1/* origin: FreeBSD /usr/src/lib/msun/src/e_pow.c */
2/*
3 * ====================================================
4 * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12// pow(x,y) return x**y
13//
14// n
15// Method: Let x = 2 * (1+f)
16// 1. Compute and return log2(x) in two pieces:
17// log2(x) = w1 + w2,
18// where w1 has 53-24 = 29 bit trailing zeros.
19// 2. Perform y*log2(x) = n+y' by simulating multi-precision
20// arithmetic, where |y'|<=0.5.
21// 3. Return x**y = 2**n*exp(y'*log2)
22//
23// Special cases:
24// 1. (anything) ** 0 is 1
25// 2. 1 ** (anything) is 1
26// 3. (anything except 1) ** NAN is NAN
27// 4. NAN ** (anything except 0) is NAN
28// 5. +-(|x| > 1) ** +INF is +INF
29// 6. +-(|x| > 1) ** -INF is +0
30// 7. +-(|x| < 1) ** +INF is +0
31// 8. +-(|x| < 1) ** -INF is +INF
32// 9. -1 ** +-INF is 1
33// 10. +0 ** (+anything except 0, NAN) is +0
34// 11. -0 ** (+anything except 0, NAN, odd integer) is +0
35// 12. +0 ** (-anything except 0, NAN) is +INF, raise divbyzero
36// 13. -0 ** (-anything except 0, NAN, odd integer) is +INF, raise divbyzero
37// 14. -0 ** (+odd integer) is -0
38// 15. -0 ** (-odd integer) is -INF, raise divbyzero
39// 16. +INF ** (+anything except 0,NAN) is +INF
40// 17. +INF ** (-anything except 0,NAN) is +0
41// 18. -INF ** (+odd integer) is -INF
42// 19. -INF ** (anything) = -0 ** (-anything), (anything except odd integer)
43// 20. (anything) ** 1 is (anything)
44// 21. (anything) ** -1 is 1/(anything)
45// 22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
46// 23. (-anything except 0 and inf) ** (non-integer) is NAN
47//
48// Accuracy:
49// pow(x,y) returns x**y nearly rounded. In particular
50// pow(integer,integer)
51// always returns the correct integer provided it is
52// representable.
53//
54// Constants :
55// The hexadecimal values are the intended ones for the following
56// constants. The decimal values may be used, provided that the
57// compiler will convert from decimal to binary accurately enough
58// to produce the hexadecimal values shown.
59//
60use super::{fabs, get_high_word, scalbn, sqrt, with_set_high_word, with_set_low_word};
61
62const BP: [f64; 2] = [1.0, 1.5];
63const DP_H: [f64; 2] = [0.0, 5.84962487220764160156e-01]; /* 0x3fe2b803_40000000 */
64const DP_L: [f64; 2] = [0.0, 1.35003920212974897128e-08]; /* 0x3E4CFDEB, 0x43CFD006 */
65const TWO53: f64 = 9007199254740992.0; /* 0x43400000_00000000 */
66const HUGE: f64 = 1.0e300;
67const TINY: f64 = 1.0e-300;
68
69// poly coefs for (3/2)*(log(x)-2s-2/3*s**3:
70const L1: f64 = 5.99999999999994648725e-01; /* 0x3fe33333_33333303 */
71const L2: f64 = 4.28571428578550184252e-01; /* 0x3fdb6db6_db6fabff */
72const L3: f64 = 3.33333329818377432918e-01; /* 0x3fd55555_518f264d */
73const L4: f64 = 2.72728123808534006489e-01; /* 0x3fd17460_a91d4101 */
74const L5: f64 = 2.30660745775561754067e-01; /* 0x3fcd864a_93c9db65 */
75const L6: f64 = 2.06975017800338417784e-01; /* 0x3fca7e28_4a454eef */
76const P1: f64 = 1.66666666666666019037e-01; /* 0x3fc55555_5555553e */
77const P2: f64 = -2.77777777770155933842e-03; /* 0xbf66c16c_16bebd93 */
78const P3: f64 = 6.61375632143793436117e-05; /* 0x3f11566a_af25de2c */
79const P4: f64 = -1.65339022054652515390e-06; /* 0xbebbbd41_c5d26bf1 */
80const P5: f64 = 4.13813679705723846039e-08; /* 0x3e663769_72bea4d0 */
81const LG2: f64 = 6.93147180559945286227e-01; /* 0x3fe62e42_fefa39ef */
82const LG2_H: f64 = 6.93147182464599609375e-01; /* 0x3fe62e43_00000000 */
83const LG2_L: f64 = -1.90465429995776804525e-09; /* 0xbe205c61_0ca86c39 */
84const OVT: f64 = 8.0085662595372944372e-017; /* -(1024-log2(ovfl+.5ulp)) */
85const CP: f64 = 9.61796693925975554329e-01; /* 0x3feec709_dc3a03fd =2/(3ln2) */
86const CP_H: f64 = 9.61796700954437255859e-01; /* 0x3feec709_e0000000 =(float)cp */
87const CP_L: f64 = -7.02846165095275826516e-09; /* 0xbe3e2fe0_145b01f5 =tail of cp_h*/
88const IVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547_652b82fe =1/ln2 */
89const IVLN2_H: f64 = 1.44269502162933349609e+00; /* 0x3ff71547_60000000 =24b 1/ln2*/
90const IVLN2_L: f64 = 1.92596299112661746887e-08; /* 0x3e54ae0b_f85ddf44 =1/ln2 tail*/
91
92/// Returns `x` to the power of `y` (f64).
