1 use crate::f64::consts;
2 use crate::num::FpCategory as Fp;
12 assert_eq!(f64::NAN.min(2.0), 2.0);
13 assert_eq!(2.0f64.min(f64::NAN), 2.0);
18 assert_eq!(f64::NAN.max(2.0), 2.0);
19 assert_eq!(2.0f64.max(f64::NAN), 2.0);
24 let nan: f64 = f64::NAN;
25 assert!(nan.is_nan());
26 assert!(!nan.is_infinite());
27 assert!(!nan.is_finite());
28 assert!(!nan.is_normal());
29 assert!(nan.is_sign_positive());
30 assert!(!nan.is_sign_negative());
31 assert_eq!(Fp::Nan, nan.classify());
36 let inf: f64 = f64::INFINITY;
37 assert!(inf.is_infinite());
38 assert!(!inf.is_finite());
39 assert!(inf.is_sign_positive());
40 assert!(!inf.is_sign_negative());
41 assert!(!inf.is_nan());
42 assert!(!inf.is_normal());
43 assert_eq!(Fp::Infinite, inf.classify());
47 fn test_neg_infinity() {
48 let neg_inf: f64 = f64::NEG_INFINITY;
49 assert!(neg_inf.is_infinite());
50 assert!(!neg_inf.is_finite());
51 assert!(!neg_inf.is_sign_positive());
52 assert!(neg_inf.is_sign_negative());
53 assert!(!neg_inf.is_nan());
54 assert!(!neg_inf.is_normal());
55 assert_eq!(Fp::Infinite, neg_inf.classify());
60 let zero: f64 = 0.0f64;
61 assert_eq!(0.0, zero);
62 assert!(!zero.is_infinite());
63 assert!(zero.is_finite());
64 assert!(zero.is_sign_positive());
65 assert!(!zero.is_sign_negative());
66 assert!(!zero.is_nan());
67 assert!(!zero.is_normal());
68 assert_eq!(Fp::Zero, zero.classify());
73 let neg_zero: f64 = -0.0;
74 assert_eq!(0.0, neg_zero);
75 assert!(!neg_zero.is_infinite());
76 assert!(neg_zero.is_finite());
77 assert!(!neg_zero.is_sign_positive());
78 assert!(neg_zero.is_sign_negative());
79 assert!(!neg_zero.is_nan());
80 assert!(!neg_zero.is_normal());
81 assert_eq!(Fp::Zero, neg_zero.classify());
84 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
87 let one: f64 = 1.0f64;
89 assert!(!one.is_infinite());
90 assert!(one.is_finite());
91 assert!(one.is_sign_positive());
92 assert!(!one.is_sign_negative());
93 assert!(!one.is_nan());
94 assert!(one.is_normal());
95 assert_eq!(Fp::Normal, one.classify());
100 let nan: f64 = f64::NAN;
101 let inf: f64 = f64::INFINITY;
102 let neg_inf: f64 = f64::NEG_INFINITY;
103 assert!(nan.is_nan());
104 assert!(!0.0f64.is_nan());
105 assert!(!5.3f64.is_nan());
106 assert!(!(-10.732f64).is_nan());
107 assert!(!inf.is_nan());
108 assert!(!neg_inf.is_nan());
112 fn test_is_infinite() {
113 let nan: f64 = f64::NAN;
114 let inf: f64 = f64::INFINITY;
115 let neg_inf: f64 = f64::NEG_INFINITY;
116 assert!(!nan.is_infinite());
117 assert!(inf.is_infinite());
118 assert!(neg_inf.is_infinite());
119 assert!(!0.0f64.is_infinite());
120 assert!(!42.8f64.is_infinite());
121 assert!(!(-109.2f64).is_infinite());
125 fn test_is_finite() {
126 let nan: f64 = f64::NAN;
127 let inf: f64 = f64::INFINITY;
128 let neg_inf: f64 = f64::NEG_INFINITY;
129 assert!(!nan.is_finite());
130 assert!(!inf.is_finite());
131 assert!(!neg_inf.is_finite());
132 assert!(0.0f64.is_finite());
133 assert!(42.8f64.is_finite());
134 assert!((-109.2f64).is_finite());
137 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
139 fn test_is_normal() {
140 let nan: f64 = f64::NAN;
141 let inf: f64 = f64::INFINITY;
142 let neg_inf: f64 = f64::NEG_INFINITY;
143 let zero: f64 = 0.0f64;
144 let neg_zero: f64 = -0.0;
