127, 127), |
125 | | 3 => (-15, 15), |
126 | | 4 => (-63, 63), |
127 | | 5 => (-10, 10), |
128 | | 6 => (-15, 15), |
129 | | 7 => (-8, 8), |
130 | | 8 => (-42, 42), |
131 | | 9 => (-7, 7), |
132 | | 10 => (-10, 10), |
133 | | 11 => (-6, 6), |
134 | | 12 => (-15, 15), |
135 | | 13 => (-6, 6), |
136 | | 14 => (-8, 8), |
137 | | 15 => (-6, 6), |
138 | | 16 => (-31, 31), |
139 | | 17 => (-5, 5), |
140 | | 18 => (-7, 7), |
141 | | 19 => (-5, 5), |
142 | | 20 => (-10, 10), |
143 | | 21 => (-5, 5), |
144 | | 22 => (-6, 6), |
145 | | 23 => (-5, 5), |
146 | | 24 => (-15, 15), |
147 | | 25 => (-5, 5), |
148 | | 26 => (-6, 6), |
149 | | 27 => (-5, 5), |
150 | | 28 => (-8, 8), |
151 | | 29 => (-4, 4), |
152 | | 30 => (-6, 6), |
153 | | 31 => (-4, 4), |
154 | | 32 => (-25, 25), |
155 | | 33 => (-4, 4), |
156 | | 34 => (-5, 5), |
157 | | 35 => (-4, 4), |
158 | | 36 => (-7, 7), |
159 | | _ => (0, 0), |
160 | | } |
161 | | } |
162 | | |
163 | | /// Get the exponent limit as a const fn. |
164 | | #[must_use] |
165 | | #[inline(always)] |
166 | | #[cfg(all(feature = "power-of-two", not(feature = "radix")))] |
167 | | pub const fn f32_exponent_limit(radix: u32) -> (i64, i64) { |
168 | | match radix { |
169 | | 2 => (-127, 127), |
170 | | 4 => (-63, 63), |
171 | | 8 => (-42, 42), |
172 | | 10 => (-10, 10), |
173 | | 16 => (-31, 31), |
174 | | 32 => (-25, 25), |
175 | | _ => (0, 0), |
176 | | } |
177 | | } |
178 | | |
179 | | /// Get the exponent limit as a const fn. |
180 | | #[must_use] |
181 | | #[inline(always)] |
182 | | #[cfg(not(feature = "power-of-two"))] |
183 | 0 | pub const fn f32_exponent_limit(radix: u32) -> (i64, i64) { |
184 | 0 | match radix { |
185 | 0 | 10 => (-10, 10), |
186 | 0 | _ => (0, 0), |
187 | | } |
188 | 0 | } |
189 | | |
190 | | /// Get the mantissa limit as a const fn. |
191 | | #[must_use] |
192 | | #[inline(always)] |
193 | | #[cfg(feature = "radix")] |
194 | | pub const fn f32_mantissa_limit(radix: u32) -> i64 { |
195 | | match radix { |
196 | | 2 => 24, |
197 | | 3 => 15, |
198 | | 4 => 12, |
199 | | 5 => 10, |
200 | | 6 => 9, |
201 | | 7 => 8, |
202 | | 8 => 8, |
203 | | 9 => 7, |
204 | | 10 => 7, |
205 | | 11 => 6, |
206 | | 12 => 6, |
207 | | 13 => 6, |
208 | | 14 => 6, |
209 | | 15 => 6, |
210 | | 16 => 6, |
211 | | 17 => 5, |
212 | | 18 => 5, |
213 | | 19 => 5, |
214 | | 20 => 5, |
215 | | 21 => 5, |
216 | | 22 => 5, |
217 | | 23 => 5, |
218 | | 24 => 5, |
219 | | 25 => 5, |
220 | | 26 => 5, |
221 | | 27 => 5, |
222 | | 28 => 4, |
223 | | 29 => 4, |
224 | | 30 => 4, |
225 | | 31 => 4, |
226 | | 32 => 4, |
227 | | 33 => 4, |
228 | | 34 => 4, |
229 | | 35 => 4, |
230 | | 36 => 4, |
231 | | _ => 0, |
232 | | } |
233 | | } |
234 | | |
235 | | /// Get the mantissa limit as a const fn. |
236 | | #[must_use] |
237 | | #[inline(always)] |
238 | | #[cfg(all(feature = "power-of-two", not(feature = "radix")))] |
239 | | pub const fn f32_mantissa_limit(radix: u32) -> i64 { |
240 | | match radix { |
241 | | 2 => 24, |
242 | | 4 => 12, |
243 | | 8 => 8, |
244 | | 10 => 7, |
245 | | 16 => 6, |
