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 | // |
60 | use super::{fabs, get_high_word, scalbn, sqrt, with_set_high_word, with_set_low_word}; |
61 | |
62 | const BP: [f64; 2] = [1.0, 1.5]; |
63 | const DP_H: [f64; 2] = [0.0, 5.84962487220764160156e-01]; /* 0x3fe2b803_40000000 */ |
64 | const DP_L: [f64; 2] = [0.0, 1.35003920212974897128e-08]; /* 0x3E4CFDEB, 0x43CFD006 */ |
65 | const TWO53: f64 = 9007199254740992.0; /* 0x43400000_00000000 */ |
66 | const HUGE: f64 = 1.0e300; |
67 | const TINY: f64 = 1.0e-300; |
68 | |
69 | // poly coefs for (3/2)*(log(x)-2s-2/3*s**3: |
70 | const L1: f64 = 5.99999999999994648725e-01; /* 0x3fe33333_33333303 */ |
71 | const L2: f64 = 4.28571428578550184252e-01; /* 0x3fdb6db6_db6fabff */ |
72 | const L3: f64 = 3.33333329818377432918e-01; /* 0x3fd55555_518f264d */ |
73 | const L4: f64 = 2.72728123808534006489e-01; /* 0x3fd17460_a91d4101 */ |
74 | const L5: f64 = 2.30660745775561754067e-01; /* 0x3fcd864a_93c9db65 */ |
75 | const L6: f64 = 2.06975017800338417784e-01; /* 0x3fca7e28_4a454eef */ |
76 | const P1: f64 = 1.66666666666666019037e-01; /* 0x3fc55555_5555553e */ |
77 | const P2: f64 = -2.77777777770155933842e-03; /* 0xbf66c16c_16bebd93 */ |
78 | const P3: f64 = 6.61375632143793436117e-05; /* 0x3f11566a_af25de2c */ |
79 | const P4: f64 = -1.65339022054652515390e-06; /* 0xbebbbd41_c5d26bf1 */ |
80 | const P5: f64 = 4.13813679705723846039e-08; /* 0x3e663769_72bea4d0 */ |
81 | const LG2: f64 = 6.93147180559945286227e-01; /* 0x3fe62e42_fefa39ef */ |
82 | const LG2_H: f64 = 6.93147182464599609375e-01; /* 0x3fe62e43_00000000 */ |
83 | const LG2_L: f64 = -1.90465429995776804525e-09; /* 0xbe205c61_0ca86c39 */ |
84 | const OVT: f64 = 8.0085662595372944372e-017; /* -(1024-log2(ovfl+.5ulp)) */ |
85 | const CP: f64 = 9.61796693925975554329e-01; /* 0x3feec709_dc3a03fd =2/(3ln2) */ |
86 | const CP_H: f64 = 9.61796700954437255859e-01; /* 0x3feec709_e0000000 =(float)cp */ |
87 | const CP_L: f64 = -7.02846165095275826516e-09; /* 0xbe3e2fe0_145b01f5 =tail of cp_h*/ |
88 | const IVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547_652b82fe =1/ln2 */ |
89 | const IVLN2_H: f64 = 1.44269502162933349609e+00; /* 0x3ff71547_60000000 =24b 1/ln2*/ |
90 | const IVLN2_L: f64 = 1.92596299112661746887e-08; /* 0x3e54ae0b_f85ddf44 =1/ln2 tail*/ |
91 | |
92 | #[cfg_attr (all(test, assert_no_panic), no_panic::no_panic)] |
93 | pub 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)] |
412 | mod 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 | |