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author | Ulrich Drepper <drepper@redhat.com> | 1999-07-14 00:54:57 +0000 |
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committer | Ulrich Drepper <drepper@redhat.com> | 1999-07-14 00:54:57 +0000 |
commit | abfbdde177c3a7155070dda1b2cdc8292054cc26 (patch) | |
tree | e021306b596381fbf8311d2b7eb294e918ff17c8 /sysdeps/libm-ieee754/e_pow.c | |
parent | 86421aa57ecfd70963ae66848bd6a6dd3b8e0fe6 (diff) | |
download | glibc-abfbdde177c3a7155070dda1b2cdc8292054cc26.tar.gz glibc-abfbdde177c3a7155070dda1b2cdc8292054cc26.tar.xz glibc-abfbdde177c3a7155070dda1b2cdc8292054cc26.zip |
Update.
Diffstat (limited to 'sysdeps/libm-ieee754/e_pow.c')
-rw-r--r-- | sysdeps/libm-ieee754/e_pow.c | 352 |
1 files changed, 0 insertions, 352 deletions
diff --git a/sysdeps/libm-ieee754/e_pow.c b/sysdeps/libm-ieee754/e_pow.c deleted file mode 100644 index 1e1496f00d..0000000000 --- a/sysdeps/libm-ieee754/e_pow.c +++ /dev/null @@ -1,352 +0,0 @@ -/* @(#)e_pow.c 5.1 93/09/24 */ -/* - * ==================================================== - * 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. - * ==================================================== - */ -/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25, - for performance improvement on pipelined processors. -*/ - -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; -#endif - -/* __ieee754_pow(x,y) return x**y - * - * n - * Method: Let x = 2 * (1+f) - * 1. Compute and return log2(x) in two pieces: - * log2(x) = w1 + w2, - * where w1 has 53-24 = 29 bit trailing zeros. - * 2. Perform y*log2(x) = n+y' by simulating muti-precision - * arithmetic, where |y'|<=0.5. - * 3. Return x**y = 2**n*exp(y'*log2) - * - * Special cases: - * 1. (anything) ** 0 is 1 - * 2. (anything) ** 1 is itself - * 3. (anything) ** NAN is NAN - * 4. NAN ** (anything except 0) is NAN - * 5. +-(|x| > 1) ** +INF is +INF - * 6. +-(|x| > 1) ** -INF is +0 - * 7. +-(|x| < 1) ** +INF is +0 - * 8. +-(|x| < 1) ** -INF is +INF - * 9. +-1 ** +-INF is NAN - * 10. +0 ** (+anything except 0, NAN) is +0 - * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 - * 12. +0 ** (-anything except 0, NAN) is +INF - * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF - * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) - * 15. +INF ** (+anything except 0,NAN) is +INF - * 16. +INF ** (-anything except 0,NAN) is +0 - * 17. -INF ** (anything) = -0 ** (-anything) - * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) - * 19. (-anything except 0 and inf) ** (non-integer) is NAN - * - * Accuracy: - * pow(x,y) returns x**y nearly rounded. In particular - * pow(integer,integer) - * always returns the correct integer provided it is - * representable. - * - * Constants : - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - */ - -#include "math.h" -#include "math_private.h" -#define zero C[0] -#define one C[1] -#define two C[2] -#define two53 C[3] -#define huge C[4] -#define tiny C[5] -#define L1 C[6] -#define L2 C[7] -#define L3 C[8] -#define L4 C[9] -#define L5 C[10] -#define L6 C[11] -#define P1 C[12] -#define P2 C[13] -#define P3 C[14] -#define P4 C[15] -#define P5 C[16] -#define lg2 C[17] -#define lg2_h C[18] -#define lg2_l C[19] -#define ovt C[20] -#define cp C[21] -#define cp_h