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/* e_powf.c -- float version of e_pow.c. |
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
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*/ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunPro, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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#include "math.h" |
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#include "math_private.h" |
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static const volatile float huge = 1.0e+30, tiny = 1.0e-30; |
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static const float |
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bp[] = {1.0, 1.5,}, |
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dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ |
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dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ |
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zero = 0.0, |
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one = 1.0, |
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two = 2.0, |
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two24 = 16777216.0, /* 0x4b800000 */ |
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/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ |
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L1 = 6.0000002384e-01, /* 0x3f19999a */ |
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L2 = 4.2857143283e-01, /* 0x3edb6db7 */ |
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L3 = 3.3333334327e-01, /* 0x3eaaaaab */ |
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L4 = 2.7272811532e-01, /* 0x3e8ba305 */ |
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L5 = 2.3066075146e-01, /* 0x3e6c3255 */ |
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L6 = 2.0697501302e-01, /* 0x3e53f142 */ |
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P1 = 1.6666667163e-01, /* 0x3e2aaaab */ |
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P2 = -2.7777778450e-03, /* 0xbb360b61 */ |
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P3 = 6.6137559770e-05, /* 0x388ab355 */ |
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P4 = -1.6533901999e-06, /* 0xb5ddea0e */ |
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P5 = 4.1381369442e-08, /* 0x3331bb4c */ |
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lg2 = 6.9314718246e-01, /* 0x3f317218 */ |
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lg2_h = 6.93145752e-01, /* 0x3f317200 */ |
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lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ |
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ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ |
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cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ |
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cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */ |
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cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */ |
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ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ |
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ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ |
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ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ |
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float |
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powf(float x, float y) |
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{ |
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float z,ax,z_h,z_l,p_h,p_l; |
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float yy1,t1,t2,r,s,t,u,v,w; |
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int32_t i,j,k,yisint,n; |
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int32_t hx,hy,ix,iy,is; |
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GET_FLOAT_WORD(hx,x); |
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GET_FLOAT_WORD(hy,y); |
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ix = hx&0x7fffffff; iy = hy&0x7fffffff; |
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/* y==zero: x**0 = 1 */ |
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if(iy==0) return one; |
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/* x==1: 1**y = 1, even if y is NaN */ |
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if (hx==0x3f800000) return one; |
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/* +-NaN return x+y */ |
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if(ix > 0x7f800000 || |
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iy > 0x7f800000) |
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return x+y; |
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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) 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) yisint = 2-(j&1); |
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} |
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} |
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/* special value of y */ |
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if (iy==0x7f800000) { /* y is +-inf */ |
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if (ix==0x3f800000) |
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return one; /* (-1)**+-inf is NaN */ |
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else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */ |
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return (hy>=0)? y: zero; |
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else /* (|x|<1)**-,+inf = inf,0 */ |
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return (hy<0)?-y: zero; |
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} |
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if(iy==0x3f800000) { /* y is +-1 */ |
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if(hy<0) return one/x; else return x; |
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} |
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if(hy==0x40000000) return x*x; /* y is 2 */ |
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if(hy==0x3f000000) { /* y is 0.5 */ |
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if(hx>=0) /* x >= +0 */ |
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return sqrtf(x); |
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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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z = ax; /*x is +-0,+-inf,+-1*/ |
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if(hy<0) z = one/z; /* z = (1/|x|) */ |
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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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return z; |
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} |
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/* (x<0)**(non-int) is NaN */ |
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if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); |
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/* |y| is huge */ |
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if(iy>0x4d000000) { /* if |y| > 2**27 */ |
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/* over/underflow if x is not close to one */ |
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if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny; |
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if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny; |
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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-one; /* t has 20 trailing zeros */ |
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w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)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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GET_FLOAT_WORD(is,t1); |
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SET_FLOAT_WORD(t1,is&0xfffff000); |
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t2 = v-(t1-u); |
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} else { |
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float s2,s_h,s_l,t_h,t_l; |
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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; n -= 24; GET_FLOAT_WORD(ix,ax); } |
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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) k=0; /* |x|<sqrt(3/2) */ |
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else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */ |
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else {k=0;n+=1;ix -= 0x00800000;} |
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SET_FLOAT_WORD(ax,ix); |
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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]; /* bp[0]=1.0, bp[1]=1.5 */ |
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v = one/(ax+bp[k]); |
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s = u*v; |
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s_h = s; |
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GET_FLOAT_WORD(is,s_h); |
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SET_FLOAT_WORD(s_h,is&0xfffff000); |
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/* t_h=ax+bp[k] High */ |
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SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21)); |
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t_l = ax - (t_h-bp[k]); |
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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 = (float)3.0+s2+r; |
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GET_FLOAT_WORD(is,t_h); |
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SET_FLOAT_WORD(t_h,is&0xfffff000); |
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t_l = r-((t_h-(float)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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GET_FLOAT_WORD(is,p_h); |
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SET_FLOAT_WORD(p_h,is&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]; |
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/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ |
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t = (float)n; |
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t1 = (((z_h+z_l)+dp_h[k])+t); |
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GET_FLOAT_WORD(is,t1); |
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SET_FLOAT_WORD(t1,is&0xfffff000); |
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t2 = z_l-(((t1-t)-dp_h[k])-z_h); |
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} |
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s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ |
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if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) |
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s = -one; /* (-ve)**(odd int) */ |
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/* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */ |
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GET_FLOAT_WORD(is,y); |
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SET_FLOAT_WORD(yy1,is&0xfffff000); |
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p_l = (y-yy1)*t1+y*t2; |
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p_h = yy1*t1; |
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z = p_l+p_h; |
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GET_FLOAT_WORD(j,z); |
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if (j>0x43000000) /* if z > 128 */ |
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return s*huge*huge; /* overflow */ |
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else if (j==0x43000000) { /* if z == 128 */ |
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if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ |
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} |
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else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */ |
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return s*tiny*tiny; /* underflow */ |
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else if (j==0xc3160000){ /* z == -150 */ |
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if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ |
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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) { /* 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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SET_FLOAT_WORD(t,n&~(0x007fffff>>k)); |
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n = ((n&0x007fffff)|0x00800000)>>(23-k); |
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if(j<0) n = -n; |
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p_h -= t; |
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} |
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t = p_l+p_h; |
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GET_FLOAT_WORD(is,t); |
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SET_FLOAT_WORD(t,is&0xfffff000); |
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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-two)-(w+z*w); |
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z = one-(r-z); |
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GET_FLOAT_WORD(j,z); |
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j += (n<<23); |
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if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */ |
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else SET_FLOAT_WORD(z,j); |
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return s*z; |
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} |
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DEF_STD(powf); |