/build/cargo-vendor-dir/libm-0.2.15/src/math/pow.rs

Source
/* 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(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_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());
    }
}

Coverage Report

Created: 2025-06-23 13:53

Line	Count	Source
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 multi-precision
20		// arithmetic, where \|y'\|<=0.5.
21		// 3. Return xy = 2nexp(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-2/3s**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
92		/// Returns `x` to the power of `y` (f64).
93		#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
94	0	pub fn pow(x: f64, y: f64) -> f64 {
95	0	let t1: f64;
96	0	let t2: f64;
97	0
98	0	let (hx, lx): (i32, u32) = ((x.to_bits() >> 32) as i32, x.to_bits() as u32);
99	0	let (hy, ly): (i32, u32) = ((y.to_bits() >> 32) as i32, y.to_bits() as u32);
100	0
101	0	let mut ix: i32 = hx & 0x7fffffff_i32;
102	0	let iy: i32 = hy & 0x7fffffff_i32;
103	0
104	0	/* x*0 = 1, even if x is NaN /
105	0	if ((iy as u32) \| ly) == 0 {
106	0	return 1.0;
107	0	}
108	0
109	0	/* 1*y = 1, even if y is NaN /
110	0	if hx == 0x3ff00000 && lx == 0 {
111	0	return 1.0;
112	0	}
113	0
114	0	/* NaN if either arg is NaN */
115	0	if ix > 0x7ff00000
116	0	\|\| (ix == 0x7ff00000 && lx != 0)
117	0	\|\| iy > 0x7ff00000
118	0	\|\| (iy == 0x7ff00000 && ly != 0)
119		{
120	0	return x + y;
121	0	}
122	0
123	0	/* determine if y is an odd int when x < 0
124	0	* yisint = 0 ... y is not an integer
125	0	* yisint = 1 ... y is an odd int
126	0	* yisint = 2 ... y is an even int
127	0	*/
128	0	let mut yisint: i32 = 0;
129	0	let mut k: i32;
130	0	let mut j: i32;
131	0	if hx < 0 {
132	0	if iy >= 0x43400000 {
133	0	yisint = 2; /* even integer y */
134	0	} else if iy >= 0x3ff00000 {
135	0	k = (iy >> 20) - 0x3ff; /* exponent */
136	0
137	0	if k > 20 {
138	0	j = (ly >> (52 - k)) as i32;
139	0
140	0	if (j << (52 - k)) == (ly as i32) {
141	0	yisint = 2 - (j & 1);
142	0	}
143	0	} else if ly == 0 {
144	0	j = iy >> (20 - k);
145	0
146	0	if (j << (20 - k)) == iy {
147	0	yisint = 2 - (j & 1);
148	0	}
149	0	}
150	0	}
151	0	}
152
153	0	if ly == 0 {
154		/* special value of y */
155	0	if iy == 0x7ff00000 {
156		/* y is +-inf */
157
158	0	return if ((ix - 0x3ff00000) \| (lx as i32)) == 0 {
159		/* (-1)*+-inf is 1 /
160	0	1.0
161	0	} else if ix >= 0x3ff00000 {
162		/* (\|x\|>1)*+-inf = inf,0 /
163	0	if hy >= 0 { y } else { 0.0 }
164		} else {
165		/* (\|x\|<1)*+-inf = 0,inf /
166	0	if hy >= 0 { 0.0 } else { -y }
167		};
168	0	}
169	0
170	0	if iy == 0x3ff00000 {