C[22] -#define cp_l C[23] -#define ivln2 C[24] -#define ivln2_h C[25] -#define ivln2_l C[26] - -#ifdef __STDC__ -static const double -#else -static double -#endif -bp[] = {1.0, 1.5,}, -dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ -dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ -C[] = { -0.0, -1.0, -2.0, -9007199254740992.0 , -1.0e300, -1.0e-300, -5.99999999999994648725e-01 , -4.28571428578550184252e-01 , -3.33333329818377432918e-01 , -2.72728123808534006489e-01 , -2.30660745775561754067e-01 , -2.06975017800338417784e-01 , -1.66666666666666019037e-01 , --2.77777777770155933842e-03 , -6.61375632143793436117e-05 , --1.65339022054652515390e-06 , -4.13813679705723846039e-08 , -6.93147180559945286227e-01 , -6.93147182464599609375e-01 , --1.90465429995776804525e-09 , -8.0085662595372944372e-0017 , -9.61796693925975554329e-01 , -9.61796700954437255859e-01 , --7.02846165095275826516e-09 , -1.44269504088896338700e+00 , -1.44269502162933349609e+00 , -1.92596299112661746887e-08 }; - -#ifdef __STDC__ - double __ieee754_pow(double x, double y) -#else - double __ieee754_pow(x,y) - double x, y; -#endif -{ - double z,ax,z_h,z_l,p_h,p_l; - double y1,t1,t2,r,s,t,u,v,w, t12,t14,r_1,r_2,r_3; - int32_t i,j,k,yisint,n; - int32_t hx,hy,ix,iy; - u_int32_t lx,ly; - - EXTRACT_WORDS(hx,lx,x); - EXTRACT_WORDS(hy,ly,y); - ix = hx&0x7fffffff; iy = hy&0x7fffffff; - - /* y==zero: x**0 = 1 */ - if((iy|ly)==0) return C[1]; - - /* +-NaN return x+y */ - if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || - iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) - 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>=0x43400000) yisint = 2; /* even integer y */ - else if(iy>=0x3ff00000) { - k = (iy>>20)-0x3ff; /* exponent */ - if(k>20) { - j = ly>>(52-k); - if((u_int32_t)(j<<(52-k))==ly) yisint = 2-(j&1); - } else if(ly==0) { - j = iy>>(20-k); - if((int32_t)(j<<(20-k))==iy) yisint = 2-(j&1); - } - } - } - - /* special value of y */ - if(ly==0) { - if (iy==0x7ff00000) { /* y is +-inf */ - if(((ix-0x3ff00000)|lx)==0) - return y - y; /* inf**+-1 is NaN */ - else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ - return (hy>=0)? y: C[0]; - else /* (|x|<1)**-,+inf = inf,0 */ - return (hy<0)?-y: C[0]; - } - if(iy==0x3ff00000) { /* y is +-1 */ - if(hy<0) return C[1]/x; else return x; - } - if(hy==0x40000000) return x*x; /* y is 2 */ - if(hy==0x3fe00000) { /* y is 0.5 */ - if(hx>=0) /* x >= +0 */ - return __ieee754_sqrt(x); - } - } - - ax = fabs(x); - /* special value of x */ - if(lx==0) { - if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ - z = ax; /*x is +-0,+-inf,+-1*/ - if(hy<0) z = C[1]/z; /* z = (1/|x|) */ - if(hx<0) { - if(((ix-0x3ff00000)|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; - } - } - - /* (x<0)**(non-int) is NaN */ - if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); - - /* |y| is huge */ - if(iy>0x41e00000) { /* if |y| > 2**31 */ - if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ - if(ix<=0x3fefffff) return (hy<0)? C[4]*C[4]:C[5]*C[5]; - if(ix>=0x3ff00000) return (hy>0)? C[4]*C[4]:C[5]*C[5]; - } - /* over/underflow if x is not close to one */ - if(ix<0x3fefffff) return (hy<0)? C[4]*C[4]:C[5]*C[5]; - if(ix>0x3ff00000) return (hy>0)? C[4]*C[4]:C[5]*C[5]; - /* now |1-x| is tiny <= 2**-20, suffice to