246 | | 32 => 4, |
247 | | _ => 0, |
248 | | } |
249 | | } |
250 | | |
251 | | /// Get the mantissa limit as a const fn. |
252 | | #[must_use] |
253 | | #[inline(always)] |
254 | | #[cfg(not(feature = "power-of-two"))] |
255 | 0 | pub const fn f32_mantissa_limit(radix: u32) -> i64 { |
256 | 0 | match radix { |
257 | 0 | 10 => 7, |
258 | 0 | _ => 0, |
259 | | } |
260 | 0 | } |
261 | | |
262 | | /// Get the exponent limit as a const fn. |
263 | | #[must_use] |
264 | | #[inline(always)] |
265 | | #[cfg(feature = "radix")] |
266 | | pub const fn f64_exponent_limit(radix: u32) -> (i64, i64) { |
267 | | match radix { |
268 | | 2 => (-1023, 1023), |
269 | | 3 => (-33, 33), |
270 | | 4 => (-511, 511), |
271 | | 5 => (-22, 22), |
272 | | 6 => (-33, 33), |
273 | | 7 => (-18, 18), |
274 | | 8 => (-341, 341), |
275 | | 9 => (-16, 16), |
276 | | 10 => (-22, 22), |
277 | | 11 => (-15, 15), |
278 | | 12 => (-33, 33), |
279 | | 13 => (-14, 14), |
280 | | 14 => (-18, 18), |
281 | | 15 => (-13, 13), |
282 | | 16 => (-255, 255), |
283 | | 17 => (-12, 12), |
284 | | 18 => (-16, 16), |
285 | | 19 => (-12, 12), |
286 | | 20 => (-22, 22), |
287 | | 21 => (-12, 12), |
288 | | 22 => (-15, 15), |
289 | | 23 => (-11, 11), |
290 | | 24 => (-33, 33), |
291 | | 25 => (-11, 11), |
292 | | 26 => (-14, 14), |
293 | | 27 => (-11, 11), |
294 | | 28 => (-18, 18), |
295 | | 29 => (-10, 10), |
296 | | 30 => (-13, 13), |
297 | | 31 => (-10, 10), |
298 | | 32 => (-204, 204), |
299 | | 33 => (-10, 10), |
300 | | 34 => (-12, 12), |
301 | | 35 => (-10, 10), |
302 | | 36 => (-16, 16), |
303 | | _ => (0, 0), |
304 | | } |
305 | | } |
306 | | |
307 | | // Get the exponent limit as a const fn. |
308 | | #[must_use] |
309 | | #[inline(always)] |
310 | | #[cfg(all(feature = "power-of-two", not(feature = "radix")))] |
311 | | pub const fn f64_exponent_limit(radix: u32) -> (i64, i64) { |
312 | | match radix { |
313 | | 2 => (-1023, 1023), |
314 | | 4 => (-511, 511), |
315 | | 8 => (-341, 341), |
316 | | 10 => (-22, 22), |
317 | | 16 => (-255, 255), |
318 | | 32 => (-204, 204), |
319 | | _ => (0, 0), |
320 | | } |
321 | | } |
322 | | |
323 | | /// Get the exponent limit as a const fn. |
324 | | #[must_use] |
325 | | #[inline(always)] |
326 | | #[cfg(not(feature = "power-of-two"))] |
327 | 734 | pub const fn f64_exponent_limit(radix: u32) -> (i64, i64) { |
328 | 734 | match radix { |
329 | 734 | 10 => (-22, 22), |
330 | 0 | _ => (0, 0), |
331 | | } |
332 | 734 | } |
333 | | |
334 | | /// Get the mantissa limit as a const fn. |
335 | | #[must_use] |
336 | | #[inline(always)] |
337 | | #[cfg(feature = "radix")] |
338 | | pub const fn f64_mantissa_limit(radix: u32) -> i64 { |
339 | | match radix { |
340 | | 2 => 53, |
341 | | 3 => 33, |
342 | | 4 => 26, |
343 | | 5 => 22, |
344 | | 6 => 20, |
345 | | 7 => 18, |
346 | | 8 => 17, |
347 | | 9 => 16, |
348 | | 10 => 15, |
349 | | 11 => 15, |
350 | | 12 => 14, |
351 | | 13 => 14, |
352 | | 14 => 13, |
353 | | 15 => 13, |
354 | | 16 => 13, |
355 | | 17 => 12, |
356 | | 18 => 12, |
357 | | 19 => 12, |
358 | | 20 => 12, |