171		/* y is +-1 */
172	0	return if hy >= 0 { x } else { 1.0 / x };
173	0	}
174	0
175	0	if hy == 0x40000000 {
176		/* y is 2 */
177	0	return x * x;
178	0	}
179	0
180	0	if hy == 0x3fe00000 {
181		/* y is 0.5 */
182	0	if hx >= 0 {
183		/* x >= +0 */
184	0	return sqrt(x);
185	0	}
186	0	}
187	0	}
188
189	0	let mut ax: f64 = fabs(x);
190	0	if lx == 0 {
191		/* special value of x */
192	0	if ix == 0x7ff00000 \|\| ix == 0 \|\| ix == 0x3ff00000 {
193		/* x is +-0,+-inf,+-1 */
194	0	let mut z: f64 = ax;
195	0
196	0	if hy < 0 {
197	0	/* z = (1/\|x\|) */
198	0	z = 1.0 / z;
199	0	}
200
201	0	if hx < 0 {
202	0	if ((ix - 0x3ff00000) \| yisint) == 0 {
203	0	z = (z - z) / (z - z); /* (-1)*non-int is NaN /
204	0	} else if yisint == 1 {
205	0	z = -z; /* (x<0)odd = -(\|x\|odd) */
206	0	}
207	0	}
208
209	0	return z;
210	0	}
211	0	}
212
213	0	let mut s: f64 = 1.0; /* sign of result */
214	0	if hx < 0 {
215	0	if yisint == 0 {
216		/* (x<0)*(non-int) is NaN /
217	0	return (x - x) / (x - x);
218	0	}
219	0
220	0	if yisint == 1 {
221	0	/* (x<0)*(odd int) /
222	0	s = -1.0;
223	0	}
224	0	}
225
226		/* \|y\| is HUGE */
227	0	if iy > 0x41e00000 {
228		/* if \|y\| > 2*31 /
229	0	if iy > 0x43f00000 {
230		/* if \|y\| > 2*64, must o/uflow /
231	0	if ix <= 0x3fefffff {
232	0	return if hy < 0 { HUGE * HUGE } else { TINY * TINY };
233	0	}
234	0
235	0	if ix >= 0x3ff00000 {
236	0	return if hy > 0 { HUGE * HUGE } else { TINY * TINY };
237	0	}
238	0	}
239
240		/* over/underflow if x is not close to one */
241	0	if ix < 0x3fefffff {
242	0	return if hy < 0 {
243	0	s * HUGE * HUGE
244		} else {
245	0	s * TINY * TINY
246		};
247	0	}
248	0	if ix > 0x3ff00000 {
249	0	return if hy > 0 {
250	0	s * HUGE * HUGE
251		} else {
252	0	s * TINY * TINY
253		};
254	0	}
255	0
256	0	/* now \|1-x\| is TINY <= 2**-20, suffice to compute
257	0	log(x) by x-x^2/2+x^3/3-x^4/4 */
258	0	let t: f64 = ax - 1.0; /* t has 20 trailing zeros */
259	0	let w: f64 = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
260	0	let u: f64 = IVLN2_H * t; /* ivln2_h has 21 sig. bits */
261	0	let v: f64 = t * IVLN2_L - w * IVLN2;
262	0	t1 = with_set_low_word(u + v, 0);
263	0	t2 = v - (t1 - u);
264		} else {
265		// double ss,s2,s_h,s_l,t_h,t_l;
266	0	let mut n: i32 = 0;
267	0
268	0	if ix < 0x00100000 {
269	0	/* take care subnormal number */
270	0	ax *= TWO53;
271	0	n -= 53;
272	0	ix = get_high_word(ax) as i32;
273	0	}
274
275	0	n += (ix >> 20) - 0x3ff;
276	0	j = ix & 0x000fffff;
277	0
278	0	/* determine interval */
279	0	let k: i32;
280	0	ix = j \| 0x3ff00000; /* normalize ix */
281	0	if j <= 0x3988E {
282	0	/* \|x\|<sqrt(3/2) */
