1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
/* origin: FreeBSD /usr/src/lib/msun/src/e_pow.c */
/*
 * ====================================================
 * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
 *
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

// pow(x,y) return x**y
//
//                    n
// Method:  Let x =  2   * (1+f)
//      1. Compute and return log2(x) in two pieces:
//              log2(x) = w1 + w2,
//         where w1 has 53-24 = 29 bit trailing zeros.
//      2. Perform y*log2(x) = n+y' by simulating muti-precision
//         arithmetic, where |y'|<=0.5.
//      3. Return x**y = 2**n*exp(y'*log2)
//
// Special cases:
//      1.  (anything) ** 0  is 1
//      2.  1 ** (anything)  is 1
//      3.  (anything except 1) ** NAN is NAN
//      4.  NAN ** (anything except 0) is NAN
//      5.  +-(|x| > 1) **  +INF is +INF
//      6.  +-(|x| > 1) **  -INF is +0
//      7.  +-(|x| < 1) **  +INF is +0
//      8.  +-(|x| < 1) **  -INF is +INF
//      9.  -1          ** +-INF is 1
//      10. +0 ** (+anything except 0, NAN)               is +0
//      11. -0 ** (+anything except 0, NAN, odd integer)  is +0
//      12. +0 ** (-anything except 0, NAN)               is +INF, raise divbyzero
//      13. -0 ** (-anything except 0, NAN, odd integer)  is +INF, raise divbyzero
//      14. -0 ** (+odd integer) is -0
//      15. -0 ** (-odd integer) is -INF, raise divbyzero
//      16. +INF ** (+anything except 0,NAN) is +INF
//      17. +INF ** (-anything except 0,NAN) is +0
//      18. -INF ** (+odd integer) is -INF
//      19. -INF ** (anything) = -0 ** (-anything), (anything except odd integer)
//      20. (anything) ** 1 is (anything)
//      21. (anything) ** -1 is 1/(anything)
//      22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
//      23. (-anything except 0 and inf) ** (non-integer) is NAN
//
// Accuracy:
//      pow(x,y) returns x**y nearly rounded. In particular
//                      pow(integer,integer)
//      always returns the correct integer provided it is
//      representable.
//
// Constants :
// The hexadecimal values are the intended ones for the following
// constants. The decimal values may be used, provided that the
// compiler will convert from decimal to binary accurately enough
// to produce the hexadecimal values shown.
//
use super::{fabs, get_high_word, scalbn, sqrt, with_set_high_word, with_set_low_word};

const BP: [f64; 2] = [1.0, 1.5];
const DP_H: [f64; 2] = [0.0, 5.84962487220764160156e-01]; /* 0x3fe2b803_40000000 */
const DP_L: [f64; 2] = [0.0, 1.35003920212974897128e-08]; /* 0x3E4CFDEB, 0x43CFD006 */
const TWO53: f64 = 9007199254740992.0; /* 0x43400000_00000000 */
const HUGE: f64 = 1.0e300;
const TINY: f64 = 1.0e-300;