359 | | 21 => 12, |
360 | | 22 => 11, |
361 | | 23 => 11, |
362 | | 24 => 11, |
363 | | 25 => 11, |
364 | | 26 => 11, |
365 | | 27 => 11, |
366 | | 28 => 11, |
367 | | 29 => 10, |
368 | | 30 => 10, |
369 | | 31 => 10, |
370 | | 32 => 10, |
371 | | 33 => 10, |
372 | | 34 => 10, |
373 | | 35 => 10, |
374 | | 36 => 10, |
375 | | _ => 0, |
376 | | } |
377 | | } |
378 | | |
379 | | /// Get the mantissa limit as a const fn. |
380 | | #[must_use] |
381 | | #[inline(always)] |
382 | | #[cfg(all(feature = "power-of-two", not(feature = "radix")))] |
383 | | pub const fn f64_mantissa_limit(radix: u32) -> i64 { |
384 | | match radix { |
385 | | 2 => 53, |
386 | | 4 => 26, |
387 | | 8 => 17, |
388 | | 10 => 15, |
389 | | 16 => 13, |
390 | | 32 => 10, |
391 | | _ => 0, |
392 | | } |
393 | | } |
394 | | |
395 | | /// Get the mantissa limit as a const fn. |
396 | | #[must_use] |
397 | | #[inline(always)] |
398 | | #[cfg(not(feature = "power-of-two"))] |
399 | 281 | pub const fn f64_mantissa_limit(radix: u32) -> i64 { |
400 | 281 | match radix { |
401 | 281 | 10 => 15, |
402 | 0 | _ => 0, |
403 | | } |
404 | 281 | } |
405 | | |
406 | | /// Get the exponent limit as a const fn. |
407 | | #[must_use] |
408 | | #[inline(always)] |
409 | | #[cfg(feature = "f128")] |
410 | | #[cfg(feature = "radix")] |
411 | | pub const fn f128_exponent_limit(radix: u32) -> (i64, i64) { |
412 | | match radix { |
413 | | 2 => (-16494, 16383), |
414 | | 3 => (-71, 71), |
415 | | 4 => (-8247, 8191), |
416 | | 5 => (-48, 48), |
417 | | 6 => (-71, 71), |
418 | | 7 => (-40, 40), |
419 | | 8 => (-5498, 5461), |
420 | | 9 => (-35, 35), |
421 | | 10 => (-48, 48), |
422 | | 11 => (-32, 32), |
423 | | 12 => (-71, 71), |
424 | | 13 => (-30, 30), |
425 | | 14 => (-40, 40), |
426 | | 15 => (-28, 28), |
427 | | 16 => (-4123, 4095), |
428 | | 17 => (-27, 27), |
429 | | 18 => (-35, 35), |
430 | | 19 => (-26, 26), |
431 | | 20 => (-48, 48), |
432 | | 21 => (-25, 25), |
433 | | 22 => (-32, 32), |
434 | | 23 => (-24, 24), |
435 | | 24 => (-71, 71), |
436 | | 25 => (-24, 24), |
437 | | 26 => (-30, 30), |
438 | | 27 => (-23, 23), |
439 | | 28 => (-40, 40), |
440 | | 29 => (-23, 23), |
441 | | 30 => (-28, 28), |
442 | | 31 => (-22, 22), |
443 | | 32 => (-3298, 3276), |
444 | | 33 => (-22, 22), |
445 | | 34 => (-27, 27), |
446 | | 35 => (-22, 22), |
447 | | 36 => (-35, 35), |
448 | | // Invalid radix |
449 | | _ => (0, 0), |
450 | | } |
451 | | } |
452 | | |
453 | | /// Get the exponent limit as a const fn. |
454 | | #[inline(always)] |
455 | | #[cfg(feature = "f128")] |
456 | | #[cfg(all(feature = "power-of-two", not(feature = "radix")))] |
457 | | pub const fn f128_exponent_limit(radix: u32) -> (i64, i64) { |
458 | | match radix { |
459 | | 2 => (-16494, 16383), |
460 | | 4 => (-8247, 8191), |
461 | | 8 => (-5498, 5461), |
462 | | 10 => (-48, 48), |
463 | | 16 => (-4123, 4095), |
464 | | 32 => (-3298, 3276), |
465 | | // Invalid radix |
466 | | _ => (0, 0), |
467 | | } |
468 | | } |
469 | | |
470 | | /// Get the exponent limit as a const fn. |
