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 muti-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#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
93pub fn pow(x: f64, y: f64) -> f64 {
94 let t1: f64;
95 let t2: f64;
96
97 let (hx, lx): (i32, u32) = ((x.to_bits() >> 32) as i32, x.to_bits() as u32);
98 let (hy, ly): (i32, u32) = ((y.to_bits() >> 32) as i32, y.to_bits() as u32);
99
100 let mut ix: i32 = (hx & 0x7fffffff) as i32;
101 let iy: i32 = (hy & 0x7fffffff) as i32;
102
103 /* x**0 = 1, even if x is NaN */
104 if ((iy as u32) | ly) == 0 {
105 return 1.0;
106 }
107
108 /* 1**y = 1, even if y is NaN */
109 if hx == 0x3ff00000 && lx == 0 {
110 return 1.0;
111 }
112
113 /* NaN if either arg is NaN */
114 if ix > 0x7ff00000
115 || (ix == 0x7ff00000 && lx != 0)
116 || iy > 0x7ff00000
117 || (iy == 0x7ff00000 && ly != 0)
118 {
119 return x + y;
120 }
121
122 /* determine if y is an odd int when x < 0
123 * yisint = 0 ... y is not an integer
124 * yisint = 1 ... y is an odd int
125 * yisint = 2 ... y is an even int
126 */
127 let mut yisint: i32 = 0;
128 let mut k: i32;
129 let mut j: i32;
130 if hx < 0 {
131 if iy >= 0x43400000 {
132 yisint = 2; /* even integer y */
133 } else if iy >= 0x3ff00000 {
134 k = (iy >> 20) - 0x3ff; /* exponent */
135
136 if k > 20 {
137 j = (ly >> (52 - k)) as i32;
138
139 if (j << (52 - k)) == (ly as i32) {
140 yisint = 2 - (j & 1);
141 }
142 } else if ly == 0 {
143 j = iy >> (20 - k);
144
145 if (j << (20 - k)) == iy {
146 yisint = 2 - (j & 1);
147 }
148 }
149 }
150 }
151
152 if ly == 0 {
153 /* special value of y */
154 if iy == 0x7ff00000 {
155 /* y is +-inf */
156
157 return if ((ix - 0x3ff00000) | (lx as i32)) == 0 {
158 /* (-1)**+-inf is 1 */
159 1.0
160 } else if ix >= 0x3ff00000 {
161 /* (|x|>1)**+-inf = inf,0 */
162 if hy >= 0 {
163 y
164 } else {
165 0.0
166 }
167 } else {
168 /* (|x|<1)**+-inf = 0,inf */
169 if hy >= 0 {
170 0.0
171 } else {
172 -y
173 }
174 };
175 }
176
177 if iy == 0x3ff00000 {
178 /* y is +-1 */
179 return if hy >= 0 { x } else { 1.0 / x };
180 }
181
182 if hy == 0x40000000 {
183 /* y is 2 */
184 return x * x;
185 }
186
187 if hy == 0x3fe00000 {
188 /* y is 0.5 */
189 if hx >= 0 {
190 /* x >= +0 */
191 return sqrt(x);
192 }
193 }
194 }
195
196 let mut ax: f64 = fabs(x);
197 if lx == 0 {
198 /* special value of x */
199 if ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000 {
200 /* x is +-0,+-inf,+-1 */
201 let mut z: f64 = ax;
202
203 if hy < 0 {
204 /* z = (1/|x|) */
205 z = 1.0 / z;
206 }
207
208 if hx < 0 {
209 if ((ix - 0x3ff00000) | yisint) == 0 {
210 z = (z - z) / (z - z); /* (-1)**non-int is NaN */
211 } else if yisint == 1 {
212 z = -z; /* (x<0)**odd = -(|x|**odd) */
213 }
214 }
215
216 return z;
217 }
218 }
219
220 let mut s: f64 = 1.0; /* sign of result */
221 if hx < 0 {
222 if yisint == 0 {
223 /* (x<0)**(non-int) is NaN */
224 return (x - x) / (x - x);
225 }
226
227 if yisint == 1 {
228 /* (x<0)**(odd int) */