// poly coefs for (3/2)*(log(x)-2s-2/3*s**3:
const L1: f64 = 5.99999999999994648725e-01; /* 0x3fe33333_33333303 */
const L2: f64 = 4.28571428578550184252e-01; /* 0x3fdb6db6_db6fabff */
const L3: f64 = 3.33333329818377432918e-01; /* 0x3fd55555_518f264d */
const L4: f64 = 2.72728123808534006489e-01; /* 0x3fd17460_a91d4101 */
const L5: f64 = 2.30660745775561754067e-01; /* 0x3fcd864a_93c9db65 */
const L6: f64 = 2.06975017800338417784e-01; /* 0x3fca7e28_4a454eef */
const P1: f64 = 1.66666666666666019037e-01; /* 0x3fc55555_5555553e */
const P2: f64 = -2.77777777770155933842e-03; /* 0xbf66c16c_16bebd93 */
const P3: f64 = 6.61375632143793436117e-05; /* 0x3f11566a_af25de2c */
const P4: f64 = -1.65339022054652515390e-06; /* 0xbebbbd41_c5d26bf1 */
const P5: f64 = 4.13813679705723846039e-08; /* 0x3e663769_72bea4d0 */
const LG2: f64 = 6.93147180559945286227e-01; /* 0x3fe62e42_fefa39ef */
const LG2_H: f64 = 6.93147182464599609375e-01; /* 0x3fe62e43_00000000 */
const LG2_L: f64 = -1.90465429995776804525e-09; /* 0xbe205c61_0ca86c39 */
const OVT: f64 = 8.0085662595372944372e-017; /* -(1024-log2(ovfl+.5ulp)) */
const CP: f64 = 9.61796693925975554329e-01; /* 0x3feec709_dc3a03fd =2/(3ln2) */
const CP_H: f64 = 9.61796700954437255859e-01; /* 0x3feec709_e0000000 =(float)cp */
const CP_L: f64 = -7.02846165095275826516e-09; /* 0xbe3e2fe0_145b01f5 =tail of cp_h*/
const IVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547_652b82fe =1/ln2 */
const IVLN2_H: f64 = 1.44269502162933349609e+00; /* 0x3ff71547_60000000 =24b 1/ln2*/
const IVLN2_L: f64 = 1.92596299112661746887e-08; /* 0x3e54ae0b_f85ddf44 =1/ln2 tail*/

#[inline]
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub fn pow(x: f64, y: f64) -> f64 {
    let t1: f64;
    let t2: f64;

    let (hx, lx): (i32, u32) = ((x.to_bits() >> 32) as i32, x.to_bits() as u32);
    let (hy, ly): (i32, u32) = ((y.to_bits() >> 32) as i32, y.to_bits() as u32);

    let mut ix: i32 = (hx & 0x7fffffff) as i32;
    let iy: i32 = (hy & 0x7fffffff) as i32;

    /* x**0 = 1, even if x is NaN */
    if ((iy as u32) | ly) == 0 {
        return 1.0;
    }

    /* 1**y = 1, even if y is NaN */
    if hx == 0x3ff00000 && lx == 0 {
        return 1.0;
    }

    /* NaN if either arg is NaN */
    if ix > 0x7ff00000
        || (ix == 0x7ff00000 && lx != 0)
        || iy > 0x7ff00000
        || (iy == 0x7ff00000 && ly != 0)
    {
        return x + y;
    }

    /* determine if y is an odd int when x < 0
     * yisint = 0       ... y is not an integer
     * yisint = 1       ... y is an odd int
     * yisint = 2       ... y is an even int
     */
    let mut yisint: i32 = 0;
    let mut k: i32;
    let mut j: i32;
    if hx < 0 {
        if iy >= 0x43400000 {
            yisint = 2; /* even integer y */
        } else if iy >= 0x3ff00000 {
            k = (iy >> 20) - 0x3ff; /* exponent */

            if k > 20 {
                j = (ly >> (52 - k)) as i32;

                if (j << (52 - k)) == (ly as i32) {
                    yisint = 2 - (j & 1);
                }
            } else if ly == 0 {
                j = iy >> (20 - k);

                if (j << (20 - k)) == iy {
                    yisint = 2 - (j & 1);
                }
            }
        }
    }

    if ly == 0 {
        /* special value of y */
        if iy == 0x7ff00000 {
            /* y is +-inf */

            return if ((ix - 0x3ff00000) | (lx as i32)) == 0 {
                /* (-1)**+-inf is 1 */
                1.0
            } else if ix >= 0x3ff00000 {
                /* (|x|>1)**+-inf = inf,0 */
                if hy >= 0 {
                    y
                } else {
                    0.0
                }
            } else {
                /* (|x|<1)**+-inf = 0,inf */
                if hy >= 0 {
                    0.0
                } else {
                    -y
                }
            };
        }

        if iy == 0x3ff00000 {
            /* y is +-1 */
            return if hy >= 0 { x } else { 1.0 / x };
        }

        if hy == 0x40000000 {
            /* y is 2 */
            return x * x;
        }

        if hy == 0x3fe00000 {
            /* y is 0.5 */
            if hx >= 0 {
                /* x >= +0 */
                return sqrt(x);
            }
        }
    }