283	0	k = 0;
284	0	} else if j < 0xBB67A {
285	0	/* \|x\|<sqrt(3) */
286	0	k = 1;
287	0	} else {
288	0	k = 0;
289	0	n += 1;
290	0	ix -= 0x00100000;
291	0	}
292	0	ax = with_set_high_word(ax, ix as u32);
293	0
294	0	/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
295	0	let u: f64 = ax - i!(BP, k as usize); /* bp[0]=1.0, bp[1]=1.5 */
296	0	let v: f64 = 1.0 / (ax + i!(BP, k as usize));
297	0	let ss: f64 = u * v;
298	0	let s_h = with_set_low_word(ss, 0);
299	0
300	0	/* t_h=ax+bp[k] High */
301	0	let t_h: f64 = with_set_high_word(
302	0	0.0,
303	0	((ix as u32 >> 1) \| 0x20000000) + 0x00080000 + ((k as u32) << 18),
304	0	);
305	0	let t_l: f64 = ax - (t_h - i!(BP, k as usize));
306	0	let s_l: f64 = v * ((u - s_h * t_h) - s_h * t_l);
307	0
308	0	/* compute log(ax) */
309	0	let s2: f64 = ss * ss;
310	0	let mut r: f64 = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
311	0	r += s_l * (s_h + ss);
312	0	let s2: f64 = s_h * s_h;
313	0	let t_h: f64 = with_set_low_word(3.0 + s2 + r, 0);
314	0	let t_l: f64 = r - ((t_h - 3.0) - s2);
315	0
316	0	/* u+v = ss(1+...) /
317	0	let u: f64 = s_h * t_h;
318	0	let v: f64 = s_l * t_h + t_l * ss;
319	0
320	0	/* 2/(3log2)(ss+...) /
321	0	let p_h: f64 = with_set_low_word(u + v, 0);
322	0	let p_l = v - (p_h - u);
323	0	let z_h: f64 = CP_H * p_h; /* cp_h+cp_l = 2/(3log2) /
324	0	let z_l: f64 = CP_L * p_h + p_l * CP + i!(DP_L, k as usize);
325	0
326	0	/* log2(ax) = (ss+..)2/(3log2) = n + dp_h + z_h + z_l */
327	0	let t: f64 = n as f64;
328	0	t1 = with_set_low_word(((z_h + z_l) + i!(DP_H, k as usize)) + t, 0);
329	0	t2 = z_l - (((t1 - t) - i!(DP_H, k as usize)) - z_h);
330		}
331
332		/* split up y into y1+y2 and compute (y1+y2)(t1+t2) /
333	0	let y1: f64 = with_set_low_word(y, 0);
334	0	let p_l: f64 = (y - y1) * t1 + y * t2;
335	0	let mut p_h: f64 = y1 * t1;
336	0	let z: f64 = p_l + p_h;
337	0	let mut j: i32 = (z.to_bits() >> 32) as i32;
338	0	let i: i32 = z.to_bits() as i32;
339	0	// let (j, i): (i32, i32) = ((z.to_bits() >> 32) as i32, z.to_bits() as i32);
340	0
341	0	if j >= 0x40900000 {
342		/* z >= 1024 */
343	0	if (j - 0x40900000) \| i != 0 {
344		/* if z > 1024 */
345	0	return s * HUGE * HUGE; /* overflow */
346	0	}
347	0
348	0	if p_l + OVT > z - p_h {
349	0	return s * HUGE * HUGE; /* overflow */
350	0	}
351	0	} else if (j & 0x7fffffff) >= 0x4090cc00 {
352		/* z <= -1075 */
353		// FIXME: instead of abs(j) use unsigned j
354
355	0	if (((j as u32) - 0xc090cc00) \| (i as u32)) != 0 {
356		/* z < -1075 */
357	0	return s * TINY * TINY; /* underflow */
358	0	}
359	0
360	0	if p_l <= z - p_h {
361	0	return s * TINY * TINY; /* underflow */
