Jorge Aparicio
328 lines
9.3 KiB
Rust
328 lines
9.3 KiB
Rust
use super::{fabsf, scalbnf, sqrtf};
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const BP: [f32; 2] = [1.0, 1.5];
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const DP_H: [f32; 2] = [0.0, 5.84960938e-01]; /* 0x3f15c000 */
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const DP_L: [f32; 2] = [0.0, 1.56322085e-06]; /* 0x35d1cfdc */
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const TWO24: f32 = 16777216.0; /* 0x4b800000 */
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const HUGE: f32 = 1.0e30;
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const TINY: f32 = 1.0e-30;
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const L1: f32 = 6.0000002384e-01; /* 0x3f19999a */
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const L2: f32 = 4.2857143283e-01; /* 0x3edb6db7 */
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const L3: f32 = 3.3333334327e-01; /* 0x3eaaaaab */
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const L4: f32 = 2.7272811532e-01; /* 0x3e8ba305 */
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const L5: f32 = 2.3066075146e-01; /* 0x3e6c3255 */
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const L6: f32 = 2.0697501302e-01; /* 0x3e53f142 */
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const P1: f32 = 1.6666667163e-01; /* 0x3e2aaaab */
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const P2: f32 = -2.7777778450e-03; /* 0xbb360b61 */
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const P3: f32 = 6.6137559770e-05; /* 0x388ab355 */
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const P4: f32 = -1.6533901999e-06; /* 0xb5ddea0e */
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const P5: f32 = 4.1381369442e-08; /* 0x3331bb4c */
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const LG2: f32 = 6.9314718246e-01; /* 0x3f317218 */
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const LG2_H: f32 = 6.93145752e-01; /* 0x3f317200 */
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const LG2_L: f32 = 1.42860654e-06; /* 0x35bfbe8c */
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const OVT: f32 = 4.2995665694e-08; /* -(128-log2(ovfl+.5ulp)) */
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const CP: f32 = 9.6179670095e-01; /* 0x3f76384f =2/(3ln2) */
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const CP_H: f32 = 9.6191406250e-01; /* 0x3f764000 =12b cp */
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const CP_L: f32 = -1.1736857402e-04; /* 0xb8f623c6 =tail of cp_h */
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const IVLN2: f32 = 1.4426950216e+00;
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const IVLN2_H: f32 = 1.4426879883e+00;
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const IVLN2_L: f32 = 7.0526075433e-06;
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#[inline]
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pub fn powf(x: f32, y: f32) -> f32 {
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let mut z: f32;
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let mut ax: f32;
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let z_h: f32;
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let z_l: f32;
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let mut p_h: f32;
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let mut p_l: f32;
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let y1: f32;
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let mut t1: f32;
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let t2: f32;
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let mut r: f32;
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let s: f32;
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let mut sn: f32;
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let mut t: f32;
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let mut u: f32;
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let mut v: f32;
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let mut w: f32;
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let i: i32;
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let mut j: i32;
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let mut k: i32;
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let mut yisint: i32;
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let mut n: i32;
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let hx: i32;
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let hy: i32;
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let mut ix: i32;
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let iy: i32;
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let mut is: i32;
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hx = x.to_bits() as i32;
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hy = y.to_bits() as i32;
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ix = hx & 0x7fffffff;
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iy = hy & 0x7fffffff;
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/* x**0 = 1, even if x is NaN */
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if iy == 0 {
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return 1.0;
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}
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/* 1**y = 1, even if y is NaN */
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if hx == 0x3f800000 {
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return 1.0;
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}
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/* NaN if either arg is NaN */
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if ix > 0x7f800000 || iy > 0x7f800000 {
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return x + y;
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}
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/* determine if y is an odd int when x < 0
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* yisint = 0 ... y is not an integer
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* yisint = 1 ... y is an odd int
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* yisint = 2 ... y is an even int
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*/
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yisint = 0;
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if hx < 0 {
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if iy >= 0x4b800000 {
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yisint = 2; /* even integer y */
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} else if iy >= 0x3f800000 {
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k = (iy >> 23) - 0x7f; /* exponent */
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j = iy >> (23 - k);
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if (j << (23 - k)) == iy {
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yisint = 2 - (j & 1);
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}
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}
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}
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/* special value of y */
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if iy == 0x7f800000 {
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/* y is +-inf */
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if ix == 0x3f800000 {
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/* (-1)**+-inf is 1 */
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return 1.0;
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} else if ix > 0x3f800000 {
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/* (|x|>1)**+-inf = inf,0 */