    let mut ax: f64 = fabs(x);
    if lx == 0 {
        /* special value of x */
        if ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000 {
            /* x is +-0,+-inf,+-1 */
            let mut z: f64 = ax;

            if hy < 0 {
                /* z = (1/|x|) */
                z = 1.0 / z;
            }

            if hx < 0 {
                if ((ix - 0x3ff00000) | yisint) == 0 {
                    z = (z - z) / (z - z); /* (-1)**non-int is NaN */
                } else if yisint == 1 {
                    z = -z; /* (x<0)**odd = -(|x|**odd) */
                }
            }

            return z;
        }
    }

    let mut s: f64 = 1.0; /* sign of result */
    if hx < 0 {
        if yisint == 0 {
            /* (x<0)**(non-int) is NaN */
            return (x - x) / (x - x);
        }

        if yisint == 1 {
            /* (x<0)**(odd int) */
            s = -1.0;
        }
    }

    /* |y| is HUGE */
    if iy > 0x41e00000 {
        /* if |y| > 2**31 */
        if iy > 0x43f00000 {
            /* if |y| > 2**64, must o/uflow */
            if ix <= 0x3fefffff {
                return if hy < 0 { HUGE * HUGE } else { TINY * TINY };
            }

            if ix >= 0x3ff00000 {
                return if hy > 0 { HUGE * HUGE } else { TINY * TINY };
            }
        }

        /* over/underflow if x is not close to one */
        if ix < 0x3fefffff {
            return if hy < 0 {
                s * HUGE * HUGE
            } else {
                s * TINY * TINY
            };
        }
        if ix > 0x3ff00000 {
            return if hy > 0 {
                s * HUGE * HUGE
            } else {
                s * TINY * TINY
            };
        }

        /* now |1-x| is TINY <= 2**-20, suffice to compute
        log(x) by x-x^2/2+x^3/3-x^4/4 */
        let t: f64 = ax - 1.0; /* t has 20 trailing zeros */
        let w: f64 = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
        let u: f64 = IVLN2_H * t; /* ivln2_h has 21 sig. bits */
        let v: f64 = t * IVLN2_L - w * IVLN2;
        t1 = with_set_low_word(u + v, 0);
        t2 = v - (t1 - u);
    } else {
        // double ss,s2,s_h,s_l,t_h,t_l;
        let mut n: i32 = 0;

        if ix < 0x00100000 {
            /* take care subnormal number */
            ax *= TWO53;
            n -= 53;
            ix = get_high_word(ax) as i32;
        }

        n += (ix >> 20) - 0x3ff;
        j = ix & 0x000fffff;

        /* determine interval */
        let k: i32;
        ix = j | 0x3ff00000; /* normalize ix */
        if j <= 0x3988E {
            /* |x|<sqrt(3/2) */
            k = 0;
        } else if j < 0xBB67A {
            /* |x|<sqrt(3)   */
            k = 1;
        } else {
            k = 0;
            n += 1;
            ix -= 0x00100000;
        }
        ax = with_set_high_word(ax, ix as u32);

        /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
        let u: f64 = ax - BP[k as usize]; /* bp[0]=1.0, bp[1]=1.5 */
        let v: f64 = 1.0 / (ax + BP[k as usize]);
        let ss: f64 = u * v;
        let s_h = with_set_low_word(ss, 0);

        /* t_h=ax+bp[k] High */
        let t_h: f64 = with_set_high_word(
            0.0,
            ((ix as u32 >> 1) | 0x20000000) + 0x00080000 + ((k as u32) << 18),
        );
        let t_l: f64 = ax - (t_h - BP[k as usize]);
        let s_l: f64 = v * ((u - s_h * t_h) - s_h * t_l);

        /* compute log(ax) */
        let s2: f64 = ss * ss;
        let mut r: f64 = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
        r += s_l * (s_h + ss);
        let s2: f64 = s_h * s_h;
        let t_h: f64 = with_set_low_word(3.0 + s2 + r, 0);
        let t_l: f64 = r - ((t_h - 3.0) - s2);

        /* u+v = ss*(1+...) */
        let u: f64 = s_h * t_h;
        let v: f64 = s_l * t_h + t_l * ss;

