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-rw-r--r--vendor/compiler_builtins/libm/src/math/powf.rs342
1 files changed, 342 insertions, 0 deletions
diff --git a/vendor/compiler_builtins/libm/src/math/powf.rs b/vendor/compiler_builtins/libm/src/math/powf.rs
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+/* 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|<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
+}
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