145 assert!(!nan.is_normal());
146 assert!(!inf.is_normal());
147 assert!(!neg_inf.is_normal());
148 assert!(!zero.is_normal());
149 assert!(!neg_zero.is_normal());
150 assert!(1f64.is_normal());
151 assert!(1e-307f64.is_normal());
152 assert!(!1e-308f64.is_normal());
155 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
158 let nan: f64 = f64::NAN;
159 let inf: f64 = f64::INFINITY;
160 let neg_inf: f64 = f64::NEG_INFINITY;
161 let zero: f64 = 0.0f64;
162 let neg_zero: f64 = -0.0;
163 assert_eq!(nan.classify(), Fp::Nan);
164 assert_eq!(inf.classify(), Fp::Infinite);
165 assert_eq!(neg_inf.classify(), Fp::Infinite);
166 assert_eq!(zero.classify(), Fp::Zero);
167 assert_eq!(neg_zero.classify(), Fp::Zero);
168 assert_eq!(1e-307f64.classify(), Fp::Normal);
169 assert_eq!(1e-308f64.classify(), Fp::Subnormal);
174 assert_approx_eq!(1.0f64.floor(), 1.0f64);
175 assert_approx_eq!(1.3f64.floor(), 1.0f64);
176 assert_approx_eq!(1.5f64.floor(), 1.0f64);
177 assert_approx_eq!(1.7f64.floor(), 1.0f64);
178 assert_approx_eq!(0.0f64.floor(), 0.0f64);
179 assert_approx_eq!((-0.0f64).floor(), -0.0f64);
180 assert_approx_eq!((-1.0f64).floor(), -1.0f64);
181 assert_approx_eq!((-1.3f64).floor(), -2.0f64);
182 assert_approx_eq!((-1.5f64).floor(), -2.0f64);
183 assert_approx_eq!((-1.7f64).floor(), -2.0f64);
188 assert_approx_eq!(1.0f64.ceil(), 1.0f64);
189 assert_approx_eq!(1.3f64.ceil(), 2.0f64);
190 assert_approx_eq!(1.5f64.ceil(), 2.0f64);
191 assert_approx_eq!(1.7f64.ceil(), 2.0f64);
192 assert_approx_eq!(0.0f64.ceil(), 0.0f64);
193 assert_approx_eq!((-0.0f64).ceil(), -0.0f64);
194 assert_approx_eq!((-1.0f64).ceil(), -1.0f64);
195 assert_approx_eq!((-1.3f64).ceil(), -1.0f64);
196 assert_approx_eq!((-1.5f64).ceil(), -1.0f64);
197 assert_approx_eq!((-1.7f64).ceil(), -1.0f64);
202 assert_approx_eq!(1.0f64.round(), 1.0f64);
203 assert_approx_eq!(1.3f64.round(), 1.0f64);
204 assert_approx_eq!(1.5f64.round(), 2.0f64);
205 assert_approx_eq!(1.7f64.round(), 2.0f64);
206 assert_approx_eq!(0.0f64.round(), 0.0f64);
207 assert_approx_eq!((-0.0f64).round(), -0.0f64);
208 assert_approx_eq!((-1.0f64).round(), -1.0f64);
209 assert_approx_eq!((-1.3f64).round(), -1.0f64);
210 assert_approx_eq!((-1.5f64).round(), -2.0f64);
211 assert_approx_eq!((-1.7f64).round(), -2.0f64);
216 assert_approx_eq!(1.0f64.trunc(), 1.0f64);
217 assert_approx_eq!(1.3f64.trunc(), 1.0f64);
218 assert_approx_eq!(1.5f64.trunc(), 1.0f64);
219 assert_approx_eq!(1.7f64.trunc(), 1.0f64);
220 assert_approx_eq!(0.0f64.trunc(), 0.0f64);
221 assert_approx_eq!((-0.0f64).trunc(), -0.0f64);
222 assert_approx_eq!((-1.0f64).trunc(), -1.0f64);
223 assert_approx_eq!((-1.3f64).trunc(), -1.0f64);
224 assert_approx_eq!((-1.5f64).trunc(), -1.0f64);
225 assert_approx_eq!((-1.7f64).trunc(), -1.0f64);
230 assert_approx_eq!(1.0f64.fract(), 0.0f64);
231 assert_approx_eq!(1.3f64.fract(), 0.3f64);
232 assert_approx_eq!(1.5f64.fract(), 0.5f64);
233 assert_approx_eq!(1.7f64.fract(), 0.7f64);
234 assert_approx_eq!(0.0f64.fract(), 0.0f64);
235 assert_approx_eq!((-0.0f64).fract(), -0.0f64);
236 assert_approx_eq!((-1.0f64).fract(), -0.0f64);
237 assert_approx_eq!((-1.3f64).fract(), -0.3f64);
238 assert_approx_eq!((-1.5f64).fract(), -0.5f64);