471 | | #[must_use] |
472 | | #[inline(always)] |
473 | | #[cfg(feature = "f128")] |
474 | | #[cfg(not(feature = "power-of-two"))] |
475 | | pub const fn f128_exponent_limit(radix: u32) -> (i64, i64) { |
476 | | match radix { |
477 | | 10 => (-48, 48), |
478 | | // Invalid radix |
479 | | _ => (0, 0), |
480 | | } |
481 | | } |
482 | | |
483 | | /// Get the mantissa limit as a const fn. |
484 | | #[must_use] |
485 | | #[inline(always)] |
486 | | #[cfg(feature = "f128")] |
487 | | #[cfg(feature = "radix")] |
488 | | pub const fn f128_mantissa_limit(radix: u32) -> i64 { |
489 | | match radix { |
490 | | 2 => 113, |
491 | | 3 => 71, |
492 | | 4 => 56, |
493 | | 5 => 48, |
494 | | 6 => 43, |
495 | | 7 => 40, |
496 | | 8 => 37, |
497 | | 9 => 35, |
498 | | 10 => 34, |
499 | | 11 => 32, |
500 | | 12 => 31, |
501 | | 13 => 30, |
502 | | 14 => 29, |
503 | | 15 => 28, |
504 | | 16 => 28, |
505 | | 17 => 27, |
506 | | 18 => 27, |
507 | | 19 => 26, |
508 | | 20 => 26, |
509 | | 21 => 25, |
510 | | 22 => 25, |
511 | | 23 => 24, |
512 | | 24 => 24, |
513 | | 25 => 24, |
514 | | 26 => 24, |
515 | | 27 => 23, |
516 | | 28 => 23, |
517 | | 29 => 23, |
518 | | 30 => 23, |
519 | | 31 => 22, |
520 | | 32 => 22, |
521 | | 33 => 22, |
522 | | 34 => 22, |
523 | | 35 => 22, |
524 | | 36 => 21, |
525 | | // Invalid radix |
526 | | _ => 0, |
527 | | } |
528 | | } |
529 | | |
530 | | /// Get the mantissa limit as a const fn. |
531 | | #[must_use] |
532 | | #[inline(always)] |
533 | | #[cfg(feature = "f128")] |
534 | | #[cfg(all(feature = "power-of-two", not(feature = "radix")))] |
535 | | pub const fn f128_mantissa_limit(radix: u32) -> i64 { |
536 | | match radix { |
537 | | 2 => 113, |
538 | | 4 => 56, |
539 | | 8 => 37, |
540 | | 10 => 34, |
541 | | 16 => 28, |
542 | | 32 => 22, |
543 | | // Invalid radix |
544 | | _ => 0, |
545 | | } |
546 | | } |
547 | | |
548 | | /// Get the mantissa limit as a const fn. |
549 | | #[must_use] |
550 | | #[inline(always)] |
551 | | #[cfg(feature = "f128")] |
552 | | #[cfg(not(feature = "power-of-two"))] |
553 | | pub const fn f128_mantissa_limit(radix: u32) -> i64 { |
554 | | match radix { |
555 | | 10 => 34, |
556 | | // Invalid radix |
557 | | _ => 0, |
558 | | } |
559 | | } |
560 | | |
561 | | // POWER LIMITS |
562 | | // ------------ |
563 | | |
564 | | // The code used to generate these limits is as follows: |
565 | | // |
566 | | // ```text |
567 | | // import math |
568 | | // |
569 | | // def find_power(base, max_value): |
570 | | // '''Using log is unreliable, since it uses float math.''' |
571 | | // |
572 | | // power = 0 |
573 | | // while base**power < max_value: |
574 | | // power += 1 |
575 | | // return power - 1 |
576 | | // |
577 | | // def print_function(bits): |
578 | | // print('#[inline(always)]') |
579 | | // print(f'pub const fn u{bits}_power_limit(radix: u32) -> u32 {{') |
580 | | // print(' match radix {') |
581 | | // max_value = 2**bits - 1 |
582 | | // for radix in range(2, 37): |
583 | | // power = find_power(radix, max_value) |
584 | | // print(f' {radix} => {power},') |