        /* 2/(3log2)*(ss+...) */
        let p_h: f64 = with_set_low_word(u + v, 0);
        let p_l = v - (p_h - u);
        let z_h: f64 = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */
        let z_l: f64 = CP_L * p_h + p_l * CP + DP_L[k as usize];

        /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
        let t: f64 = n as f64;
        t1 = with_set_low_word(((z_h + z_l) + DP_H[k as usize]) + t, 0);
        t2 = z_l - (((t1 - t) - DP_H[k as usize]) - z_h);
    }

    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
    let y1: f64 = with_set_low_word(y, 0);
    let p_l: f64 = (y - y1) * t1 + y * t2;
    let mut p_h: f64 = y1 * t1;
    let z: f64 = p_l + p_h;
    let mut j: i32 = (z.to_bits() >> 32) as i32;
    let i: i32 = z.to_bits() as i32;
    // let (j, i): (i32, i32) = ((z.to_bits() >> 32) as i32, z.to_bits() as i32);

    if j >= 0x40900000 {
        /* z >= 1024 */
        if (j - 0x40900000) | i != 0 {
            /* if z > 1024 */
            return s * HUGE * HUGE; /* overflow */
        }

        if p_l + OVT > z - p_h {
            return s * HUGE * HUGE; /* overflow */
        }
    } else if (j & 0x7fffffff) >= 0x4090cc00 {
        /* z <= -1075 */
        // FIXME: instead of abs(j) use unsigned j

        if (((j as u32) - 0xc090cc00) | (i as u32)) != 0 {
            /* z < -1075 */
            return s * TINY * TINY; /* underflow */
        }

        if p_l <= z - p_h {
            return s * TINY * TINY; /* underflow */
        }
    }

    /* compute 2**(p_h+p_l) */
    let i: i32 = j & (0x7fffffff as i32);
    k = (i >> 20) - 0x3ff;
    let mut n: i32 = 0;

    if i > 0x3fe00000 {
        /* if |z| > 0.5, set n = [z+0.5] */
        n = j + (0x00100000 >> (k + 1));
        k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
        let t: f64 = with_set_high_word(0.0, (n & !(0x000fffff >> k)) as u32);
        n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
        if j < 0 {
            n = -n;
        }
        p_h -= t;
    }

    let t: f64 = with_set_low_word(p_l + p_h, 0);
    let u: f64 = t * LG2_H;
    let v: f64 = (p_l - (t - p_h)) * LG2 + t * LG2_L;
    let mut z: f64 = u + v;
    let w: f64 = v - (z - u);
    let t: f64 = z * z;
    let t1: f64 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
    let r: f64 = (z * t1) / (t1 - 2.0) - (w + z * w);
    z = 1.0 - (r - z);
    j = get_high_word(z) as i32;
    j += n << 20;

    if (j >> 20) <= 0 {
        /* subnormal output */
        z = scalbn(z, n);
    } else {
        z = with_set_high_word(z, j as u32);
    }

    s * z
}

#[cfg(test)]
mod tests {
    extern crate core;

    use self::core::f64::consts::{E, PI};
    use self::core::f64::{EPSILON, INFINITY, MAX, MIN, MIN_POSITIVE, NAN, NEG_INFINITY};
    use super::pow;

    const POS_ZERO: &[f64] = &[0.0];
    const NEG_ZERO: &[f64] = &[-0.0];
    const POS_ONE: &[f64] = &[1.0];
    const NEG_ONE: &[f64] = &[-1.0];
    const POS_FLOATS: &[f64] = &[99.0 / 70.0, E, PI];
    const NEG_FLOATS: &[f64] = &[-99.0 / 70.0, -E, -PI];
    const POS_SMALL_FLOATS: &[f64] = &[(1.0 / 2.0), MIN_POSITIVE, EPSILON];
    const NEG_SMALL_FLOATS: &[f64] = &[-(1.0 / 2.0), -MIN_POSITIVE, -EPSILON];
    const POS_EVENS: &[f64] = &[2.0, 6.0, 8.0, 10.0, 22.0, 100.0, MAX];
    const NEG_EVENS: &[f64] = &[MIN, -100.0, -22.0, -10.0, -8.0, -6.0, -2.0];
    const POS_ODDS: &[f64] = &[3.0, 7.0];
    const NEG_ODDS: &[f64] = &[-7.0, -3.0];
    const NANS: &[f64] = &[NAN];
    const POS_INF: &[f64] = &[INFINITY];
    const NEG_INF: &[f64] = &[NEG_INFINITY];