239 assert_approx_eq!((-1.7f64).fract(), -0.7f64);
244 assert_eq!(f64::INFINITY.abs(), f64::INFINITY);
245 assert_eq!(1f64.abs(), 1f64);
246 assert_eq!(0f64.abs(), 0f64);
247 assert_eq!((-0f64).abs(), 0f64);
248 assert_eq!((-1f64).abs(), 1f64);
249 assert_eq!(f64::NEG_INFINITY.abs(), f64::INFINITY);
250 assert_eq!((1f64 / f64::NEG_INFINITY).abs(), 0f64);
251 assert!(f64::NAN.abs().is_nan());
256 assert_eq!(f64::INFINITY.signum(), 1f64);
257 assert_eq!(1f64.signum(), 1f64);
258 assert_eq!(0f64.signum(), 1f64);
259 assert_eq!((-0f64).signum(), -1f64);
260 assert_eq!((-1f64).signum(), -1f64);
261 assert_eq!(f64::NEG_INFINITY.signum(), -1f64);
262 assert_eq!((1f64 / f64::NEG_INFINITY).signum(), -1f64);
263 assert!(f64::NAN.signum().is_nan());
267 fn test_is_sign_positive() {
268 assert!(f64::INFINITY.is_sign_positive());
269 assert!(1f64.is_sign_positive());
270 assert!(0f64.is_sign_positive());
271 assert!(!(-0f64).is_sign_positive());
272 assert!(!(-1f64).is_sign_positive());
273 assert!(!f64::NEG_INFINITY.is_sign_positive());
274 assert!(!(1f64 / f64::NEG_INFINITY).is_sign_positive());
275 assert!(f64::NAN.is_sign_positive());
276 assert!(!(-f64::NAN).is_sign_positive());
280 fn test_is_sign_negative() {
281 assert!(!f64::INFINITY.is_sign_negative());
282 assert!(!1f64.is_sign_negative());
283 assert!(!0f64.is_sign_negative());
284 assert!((-0f64).is_sign_negative());
285 assert!((-1f64).is_sign_negative());
286 assert!(f64::NEG_INFINITY.is_sign_negative());
287 assert!((1f64 / f64::NEG_INFINITY).is_sign_negative());
288 assert!(!f64::NAN.is_sign_negative());
289 assert!((-f64::NAN).is_sign_negative());
294 let tiny = f64::from_bits(1);
295 let tiny_up = f64::from_bits(2);
296 let max_down = f64::from_bits(0x7fef_ffff_ffff_fffe);
297 let largest_subnormal = f64::from_bits(0x000f_ffff_ffff_ffff);
298 let smallest_normal = f64::from_bits(0x0010_0000_0000_0000);
300 // Check that NaNs roundtrip.
302 let nan1 = f64::from_bits(f64::NAN.to_bits() ^ 0x000a_aaaa_aaaa_aaaa);
303 let nan2 = f64::from_bits(f64::NAN.to_bits() ^ 0x0005_5555_5555_5555);
304 assert_eq!(nan0.next_up().to_bits(), nan0.to_bits());
305 assert_eq!(nan1.next_up().to_bits(), nan1.to_bits());
306 assert_eq!(nan2.next_up().to_bits(), nan2.to_bits());
308 assert_eq!(f64::NEG_INFINITY.next_up(), f64::MIN);
309 assert_eq!(f64::MIN.next_up(), -max_down);
310 assert_eq!((-1.0 - f64::EPSILON).next_up(), -1.0);
311 assert_eq!((-smallest_normal).next_up(), -largest_subnormal);
312 assert_eq!((-tiny_up).next_up(), -tiny);
313 assert_eq!((-tiny).next_up().to_bits(), (-0.0f64).to_bits());
314 assert_eq!((-0.0f64).next_up(), tiny);
315 assert_eq!(0.0f64.next_up(), tiny);
316 assert_eq!(tiny.next_up(), tiny_up);
317 assert_eq!(largest_subnormal.next_up(), smallest_normal);
318 assert_eq!(1.0f64.next_up(), 1.0 + f64::EPSILON);
319 assert_eq!(f64::MAX.next_up(), f64::INFINITY);
320 assert_eq!(f64::INFINITY.next_up(), f64::INFINITY);
324 fn test_next_down() {
325 let tiny = f64::from_bits(1);
326 let tiny_up = f64::from_bits(2);
327 let max_down = f64::from_bits(0x7fef_ffff_ffff_fffe);
328 let largest_subnormal = f64::from_bits(0x000f_ffff_ffff_ffff);
329 let smallest_normal = f64::from_bits(0x0010_0000_0000_0000);
331 // Check that NaNs roundtrip.