585 | | // print(' // Any other radix should be unreachable.') |
586 | | // print(' _ => 1,') |
587 | | // print(' }') |
588 | | // print('}') |
589 | | // print('') |
590 | | // |
591 | | // print_function(32) |
592 | | // print_function(64) |
593 | | // ``` |
594 | | |
595 | | /// Get the maximum value for `radix^N` that can be represented in a u32. |
596 | | /// This is calculated as `⌊log(2^32 - 1, b)⌋`. |
597 | | #[must_use] |
598 | | #[inline(always)] |
599 | | #[cfg(feature = "radix")] |
600 | | pub const fn u32_power_limit(radix: u32) -> u32 { |
601 | | match radix { |
602 | | 2 => 31, |
603 | | 3 => 20, |
604 | | 4 => 15, |
605 | | 5 => 13, |
606 | | 6 => 12, |
607 | | 7 => 11, |
608 | | 8 => 10, |
609 | | 9 => 10, |
610 | | 10 => 9, |
611 | | 11 => 9, |
612 | | 12 => 8, |
613 | | 13 => 8, |
614 | | 14 => 8, |
615 | | 15 => 8, |
616 | | 16 => 7, |
617 | | 17 => 7, |
618 | | 18 => 7, |
619 | | 19 => 7, |
620 | | 20 => 7, |
621 | | 21 => 7, |
622 | | 22 => 7, |
623 | | 23 => 7, |
624 | | 24 => 6, |
625 | | 25 => 6, |
626 | | 26 => 6, |
627 | | 27 => 6, |
628 | | 28 => 6, |
629 | | 29 => 6, |
630 | | 30 => 6, |
631 | | 31 => 6, |
632 | | 32 => 6, |
633 | | 33 => 6, |
634 | | 34 => 6, |
635 | | 35 => 6, |
636 | | 36 => 6, |
637 | | // Any other radix should be unreachable. |
638 | | _ => 1, |
639 | | } |
640 | | } |
641 | | |
642 | | /// This is calculated as `⌊log(2^32 - 1, b)⌋`. |
643 | | #[must_use] |
644 | | #[inline(always)] |
645 | | #[cfg(all(feature = "power-of-two", not(feature = "radix")))] |
646 | | pub const fn u32_power_limit(radix: u32) -> u32 { |
647 | | match radix { |
648 | | 2 => 31, |
649 | | 4 => 15, |
650 | | 5 => 13, |
651 | | 8 => 10, |
652 | | 10 => 9, |
653 | | 16 => 7, |
654 | | 32 => 6, |
655 | | // Any other radix should be unreachable. |
656 | | _ => 1, |
657 | | } |
658 | | } |
659 | | |
660 | | /// This is calculated as `⌊log(2^32 - 1, b)⌋`. |
661 | | #[must_use] |
662 | | #[inline(always)] |
663 | | #[cfg(not(feature = "power-of-two"))] |
664 | 0 | pub const fn u32_power_limit(radix: u32) -> u32 { |
665 | 0 | match radix { |
666 | 0 | 5 => 13, |
667 | 0 | 10 => 9, |
668 | | // Any other radix should be unreachable. |
669 | 0 | _ => 1, |
670 | | } |
671 | 0 | } |
672 | | |
673 | | /// Get the maximum value for `radix^N` that can be represented in a u64. |
674 | | /// This is calculated as `⌊log(2^64 - 1, b)⌋`. |
675 | | #[must_use] |
676 | | #[inline(always)] |
677 | | #[cfg(feature = "radix")] |
678 | | pub const fn u64_power_limit(radix: u32) -> u32 { |
679 | | match radix { |
680 | | 2 => 63, |
681 | | 3 => 40, |
682 | | 4 => 31, |
683 | | 5 => 27, |
684 | | 6 => 24, |
685 | | 7 => 22, |
686 | | 8 => 21, |
687 | | 9 => 20, |
688 | | 10 => 19, |
689 | | 11 => 18, |
690 | | 12 => 17, |
691 | | 13 => 17, |
692 | | 14 => 16, |
693 | | 15 => 16, |
694 | | 16 => 15, |
695 | | 17 => 15, |
696 | | 18 => 15, |
697 | | 19 => 15, |
698 | | 20 => 14, |
699 | | 21 => 14, |
700 | | 22 => 14, |
701 | | 23 => 14, |
702 | | 24 => 13, |
703 | | 25 => 13, |
704 | | 26 => 13, |
