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authorDaniel Baumann <daniel.baumann@progress-linux.org>2024-04-19 00:47:55 +0000
committerDaniel Baumann <daniel.baumann@progress-linux.org>2024-04-19 00:47:55 +0000
commit26a029d407be480d791972afb5975cf62c9360a6 (patch)
treef435a8308119effd964b339f76abb83a57c29483 /third_party/rust/libm/src/math/pow.rs
parentInitial commit. (diff)
downloadfirefox-26a029d407be480d791972afb5975cf62c9360a6.tar.xz
firefox-26a029d407be480d791972afb5975cf62c9360a6.zip
Adding upstream version 124.0.1.upstream/124.0.1
Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
Diffstat (limited to 'third_party/rust/libm/src/math/pow.rs')
-rw-r--r--third_party/rust/libm/src/math/pow.rs637
1 files changed, 637 insertions, 0 deletions
diff --git a/third_party/rust/libm/src/math/pow.rs b/third_party/rust/libm/src/math/pow.rs
new file mode 100644
index 0000000000..6a19ae6011
--- /dev/null
+++ b/third_party/rust/libm/src/math/pow.rs
@@ -0,0 +1,637 @@
+/* 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*/
+
+#[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 - 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 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: &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 {} 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());
+ }
+}