| /* origin: FreeBSD /usr/src/lib/msun/src/e_powf.c */ |
| /* |
| * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected]. |
| */ |
| /* |
| * ==================================================== |
| * 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|<sqrt(3/2) */ |
| k = 0; |
| } else if j < 0x5db3d7 { |
| /* |x|<sqrt(3) */ |
| k = 1; |
| } else { |
| k = 0; |
| n += 1; |
| ix -= 0x00800000; |
| } |
| ax = f32::from_bits(ix as u32); |
| |
| /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ |
| u = ax - i!(BP, k as usize); /* bp[0]=1.0, bp[1]=1.5 */ |
| v = 1.0 / (ax + i!(BP, k as usize)); |
| s = u * v; |
| s_h = s; |
| is = s_h.to_bits() as i32; |
| s_h = f32::from_bits(is as u32 & 0xfffff000); |
| /* t_h=ax+bp[k] High */ |
| is = (((ix as u32 >> 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 |
| } |