705 | | 27 => 13, |
706 | | 28 => 13, |
707 | | 29 => 13, |
708 | | 30 => 13, |
709 | | 31 => 12, |
710 | | 32 => 12, |
711 | | 33 => 12, |
712 | | 34 => 12, |
713 | | 35 => 12, |
714 | | 36 => 12, |
715 | | // Any other radix should be unreachable. |
716 | | _ => 1, |
717 | | } |
718 | | } |
719 | | |
720 | | /// Get the maximum value for `radix^N` that can be represented in a u64. |
721 | | /// This is calculated as `⌊log(2^64 - 1, b)⌋`. |
722 | | #[must_use] |
723 | | #[inline(always)] |
724 | | #[cfg(all(feature = "power-of-two", not(feature = "radix")))] |
725 | | pub const fn u64_power_limit(radix: u32) -> u32 { |
726 | | match radix { |
727 | | 2 => 63, |
728 | | 4 => 31, |
729 | | 5 => 27, |
730 | | 8 => 21, |
731 | | 10 => 19, |
732 | | 16 => 15, |
733 | | 32 => 12, |
734 | | // Any other radix should be unreachable. |
735 | | _ => 1, |
736 | | } |
737 | | } |
738 | | |
739 | | #[must_use] |
740 | | #[inline(always)] |
741 | | #[cfg(not(feature = "power-of-two"))] |
742 | 28 | pub const fn u64_power_limit(radix: u32) -> u32 { |
743 | 28 | match radix { |
744 | 14 | 5 => 27, |
745 | 14 | 10 => 19, |
746 | | // Any other radix should be unreachable. |
747 | 0 | _ => 1, |
748 | | } |
749 | 28 | } |
750 | | |
751 | | // MAX DIGITS |
752 | | // ---------- |
753 | | |
754 | | /// Calculate the maximum number of digits possible in the mantissa. |
755 | | /// |
756 | | /// Returns the maximum number of digits plus one. |
757 | | /// |
758 | | /// We can exactly represent a float in radix `b` from radix 2 if |
759 | | /// `b` is divisible by 2. This function calculates the exact number of |
760 | | /// digits required to exactly represent that float. This makes sense, |
761 | | /// and the exact reference and I quote is: |
762 | | /// |
763 | | /// > A necessary and sufficient condition for all numbers representable in |
764 | | /// > radix β |
765 | | /// > with a finite number of digits to be representable in radix γ with a |
766 | | /// > finite number of digits is that β should divide an integer power of γ. |
767 | | /// |
768 | | /// According to the "Handbook of Floating Point Arithmetic", |
769 | | /// for IEEE754, with `emin` being the min exponent, `p2` being the |
770 | | /// precision, and `b` being the radix, the number of digits follows as: |
771 | | /// |
772 | | /// `−emin + p2 + ⌊(emin + 1) log(2, b) − log(1 − 2^(−p2), b)⌋` |
773 | | /// |
774 | | /// For f16, this follows as: |
775 | | /// emin = -14 |
776 | | /// p2 = 11 |
777 | | /// |
778 | | /// For bfloat16 , this follows as: |
779 | | /// emin = -126 |
780 | | /// p2 = 8 |
781 | | /// |
782 | | /// For f32, this follows as: |
783 | | /// emin = -126 |
784 | | /// p2 = 24 |
785 | | /// |
786 | | /// For f64, this follows as: |
787 | | /// emin = -1022 |
788 | | /// p2 = 53 |
789 | | /// |
790 | | /// For f128, this follows as: |
791 | | /// emin = -16382 |
792 | | /// p2 = 113 |
793 | | /// |
794 | | /// In Python: |
795 | | /// `-emin + p2 + math.floor((emin+ 1)*math.log(2, b)-math.log(1-2**(-p2), |
796 | | /// b))` |
797 | | /// |