362	0	}
363	0	}
364
365		/* compute 2*(p_h+p_l) /
366	0	let i: i32 = j & 0x7fffffff_i32;
367	0	k = (i >> 20) - 0x3ff;
368	0	let mut n: i32 = 0;
369	0
370	0	if i > 0x3fe00000 {
371		/* if \|z\| > 0.5, set n = [z+0.5] */
372	0	n = j + (0x00100000 >> (k + 1));
373	0	k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
374	0	let t: f64 = with_set_high_word(0.0, (n & !(0x000fffff >> k)) as u32);
375	0	n = ((n & 0x000fffff) \| 0x00100000) >> (20 - k);
376	0	if j < 0 {
377	0	n = -n;
378	0	}
379	0	p_h -= t;
380	0	}
381
382	0	let t: f64 = with_set_low_word(p_l + p_h, 0);
383	0	let u: f64 = t * LG2_H;
384	0	let v: f64 = (p_l - (t - p_h)) * LG2 + t * LG2_L;
385	0	let mut z: f64 = u + v;
386	0	let w: f64 = v - (z - u);
387	0	let t: f64 = z * z;
388	0	let t1: f64 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
389	0	let r: f64 = (z * t1) / (t1 - 2.0) - (w + z * w);
390	0	z = 1.0 - (r - z);
391	0	j = get_high_word(z) as i32;
392	0	j += n << 20;
393	0
394	0	if (j >> 20) <= 0 {
395	0	/* subnormal output */
396	0	z = scalbn(z, n);
397	0	} else {
398	0	z = with_set_high_word(z, j as u32);
399	0	}
400
401	0	s * z
402	0	}
403
404		#[cfg(test)]
405		mod tests {
406		extern crate core;
407
408		use self::core::f64::consts::{E, PI};
409		use super::pow;
410
411		const POS_ZERO: &[f64] = &[0.0];
412		const NEG_ZERO: &[f64] = &[-0.0];
413		const POS_ONE: &[f64] = &[1.0];
414		const NEG_ONE: &[f64] = &[-1.0];
415		const POS_FLOATS: &[f64] = &[99.0 / 70.0, E, PI];
416		const NEG_FLOATS: &[f64] = &[-99.0 / 70.0, -E, -PI];
417		const POS_SMALL_FLOATS: &[f64] = &[(1.0 / 2.0), f64::MIN_POSITIVE, f64::EPSILON];
418		const NEG_SMALL_FLOATS: &[f64] = &[-(1.0 / 2.0), -f64::MIN_POSITIVE, -f64::EPSILON];
419		const POS_EVENS: &[f64] = &[2.0, 6.0, 8.0, 10.0, 22.0, 100.0, f64::MAX];
420		const NEG_EVENS: &[f64] = &[f64::MIN, -100.0, -22.0, -10.0, -8.0, -6.0, -2.0];
421		const POS_ODDS: &[f64] = &[3.0, 7.0];
422		const NEG_ODDS: &[f64] = &[-7.0, -3.0];
423		const NANS: &[f64] = &[f64::NAN];
424		const POS_INF: &[f64] = &[f64::INFINITY];
425		const NEG_INF: &[f64] = &[f64::NEG_INFINITY];
426
427		const ALL: &[&[f64]] = &[
428		POS_ZERO,
429		NEG_ZERO,
430		NANS,
431		NEG_SMALL_FLOATS,
432		POS_SMALL_FLOATS,
433		NEG_FLOATS,
434		POS_FLOATS,
435		NEG_EVENS,
436		POS_EVENS,
437		NEG_ODDS,
438		POS_ODDS,
439		NEG_INF,
440		POS_INF,
441		NEG_ONE,
442		POS_ONE,
443		];
444		const POS: &[&[f64]] = &[POS_ZERO, POS_ODDS, POS_ONE, POS_FLOATS, POS_EVENS, POS_INF];
445		const NEG: &[&[f64]] = &[NEG_ZERO, NEG_ODDS, NEG_ONE, NEG_FLOATS, NEG_EVENS, NEG_INF];
446
