| /* 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()); |
| } |
| } |