229 s = -1.0;
230 }
231 }
232
233 /* |y| is HUGE */
234 if iy > 0x41e00000 {
235 /* if |y| > 2**31 */
236 if iy > 0x43f00000 {
237 /* if |y| > 2**64, must o/uflow */
238 if ix <= 0x3fefffff {
239 return if hy < 0 { HUGE * HUGE } else { TINY * TINY };
240 }
241
242 if ix >= 0x3ff00000 {
243 return if hy > 0 { HUGE * HUGE } else { TINY * TINY };
244 }
245 }
246
247 /* over/underflow if x is not close to one */
248 if ix < 0x3fefffff {
249 return if hy < 0 {
250 s * HUGE * HUGE
251 } else {
252 s * TINY * TINY
253 };
254 }
255 if ix > 0x3ff00000 {
256 return if hy > 0 {
257 s * HUGE * HUGE
258 } else {
259 s * TINY * TINY
260 };
261 }
262
263 /* now |1-x| is TINY <= 2**-20, suffice to compute
264 log(x) by x-x^2/2+x^3/3-x^4/4 */
265 let t: f64 = ax - 1.0; /* t has 20 trailing zeros */
266 let w: f64 = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
267 let u: f64 = IVLN2_H * t; /* ivln2_h has 21 sig. bits */
268 let v: f64 = t * IVLN2_L - w * IVLN2;
269 t1 = with_set_low_word(u + v, 0);
270 t2 = v - (t1 - u);
271 } else {
272 // double ss,s2,s_h,s_l,t_h,t_l;
273 let mut n: i32 = 0;
274
275 if ix < 0x00100000 {
276 /* take care subnormal number */
277 ax *= TWO53;
278 n -= 53;
279 ix = get_high_word(ax) as i32;
280 }
281
282 n += (ix >> 20) - 0x3ff;
283 j = ix & 0x000fffff;
284
285 /* determine interval */
286 let k: i32;
287 ix = j | 0x3ff00000; /* normalize ix */
288 if j <= 0x3988E {
289 /* |x|<sqrt(3/2) */
290 k = 0;
291 } else if j < 0xBB67A {
292 /* |x|<sqrt(3) */
293 k = 1;
294 } else {
295 k = 0;
296 n += 1;
297 ix -= 0x00100000;
298 }
299 ax = with_set_high_word(ax, ix as u32);
300
301 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
302 let u: f64 = ax - i!(BP, k as usize); /* bp[0]=1.0, bp[1]=1.5 */
303 let v: f64 = 1.0 / (ax + i!(BP, k as usize));
304 let ss: f64 = u * v;
305 let s_h = with_set_low_word(ss, 0);
306
307 /* t_h=ax+bp[k] High */
308 let t_h: f64 = with_set_high_word(
309 0.0,
310 ((ix as u32 >> 1) | 0x20000000) + 0x00080000 + ((k as u32) << 18),
311 );
312 let t_l: f64 = ax - (t_h - i!(BP, k as usize));
313 let s_l: f64 = v * ((u - s_h * t_h) - s_h * t_l);
314
315 /* compute log(ax) */
316 let s2: f64 = ss * ss;
317 let mut r: f64 = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
318 r += s_l * (s_h + ss);
319 let s2: f64 = s_h * s_h;
320 let t_h: f64 = with_set_low_word(3.0 + s2 + r, 0);
321 let t_l: f64 = r - ((t_h - 3.0) - s2);
322
323 /* u+v = ss*(1+...) */
324 let u: f64 = s_h * t_h;
325 let v: f64 = s_l * t_h + t_l * ss;
326
327 /* 2/(3log2)*(ss+...) */
328 let p_h: f64 = with_set_low_word(u + v, 0);
329 let p_l = v - (p_h - u);
330 let z_h: f64 = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */
331 let z_l: f64 = CP_L * p_h + p_l * CP + i!(DP_L, k as usize);
332
333 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
334 let t: f64 = n as f64;
335 t1 = with_set_low_word(((z_h + z_l) + i!(DP_H, k as usize)) + t, 0);
336 t2 = z_l - (((t1 - t) - i!(DP_H, k as usize)) - z_h);