447		fn pow_test(base: f64, exponent: f64, expected: f64) {
448		let res = pow(base, exponent);
449		assert!(
450		if expected.is_nan() {
451		res.is_nan()
452		} else {
453		pow(base, exponent) == expected
454		},
455		"{base} ** {exponent} was {res} instead of {expected}",
456		);
457		}
458
459		fn test_sets_as_base(sets: &[&[f64]], exponent: f64, expected: f64) {
460		sets.iter()
461		.for_each(\|s\| s.iter().for_each(\|val\| pow_test(*val, exponent, expected)));
462		}
463
464		fn test_sets_as_exponent(base: f64, sets: &[&[f64]], expected: f64) {
465		sets.iter()
466		.for_each(\|s\| s.iter().for_each(\|val\| pow_test(base, *val, expected)));
467		}
468
469		fn test_sets(sets: &[&[f64]], computed: &dyn Fn(f64) -> f64, expected: &dyn Fn(f64) -> f64) {
470		sets.iter().for_each(\|s\| {
471		s.iter().for_each(\|val\| {
472		let exp = expected(*val);
473		let res = computed(*val);
474
475		#[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
476		let exp = force_eval!(exp);
477		#[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
478		let res = force_eval!(res);
479		assert!(
480		if exp.is_nan() {
481		res.is_nan()
482		} else {
483		exp == res
484		},
485		"test for {val} was {res} instead of {exp}",
486		);
487		})
488		});
489		}
490
491		#[test]
492		fn zero_as_exponent() {
493		test_sets_as_base(ALL, 0.0, 1.0);
494		test_sets_as_base(ALL, -0.0, 1.0);
495		}
496
497		#[test]
498		fn one_as_base() {
499		test_sets_as_exponent(1.0, ALL, 1.0);
500		}
501
502		#[test]
503		fn nan_inputs() {
504		// NAN as the base:
505		// (f64::NAN ^ anything but 0 should be f64::NAN)
506		test_sets_as_exponent(f64::NAN, &ALL[2..], f64::NAN);
507
508		// f64::NAN as the exponent:
509		// (anything but 1 ^ f64::NAN should be f64::NAN)
510		test_sets_as_base(&ALL[..(ALL.len() - 2)], f64::NAN, f64::NAN);
511		}
512
513		#[test]
514		fn infinity_as_base() {
515		// Positive Infinity as the base:
516		// (+Infinity ^ positive anything but 0 and f64::NAN should be +Infinity)
517		test_sets_as_exponent(f64::INFINITY, &POS[1..], f64::INFINITY);
518
519		// (+Infinity ^ negative anything except 0 and f64::NAN should be 0.0)
520		test_sets_as_exponent(f64::INFINITY, &NEG[1..], 0.0);
521
522		// Negative Infinity as the base:
523		// (-Infinity ^ positive odd ints should be -Infinity)
524		test_sets_as_exponent(f64::NEG_INFINITY, &[POS_ODDS], f64::NEG_INFINITY);
525
526		// (-Infinity ^ anything but odd ints should be == -0 ^ (-anything))
527		// We can lump in pos/neg odd ints here because they don't seem to
528		// cause panics (div by zero) in release mode (I think).