93#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
94pub fn pow(x: f64, y: f64) -> f64 {
95 let t1: f64;
96 let t2: f64;
97
98 let (hx, lx): (i32, u32) = ((x.to_bits() >> 32) as i32, x.to_bits() as u32);
99 let (hy, ly): (i32, u32) = ((y.to_bits() >> 32) as i32, y.to_bits() as u32);
100
101 let mut ix: i32 = hx & 0x7fffffff_i32;
102 let iy: i32 = hy & 0x7fffffff_i32;
103
104 /* x**0 = 1, even if x is NaN */
105 if ((iy as u32) | ly) == 0 {
106 return 1.0;
107 }
108
109 /* 1**y = 1, even if y is NaN */
110 if hx == 0x3ff00000 && lx == 0 {
111 return 1.0;
112 }
113
114 /* NaN if either arg is NaN */
115 if ix > 0x7ff00000
116 || (ix == 0x7ff00000 && lx != 0)
117 || iy > 0x7ff00000
118 || (iy == 0x7ff00000 && ly != 0)
119 {
120 return x + y;
121 }
122
123 /* determine if y is an odd int when x < 0
124 * yisint = 0 ... y is not an integer
125 * yisint = 1 ... y is an odd int
126 * yisint = 2 ... y is an even int
127 */
128 let mut yisint: i32 = 0;
129 let mut k: i32;
130 let mut j: i32;
131 if hx < 0 {
132 if iy >= 0x43400000 {
133 yisint = 2; /* even integer y */
134 } else if iy >= 0x3ff00000 {
135 k = (iy >> 20) - 0x3ff; /* exponent */
136
137 if k > 20 {
138 j = (ly >> (52 - k)) as i32;
139
140 if (j << (52 - k)) == (ly as i32) {
141 yisint = 2 - (j & 1);
142 }
143 } else if ly == 0 {
144 j = iy >> (20 - k);
145
146 if (j << (20 - k)) == iy {
147 yisint = 2 - (j & 1);
148 }
149 }
150 }
151 }
152
153 if ly == 0 {
154 /* special value of y */
155 if iy == 0x7ff00000 {
156 /* y is +-inf */
157
158 return if ((ix - 0x3ff00000) | (lx as i32)) == 0 {
159 /* (-1)**+-inf is 1 */
160 1.0
161 } else if ix >= 0x3ff00000 {
162 /* (|x|>1)**+-inf = inf,0 */
163 if hy >= 0 { y } else { 0.0 }
164 } else {
165 /* (|x|<1)**+-inf = 0,inf */
166 if hy >= 0 { 0.0 } else { -y }
167 };
168 }
169
170 if iy == 0x3ff00000 {
171 /* y is +-1 */
172 return if hy >= 0 { x } else { 1.0 / x };
173 }
174
175 if hy == 0x40000000 {
176 /* y is 2 */
177 return x * x;
178 }
179
180 if hy == 0x3fe00000 {
181 /* y is 0.5 */
182 if hx >= 0 {
183 /* x >= +0 */
184 return sqrt(x);
185 }
186 }
187 }
188
189 let mut ax: f64 = fabs(x);
190 if lx == 0 {
191 /* special value of x */
192 if ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000 {
193 /* x is +-0,+-inf,+-1 */
194 let mut z: f64 = ax;
195
196 if hy < 0 {
197 /* z = (1/|x|) */
198 z = 1.0 / z;
199 }
200
201 if hx < 0 {
202 if ((ix - 0x3ff00000) | yisint) == 0 {
203 z = (z - z) / (z - z); /* (-1)**non-int is NaN */
204 } else if yisint == 1 {
205 z = -z; /* (x<0)**odd = -(|x|**odd) */
206 }
207 }
208
209 return z;
210 }
211 }
212
213 let mut s: f64 = 1.0; /* sign of result */
214 if hx < 0 {
215 if yisint == 0 {
216 /* (x<0)**(non-int) is NaN */
217 return (x - x) / (x - x);
218 }
219
220 if yisint == 1 {
221 /* (x<0)**(odd int) */
222 s = -1.0;
223 }
224 }
225
226 /* |y| is HUGE */
227 if iy > 0x41e00000 {
228 /* if |y| > 2**31 */
229 if iy > 0x43f00000 {