333 let nan1 = f64::from_bits(f64::NAN.to_bits() ^ 0x000a_aaaa_aaaa_aaaa);
334 let nan2 = f64::from_bits(f64::NAN.to_bits() ^ 0x0005_5555_5555_5555);
335 assert_eq!(nan0.next_down().to_bits(), nan0.to_bits());
336 assert_eq!(nan1.next_down().to_bits(), nan1.to_bits());
337 assert_eq!(nan2.next_down().to_bits(), nan2.to_bits());
339 assert_eq!(f64::NEG_INFINITY.next_down(), f64::NEG_INFINITY);
340 assert_eq!(f64::MIN.next_down(), f64::NEG_INFINITY);
341 assert_eq!((-max_down).next_down(), f64::MIN);
342 assert_eq!((-1.0f64).next_down(), -1.0 - f64::EPSILON);
343 assert_eq!((-largest_subnormal).next_down(), -smallest_normal);
344 assert_eq!((-tiny).next_down(), -tiny_up);
345 assert_eq!((-0.0f64).next_down(), -tiny);
346 assert_eq!((0.0f64).next_down(), -tiny);
347 assert_eq!(tiny.next_down().to_bits(), 0.0f64.to_bits());
348 assert_eq!(tiny_up.next_down(), tiny);
349 assert_eq!(smallest_normal.next_down(), largest_subnormal);
350 assert_eq!((1.0 + f64::EPSILON).next_down(), 1.0f64);
351 assert_eq!(f64::MAX.next_down(), max_down);
352 assert_eq!(f64::INFINITY.next_down(), f64::MAX);
357 let nan: f64 = f64::NAN;
358 let inf: f64 = f64::INFINITY;
359 let neg_inf: f64 = f64::NEG_INFINITY;
360 assert_approx_eq!(12.3f64.mul_add(4.5, 6.7), 62.05);
361 assert_approx_eq!((-12.3f64).mul_add(-4.5, -6.7), 48.65);
362 assert_approx_eq!(0.0f64.mul_add(8.9, 1.2), 1.2);
363 assert_approx_eq!(3.4f64.mul_add(-0.0, 5.6), 5.6);
364 assert!(nan.mul_add(7.8, 9.0).is_nan());
365 assert_eq!(inf.mul_add(7.8, 9.0), inf);
366 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
367 assert_eq!(8.9f64.mul_add(inf, 3.2), inf);
368 assert_eq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf);
373 let nan: f64 = f64::NAN;
374 let inf: f64 = f64::INFINITY;
375 let neg_inf: f64 = f64::NEG_INFINITY;
376 assert_eq!(1.0f64.recip(), 1.0);
377 assert_eq!(2.0f64.recip(), 0.5);
378 assert_eq!((-0.4f64).recip(), -2.5);
379 assert_eq!(0.0f64.recip(), inf);
380 assert!(nan.recip().is_nan());
381 assert_eq!(inf.recip(), 0.0);
382 assert_eq!(neg_inf.recip(), 0.0);
387 let nan: f64 = f64::NAN;
388 let inf: f64 = f64::INFINITY;
389 let neg_inf: f64 = f64::NEG_INFINITY;
390 assert_eq!(1.0f64.powi(1), 1.0);
391 assert_approx_eq!((-3.1f64).powi(2), 9.61);
392 assert_approx_eq!(5.9f64.powi(-2), 0.028727);
393 assert_eq!(8.3f64.powi(0), 1.0);
394 assert!(nan.powi(2).is_nan());
395 assert_eq!(inf.powi(3), inf);
396 assert_eq!(neg_inf.powi(2), inf);
401 let nan: f64 = f64::NAN;
402 let inf: f64 = f64::INFINITY;
403 let neg_inf: f64 = f64::NEG_INFINITY;
404 assert_eq!(1.0f64.powf(1.0), 1.0);
405 assert_approx_eq!(3.4f64.powf(4.5), 246.408183);
406 assert_approx_eq!(2.7f64.powf(-3.2), 0.041652);
407 assert_approx_eq!((-3.1f64).powf(2.0), 9.61);
408 assert_approx_eq!(5.9f64.powf(-2.0), 0.028727);
409 assert_eq!(8.3f64.powf(0.0), 1.0);
410 assert!(nan.powf(2.0).is_nan());
411 assert_eq!(inf.powf(2.0), inf);
412 assert_eq!(neg_inf.powf(3.0), neg_inf);
416 fn test_sqrt_domain() {
417 assert!(f64::NAN.sqrt().is_nan());
418 assert!(f64::NEG_INFINITY.sqrt().is_nan());
419 assert!((-1.0f64).sqrt().is_nan());
420 assert_eq!((-0.0f64).sqrt(), -0.0);
421 assert_eq!(0.0f64.sqrt(), 0.0);
422 assert_eq!(1.0f64.sqrt(), 1.0);
423 assert_eq!(f64::INFINITY.sqrt(), f64::INFINITY);
428 assert_eq!(1.0, 0.0f64.exp());
429 assert_approx_eq!(2.718282, 1.0f64.exp());
430 assert_approx_eq!(148.413159, 5.0f64.exp());
432 let inf: f64 = f64::INFINITY;
433 let neg_inf: f64 = f64::NEG_INFINITY;
434 let nan: f64 = f64::NAN;
435 assert_eq!(inf, inf.exp());
436 assert_eq!(0.0, neg_inf.exp());
437 assert!(nan.exp().is_nan());
442 assert_eq!(32.0, 5.0f64.exp2());
443 assert_eq!(1.0, 0.0f64.exp2());
445 let inf: f64 = f64::INFINITY;
446 let neg_inf: f64 = f64::NEG_INFINITY;
447 let nan: f64 = f64::NAN;
448 assert_eq!(inf, inf.exp2());
449 assert_eq!(0.0, neg_inf.exp2());