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return if hy >= 0 { y } else { 0.0 };
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} else {
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/* (|x|<1)**+-inf = 0,inf */
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return if hy >= 0 { 0.0 } else { -y };
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}
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}
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if iy == 0x3f800000 {
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/* y is +-1 */
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return if hy >= 0 { x } else { 1.0 / x };
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}
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if hy == 0x40000000 {
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/* y is 2 */
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return x * x;
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}
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if hy == 0x3f000000 {
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/* y is 0.5 */
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if hx >= 0 {
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/* x >= +0 */
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return sqrtf(x);
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}
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}
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ax = fabsf(x);
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/* special value of x */
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if ix == 0x7f800000 || ix == 0 || ix == 0x3f800000 {
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/* x is +-0,+-inf,+-1 */
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z = ax;
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if hy < 0 {
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/* z = (1/|x|) */
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z = 1.0 / z;
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}
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if hx < 0 {
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if ((ix - 0x3f800000) | yisint) == 0 {
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z = (z - z) / (z - z); /* (-1)**non-int is NaN */
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} else if yisint == 1 {
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z = -z; /* (x<0)**odd = -(|x|**odd) */
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}
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}
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return z;
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}
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sn = 1.0; /* sign of result */
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if hx < 0 {
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if yisint == 0 {
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/* (x<0)**(non-int) is NaN */
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return (x - x) / (x - x);
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}
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if yisint == 1 {
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/* (x<0)**(odd int) */
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sn = -1.0;
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}
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}
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/* |y| is HUGE */
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if iy > 0x4d000000 {
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/* if |y| > 2**27 */
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/* over/underflow if x is not close to one */
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if ix < 0x3f7ffff8 {
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return if hy < 0 {
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sn * HUGE * HUGE
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} else {
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sn * TINY * TINY
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};
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}
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if ix > 0x3f800007 {
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return if hy > 0 {
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sn * HUGE * HUGE
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} else {
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sn * TINY * TINY
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};
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}
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/* now |1-x| is TINY <= 2**-20, suffice to compute
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log(x) by x-x^2/2+x^3/3-x^4/4 */
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t = ax - 1.; /* t has 20 trailing zeros */
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w = (t * t) * (0.5 - t * (0.333333333333 - t * 0.25));
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u = IVLN2_H * t; /* IVLN2_H has 16 sig. bits */
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v = t * IVLN2_L - w * IVLN2;
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t1 = u + v;
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is = t1.to_bits() as i32;
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t1 = f32::from_bits(is as u32 & 0xfffff000);
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t2 = v - (t1 - u);
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} else {
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let mut s2: f32;
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let mut s_h: f32;
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let s_l: f32;
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let mut t_h: f32;
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let mut t_l: f32;
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n = 0;
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/* take care subnormal number */
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if ix < 0x00800000 {
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ax *= TWO24;
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n -= 24;
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ix = ax.to_bits() as i32;
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}
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n += ((ix) >> 23) - 0x7f;
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j = ix & 0x007fffff;
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/* determine interval */
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ix = j | 0x3f800000; /* normalize ix */
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if j <= 0x1cc471 {
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/* |x|<sqrt(3/2) */
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k = 0;
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} else if j < 0x5db3d7 {
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/* |x|<sqrt(3) */
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k = 1;
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} else {
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k = 0;
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n += 1;
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ix -= 0x00800000;
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}
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ax = f32::from_bits(ix as u32);
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/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
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u = ax - BP[k as usize]; /* bp[0]=1.0, bp[1]=1.5 */