    const ALL: &[&[f64]] = &[
        POS_ZERO,
        NEG_ZERO,
        NANS,
        NEG_SMALL_FLOATS,
        POS_SMALL_FLOATS,
        NEG_FLOATS,
        POS_FLOATS,
        NEG_EVENS,
        POS_EVENS,
        NEG_ODDS,
        POS_ODDS,
        NEG_INF,
        POS_INF,
        NEG_ONE,
        POS_ONE,
    ];
    const POS: &[&[f64]] = &[POS_ZERO, POS_ODDS, POS_ONE, POS_FLOATS, POS_EVENS, POS_INF];
    const NEG: &[&[f64]] = &[NEG_ZERO, NEG_ODDS, NEG_ONE, NEG_FLOATS, NEG_EVENS, NEG_INF];

    fn pow_test(base: f64, exponent: f64, expected: f64) {
        let res = pow(base, exponent);
        assert!(
            if expected.is_nan() {
                res.is_nan()
            } else {
                pow(base, exponent) == expected
            },
            "{} ** {} was {} instead of {}",
            base,
            exponent,
            res,
            expected
        );
    }

    fn test_sets_as_base(sets: &[&[f64]], exponent: f64, expected: f64) {
        sets.iter()
            .for_each(|s| s.iter().for_each(|val| pow_test(*val, exponent, expected)));
    }

    fn test_sets_as_exponent(base: f64, sets: &[&[f64]], expected: f64) {
        sets.iter()
            .for_each(|s| s.iter().for_each(|val| pow_test(base, *val, expected)));
    }

    fn test_sets(sets: &[&[f64]], computed: &Fn(f64) -> f64, expected: &Fn(f64) -> f64) {
        sets.iter().for_each(|s| {
            s.iter().for_each(|val| {
                let exp = expected(*val);
                let res = computed(*val);

                assert!(
                    if exp.is_nan() {
                        res.is_nan()
                    } else {
                        exp == res
                    },
                    "test for {} was {} instead of {}",
                    val,
                    res,
                    exp
                );
            })
        });
    }

    #[test]
    fn zero_as_exponent() {
        test_sets_as_base(ALL, 0.0, 1.0);
        test_sets_as_base(ALL, -0.0, 1.0);
    }

    #[test]
    fn one_as_base() {
        test_sets_as_exponent(1.0, ALL, 1.0);
    }

    #[test]
    fn nan_inputs() {
        // NAN as the base:
        // (NAN ^ anything *but 0* should be NAN)
        test_sets_as_exponent(NAN, &ALL[2..], NAN);

        // NAN as the exponent:
        // (anything *but 1* ^ NAN should be NAN)
        test_sets_as_base(&ALL[..(ALL.len() - 2)], NAN, NAN);
    }

    #[test]
    fn infinity_as_base() {
        // Positive Infinity as the base:
        // (+Infinity ^ positive anything but 0 and NAN should be +Infinity)
        test_sets_as_exponent(INFINITY, &POS[1..], INFINITY);

        // (+Infinity ^ negative anything except 0 and NAN should be 0.0)
        test_sets_as_exponent(INFINITY, &NEG[1..], 0.0);

        // Negative Infinity as the base:
        // (-Infinity ^ positive odd ints should be -Infinity)
        test_sets_as_exponent(NEG_INFINITY, &[POS_ODDS], NEG_INFINITY);

        // (-Infinity ^ anything but odd ints should be == -0 ^ (-anything))
        // We can lump in pos/neg odd ints here because they don't seem to
        // cause panics (div by zero) in release mode (I think).
        test_sets(ALL, &|v: f64| pow(NEG_INFINITY, v), &|v: f64| pow(-0.0, -v));
    }

