/* origin: FreeBSD /usr/src/lib/msun/src/e_powf.c */ /* * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ use super::{fabsf, scalbnf, sqrtf}; const BP: [f32; 2] = [1.0, 1.5]; const DP_H: [f32; 2] = [0.0, 5.84960938e-01]; /* 0x3f15c000 */ const DP_L: [f32; 2] = [0.0, 1.56322085e-06]; /* 0x35d1cfdc */ const TWO24: f32 = 16777216.0; /* 0x4b800000 */ const HUGE: f32 = 1.0e30; const TINY: f32 = 1.0e-30; const L1: f32 = 6.0000002384e-01; /* 0x3f19999a */ const L2: f32 = 4.2857143283e-01; /* 0x3edb6db7 */ const L3: f32 = 3.3333334327e-01; /* 0x3eaaaaab */ const L4: f32 = 2.7272811532e-01; /* 0x3e8ba305 */ const L5: f32 = 2.3066075146e-01; /* 0x3e6c3255 */ const L6: f32 = 2.0697501302e-01; /* 0x3e53f142 */ const P1: f32 = 1.6666667163e-01; /* 0x3e2aaaab */ const P2: f32 = -2.7777778450e-03; /* 0xbb360b61 */ const P3: f32 = 6.6137559770e-05; /* 0x388ab355 */ const P4: f32 = -1.6533901999e-06; /* 0xb5ddea0e */ const P5: f32 = 4.1381369442e-08; /* 0x3331bb4c */ const LG2: f32 = 6.9314718246e-01; /* 0x3f317218 */ const LG2_H: f32 = 6.93145752e-01; /* 0x3f317200 */ const LG2_L: f32 = 1.42860654e-06; /* 0x35bfbe8c */ const OVT: f32 = 4.2995665694e-08; /* -(128-log2(ovfl+.5ulp)) */ const CP: f32 = 9.6179670095e-01; /* 0x3f76384f =2/(3ln2) */ const CP_H: f32 = 9.6191406250e-01; /* 0x3f764000 =12b cp */ const CP_L: f32 = -1.1736857402e-04; /* 0xb8f623c6 =tail of cp_h */ const IVLN2: f32 = 1.4426950216e+00; const IVLN2_H: f32 = 1.4426879883e+00; const IVLN2_L: f32 = 7.0526075433e-06; #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] pub fn powf(x: f32, y: f32) -> f32 { let mut z: f32; let mut ax: f32; let z_h: f32; let z_l: f32; let mut p_h: f32; let mut p_l: f32; let y1: f32; let mut t1: f32; let t2: f32; let mut r: f32; let s: f32; let mut sn: f32; let mut t: f32; let mut u: f32; let mut v: f32; let mut w: f32; let i: i32; let mut j: i32; let mut k: i32; let mut yisint: i32; let mut n: i32; let hx: i32; let hy: i32; let mut ix: i32; let iy: i32; let mut is: i32; hx = x.to_bits() as i32; hy = y.to_bits() as i32; ix = hx & 0x7fffffff; iy = hy & 0x7fffffff; /* x**0 = 1, even if x is NaN */ if iy == 0 { return 1.0; } /* 1**y = 1, even if y is NaN */ if hx == 0x3f800000 { return 1.0; } /* NaN if either arg is NaN */ if ix > 0x7f800000 || iy > 0x7f800000 { 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 */ yisint = 0; if hx < 0 { if iy >= 0x4b800000 { yisint = 2; /* even integer y */ } else if iy >= 0x3f800000 { k = (iy >> 23) - 0x7f; /* exponent */ j = iy >> (23 - k); if (j << (23 - k)) == iy { yisint = 2 - (j & 1); } } } /* special value of y */ if iy == 0x7f800000 { /* y is +-inf */ if ix == 0x3f800000 { /* (-1)**+-inf is 1 */ return 1.0; } else if ix > 0x3f800000 { /* (|x|>1)**+-inf = inf,0 */ return if hy >= 0 { y } else { 0.0 }; } else { /* (|x|<1)**+-inf = 0,inf */ return if hy >= 0 { 0.0 } else { -y }; } } if iy == 0x3f800000 { /* y is +-1 */ return if hy >= 0 { x } else { 1.0 / x }; } if hy == 0x40000000 { /* y is 2 */ return x * x; } if hy == 0x3f000000 /* y is 0.5 */ && hx >= 0 { /* x >= +0 */ return sqrtf(x); } ax = fabsf(x); /* special value of x */ if ix == 0x7f800000 || ix == 0 || ix == 0x3f800000 { /* x is +-0,+-inf,+-1 */ z = ax; if hy < 0 { /* z = (1/|x|) */ z = 1.0 / z; } if hx < 0 { if ((ix - 0x3f800000) | 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; } sn = 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) */ sn = -1.0; } } /* |y| is HUGE */ if iy > 0x4d000000 { /* if |y| > 2**27 */ /* over/underflow if x is not close to one */ if ix < 0x3f7ffff8 { return if hy < 0 { sn * HUGE * HUGE } else { sn * TINY * TINY }; } if ix > 0x3f800007 { return if hy > 0 { sn * HUGE * HUGE } else { sn * 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 */ t = ax - 1.; /* t has 20 trailing zeros */ w = (t * t) * (0.5 - t * (0.333333333333 - t * 0.25)); u = IVLN2_H * t; /* IVLN2_H has 16 sig. bits */ v = t * IVLN2_L - w * IVLN2; t1 = u + v; is = t1.to_bits() as i32; t1 = f32::from_bits(is as u32 & 0xfffff000); t2 = v - (t1 - u); } else { let mut s2: f32; let mut s_h: f32; let s_l: f32; let mut t_h: f32; let mut t_l: f32; n = 0; /* take care subnormal number */ if ix < 0x00800000 { ax *= TWO24; n -= 24; ix = ax.to_bits() as i32; } n += ((ix) >> 23) - 0x7f; j = ix & 0x007fffff; /* determine interval */ ix = j | 0x3f800000; /* normalize ix */ if j <= 0x1cc471 { /* |x|> 1) & 0xfffff000) | 0x20000000) as i32; t_h = f32::from_bits(is as u32 + 0x00400000 + ((k as u32) << 21)); t_l = ax - (t_h - i!(BP, k as usize)); s_l = v * ((u - s_h * t_h) - s_h * t_l); /* compute log(ax) */ s2 = s * s; r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6))))); r += s_l * (s_h + s); s2 = s_h * s_h; t_h = 3.0 + s2 + r; is = t_h.to_bits() as i32; t_h = f32::from_bits(is as u32 & 0xfffff000); t_l = r - ((t_h - 3.0) - s2); /* u+v = s*(1+...) */ u = s_h * t_h; v = s_l * t_h + t_l * s; /* 2/(3log2)*(s+...) */ p_h = u + v; is = p_h.to_bits() as i32; p_h = f32::from_bits(is as u32 & 0xfffff000); p_l = v - (p_h - u); z_h = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */ z_l = CP_L * p_h + p_l * CP + i!(DP_L, k as usize); /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ t = n as f32; t1 = ((z_h + z_l) + i!(DP_H, k as usize)) + t; is = t1.to_bits() as i32; t1 = f32::from_bits(is as u32 & 0xfffff000); 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) */ is = y.to_bits() as i32; y1 = f32::from_bits(is as u32 & 0xfffff000); p_l = (y - y1) * t1 + y * t2; p_h = y1 * t1; z = p_l + p_h; j = z.to_bits() as i32; if j > 0x43000000 { /* if z > 128 */ return sn * HUGE * HUGE; /* overflow */ } else if j == 0x43000000 { /* if z == 128 */ if p_l + OVT > z - p_h { return sn * HUGE * HUGE; /* overflow */ } } else if (j & 0x7fffffff) > 0x43160000 { /* z < -150 */ // FIXME: check should be (uint32_t)j > 0xc3160000 return sn * TINY * TINY; /* underflow */ } else if j as u32 == 0xc3160000 /* z == -150 */ && p_l <= z - p_h { return sn * TINY * TINY; /* underflow */ } /* * compute 2**(p_h+p_l) */ i = j & 0x7fffffff; k = (i >> 23) - 0x7f; n = 0; if i > 0x3f000000 { /* if |z| > 0.5, set n = [z+0.5] */ n = j + (0x00800000 >> (k + 1)); k = ((n & 0x7fffffff) >> 23) - 0x7f; /* new k for n */ t = f32::from_bits(n as u32 & !(0x007fffff >> k)); n = ((n & 0x007fffff) | 0x00800000) >> (23 - k); if j < 0 { n = -n; } p_h -= t; } t = p_l + p_h; is = t.to_bits() as i32; t = f32::from_bits(is as u32 & 0xffff8000); u = t * LG2_H; v = (p_l - (t - p_h)) * LG2 + t * LG2_L; z = u + v; w = v - (z - u); t = z * z; t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5)))); r = (z * t1) / (t1 - 2.0) - (w + z * w); z = 1.0 - (r - z); j = z.to_bits() as i32; j += n << 23; if (j >> 23) <= 0 { /* subnormal output */ z = scalbnf(z, n); } else { z = f32::from_bits(j as u32); } sn * z }