mirror of
https://github.com/rust-lang/rust.git
synced 2025-11-24 11:16:53 +00:00
ecf6d3c6ce
Currently, attributes for `no-panic` are gated behind both the `test` config and `assert_no_panic`, because `no-panic` is a dev dependency (so only available with test configuration). However, we only emit `assert_no_panic` when the test config is also set anyway, so there isn't any need to gate on both. Replace gates on `all(test, assert_no_panic)` with only `assert_no_panic`. This is simpler, and also has the benefit that attempting to check for panics without `--test` errors.
625 lines
21 KiB
Rust
625 lines
21 KiB
Rust
/* 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 multi-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*/
|
|
|
|
/// Returns `x` to the power of `y` (f64).
|
|
#[cfg_attr(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_i32;
|
|
let iy: i32 = hy & 0x7fffffff_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 - i!(BP, k as usize); /* bp[0]=1.0, bp[1]=1.5 */
|
|
let v: f64 = 1.0 / (ax + i!(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 - i!(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 + i!(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) + i!(DP_H, k as usize)) + t, 0);
|
|
t2 = z_l - (((t1 - t) - i!(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_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 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), f64::MIN_POSITIVE, f64::EPSILON];
|
|
const NEG_SMALL_FLOATS: &[f64] = &[-(1.0 / 2.0), -f64::MIN_POSITIVE, -f64::EPSILON];
|
|
const POS_EVENS: &[f64] = &[2.0, 6.0, 8.0, 10.0, 22.0, 100.0, f64::MAX];
|
|
const NEG_EVENS: &[f64] = &[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] = &[f64::NAN];
|
|
const POS_INF: &[f64] = &[f64::INFINITY];
|
|
const NEG_INF: &[f64] = &[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
|
|
},
|
|
"{base} ** {exponent} was {res} instead of {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: &dyn Fn(f64) -> f64, expected: &dyn Fn(f64) -> f64) {
|
|
sets.iter().for_each(|s| {
|
|
s.iter().for_each(|val| {
|
|
let exp = expected(*val);
|
|
let res = computed(*val);
|
|
|
|
#[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
|
|
let exp = force_eval!(exp);
|
|
#[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
|
|
let res = force_eval!(res);
|
|
assert!(
|
|
if exp.is_nan() {
|
|
res.is_nan()
|
|
} else {
|
|
exp == res
|
|
},
|
|
"test for {val} was {res} instead of {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:
|
|
// (f64::NAN ^ anything *but 0* should be f64::NAN)
|
|
test_sets_as_exponent(f64::NAN, &ALL[2..], f64::NAN);
|
|
|
|
// f64::NAN as the exponent:
|
|
// (anything *but 1* ^ f64::NAN should be f64::NAN)
|
|
test_sets_as_base(&ALL[..(ALL.len() - 2)], f64::NAN, f64::NAN);
|
|
}
|
|
|
|
#[test]
|
|
fn infinity_as_base() {
|
|
// Positive Infinity as the base:
|
|
// (+Infinity ^ positive anything but 0 and f64::NAN should be +Infinity)
|
|
test_sets_as_exponent(f64::INFINITY, &POS[1..], f64::INFINITY);
|
|
|
|
// (+Infinity ^ negative anything except 0 and f64::NAN should be 0.0)
|
|
test_sets_as_exponent(f64::INFINITY, &NEG[1..], 0.0);
|
|
|
|
// Negative Infinity as the base:
|
|
// (-Infinity ^ positive odd ints should be -Infinity)
|
|
test_sets_as_exponent(f64::NEG_INFINITY, &[POS_ODDS], f64::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(f64::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 f64::NAN as the base)
|
|
test_sets_as_base(&ALL[5..(ALL.len() - 2)], f64::INFINITY, f64::INFINITY);
|
|
|
|
// (pos/neg > 1 ^ -Infinity should be 0.0)
|
|
test_sets_as_base(&ALL[5..ALL.len() - 2], f64::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 f64::NAN as the base)
|
|
test_sets_as_base(base_below_one, f64::INFINITY, 0.0);
|
|
|
|
// (pos/neg < 1 ^ -Infinity should be Infinity)
|
|
test_sets_as_base(base_below_one, f64::NEG_INFINITY, f64::INFINITY);
|
|
|
|
// Positive/Negative 1 as the base:
|
|
// (pos/neg 1 ^ Infinity should be 1)
|
|
test_sets_as_base(&[NEG_ONE, POS_ONE], f64::INFINITY, 1.0);
|
|
|
|
// (pos/neg 1 ^ -Infinity should be 1)
|
|
test_sets_as_base(&[NEG_ONE, POS_ONE], f64::NEG_INFINITY, 1.0);
|
|
}
|
|
|
|
#[test]
|
|
fn zero_as_base() {
|
|
// Positive Zero as the base:
|
|
// (+0 ^ anything positive but 0 and f64::NAN should be +0)
|
|
test_sets_as_exponent(0.0, &POS[1..], 0.0);
|
|
|
|
// (+0 ^ anything negative but 0 and f64::NAN should be Infinity)
|
|
// (this should panic because we're dividing by zero)
|
|
test_sets_as_exponent(0.0, &NEG[1..], f64::INFINITY);
|
|
|
|
// Negative Zero as the base:
|
|
// (-0 ^ anything positive but 0, f64::NAN, and odd ints should be +0)
|
|
test_sets_as_exponent(-0.0, &POS[3..], 0.0);
|
|
|
|
// (-0 ^ anything negative but 0, f64::NAN, and odd ints should be Infinity)
|
|
// (should panic because of divide by zero)
|
|
test_sets_as_exponent(-0.0, &NEG[3..], f64::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], f64::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), &|_| f64::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());
|
|
}
|
|
}
|