450 assert!(nan.exp2().is_nan());
455 let nan: f64 = f64::NAN;
456 let inf: f64 = f64::INFINITY;
457 let neg_inf: f64 = f64::NEG_INFINITY;
458 assert_approx_eq!(1.0f64.exp().ln(), 1.0);
459 assert!(nan.ln().is_nan());
460 assert_eq!(inf.ln(), inf);
461 assert!(neg_inf.ln().is_nan());
462 assert!((-2.3f64).ln().is_nan());
463 assert_eq!((-0.0f64).ln(), neg_inf);
464 assert_eq!(0.0f64.ln(), neg_inf);
465 assert_approx_eq!(4.0f64.ln(), 1.386294);
470 let nan: f64 = f64::NAN;
471 let inf: f64 = f64::INFINITY;
472 let neg_inf: f64 = f64::NEG_INFINITY;
473 assert_eq!(10.0f64.log(10.0), 1.0);
474 assert_approx_eq!(2.3f64.log(3.5), 0.664858);
475 assert_eq!(1.0f64.exp().log(1.0f64.exp()), 1.0);
476 assert!(1.0f64.log(1.0).is_nan());
477 assert!(1.0f64.log(-13.9).is_nan());
478 assert!(nan.log(2.3).is_nan());
479 assert_eq!(inf.log(10.0), inf);
480 assert!(neg_inf.log(8.8).is_nan());
481 assert!((-2.3f64).log(0.1).is_nan());
482 assert_eq!((-0.0f64).log(2.0), neg_inf);
483 assert_eq!(0.0f64.log(7.0), neg_inf);
488 let nan: f64 = f64::NAN;
489 let inf: f64 = f64::INFINITY;
490 let neg_inf: f64 = f64::NEG_INFINITY;
491 assert_approx_eq!(10.0f64.log2(), 3.321928);
492 assert_approx_eq!(2.3f64.log2(), 1.201634);
493 assert_approx_eq!(1.0f64.exp().log2(), 1.442695);
494 assert!(nan.log2().is_nan());
495 assert_eq!(inf.log2(), inf);
496 assert!(neg_inf.log2().is_nan());
497 assert!((-2.3f64).log2().is_nan());
498 assert_eq!((-0.0f64).log2(), neg_inf);
499 assert_eq!(0.0f64.log2(), neg_inf);
504 let nan: f64 = f64::NAN;
505 let inf: f64 = f64::INFINITY;
506 let neg_inf: f64 = f64::NEG_INFINITY;
507 assert_eq!(10.0f64.log10(), 1.0);
508 assert_approx_eq!(2.3f64.log10(), 0.361728);
509 assert_approx_eq!(1.0f64.exp().log10(), 0.434294);
510 assert_eq!(1.0f64.log10(), 0.0);
511 assert!(nan.log10().is_nan());
512 assert_eq!(inf.log10(), inf);
513 assert!(neg_inf.log10().is_nan());
514 assert!((-2.3f64).log10().is_nan());
515 assert_eq!((-0.0f64).log10(), neg_inf);
516 assert_eq!(0.0f64.log10(), neg_inf);
520 fn test_to_degrees() {
521 let pi: f64 = consts::PI;
522 let nan: f64 = f64::NAN;
523 let inf: f64 = f64::INFINITY;
524 let neg_inf: f64 = f64::NEG_INFINITY;
525 assert_eq!(0.0f64.to_degrees(), 0.0);
526 assert_approx_eq!((-5.8f64).to_degrees(), -332.315521);
527 assert_eq!(pi.to_degrees(), 180.0);
528 assert!(nan.to_degrees().is_nan());
529 assert_eq!(inf.to_degrees(), inf);
530 assert_eq!(neg_inf.to_degrees(), neg_inf);
534 fn test_to_radians() {
535 let pi: f64 = consts::PI;
536 let nan: f64 = f64::NAN;
537 let inf: f64 = f64::INFINITY;
538 let neg_inf: f64 = f64::NEG_INFINITY;
539 assert_eq!(0.0f64.to_radians(), 0.0);
540 assert_approx_eq!(154.6f64.to_radians(), 2.698279);
541 assert_approx_eq!((-332.31f64).to_radians(), -5.799903);
542 assert_eq!(180.0f64.to_radians(), pi);
543 assert!(nan.to_radians().is_nan());
544 assert_eq!(inf.to_radians(), inf);
545 assert_eq!(neg_inf.to_radians(), neg_inf);
550 assert_eq!(0.0f64.asinh(), 0.0f64);
551 assert_eq!((-0.0f64).asinh(), -0.0f64);
553 let inf: f64 = f64::INFINITY;
554 let neg_inf: f64 = f64::NEG_INFINITY;
555 let nan: f64 = f64::NAN;
556 assert_eq!(inf.asinh(), inf);
557 assert_eq!(neg_inf.asinh(), neg_inf);
558 assert!(nan.asinh().is_nan());
559 assert!((-0.0f64).asinh().is_sign_negative());
561 assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64);
562 assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64);
563 // regression test for the catastrophic cancellation fixed in 72486
564 assert_approx_eq!((-67452098.07139316f64).asinh(), -18.72007542627454439398548429400083);
569 assert_eq!(1.0f64.acosh(), 0.0f64);
570 assert!(0.999f64.acosh().is_nan());
572 let inf: f64 = f64::INFINITY;
573 let neg_inf: f64 = f64::NEG_INFINITY;
574 let nan: f64 = f64::NAN;
575 assert_eq!(inf.acosh(), inf);
576 assert!(neg_inf.acosh().is_nan());