compute - log(x) by x-x^2/2+x^3/3-x^4/4 */ - t = x-1; /* t has 20 trailing zeros */ - w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); - u = C[25]*t; /* ivln2_h has 21 sig. bits */ - v = t*C[26]-w*C[24]; - t1 = u+v; - SET_LOW_WORD(t1,0); - t2 = v-(t1-u); - } else { - double s2,s_h,s_l,t_h,t_l,s22,s24,s26,r1,r2,r3; - n = 0; - /* take care subnormal number */ - if(ix<0x00100000) - {ax *= C[3]; n -= 53; GET_HIGH_WORD(ix,ax); } - n += ((ix)>>20)-0x3ff; - j = ix&0x000fffff; - /* determine interval */ - ix = j|0x3ff00000; /* normalize ix */ - if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ - else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ - else {k=0;n+=1;ix -= 0x00100000;} - SET_HIGH_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 = C[1]/(ax+bp[k]); - s = u*v; - s_h = s; - SET_LOW_WORD(s_h,0); - /* t_h=ax+bp[k] High */ - t_h = C[0]; - SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18)); - 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; -#ifdef DO_NOT_USE_THIS - r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); -#else - r1 = C[10]+s2*C[11]; s22=s2*s2; - r2 = C[8]+s2*C[9]; s24=s22*s22; - r3 = C[6]+s2*C[7]; s26=s24*s22; - r = r3*s22 + r2*s24 + r1*s26; -#endif - r += s_l*(s_h+s); - s2 = s_h*s_h; - t_h = 3.0+s2+r; - SET_LOW_WORD(t_h,0); - 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; - SET_LOW_WORD(p_h,0); - p_l = v-(p_h-u); - z_h = C[22]*p_h; /* cp_h+cp_l = 2/(3*log2) */ - z_l = C[23]*p_h+p_l*C[21]+dp_l[k]; - /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ - t = (double)n; - t1 = (((z_h+z_l)+dp_h[k])+t); - SET_LOW_WORD(t1,0); - t2 = z_l-(((t1-t)-dp_h[k])-z_h); - } - - s = C[1]; /* s (sign of result -ve**odd) = -1 else = 1 */ - if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) - s = -C[1];/* (-ve)**(odd int) */ - - /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ - y1 = y; - SET_LOW_WORD(y1,0); - p_l = (y-y1)*t1+y*t2; - p_h = y1*t1; - z = p_l+p_h; - EXTRACT_WORDS(j,i,z); - if (j>=0x40900000) { /* z >= 1024 */ - if(((j-0x40900000)|i)!=0) /* if z > 1024 */ - return s*C[4]*C[4]; /* overflow */ - else { - if(p_l+C[20]>z-p_h) return s*C[4]*C[4]; /* overflow */ - } - } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ - if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ - return s*C[5]*C[5]; /* underflow */ - else { - if(p_l<=z-p_h) return s*C[5]*C[5]; /* underflow */ - } - } - /* - * compute 2**(p_h+p_l) - */ - i = j&0x7fffffff; - k = (i>>20)-0x3ff; - n = 0; - if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ - n = j+(0x00100000>>(k+1)); - k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ - t = C[0]; - SET_HIGH_WORD(t,n&~(0x000fffff>>k)); - n = ((n&0x000fffff)|0x00100000)>>(20-k); - if(j<0) n = -n; - p_h -= t; - } - t = p_l+p_h; - SET_LOW_WORD(t,0); - u = t*C[18]; - v = (p_l-(t-p_h))*C[17]+t*C[19]; - z = u+v; - w = v-(z-u); - t = z*z; -#ifdef DO_NOT_USE_THIS - t1 = z - t*(C[12]+t*(C[13]+t*(C[14]+t*(C[15]+t*C[16])))); -#else - r_1 = C[15]+t*C[16]; t12 = t*t; - r_2 = C[13]+t*C[14]; t14 = t12*t12; - r_3 = t*C[12]; - t1 = z - r_3 - t12*r_2 - t14*r_1; -#endif - r = (z*t1)/(t1-C[2])-(w+z*w); - z = C[1]-(r-z); - GET_HIGH_WORD(j,z); - j += (n<<20); - if((j>>20)<=0) z = __scalbn(z,n); /* subnormal output */ - else SET_HIGH_WORD(z,j); - return s*z; -} |