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v = 1.0 / (ax + BP[k as usize]);
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s = u * v;
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s_h = s;
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is = s_h.to_bits() as i32;
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s_h = f32::from_bits(is as u32 & 0xfffff000);
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/* t_h=ax+bp[k] High */
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is = (((ix as u32 >> 1) & 0xfffff000) | 0x20000000) as i32;
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t_h = f32::from_bits(is as u32 + 0x00400000 + ((k as u32) << 21));
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t_l = ax - (t_h - BP[k as usize]);
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s_l = v * ((u - s_h * t_h) - s_h * t_l);
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/* compute log(ax) */
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s2 = s * s;
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r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
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r += s_l * (s_h + s);
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s2 = s_h * s_h;
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t_h = 3.0 + s2 + r;
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is = t_h.to_bits() as i32;
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t_h = f32::from_bits(is as u32 & 0xfffff000);
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t_l = r - ((t_h - 3.0) - s2);
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/* u+v = s*(1+...) */
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u = s_h * t_h;
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v = s_l * t_h + t_l * s;
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/* 2/(3log2)*(s+...) */
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p_h = u + v;
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is = p_h.to_bits() as i32;
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p_h = f32::from_bits(is as u32 & 0xfffff000);
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p_l = v - (p_h - u);
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z_h = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */
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z_l = CP_L * p_h + p_l * CP + DP_L[k as usize];
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/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
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t = n as f32;
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t1 = ((z_h + z_l) + DP_H[k as usize]) + t;
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is = t1.to_bits() as i32;
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t1 = f32::from_bits(is as u32 & 0xfffff000);
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t2 = z_l - (((t1 - t) - DP_H[k as usize]) - z_h);
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};
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/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
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is = y.to_bits() as i32;
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y1 = f32::from_bits(is as u32 & 0xfffff000);
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p_l = (y - y1) * t1 + y * t2;
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p_h = y1 * t1;
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z = p_l + p_h;
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j = z.to_bits() as i32;
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if j > 0x43000000 {
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/* if z > 128 */
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return sn * HUGE * HUGE; /* overflow */
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} else if j == 0x43000000 {
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/* if z == 128 */
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if p_l + OVT > z - p_h {
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return sn * HUGE * HUGE; /* overflow */
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}
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} else if (j & 0x7fffffff) > 0x43160000 {
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/* z < -150 */
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// FIXME: check should be (uint32_t)j > 0xc3160000
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return sn * TINY * TINY; /* underflow */
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} else if j as u32 == 0xc3160000 {
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/* z == -150 */
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if p_l <= z - p_h {
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return sn * TINY * TINY; /* underflow */
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}
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}
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/*
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* compute 2**(p_h+p_l)
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*/
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i = j & 0x7fffffff;
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k = (i >> 23) - 0x7f;
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n = 0;
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if i > 0x3f000000 {
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/* if |z| > 0.5, set n = [z+0.5] */
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n = j + (0x00800000 >> (k + 1));
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k = ((n & 0x7fffffff) >> 23) - 0x7f; /* new k for n */
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t = f32::from_bits(n as u32 & !(0x007fffff >> k));
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n = ((n & 0x007fffff) | 0x00800000) >> (23 - k);
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if j < 0 {
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n = -n;
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}
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p_h -= t;
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}
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t = p_l + p_h;
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is = t.to_bits() as i32;
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t = f32::from_bits(is as u32 & 0xffff8000);
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u = t * LG2_H;
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v = (p_l - (t - p_h)) * LG2 + t * LG2_L;
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z = u + v;
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w = v - (z - u);
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t = z * z;
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t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
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r = (z * t1) / (t1 - 2.0) - (w + z * w);
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z = 1.0 - (r - z);
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j = z.to_bits() as i32;
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j += n << 23;
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if (j >> 23) <= 0 {
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/* subnormal output */
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z = scalbnf(z, n);
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} else {
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z = f32::from_bits(j as u32);
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}
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return sn * z;
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}
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