577 assert!(nan.acosh().is_nan());
578 assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64);
579 assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64);
584 assert_eq!(0.0f64.atanh(), 0.0f64);
585 assert_eq!((-0.0f64).atanh(), -0.0f64);
587 let inf: f64 = f64::INFINITY;
588 let neg_inf: f64 = f64::NEG_INFINITY;
589 let nan: f64 = f64::NAN;
590 assert_eq!(1.0f64.atanh(), inf);
591 assert_eq!((-1.0f64).atanh(), neg_inf);
592 assert!(2f64.atanh().atanh().is_nan());
593 assert!((-2f64).atanh().atanh().is_nan());
594 assert!(inf.atanh().is_nan());
595 assert!(neg_inf.atanh().is_nan());
596 assert!(nan.atanh().is_nan());
597 assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64);
598 assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64);
602 fn test_real_consts() {
604 let pi: f64 = consts::PI;
605 let frac_pi_2: f64 = consts::FRAC_PI_2;
606 let frac_pi_3: f64 = consts::FRAC_PI_3;
607 let frac_pi_4: f64 = consts::FRAC_PI_4;
608 let frac_pi_6: f64 = consts::FRAC_PI_6;
609 let frac_pi_8: f64 = consts::FRAC_PI_8;
610 let frac_1_pi: f64 = consts::FRAC_1_PI;
611 let frac_2_pi: f64 = consts::FRAC_2_PI;
612 let frac_2_sqrtpi: f64 = consts::FRAC_2_SQRT_PI;
613 let sqrt2: f64 = consts::SQRT_2;
614 let frac_1_sqrt2: f64 = consts::FRAC_1_SQRT_2;
615 let e: f64 = consts::E;
616 let log2_e: f64 = consts::LOG2_E;
617 let log10_e: f64 = consts::LOG10_E;
618 let ln_2: f64 = consts::LN_2;
619 let ln_10: f64 = consts::LN_10;
621 assert_approx_eq!(frac_pi_2, pi / 2f64);
622 assert_approx_eq!(frac_pi_3, pi / 3f64);
623 assert_approx_eq!(frac_pi_4, pi / 4f64);
624 assert_approx_eq!(frac_pi_6, pi / 6f64);
625 assert_approx_eq!(frac_pi_8, pi / 8f64);
626 assert_approx_eq!(frac_1_pi, 1f64 / pi);
627 assert_approx_eq!(frac_2_pi, 2f64 / pi);
628 assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt());
629 assert_approx_eq!(sqrt2, 2f64.sqrt());
630 assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt());
631 assert_approx_eq!(log2_e, e.log2());
632 assert_approx_eq!(log10_e, e.log10());
633 assert_approx_eq!(ln_2, 2f64.ln());
634 assert_approx_eq!(ln_10, 10f64.ln());
638 fn test_float_bits_conv() {
639 assert_eq!((1f64).to_bits(), 0x3ff0000000000000);
640 assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
641 assert_eq!((1337f64).to_bits(), 0x4094e40000000000);
642 assert_eq!((-14.25f64).to_bits(), 0xc02c800000000000);
643 assert_approx_eq!(f64::from_bits(0x3ff0000000000000), 1.0);
644 assert_approx_eq!(f64::from_bits(0x4029000000000000), 12.5);
645 assert_approx_eq!(f64::from_bits(0x4094e40000000000), 1337.0);
646 assert_approx_eq!(f64::from_bits(0xc02c800000000000), -14.25);
648 // Check that NaNs roundtrip their bits regardless of signaling-ness
649 // 0xA is 0b1010; 0x5 is 0b0101 -- so these two together clobbers all the mantissa bits
650 let masked_nan1 = f64::NAN.to_bits() ^ 0x000A_AAAA_AAAA_AAAA;
651 let masked_nan2 = f64::NAN.to_bits() ^ 0x0005_5555_5555_5555;
652 assert!(f64::from_bits(masked_nan1).is_nan());
653 assert!(f64::from_bits(masked_nan2).is_nan());
655 assert_eq!(f64::from_bits(masked_nan1).to_bits(), masked_nan1);
656 assert_eq!(f64::from_bits(masked_nan2).to_bits(), masked_nan2);
661 fn test_clamp_min_greater_than_max() {
662 let _ = 1.0f64.clamp(3.0, 1.0);
667 fn test_clamp_min_is_nan() {
668 let _ = 1.0f64.clamp(f64::NAN, 1.0);
673 fn test_clamp_max_is_nan() {
674 let _ = 1.0f64.clamp(3.0, f64::NAN);
678 fn test_total_cmp() {
679 use core::cmp::Ordering;
681 fn quiet_bit_mask() -> u64 {
682 1 << (f64::MANTISSA_DIGITS - 2)
685 fn min_subnorm() -> f64 {
686 f64::MIN_POSITIVE / f64::powf(2.0, f64::MANTISSA_DIGITS as f64 - 1.0)
689 fn max_subnorm() -> f64 {
690 f64::MIN_POSITIVE - min_subnorm()
694 f64::from_bits(f64::NAN.to_bits() | quiet_bit_mask())
698 f64::from_bits((f64::NAN.to_bits() & !quiet_bit_mask()) + 42)