337 }
338
339 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
340 let y1: f64 = with_set_low_word(y, 0);
341 let p_l: f64 = (y - y1) * t1 + y * t2;
342 let mut p_h: f64 = y1 * t1;
343 let z: f64 = p_l + p_h;
344 let mut j: i32 = (z.to_bits() >> 32) as i32;
345 let i: i32 = z.to_bits() as i32;
346 // let (j, i): (i32, i32) = ((z.to_bits() >> 32) as i32, z.to_bits() as i32);
347
348 if j >= 0x40900000 {
349 /* z >= 1024 */
350 if (j - 0x40900000) | i != 0 {
351 /* if z > 1024 */
352 return s * HUGE * HUGE; /* overflow */
353 }
354
355 if p_l + OVT > z - p_h {
356 return s * HUGE * HUGE; /* overflow */
357 }
358 } else if (j & 0x7fffffff) >= 0x4090cc00 {
359 /* z <= -1075 */
360 // FIXME: instead of abs(j) use unsigned j
361
362 if (((j as u32) - 0xc090cc00) | (i as u32)) != 0 {
363 /* z < -1075 */
364 return s * TINY * TINY; /* underflow */
365 }
366
367 if p_l <= z - p_h {
368 return s * TINY * TINY; /* underflow */
369 }
370 }
371
372 /* compute 2**(p_h+p_l) */
373 let i: i32 = j & (0x7fffffff as i32);
374 k = (i >> 20) - 0x3ff;
375 let mut n: i32 = 0;
376
377 if i > 0x3fe00000 {
378 /* if |z| > 0.5, set n = [z+0.5] */
379 n = j + (0x00100000 >> (k + 1));
380 k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
381 let t: f64 = with_set_high_word(0.0, (n & !(0x000fffff >> k)) as u32);
382 n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
383 if j < 0 {
384 n = -n;
385 }
386 p_h -= t;
387 }
388
389 let t: f64 = with_set_low_word(p_l + p_h, 0);
390 let u: f64 = t * LG2_H;
391 let v: f64 = (p_l - (t - p_h)) * LG2 + t * LG2_L;
392 let mut z: f64 = u + v;
393 let w: f64 = v - (z - u);
394 let t: f64 = z * z;
395 let t1: f64 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
396 let r: f64 = (z * t1) / (t1 - 2.0) - (w + z * w);
397 z = 1.0 - (r - z);
398 j = get_high_word(z) as i32;
399 j += n << 20;
400
401 if (j >> 20) <= 0 {
402 /* subnormal output */
403 z = scalbn(z, n);
404 } else {
405 z = with_set_high_word(z, j as u32);
406 }
407
408 s * z
409}
410
411#[cfg(test)]
412mod tests {
413 extern crate core;
414
415 use self::core::f64::consts::{E, PI};
416 use self::core::f64::{EPSILON, INFINITY, MAX, MIN, MIN_POSITIVE, NAN, NEG_INFINITY};
417 use super::pow;
418
419 const POS_ZERO: &[f64] = &[0.0];
420 const NEG_ZERO: &[f64] = &[-0.0];
421 const POS_ONE: &[f64] = &[1.0];
422 const NEG_ONE: &[f64] = &[-1.0];
423 const POS_FLOATS: &[f64] = &[99.0 / 70.0, E, PI];
424 const NEG_FLOATS: &[f64] = &[-99.0 / 70.0, -E, -PI];
425 const POS_SMALL_FLOATS: &[f64] = &[(1.0 / 2.0), MIN_POSITIVE, EPSILON];
426 const NEG_SMALL_FLOATS: &[f64] = &[-(1.0 / 2.0), -MIN_POSITIVE, -EPSILON];
427 const POS_EVENS: &[f64] = &[2.0, 6.0, 8.0, 10.0, 22.0, 100.0, MAX];
428 const NEG_EVENS: &[f64] = &[MIN, -100.0, -22.0, -10.0, -8.0, -6.0, -2.0];
429 const POS_ODDS: &[f64] = &[3.0, 7.0];
430 const NEG_ODDS: &[f64] = &[-7.0, -3.0];
431 const NANS: &[f64] = &[NAN];
432 const POS_INF: &[f64] = &[INFINITY];
