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8faf50e0 XL |
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 | ||
48663c56 | 92 | #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
8faf50e0 XL |
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 | |
48663c56 | 264 | log(x) by x-x^2/2+x^3/3-x^4/4 */ |
8faf50e0 XL |
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) */ | |
f9f354fc XL |
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)); | |
8faf50e0 XL |
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 | ); | |
f9f354fc | 312 | let t_l: f64 = ax - (t_h - i!(BP, k as usize)); |
8faf50e0 XL |
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) */ | |
f9f354fc | 331 | let z_l: f64 = CP_L * p_h + p_l * CP + i!(DP_L, k as usize); |
8faf50e0 XL |
332 | |
333 | /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ | |
334 | let t: f64 = n as f64; | |
f9f354fc XL |
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); | |
8faf50e0 XL |
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 | ||
48663c56 XL |
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 | ||
60c5eb7d | 481 | fn test_sets(sets: &[&[f64]], computed: &dyn Fn(f64) -> f64, expected: &dyn Fn(f64) -> f64) { |
48663c56 XL |
482 | sets.iter().for_each(|s| { |
483 | s.iter().for_each(|val| { | |
484 | let exp = expected(*val); | |
485 | let res = computed(*val); | |
486 | ||
487 | assert!( | |
488 | if exp.is_nan() { | |
489 | res.is_nan() | |
490 | } else { | |
491 | exp == res | |
492 | }, | |
493 | "test for {} was {} instead of {}", | |
494 | val, | |
495 | res, | |
496 | exp | |
497 | ); | |
498 | }) | |
499 | }); | |
500 | } | |
501 | ||
502 | #[test] | |
503 | fn zero_as_exponent() { | |
504 | test_sets_as_base(ALL, 0.0, 1.0); | |
505 | test_sets_as_base(ALL, -0.0, 1.0); | |
506 | } | |
507 | ||
508 | #[test] | |
509 | fn one_as_base() { | |
510 | test_sets_as_exponent(1.0, ALL, 1.0); | |
511 | } | |
512 | ||
513 | #[test] | |
514 | fn nan_inputs() { | |
515 | // NAN as the base: | |
516 | // (NAN ^ anything *but 0* should be NAN) | |
517 | test_sets_as_exponent(NAN, &ALL[2..], NAN); | |
518 | ||
519 | // NAN as the exponent: | |
520 | // (anything *but 1* ^ NAN should be NAN) | |
521 | test_sets_as_base(&ALL[..(ALL.len() - 2)], NAN, NAN); | |
522 | } | |
523 | ||
524 | #[test] | |
525 | fn infinity_as_base() { | |
526 | // Positive Infinity as the base: | |
527 | // (+Infinity ^ positive anything but 0 and NAN should be +Infinity) | |
528 | test_sets_as_exponent(INFINITY, &POS[1..], INFINITY); | |
529 | ||
530 | // (+Infinity ^ negative anything except 0 and NAN should be 0.0) | |
531 | test_sets_as_exponent(INFINITY, &NEG[1..], 0.0); | |
532 | ||
533 | // Negative Infinity as the base: | |
534 | // (-Infinity ^ positive odd ints should be -Infinity) | |
535 | test_sets_as_exponent(NEG_INFINITY, &[POS_ODDS], NEG_INFINITY); | |
536 | ||
537 | // (-Infinity ^ anything but odd ints should be == -0 ^ (-anything)) | |
538 | // We can lump in pos/neg odd ints here because they don't seem to | |
539 | // cause panics (div by zero) in release mode (I think). | |
540 | test_sets(ALL, &|v: f64| pow(NEG_INFINITY, v), &|v: f64| pow(-0.0, -v)); | |
541 | } | |
542 | ||
543 | #[test] | |
544 | fn infinity_as_exponent() { | |
545 | // Positive/Negative base greater than 1: | |
546 | // (pos/neg > 1 ^ Infinity should be Infinity - note this excludes NAN as the base) | |
547 | test_sets_as_base(&ALL[5..(ALL.len() - 2)], INFINITY, INFINITY); | |