701 assert_eq!(Ordering::Equal, (-q_nan()).total_cmp(&-q_nan()));
702 assert_eq!(Ordering::Equal, (-s_nan()).total_cmp(&-s_nan()));
703 assert_eq!(Ordering::Equal, (-f64::INFINITY).total_cmp(&-f64::INFINITY));
704 assert_eq!(Ordering::Equal, (-f64::MAX).total_cmp(&-f64::MAX));
705 assert_eq!(Ordering::Equal, (-2.5_f64).total_cmp(&-2.5));
706 assert_eq!(Ordering::Equal, (-1.0_f64).total_cmp(&-1.0));
707 assert_eq!(Ordering::Equal, (-1.5_f64).total_cmp(&-1.5));
708 assert_eq!(Ordering::Equal, (-0.5_f64).total_cmp(&-0.5));
709 assert_eq!(Ordering::Equal, (-f64::MIN_POSITIVE).total_cmp(&-f64::MIN_POSITIVE));
710 assert_eq!(Ordering::Equal, (-max_subnorm()).total_cmp(&-max_subnorm()));
711 assert_eq!(Ordering::Equal, (-min_subnorm()).total_cmp(&-min_subnorm()));
712 assert_eq!(Ordering::Equal, (-0.0_f64).total_cmp(&-0.0));
713 assert_eq!(Ordering::Equal, 0.0_f64.total_cmp(&0.0));
714 assert_eq!(Ordering::Equal, min_subnorm().total_cmp(&min_subnorm()));
715 assert_eq!(Ordering::Equal, max_subnorm().total_cmp(&max_subnorm()));
716 assert_eq!(Ordering::Equal, f64::MIN_POSITIVE.total_cmp(&f64::MIN_POSITIVE));
717 assert_eq!(Ordering::Equal, 0.5_f64.total_cmp(&0.5));
718 assert_eq!(Ordering::Equal, 1.0_f64.total_cmp(&1.0));
719 assert_eq!(Ordering::Equal, 1.5_f64.total_cmp(&1.5));
720 assert_eq!(Ordering::Equal, 2.5_f64.total_cmp(&2.5));
721 assert_eq!(Ordering::Equal, f64::MAX.total_cmp(&f64::MAX));
722 assert_eq!(Ordering::Equal, f64::INFINITY.total_cmp(&f64::INFINITY));
723 assert_eq!(Ordering::Equal, s_nan().total_cmp(&s_nan()));
724 assert_eq!(Ordering::Equal, q_nan().total_cmp(&q_nan()));
726 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-s_nan()));
727 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::INFINITY));
728 assert_eq!(Ordering::Less, (-f64::INFINITY).total_cmp(&-f64::MAX));
729 assert_eq!(Ordering::Less, (-f64::MAX).total_cmp(&-2.5));
730 assert_eq!(Ordering::Less, (-2.5_f64).total_cmp(&-1.5));
731 assert_eq!(Ordering::Less, (-1.5_f64).total_cmp(&-1.0));
732 assert_eq!(Ordering::Less, (-1.0_f64).total_cmp(&-0.5));
733 assert_eq!(Ordering::Less, (-0.5_f64).total_cmp(&-f64::MIN_POSITIVE));
734 assert_eq!(Ordering::Less, (-f64::MIN_POSITIVE).total_cmp(&-max_subnorm()));
735 assert_eq!(Ordering::Less, (-max_subnorm()).total_cmp(&-min_subnorm()));
736 assert_eq!(Ordering::Less, (-min_subnorm()).total_cmp(&-0.0));
737 assert_eq!(Ordering::Less, (-0.0_f64).total_cmp(&0.0));
738 assert_eq!(Ordering::Less, 0.0_f64.total_cmp(&min_subnorm()));
739 assert_eq!(Ordering::Less, min_subnorm().total_cmp(&max_subnorm()));
740 assert_eq!(Ordering::Less, max_subnorm().total_cmp(&f64::MIN_POSITIVE));
741 assert_eq!(Ordering::Less, f64::MIN_POSITIVE.total_cmp(&0.5));
742 assert_eq!(Ordering::Less, 0.5_f64.total_cmp(&1.0));
743 assert_eq!(Ordering::Less, 1.0_f64.total_cmp(&1.5));
744 assert_eq!(Ordering::Less, 1.5_f64.total_cmp(&2.5));
745 assert_eq!(Ordering::Less, 2.5_f64.total_cmp(&f64::MAX));
746 assert_eq!(Ordering::Less, f64::MAX.total_cmp(&f64::INFINITY));
747 assert_eq!(Ordering::Less, f64::INFINITY.total_cmp(&s_nan()));
748 assert_eq!(Ordering::Less, s_nan().total_cmp(&q_nan()));
750 assert_eq!(Ordering::Greater, (-s_nan()).total_cmp(&-q_nan()));
751 assert_eq!(Ordering::Greater, (-f64::INFINITY).total_cmp(&-s_nan()));
752 assert_eq!(Ordering::Greater, (-f64::MAX).total_cmp(&-f64::INFINITY));
753 assert_eq!(Ordering::Greater, (-2.5_f64).total_cmp(&-f64::MAX));
754 assert_eq!(Ordering::Greater, (-1.5_f64).total_cmp(&-2.5));
755 assert_eq!(Ordering::Greater, (-1.0_f64).total_cmp(&-1.5));
756 assert_eq!(Ordering::Greater, (-0.5_f64).total_cmp(&-1.0));
757 assert_eq!(Ordering::Greater, (-f64::MIN_POSITIVE).total_cmp(&-0.5));
758 assert_eq!(Ordering::Greater, (-max_subnorm()).total_cmp(&-f64::MIN_POSITIVE));
759 assert_eq!(Ordering::Greater, (-min_subnorm()).total_cmp(&-max_subnorm()));