230 /* if |y| > 2**64, must o/uflow */
231 if ix <= 0x3fefffff {
232 return if hy < 0 { HUGE * HUGE } else { TINY * TINY };
233 }
234
235 if ix >= 0x3ff00000 {
236 return if hy > 0 { HUGE * HUGE } else { TINY * TINY };
237 }
238 }
239
240 /* over/underflow if x is not close to one */
241 if ix < 0x3fefffff {
242 return if hy < 0 {
243 s * HUGE * HUGE
244 } else {
245 s * TINY * TINY
246 };
247 }
248 if ix > 0x3ff00000 {
249 return if hy > 0 {
250 s * HUGE * HUGE
251 } else {
252 s * TINY * TINY
253 };
254 }
255
256 /* now |1-x| is TINY <= 2**-20, suffice to compute
257 log(x) by x-x^2/2+x^3/3-x^4/4 */
258 let t: f64 = ax - 1.0; /* t has 20 trailing zeros */
259 let w: f64 = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
260 let u: f64 = IVLN2_H * t; /* ivln2_h has 21 sig. bits */
261 let v: f64 = t * IVLN2_L - w * IVLN2;
262 t1 = with_set_low_word(u + v, 0);
263 t2 = v - (t1 - u);
264 } else {
265 // double ss,s2,s_h,s_l,t_h,t_l;
266 let mut n: i32 = 0;
267
268 if ix < 0x00100000 {
269 /* take care subnormal number */
270 ax *= TWO53;
271 n -= 53;
272 ix = get_high_word(ax) as i32;
273 }
274
275 n += (ix >> 20) - 0x3ff;
276 j = ix & 0x000fffff;
277
278 /* determine interval */
279 let k: i32;
280 ix = j | 0x3ff00000; /* normalize ix */
281 if j <= 0x3988E {
282 /* |x|<sqrt(3/2) */
283 k = 0;
284 } else if j < 0xBB67A {
285 /* |x|<sqrt(3) */
286 k = 1;
287 } else {
288 k = 0;
289 n += 1;
290 ix -= 0x00100000;
291 }
292 ax = with_set_high_word(ax, ix as u32);
293
294 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
295 let u: f64 = ax - i!(BP, k as usize); /* bp[0]=1.0, bp[1]=1.5 */
296 let v: f64 = 1.0 / (ax + i!(BP, k as usize));
297 let ss: f64 = u * v;
298 let s_h = with_set_low_word(ss, 0);
299
300 /* t_h=ax+bp[k] High */
301 let t_h: f64 = with_set_high_word(
302 0.0,
303 ((ix as u32 >> 1) | 0x20000000) + 0x00080000 + ((k as u32) << 18),
304 );
305 let t_l: f64 = ax - (t_h - i!(BP, k as usize));
306 let s_l: f64 = v * ((u - s_h * t_h) - s_h * t_l);
307
308 /* compute log(ax) */
309 let s2: f64 = ss * ss;
310 let mut r: f64 = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
311 r += s_l * (s_h + ss);
312 let s2: f64 = s_h * s_h;
313 let t_h: f64 = with_set_low_word(3.0 + s2 + r, 0);
314 let t_l: f64 = r - ((t_h - 3.0) - s2);
315
316 /* u+v = ss*(1+...) */
317 let u: f64 = s_h * t_h;
318 let v: f64 = s_l * t_h + t_l * ss;
319
320 /* 2/(3log2)*(ss+...) */
321 let p_h: f64 = with_set_low_word(u + v, 0);
322 let p_l = v - (p_h - u);
323 let z_h: f64 = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */
324 let z_l: f64 = CP_L * p_h + p_l * CP + i!(DP_L, k as usize);
325
326 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
327 let t: f64 = n as f64;
328 t1 = with_set_low_word(((z_h + z_l) + i!(DP_H, k as usize)) + t, 0);
329 t2 = z_l - (((t1 - t) - i!(DP_H, k as usize)) - z_h);
330 }
331
332 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