    #[test]
    fn infinity_as_exponent() {
        // Positive/Negative base greater than 1:
        // (pos/neg > 1 ^ Infinity should be Infinity - note this excludes NAN as the base)
        test_sets_as_base(&ALL[5..(ALL.len() - 2)], INFINITY, INFINITY);

        // (pos/neg > 1 ^ -Infinity should be 0.0)
        test_sets_as_base(&ALL[5..ALL.len() - 2], NEG_INFINITY, 0.0);

        // Positive/Negative base less than 1:
        let base_below_one = &[POS_ZERO, NEG_ZERO, NEG_SMALL_FLOATS, POS_SMALL_FLOATS];

        // (pos/neg < 1 ^ Infinity should be 0.0 - this also excludes NAN as the base)
        test_sets_as_base(base_below_one, INFINITY, 0.0);

        // (pos/neg < 1 ^ -Infinity should be Infinity)
        test_sets_as_base(base_below_one, NEG_INFINITY, INFINITY);

        // Positive/Negative 1 as the base:
        // (pos/neg 1 ^ Infinity should be 1)
        test_sets_as_base(&[NEG_ONE, POS_ONE], INFINITY, 1.0);

        // (pos/neg 1 ^ -Infinity should be 1)
        test_sets_as_base(&[NEG_ONE, POS_ONE], NEG_INFINITY, 1.0);
    }

    #[test]
    fn zero_as_base() {
        // Positive Zero as the base:
        // (+0 ^ anything positive but 0 and NAN should be +0)
        test_sets_as_exponent(0.0, &POS[1..], 0.0);

        // (+0 ^ anything negative but 0 and NAN should be Infinity)
        // (this should panic because we're dividing by zero)
        test_sets_as_exponent(0.0, &NEG[1..], INFINITY);

        // Negative Zero as the base:
        // (-0 ^ anything positive but 0, NAN, and odd ints should be +0)
        test_sets_as_exponent(-0.0, &POS[3..], 0.0);

        // (-0 ^ anything negative but 0, NAN, and odd ints should be Infinity)
        // (should panic because of divide by zero)
        test_sets_as_exponent(-0.0, &NEG[3..], INFINITY);

        // (-0 ^ positive odd ints should be -0)
        test_sets_as_exponent(-0.0, &[POS_ODDS], -0.0);

        // (-0 ^ negative odd ints should be -Infinity)
        // (should panic because of divide by zero)
        test_sets_as_exponent(-0.0, &[NEG_ODDS], NEG_INFINITY);
    }

    #[test]
    fn special_cases() {
        // One as the exponent:
        // (anything ^ 1 should be anything - i.e. the base)
        test_sets(ALL, &|v: f64| pow(v, 1.0), &|v: f64| v);

        // Negative One as the exponent:
        // (anything ^ -1 should be 1/anything)
        test_sets(ALL, &|v: f64| pow(v, -1.0), &|v: f64| 1.0 / v);

        // Factoring -1 out:
        // (negative anything ^ integer should be (-1 ^ integer) * (positive anything ^ integer))
        &[POS_ZERO, NEG_ZERO, POS_ONE, NEG_ONE, POS_EVENS, NEG_EVENS]
            .iter()
            .for_each(|int_set| {
                int_set.iter().for_each(|int| {
                    test_sets(ALL, &|v: f64| pow(-v, *int), &|v: f64| {
                        pow(-1.0, *int) * pow(v, *int)
                    });
                })
            });

        // Negative base (imaginary results):
        // (-anything except 0 and Infinity ^ non-integer should be NAN)
        &NEG[1..(NEG.len() - 1)].iter().for_each(|set| {
            set.iter().for_each(|val| {
                test_sets(&ALL[3..7], &|v: f64| pow(*val, v), &|_| NAN);
            })
        });
    }

    #[test]
    fn normal_cases() {
        assert_eq!(pow(2.0, 20.0), (1 << 20) as f64);
        assert_eq!(pow(-1.0, 9.0), -1.0);
        assert!(pow(-1.0, 2.2).is_nan());
        assert!(pow(-1.0, -1.14).is_nan());
    }
}