760 assert_eq!(Ordering::Greater, (-0.0_f64).total_cmp(&-min_subnorm()));
761 assert_eq!(Ordering::Greater, 0.0_f64.total_cmp(&-0.0));
762 assert_eq!(Ordering::Greater, min_subnorm().total_cmp(&0.0));
763 assert_eq!(Ordering::Greater, max_subnorm().total_cmp(&min_subnorm()));
764 assert_eq!(Ordering::Greater, f64::MIN_POSITIVE.total_cmp(&max_subnorm()));
765 assert_eq!(Ordering::Greater, 0.5_f64.total_cmp(&f64::MIN_POSITIVE));
766 assert_eq!(Ordering::Greater, 1.0_f64.total_cmp(&0.5));
767 assert_eq!(Ordering::Greater, 1.5_f64.total_cmp(&1.0));
768 assert_eq!(Ordering::Greater, 2.5_f64.total_cmp(&1.5));
769 assert_eq!(Ordering::Greater, f64::MAX.total_cmp(&2.5));
770 assert_eq!(Ordering::Greater, f64::INFINITY.total_cmp(&f64::MAX));
771 assert_eq!(Ordering::Greater, s_nan().total_cmp(&f64::INFINITY));
772 assert_eq!(Ordering::Greater, q_nan().total_cmp(&s_nan()));
774 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-s_nan()));
775 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-f64::INFINITY));
776 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-f64::MAX));
777 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-2.5));
778 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-1.5));
779 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-1.0));
780 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-0.5));
781 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-f64::MIN_POSITIVE));
782 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-max_subnorm()));
783 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-min_subnorm()));
784 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-0.0));
785 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&0.0));
786 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&min_subnorm()));
787 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&max_subnorm()));
788 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&f64::MIN_POSITIVE));
789 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&0.5));
790 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&1.0));
791 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&1.5));
792 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&2.5));
793 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&f64::MAX));
794 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&f64::INFINITY));
795 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&s_nan()));
797 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::INFINITY));
798 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::MAX));
799 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-2.5));
800 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-1.5));
801 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-1.0));
802 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-0.5));
803 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::MIN_POSITIVE));
804 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-max_subnorm()));
805 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-min_subnorm()));
806 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-0.0));
807 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&0.0));
808 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&min_subnorm()));
809 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&max_subnorm()));
810 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::MIN_POSITIVE));
811 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&0.5));
812 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&1.0));
813 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&1.5));
814 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&2.5));
815 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::MAX));
816 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::INFINITY));
817 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&s_nan()));