333 let y1: f64 = with_set_low_word(y, 0);
334 let p_l: f64 = (y - y1) * t1 + y * t2;
335 let mut p_h: f64 = y1 * t1;
336 let z: f64 = p_l + p_h;
337 let mut j: i32 = (z.to_bits() >> 32) as i32;
338 let i: i32 = z.to_bits() as i32;
339 // let (j, i): (i32, i32) = ((z.to_bits() >> 32) as i32, z.to_bits() as i32);
340
341 if j >= 0x40900000 {
342 /* z >= 1024 */
343 if (j - 0x40900000) | i != 0 {
344 /* if z > 1024 */
345 return s * HUGE * HUGE; /* overflow */
346 }
347
348 if p_l + OVT > z - p_h {
349 return s * HUGE * HUGE; /* overflow */
350 }
351 } else if (j & 0x7fffffff) >= 0x4090cc00 {
352 /* z <= -1075 */
353 // FIXME: instead of abs(j) use unsigned j
354
355 if (((j as u32) - 0xc090cc00) | (i as u32)) != 0 {
356 /* z < -1075 */
357 return s * TINY * TINY; /* underflow */
358 }
359
360 if p_l <= z - p_h {
361 return s * TINY * TINY; /* underflow */
362 }
363 }
364
365 /* compute 2**(p_h+p_l) */
366 let i: i32 = j & 0x7fffffff_i32;
367 k = (i >> 20) - 0x3ff;
368 let mut n: i32 = 0;
369
370 if i > 0x3fe00000 {
371 /* if |z| > 0.5, set n = [z+0.5] */
372 n = j + (0x00100000 >> (k + 1));
373 k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
374 let t: f64 = with_set_high_word(0.0, (n & !(0x000fffff >> k)) as u32);
375 n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
376 if j < 0 {
377 n = -n;
378 }
379 p_h -= t;
380 }
381
382 let t: f64 = with_set_low_word(p_l + p_h, 0);
383 let u: f64 = t * LG2_H;
384 let v: f64 = (p_l - (t - p_h)) * LG2 + t * LG2_L;
385 let mut z: f64 = u + v;
386 let w: f64 = v - (z - u);
387 let t: f64 = z * z;
388 let t1: f64 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
389 let r: f64 = (z * t1) / (t1 - 2.0) - (w + z * w);
390 z = 1.0 - (r - z);
391 j = get_high_word(z) as i32;
392 j += n << 20;
393
394 if (j >> 20) <= 0 {
395 /* subnormal output */
396 z = scalbn(z, n);
397 } else {
398 z = with_set_high_word(z, j as u32);
399 }
400
401 s * z
402}
403
404#[cfg(test)]
405mod tests {
406 extern crate core;
407
408 use self::core::f64::consts::{E, PI};
409 use super::pow;
410
411 const POS_ZERO: &[f64] = &[0.0];
412 const NEG_ZERO: &[f64] = &[-0.0];
413 const POS_ONE: &[f64] = &[1.0];
414 const NEG_ONE: &[f64] = &[-1.0];
415 const POS_FLOATS: &[f64] = &[99.0 / 70.0, E, PI];
416 const NEG_FLOATS: &[f64] = &[-99.0 / 70.0, -E, -PI];
417 const POS_SMALL_FLOATS: &[f64] = &[(1.0 / 2.0), f64::MIN_POSITIVE, f64::EPSILON];
418 const NEG_SMALL_FLOATS: &[f64] = &[-(1.0 / 2.0), -f64::MIN_POSITIVE, -f64::EPSILON];
419 const POS_EVENS: &[f64] = &[2.0, 6.0, 8.0, 10.0, 22.0, 100.0, f64::MAX];
420 const NEG_EVENS: &[f64] = &[f64::MIN, -100.0, -22.0, -10.0, -8.0, -6.0, -2.0];
421 const POS_ODDS: &[f64] = &[3.0, 7.0];
422 const NEG_ODDS: &[f64] = &[-7.0, -3.0];
423 const NANS: &[f64] = &[f64::NAN];
424 const POS_INF: &[f64] = &[f64::INFINITY];
425 const NEG_INF: &[f64] = &[f64::NEG_INFINITY];
426
427 const ALL: &[&[f64]] = &[
428 POS_ZERO,
429 NEG_ZERO,
430 NANS,