798 | | /// This was used to calculate the maximum number of digits for [2, 36]. |
799 | | /// |
800 | | /// The minimum, denormal exponent can be calculated as follows: given |
801 | | /// the number of exponent bits `exp_bits`, and the number of bits |
802 | | /// in the mantissa `mantissa_bits`, we have an exponent bias |
803 | | /// `exp_bias` equal to `2^(exp_bits-1) - 1 + mantissa_bits`. We |
804 | | /// therefore have a denormal exponent `denormal_exp` equal to |
805 | | /// `1 - exp_bias` and the minimum, denormal float `min_float` is |
806 | | /// therefore `2^denormal_exp`. |
807 | | /// |
808 | | /// For f16, this follows as: |
809 | | /// exp_bits = 5 |
810 | | /// mantissa_bits = 10 |
811 | | /// exp_bias = 25 |
812 | | /// denormal_exp = -24 |
813 | | /// min_float = 5.96 * 10^−8 |
814 | | /// |
815 | | /// For bfloat16, this follows as: |
816 | | /// exp_bits = 8 |
817 | | /// mantissa_bits = 7 |
818 | | /// exp_bias = 134 |
819 | | /// denormal_exp = -133 |
820 | | /// min_float = 9.18 * 10^−41 |
821 | | /// |
822 | | /// For f32, this follows as: |
823 | | /// exp_bits = 8 |
824 | | /// mantissa_bits = 23 |
825 | | /// exp_bias = 150 |
826 | | /// denormal_exp = -149 |
827 | | /// min_float = 1.40 * 10^−45 |
828 | | /// |
829 | | /// For f64, this follows as: |
830 | | /// exp_bits = 11 |
831 | | /// mantissa_bits = 52 |
832 | | /// exp_bias = 1075 |
833 | | /// denormal_exp = -1074 |
834 | | /// min_float = 5.00 * 10^−324 |
835 | | /// |
836 | | /// For f128, this follows as: |
837 | | /// exp_bits = 15 |
838 | | /// mantissa_bits = 112 |
839 | | /// exp_bias = 16495 |
840 | | /// denormal_exp = -16494 |
841 | | /// min_float = 6.48 * 10^−4966 |
842 | | /// |
843 | | /// These match statements can be generated with the following Python |
844 | | /// code: |
845 | | /// ```python |
846 | | /// import math |
847 | | /// |
848 | | /// def digits(emin, p2, b): |
849 | | /// return -emin + p2 + math.floor((emin+ 1)*math.log(2, b)-math.log(1-2**(-p2), b)) |
850 | | /// |
851 | | /// def max_digits(emin, p2): |
852 | | /// radices = [6, 10, 12, 14, 18, 20, 22, 24 26 28, 30, 34, 36] |
853 | | /// print('match radix {') |
854 | | /// for radix in radices: |
855 | | /// value = digits(emin, p2, radix) |
856 | | /// print(f' {radix} => Some({value + 2}),') |
857 | | /// print(' // Powers of two should be unreachable.') |
858 | | /// print(' // Odd numbers will have infinite digits.') |
859 | | /// print(' _ => None,') |
860 | | /// print('}') |
861 | | /// ``` |
862 | | #[allow(clippy::doc_markdown)] // reason="not meant to be function parameters" |
863 | | pub trait MaxDigits { |
864 | | fn max_digits(radix: u32) -> Option<usize>; |
865 | | } |
866 | | |
867 | | /// emin = -126 |
868 | | /// p2 = 24 |
869 | | impl MaxDigits for f32 { |
870 | | #[inline(always)] |
871 | 0 | fn max_digits(radix: u32) -> Option<usize> { |
872 | 0 | debug_assert_radix(radix); |
873 | 0 | f32_max_digits(radix) |
874 | 0 | } |
875 | | } |
876 | | |
877 | | /// emin = -1022 |
878 | | /// p2 = 53 |