548 | ||
549 | // (pos/neg > 1 ^ -Infinity should be 0.0) | |
550 | test_sets_as_base(&ALL[5..ALL.len() - 2], NEG_INFINITY, 0.0); | |
551 | ||
552 | // Positive/Negative base less than 1: | |
553 | let base_below_one = &[POS_ZERO, NEG_ZERO, NEG_SMALL_FLOATS, POS_SMALL_FLOATS]; | |
554 | ||
555 | // (pos/neg < 1 ^ Infinity should be 0.0 - this also excludes NAN as the base) | |
556 | test_sets_as_base(base_below_one, INFINITY, 0.0); | |
557 | ||
558 | // (pos/neg < 1 ^ -Infinity should be Infinity) | |
559 | test_sets_as_base(base_below_one, NEG_INFINITY, INFINITY); | |
560 | ||
561 | // Positive/Negative 1 as the base: | |
562 | // (pos/neg 1 ^ Infinity should be 1) | |
563 | test_sets_as_base(&[NEG_ONE, POS_ONE], INFINITY, 1.0); | |
564 | ||
565 | // (pos/neg 1 ^ -Infinity should be 1) | |
566 | test_sets_as_base(&[NEG_ONE, POS_ONE], NEG_INFINITY, 1.0); | |
567 | } | |
568 | ||
569 | #[test] | |
570 | fn zero_as_base() { | |
571 | // Positive Zero as the base: | |
572 | // (+0 ^ anything positive but 0 and NAN should be +0) | |
573 | test_sets_as_exponent(0.0, &POS[1..], 0.0); | |
574 | ||
575 | // (+0 ^ anything negative but 0 and NAN should be Infinity) | |
576 | // (this should panic because we're dividing by zero) | |
577 | test_sets_as_exponent(0.0, &NEG[1..], INFINITY); | |
578 | ||
579 | // Negative Zero as the base: | |
580 | // (-0 ^ anything positive but 0, NAN, and odd ints should be +0) | |
581 | test_sets_as_exponent(-0.0, &POS[3..], 0.0); | |
582 | ||
583 | // (-0 ^ anything negative but 0, NAN, and odd ints should be Infinity) | |
584 | // (should panic because of divide by zero) | |
585 | test_sets_as_exponent(-0.0, &NEG[3..], INFINITY); | |
586 | ||
587 | // (-0 ^ positive odd ints should be -0) | |
588 | test_sets_as_exponent(-0.0, &[POS_ODDS], -0.0); | |
589 | ||
590 | // (-0 ^ negative odd ints should be -Infinity) | |
591 | // (should panic because of divide by zero) | |
592 | test_sets_as_exponent(-0.0, &[NEG_ODDS], NEG_INFINITY); | |
593 | } | |
594 | ||
595 | #[test] | |
596 | fn special_cases() { | |
597 | // One as the exponent: | |
598 | // (anything ^ 1 should be anything - i.e. the base) | |
599 | test_sets(ALL, &|v: f64| pow(v, 1.0), &|v: f64| v); | |
600 | ||
601 | // Negative One as the exponent: | |
602 | // (anything ^ -1 should be 1/anything) | |
603 | test_sets(ALL, &|v: f64| pow(v, -1.0), &|v: f64| 1.0 / v); | |
604 | ||
605 | // Factoring -1 out: | |
606 | // (negative anything ^ integer should be (-1 ^ integer) * (positive anything ^ integer)) | |
136023e0 | 607 | (&[POS_ZERO, NEG_ZERO, POS_ONE, NEG_ONE, POS_EVENS, NEG_EVENS]) |
48663c56 XL |
608 | .iter() |
609 | .for_each(|int_set| { | |
610 | int_set.iter().for_each(|int| { | |
611 | test_sets(ALL, &|v: f64| pow(-v, *int), &|v: f64| { | |
612 | pow(-1.0, *int) * pow(v, *int) | |
613 | }); | |
614 | }) | |
615 | }); | |
616 | ||
617 | // Negative base (imaginary results): | |
618 | // (-anything except 0 and Infinity ^ non-integer should be NAN) | |
136023e0 | 619 | (&NEG[1..(NEG.len() - 1)]).iter().for_each(|set| { |
48663c56 XL |
620 | set.iter().for_each(|val| { |
621 | test_sets(&ALL[3..7], &|v: f64| pow(*val, v), &|_| NAN); | |
622 | }) | |
623 | }); | |
624 | } | |
625 | ||
626 | #[test] | |
627 | fn normal_cases() { | |
628 | assert_eq!(pow(2.0, 20.0), (1 << 20) as f64); | |
629 | assert_eq!(pow(-1.0, 9.0), -1.0); | |
630 | assert!(pow(-1.0, 2.2).is_nan()); | |
631 | assert!(pow(-1.0, -1.14).is_nan()); | |
632 | } | |
8faf50e0 | 633 | } |