431 NEG_SMALL_FLOATS,
432 POS_SMALL_FLOATS,
433 NEG_FLOATS,
434 POS_FLOATS,
435 NEG_EVENS,
436 POS_EVENS,
437 NEG_ODDS,
438 POS_ODDS,
439 NEG_INF,
440 POS_INF,
441 NEG_ONE,
442 POS_ONE,
443 ];
444 const POS: &[&[f64]] = &[POS_ZERO, POS_ODDS, POS_ONE, POS_FLOATS, POS_EVENS, POS_INF];
445 const NEG: &[&[f64]] = &[NEG_ZERO, NEG_ODDS, NEG_ONE, NEG_FLOATS, NEG_EVENS, NEG_INF];
446
447 fn pow_test(base: f64, exponent: f64, expected: f64) {
448 let res = pow(base, exponent);
449 assert!(
450 if expected.is_nan() {
451 res.is_nan()
452 } else {
453 pow(base, exponent) == expected
454 },
455 "{} ** {} was {} instead of {}",
456 base,
457 exponent,
458 res,
459 expected
460 );
461 }
462
463 fn test_sets_as_base(sets: &[&[f64]], exponent: f64, expected: f64) {
464 sets.iter()
465 .for_each(|s| s.iter().for_each(|val| pow_test(*val, exponent, expected)));
466 }
467
468 fn test_sets_as_exponent(base: f64, sets: &[&[f64]], expected: f64) {
469 sets.iter()
470 .for_each(|s| s.iter().for_each(|val| pow_test(base, *val, expected)));
471 }
472
473 fn test_sets(sets: &[&[f64]], computed: &dyn Fn(f64) -> f64, expected: &dyn Fn(f64) -> f64) {
474 sets.iter().for_each(|s| {
475 s.iter().for_each(|val| {
476 let exp = expected(*val);
477 let res = computed(*val);
478
479 #[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
480 let exp = force_eval!(exp);
481 #[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
482 let res = force_eval!(res);
483 assert!(
484 if exp.is_nan() {
485 res.is_nan()
486 } else {
487 exp == res
488 },
489 "test for {} was {} instead of {}",
490 val,
491 res,
492 exp
493 );
494 })
495 });
496 }
497
498 #[test]
499 fn zero_as_exponent() {
500 test_sets_as_base(ALL, 0.0, 1.0);
501 test_sets_as_base(ALL, -0.0, 1.0);
502 }
503
504 #[test]
505 fn one_as_base() {
506 test_sets_as_exponent(1.0, ALL, 1.0);
507 }
508
509 #[test]
510 fn nan_inputs() {
511 // NAN as the base:
512 // (f64::NAN ^ anything *but 0* should be f64::NAN)
513 test_sets_as_exponent(f64::NAN, &ALL[2..], f64::NAN);
514
515 // f64::NAN as the exponent:
516 // (anything *but 1* ^ f64::NAN should be f64::NAN)
517 test_sets_as_base(&ALL[..(ALL.len() - 2)], f64::NAN, f64::NAN);
518 }
519
520 #[test]
521 fn infinity_as_base() {
522 // Positive Infinity as the base:
523 // (+Infinity ^ positive anything but 0 and f64::NAN should be +Infinity)
524 test_sets_as_exponent(f64::INFINITY, &POS[1..], f64::INFINITY);
525
526 // (+Infinity ^ negative anything except 0 and f64::NAN should be 0.0)
527 test_sets_as_exponent(f64::INFINITY, &NEG[1..], 0.0);
528
529 // Negative Infinity as the base:
530 // (-Infinity ^ positive odd ints should be -Infinity)
531 test_sets_as_exponent(f64::NEG_INFINITY, &[POS_ODDS], f64::NEG_INFINITY);
532
533 // (-Infinity ^ anything but odd ints should be == -0 ^ (-anything))
534 // We can lump in pos/neg odd ints here because they don't seem to
535 // cause panics (div by zero) in release mode (I think).