433 const NEG_INF: &[f64] = &[NEG_INFINITY];
434
435 const ALL: &[&[f64]] = &[
436 POS_ZERO,
437 NEG_ZERO,
438 NANS,
439 NEG_SMALL_FLOATS,
440 POS_SMALL_FLOATS,
441 NEG_FLOATS,
442 POS_FLOATS,
443 NEG_EVENS,
444 POS_EVENS,
445 NEG_ODDS,
446 POS_ODDS,
447 NEG_INF,
448 POS_INF,
449 NEG_ONE,
450 POS_ONE,
451 ];
452 const POS: &[&[f64]] = &[POS_ZERO, POS_ODDS, POS_ONE, POS_FLOATS, POS_EVENS, POS_INF];
453 const NEG: &[&[f64]] = &[NEG_ZERO, NEG_ODDS, NEG_ONE, NEG_FLOATS, NEG_EVENS, NEG_INF];
454
455 fn pow_test(base: f64, exponent: f64, expected: f64) {
456 let res = pow(base, exponent);
457 assert!(
458 if expected.is_nan() {
459 res.is_nan()
460 } else {
461 pow(base, exponent) == expected
462 },
463 "{} ** {} was {} instead of {}",
464 base,
465 exponent,
466 res,
467 expected
468 );
469 }
470
471 fn test_sets_as_base(sets: &[&[f64]], exponent: f64, expected: f64) {
472 sets.iter()
473 .for_each(|s| s.iter().for_each(|val| pow_test(*val, exponent, expected)));
474 }
475
476 fn test_sets_as_exponent(base: f64, sets: &[&[f64]], expected: f64) {
477 sets.iter()
478 .for_each(|s| s.iter().for_each(|val| pow_test(base, *val, expected)));
479 }
480
481 fn test_sets(sets: &[&[f64]], computed: &dyn Fn(f64) -> f64, expected: &dyn Fn(f64) -> f64) {
482 sets.iter().for_each(|s| {
483 s.iter().for_each(|val| {
484 let exp = expected(*val);
485 let res = computed(*val);
486
487 #[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
488 let exp = force_eval!(exp);
489 #[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
490 let res = force_eval!(res);
491 assert!(
492 if exp.is_nan() {
493 res.is_nan()
494 } else {
495 exp == res
496 },
497 "test for {} was {} instead of {}",
498 val,
499 res,
500 exp
501 );
502 })
503 });
504 }
505
506 #[test]
507 fn zero_as_exponent() {
508 test_sets_as_base(ALL, 0.0, 1.0);
509 test_sets_as_base(ALL, -0.0, 1.0);
510 }
511
512 #[test]
513 fn one_as_base() {
514 test_sets_as_exponent(1.0, ALL, 1.0);
515 }
516
517 #[test]
518 fn nan_inputs() {
519 // NAN as the base:
520 // (NAN ^ anything *but 0* should be NAN)
521 test_sets_as_exponent(NAN, &ALL[2..], NAN);
522
523 // NAN as the exponent:
524 // (anything *but 1* ^ NAN should be NAN)
525 test_sets_as_base(&ALL[..(ALL.len() - 2)], NAN, NAN);
526 }
527
528 #[test]
529 fn infinity_as_base() {
530 // Positive Infinity as the base:
531 // (+Infinity ^ positive anything but 0 and NAN should be +Infinity)
532 test_sets_as_exponent(INFINITY, &POS[1..], INFINITY);
533
534 // (+Infinity ^ negative anything except 0 and NAN should be 0.0)
535 test_sets_as_exponent(INFINITY, &NEG[1..], 0.0);
536
537 // Negative Infinity as the base:
538 // (-Infinity ^ positive odd ints should be -Infinity)
539 test_sets_as_exponent(NEG_INFINITY, &[POS_ODDS], NEG_INFINITY);
540
541 // (-Infinity ^ anything but odd ints should be == -0 ^ (-anything))
542 // We can lump in pos/neg odd ints here because they don't seem to
543 // cause panics (div by zero) in release mode (I think).