879 | | impl MaxDigits for f64 { |
880 | | #[inline(always)] |
881 | 14 | fn max_digits(radix: u32) -> Option<usize> { |
882 | 14 | debug_assert_radix(radix); |
883 | 14 | f64_max_digits(radix) |
884 | 14 | } |
885 | | } |
886 | | |
887 | | #[cfg(feature = "f16")] |
888 | | impl MaxDigits for f16 { |
889 | | #[inline(always)] |
890 | | fn max_digits(_: u32) -> Option<usize> { |
891 | | unimplemented!() |
892 | | } |
893 | | } |
894 | | |
895 | | #[cfg(feature = "f16")] |
896 | | impl MaxDigits for bf16 { |
897 | | #[inline(always)] |
898 | | fn max_digits(_: u32) -> Option<usize> { |
899 | | unimplemented!() |
900 | | } |
901 | | } |
902 | | |
903 | | ///// `emin = -16382` |
904 | | ///// `p2 = 113` |
905 | | //#[cfg(feature = "f128")] |
906 | | //impl MaxDigits for f128 { |
907 | | // #[inline(always)] |
908 | | // fn max_digits(radix: u32) -> Option<usize> { |
909 | | // match radix { |
910 | | // 6 => Some(10159), |
911 | | // 10 => Some(11565), |
912 | | // 12 => Some(11927), |
913 | | // 14 => Some(12194), |
914 | | // 18 => Some(12568), |
915 | | // 20 => Some(12706), |
916 | | // 22 => Some(12823), |
917 | | // 24 => Some(12924), |
918 | | // 26 => Some(13012), |
919 | | // 28 => Some(13089), |
920 | | // 30 => Some(13158), |
921 | | // 34 => Some(13277), |
922 | | // 36 => Some(13328), |
923 | | // // Powers of two should be unreachable. |
924 | | // // Odd numbers will have infinite digits. |
925 | | // _ => None, |
926 | | // } |
927 | | // } |
928 | | //} |
929 | | |
930 | | // CONST FN |
931 | | // -------- |
932 | | |
933 | | /// Get the maximum number of significant digits as a const fn. |
934 | | #[must_use] |
935 | | #[inline(always)] |
936 | 0 | pub const fn f32_max_digits(radix: u32) -> Option<usize> { |
937 | 0 | match radix { |
938 | 0 | 6 => Some(103), |
939 | 0 | 10 => Some(114), |
940 | 0 | 12 => Some(117), |
941 | 0 | 14 => Some(119), |
942 | 0 | 18 => Some(122), |
943 | 0 | 20 => Some(123), |
944 | 0 | 22 => Some(123), |
945 | 0 | 24 => Some(124), |
946 | 0 | 26 => Some(125), |
947 | 0 | 28 => Some(125), |
948 | 0 | 30 => Some(126), |
949 | 0 | 34 => Some(127), |
950 | 0 | 36 => Some(127), |
951 | | // Powers of two should be unreachable. |
952 | | // Odd numbers will have infinite digits. |
953 | 0 | _ => None, |
954 | | } |
955 | 0 | } |
956 | | |
957 | | /// Get the maximum number of significant digits as a const fn. |
958 | | #[must_use] |
959 | | #[inline(always)] |
960 | 14 | pub const fn f64_max_digits(radix: u32) -> Option<usize> { |
961 | 14 | match radix { |
962 | 0 | 6 => Some(682), |
963 | 14 | 10 => Some(769), |
964 | 0 | 12 => Some(792), |
965 | 0 | 14 => Some(808), |
966 | 0 | 18 => Some(832), |
967 | 0 | 20 => Some(840), |
968 | 0 | 22 => Some(848), |
969 | 0 | 24 => Some(854), |
970 | 0 | 26 => Some(859), |
971 | 0 | 28 => Some(864), |
972 | 0 | 30 => Some(868), |
973 | 0 | 34 => Some(876), |
974 | 0 | 36 => Some(879), |
975 | | // Powers of two should be unreachable. |
976 | | // Odd numbers will have infinite digits. |
977 | 0 | _ => None, |
978 | | } |
979 | 14 | } |