536 test_sets(ALL, &|v: f64| pow(f64::NEG_INFINITY, v), &|v: f64| {
537 pow(-0.0, -v)
538 });
539 }
540
541 #[test]
542 fn infinity_as_exponent() {
543 // Positive/Negative base greater than 1:
544 // (pos/neg > 1 ^ Infinity should be Infinity - note this excludes f64::NAN as the base)
545 test_sets_as_base(&ALL[5..(ALL.len() - 2)], f64::INFINITY, f64::INFINITY);
546
547 // (pos/neg > 1 ^ -Infinity should be 0.0)
548 test_sets_as_base(&ALL[5..ALL.len() - 2], f64::NEG_INFINITY, 0.0);
549
550 // Positive/Negative base less than 1:
551 let base_below_one = &[POS_ZERO, NEG_ZERO, NEG_SMALL_FLOATS, POS_SMALL_FLOATS];
552
553 // (pos/neg < 1 ^ Infinity should be 0.0 - this also excludes f64::NAN as the base)
554 test_sets_as_base(base_below_one, f64::INFINITY, 0.0);
555
556 // (pos/neg < 1 ^ -Infinity should be Infinity)
557 test_sets_as_base(base_below_one, f64::NEG_INFINITY, f64::INFINITY);
558
559 // Positive/Negative 1 as the base:
560 // (pos/neg 1 ^ Infinity should be 1)
561 test_sets_as_base(&[NEG_ONE, POS_ONE], f64::INFINITY, 1.0);
562
563 // (pos/neg 1 ^ -Infinity should be 1)
564 test_sets_as_base(&[NEG_ONE, POS_ONE], f64::NEG_INFINITY, 1.0);
565 }
566
567 #[test]
568 fn zero_as_base() {
569 // Positive Zero as the base:
570 // (+0 ^ anything positive but 0 and f64::NAN should be +0)
571 test_sets_as_exponent(0.0, &POS[1..], 0.0);
572
573 // (+0 ^ anything negative but 0 and f64::NAN should be Infinity)
574 // (this should panic because we're dividing by zero)
575 test_sets_as_exponent(0.0, &NEG[1..], f64::INFINITY);
576
577 // Negative Zero as the base:
578 // (-0 ^ anything positive but 0, f64::NAN, and odd ints should be +0)
579 test_sets_as_exponent(-0.0, &POS[3..], 0.0);
580
581 // (-0 ^ anything negative but 0, f64::NAN, and odd ints should be Infinity)
582 // (should panic because of divide by zero)
583 test_sets_as_exponent(-0.0, &NEG[3..], f64::INFINITY);
584
585 // (-0 ^ positive odd ints should be -0)
586 test_sets_as_exponent(-0.0, &[POS_ODDS], -0.0);
587
588 // (-0 ^ negative odd ints should be -Infinity)
589 // (should panic because of divide by zero)
590 test_sets_as_exponent(-0.0, &[NEG_ODDS], f64::NEG_INFINITY);
591 }
592
593 #[test]
594 fn special_cases() {
595 // One as the exponent:
596 // (anything ^ 1 should be anything - i.e. the base)
597 test_sets(ALL, &|v: f64| pow(v, 1.0), &|v: f64| v);
598
599 // Negative One as the exponent:
600 // (anything ^ -1 should be 1/anything)
601 test_sets(ALL, &|v: f64| pow(v, -1.0), &|v: f64| 1.0 / v);
602
603 // Factoring -1 out:
604 // (negative anything ^ integer should be (-1 ^ integer) * (positive anything ^ integer))
605 [POS_ZERO, NEG_ZERO, POS_ONE, NEG_ONE, POS_EVENS, NEG_EVENS]
606 .iter()
607 .for_each(|int_set| {
608 int_set.iter().for_each(|int| {
609 test_sets(ALL, &|v: f64| pow(-v, *int), &|v: f64| {
610 pow(-1.0, *int) * pow(v, *int)
611 });
612 })
613 });
614
615 // Negative base (imaginary results):
616 // (-anything except 0 and Infinity ^ non-integer should be NAN)
617 NEG[1..(NEG.len() - 1)].iter().for_each(|set| {
618 set.iter().for_each(|val| {
619 test_sets(&ALL[3..7], &|v: f64| pow(*val, v), &|_| f64::NAN);
620 })
621 });
622 }
623
624 #[test]
625 fn normal_cases() {
626 assert_eq!(pow(2.0, 20.0), (1 << 20) as f64);
627 assert_eq!(pow(-1.0, 9.0), -1.0);
628 assert!(pow(-1.0, 2.2).is_nan());
629 assert!(pow(-1.0, -1.14).is_nan());
630 }
631}
632