544 test_sets(ALL, &|v: f64| pow(NEG_INFINITY, v), &|v: f64| pow(-0.0, -v));
545 }
546
547 #[test]
548 fn infinity_as_exponent() {
549 // Positive/Negative base greater than 1:
550 // (pos/neg > 1 ^ Infinity should be Infinity - note this excludes NAN as the base)
551 test_sets_as_base(&ALL[5..(ALL.len() - 2)], INFINITY, INFINITY);
552
553 // (pos/neg > 1 ^ -Infinity should be 0.0)
554 test_sets_as_base(&ALL[5..ALL.len() - 2], NEG_INFINITY, 0.0);
555
556 // Positive/Negative base less than 1:
557 let base_below_one = &[POS_ZERO, NEG_ZERO, NEG_SMALL_FLOATS, POS_SMALL_FLOATS];
558
559 // (pos/neg < 1 ^ Infinity should be 0.0 - this also excludes NAN as the base)
560 test_sets_as_base(base_below_one, INFINITY, 0.0);
561
562 // (pos/neg < 1 ^ -Infinity should be Infinity)
563 test_sets_as_base(base_below_one, NEG_INFINITY, INFINITY);
564
565 // Positive/Negative 1 as the base:
566 // (pos/neg 1 ^ Infinity should be 1)
567 test_sets_as_base(&[NEG_ONE, POS_ONE], INFINITY, 1.0);
568
569 // (pos/neg 1 ^ -Infinity should be 1)
570 test_sets_as_base(&[NEG_ONE, POS_ONE], NEG_INFINITY, 1.0);
571 }
572
573 #[test]
574 fn zero_as_base() {
575 // Positive Zero as the base:
576 // (+0 ^ anything positive but 0 and NAN should be +0)
577 test_sets_as_exponent(0.0, &POS[1..], 0.0);
578
579 // (+0 ^ anything negative but 0 and NAN should be Infinity)
580 // (this should panic because we're dividing by zero)
581 test_sets_as_exponent(0.0, &NEG[1..], INFINITY);
582
583 // Negative Zero as the base:
584 // (-0 ^ anything positive but 0, NAN, and odd ints should be +0)
585 test_sets_as_exponent(-0.0, &POS[3..], 0.0);
586
587 // (-0 ^ anything negative but 0, NAN, and odd ints should be Infinity)
588 // (should panic because of divide by zero)
589 test_sets_as_exponent(-0.0, &NEG[3..], INFINITY);
590
591 // (-0 ^ positive odd ints should be -0)
592 test_sets_as_exponent(-0.0, &[POS_ODDS], -0.0);
593
594 // (-0 ^ negative odd ints should be -Infinity)
595 // (should panic because of divide by zero)
596 test_sets_as_exponent(-0.0, &[NEG_ODDS], NEG_INFINITY);
597 }
598
599 #[test]
600 fn special_cases() {
601 // One as the exponent:
602 // (anything ^ 1 should be anything - i.e. the base)
603 test_sets(ALL, &|v: f64| pow(v, 1.0), &|v: f64| v);
604
605 // Negative One as the exponent:
606 // (anything ^ -1 should be 1/anything)
607 test_sets(ALL, &|v: f64| pow(v, -1.0), &|v: f64| 1.0 / v);
608
609 // Factoring -1 out:
610 // (negative anything ^ integer should be (-1 ^ integer) * (positive anything ^ integer))
611 (&[POS_ZERO, NEG_ZERO, POS_ONE, NEG_ONE, POS_EVENS, NEG_EVENS])
612 .iter()
613 .for_each(|int_set| {
614 int_set.iter().for_each(|int| {
615 test_sets(ALL, &|v: f64| pow(-v, *int), &|v: f64| {
616 pow(-1.0, *int) * pow(v, *int)
617 });
618 })
619 });
620
621 // Negative base (imaginary results):
622 // (-anything except 0 and Infinity ^ non-integer should be NAN)
623 (&NEG[1..(NEG.len() - 1)]).iter().for_each(|set| {
624 set.iter().for_each(|val| {
625 test_sets(&ALL[3..7], &|v: f64| pow(*val, v), &|_| NAN);
626 })
627 });
628 }
629
630 #[test]
631 fn normal_cases() {
632 assert_eq!(pow(2.0, 20.0), (1 << 20) as f64);
633 assert_eq!(pow(-1.0, 9.0), -1.0);
634 assert!(pow(-1.0, 2.2).is_nan());
635 assert!(pow(-1.0, -1.14).is_nan());
636 }
637}
638