| /* 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. |
| * ==================================================== |
| */ |
| |
| #include "libm.h" |
| |
| static const float bp[] = |
| { |
| 1.0, 1.5, |
| }, |
| dp_h[] = |
| { |
| 0.0, 5.84960938e-01, |
| }, /* 0x3f15c000 */ |
| dp_l[] = |
| { |
| 0.0, 1.56322085e-06, |
| }, /* 0x35d1cfdc */ |
| two24 = 16777216.0, /* 0x4b800000 */ |
| huge = 1.0e30, |
| tiny = 1.0e-30, |
| /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ |
| L1 = 6.0000002384e-01, /* 0x3f19999a */ |
| L2 = 4.2857143283e-01, /* 0x3edb6db7 */ |
| L3 = 3.3333334327e-01, /* 0x3eaaaaab */ |
| L4 = 2.7272811532e-01, /* 0x3e8ba305 */ |
| L5 = 2.3066075146e-01, /* 0x3e6c3255 */ |
| L6 = 2.0697501302e-01, /* 0x3e53f142 */ |
| P1 = 1.6666667163e-01, /* 0x3e2aaaab */ |
| P2 = -2.7777778450e-03, /* 0xbb360b61 */ |
| P3 = 6.6137559770e-05, /* 0x388ab355 */ |
| P4 = -1.6533901999e-06, /* 0xb5ddea0e */ |
| P5 = 4.1381369442e-08, /* 0x3331bb4c */ |
| lg2 = 6.9314718246e-01, /* 0x3f317218 */ |
| lg2_h = 6.93145752e-01, /* 0x3f317200 */ |
| lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ |
| ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ |
| cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ |
| cp_h = 9.6191406250e-01, /* 0x3f764000 =12b cp */ |
| cp_l = -1.1736857402e-04, /* 0xb8f623c6 =tail of cp_h */ |
| ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ |
| ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ |
| ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ |
| |
| float powf(float x, float y) { |
| float z, ax, z_h, z_l, p_h, p_l; |
| float y1, t1, t2, r, s, sn, t, u, v, w; |
| int32_t i, j, k, yisint, n; |
| int32_t hx, hy, ix, iy, is; |
| |
| GET_FLOAT_WORD(hx, x); |
| GET_FLOAT_WORD(hy, y); |
| ix = hx & 0x7fffffff; |
| iy = hy & 0x7fffffff; |
| |
| /* x**0 = 1, even if x is NaN */ |
| if (iy == 0) |
| return 1.0f; |
| /* 1**y = 1, even if y is NaN */ |
| if (hx == 0x3f800000) |
| return 1.0f; |
| /* 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 1.0f; |
| else if (ix > 0x3f800000) /* (|x|>1)**+-inf = inf,0 */ |
| return hy >= 0 ? y : 0.0f; |
| else /* (|x|<1)**+-inf = 0,inf */ |
| return hy >= 0 ? 0.0f : -y; |
| } |
| if (iy == 0x3f800000) /* y is +-1 */ |
| return hy >= 0 ? x : 1.0f / x; |
| if (hy == 0x40000000) /* y is 2 */ |
| return x * x; |
| if (hy == 0x3f000000) { /* y is 0.5 */ |
| if (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 = 1.0f / 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 = 1.0f; /* 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 = -1.0f; |
| } |
| |
| /* |y| is huge */ |
| if (iy > 0x4d000000) { /* if |y| > 2**27 */ |
| /* over/underflow if x is not close to one */ |
| if (ix < 0x3f7ffff8) |
| return hy < 0 ? sn * huge * huge : sn * tiny * tiny; |
| if (ix > 0x3f800007) |
| return hy > 0 ? sn * huge * huge : 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) * (0.5f - t * (0.333333333333f - t * 0.25f)); |
| u = ivln2_h * t; /* ivln2_h has 16 sig. bits */ |
| v = t * ivln2_l - w * ivln2; |
| t1 = u + v; |
| GET_FLOAT_WORD(is, t1); |
| SET_FLOAT_WORD(t1, is & 0xfffff000); |
| t2 = v - (t1 - u); |
| } else { |
| float s2, s_h, s_l, t_h, t_l; |
| n = 0; |
| /* take care subnormal number */ |
| if (ix < 0x00800000) { |
| ax *= two24; |
| n -= 24; |
| GET_FLOAT_WORD(ix, ax); |
| } |
| 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; |
| } |
| SET_FLOAT_WORD(ax, ix); |
| |
| /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ |
| u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ |
| v = 1.0f / (ax + bp[k]); |
| s = u * v; |
| s_h = s; |
| GET_FLOAT_WORD(is, s_h); |
| SET_FLOAT_WORD(s_h, is & 0xfffff000); |
| /* t_h=ax+bp[k] High */ |
| is = ((ix >> 1) & 0xfffff000) | 0x20000000; |
| SET_FLOAT_WORD(t_h, is + 0x00400000 + (k << 21)); |
| t_l = ax - (t_h - bp[k]); |
| 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 = 3.0f + s2 + r; |
| GET_FLOAT_WORD(is, t_h); |
| SET_FLOAT_WORD(t_h, is & 0xfffff000); |
| t_l = r - ((t_h - 3.0f) - 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; |
| GET_FLOAT_WORD(is, p_h); |
| SET_FLOAT_WORD(p_h, is & 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 + dp_l[k]; |
| /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ |
| t = (float)n; |
| t1 = (((z_h + z_l) + dp_h[k]) + t); |
| GET_FLOAT_WORD(is, t1); |
| SET_FLOAT_WORD(t1, is & 0xfffff000); |
| t2 = z_l - (((t1 - t) - dp_h[k]) - z_h); |
| } |
| |
| /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ |
| GET_FLOAT_WORD(is, y); |
| SET_FLOAT_WORD(y1, is & 0xfffff000); |
| p_l = (y - y1) * t1 + y * t2; |
| p_h = y1 * t1; |
| z = p_l + p_h; |
| GET_FLOAT_WORD(j, z); |
| 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 == 0xc3160000) { /* z == -150 */ |
| if (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 */ |
| SET_FLOAT_WORD(t, n & ~(0x007fffff >> k)); |
| n = ((n & 0x007fffff) | 0x00800000) >> (23 - k); |
| if (j < 0) |
| n = -n; |
| p_h -= t; |
| } |
| t = p_l + p_h; |
| GET_FLOAT_WORD(is, t); |
| SET_FLOAT_WORD(t, is & 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 - 2.0f) - (w + z * w); |
| z = 1.0f - (r - z); |
| GET_FLOAT_WORD(j, z); |
| j += n << 23; |
| if ((j >> 23) <= 0) /* subnormal output */ |
| z = scalbnf(z, n); |
| else |
| SET_FLOAT_WORD(z, j); |
| return sn * z; |
| } |