529		test_sets(ALL, &\|v: f64\| pow(f64::NEG_INFINITY, v), &\|v: f64\| {
530		pow(-0.0, -v)
531		});
532		}
533
534		#[test]
535		fn infinity_as_exponent() {
536		// Positive/Negative base greater than 1:
537		// (pos/neg > 1 ^ Infinity should be Infinity - note this excludes f64::NAN as the base)
538		test_sets_as_base(&ALL[5..(ALL.len() - 2)], f64::INFINITY, f64::INFINITY);
539
540		// (pos/neg > 1 ^ -Infinity should be 0.0)
541		test_sets_as_base(&ALL[5..ALL.len() - 2], f64::NEG_INFINITY, 0.0);
542
543		// Positive/Negative base less than 1:
544		let base_below_one = &[POS_ZERO, NEG_ZERO, NEG_SMALL_FLOATS, POS_SMALL_FLOATS];
545
546		// (pos/neg < 1 ^ Infinity should be 0.0 - this also excludes f64::NAN as the base)
547		test_sets_as_base(base_below_one, f64::INFINITY, 0.0);
548
549		// (pos/neg < 1 ^ -Infinity should be Infinity)
550		test_sets_as_base(base_below_one, f64::NEG_INFINITY, f64::INFINITY);
551
552		// Positive/Negative 1 as the base:
553		// (pos/neg 1 ^ Infinity should be 1)
554		test_sets_as_base(&[NEG_ONE, POS_ONE], f64::INFINITY, 1.0);
555
556		// (pos/neg 1 ^ -Infinity should be 1)
557		test_sets_as_base(&[NEG_ONE, POS_ONE], f64::NEG_INFINITY, 1.0);
558		}
559
560		#[test]
561		fn zero_as_base() {
562		// Positive Zero as the base:
563		// (+0 ^ anything positive but 0 and f64::NAN should be +0)
564		test_sets_as_exponent(0.0, &POS[1..], 0.0);
565
566		// (+0 ^ anything negative but 0 and f64::NAN should be Infinity)
567		// (this should panic because we're dividing by zero)
568		test_sets_as_exponent(0.0, &NEG[1..], f64::INFINITY);
569
570		// Negative Zero as the base:
571		// (-0 ^ anything positive but 0, f64::NAN, and odd ints should be +0)
572		test_sets_as_exponent(-0.0, &POS[3..], 0.0);
573
574		// (-0 ^ anything negative but 0, f64::NAN, and odd ints should be Infinity)
575		// (should panic because of divide by zero)
576		test_sets_as_exponent(-0.0, &NEG[3..], f64::INFINITY);
577
578		// (-0 ^ positive odd ints should be -0)
579		test_sets_as_exponent(-0.0, &[POS_ODDS], -0.0);
580
581		// (-0 ^ negative odd ints should be -Infinity)
582		// (should panic because of divide by zero)
583		test_sets_as_exponent(-0.0, &[NEG_ODDS], f64::NEG_INFINITY);
584		}
585
586		#[test]
587		fn special_cases() {
588		// One as the exponent:
589		// (anything ^ 1 should be anything - i.e. the base)
590		test_sets(ALL, &\|v: f64\| pow(v, 1.0), &\|v: f64\| v);
591
592		// Negative One as the exponent:
593		// (anything ^ -1 should be 1/anything)
594		test_sets(ALL, &\|v: f64\| pow(v, -1.0), &\|v: f64\| 1.0 / v);
595
596		// Factoring -1 out:
597		// (negative anything ^ integer should be (-1 ^ integer) * (positive anything ^ integer))
598		[POS_ZERO, NEG_ZERO, POS_ONE, NEG_ONE, POS_EVENS, NEG_EVENS]
599		.iter()
600		.for_each(\|int_set\| {
601		int_set.iter().for_each(\|int\| {
602		test_sets(ALL, &\|v: f64\| pow(-v, *int), &\|v: f64\| {
603		pow(-1.0, int) pow(v, *int)
604		});
605		})
606		});
607
608		// Negative base (imaginary results):
609		// (-anything except 0 and Infinity ^ non-integer should be NAN)
610		NEG[1..(NEG.len() - 1)].iter().for_each(\|set\| {
611		set.iter().for_each(\|val\| {
612		test_sets(&ALL[3..7], &\|v: f64\| pow(*val, v), &\|_\| f64::NAN);
613		})
614		});
615		}
616
617		#[test]
618		fn normal_cases() {
619		assert_eq!(pow(2.0, 20.0), (1 << 20) as f64);
620		assert_eq!(pow(-1.0, 9.0), -1.0);
621		assert!(pow(-1.0, 2.2).is_nan());
622		assert!(pow(-1.0, -1.14).is_nan());
623		}
624		}