| /* |
| * ==================================================== |
| * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #include "bsd_private.h" |
| |
| double bsd__ieee754_pow(double x, double y) |
| { |
| double z,ax,z_h,z_l,p_h,p_l; |
| double y1,t1,t2,r,s,t,u,v,w; |
| 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 one; |
| |
| /* x==1: 1**y = 1, even if y is NaN */ |
| if (hx==0x3ff00000 && lx == 0) return one; |
| |
| /* y!=zero: result is NaN if either arg is NaN */ |
| if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || |
| iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) |
| return (x+0.0)+(y+0.0); |
| |
| /* 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((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 one; /* (-1)**+-inf is NaN */ |
| else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ |
| return (hy>=0)? y: zero; |
| else /* (|x|<1)**-,+inf = inf,0 */ |
| return (hy<0)?-y: zero; |
| } |
| if(iy==0x3ff00000) { /* y is +-1 */ |
| if(hy<0) return one/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 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 = one/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; |
| } |
| } |
| |
| /* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be |
| n = (hx>>31)+1; |
| but ANSI C says a right shift of a signed negative quantity is |
| implementation defined. */ |
| n = ((u_int32_t)hx>>31)-1; |
| |
| /* (x<0)**(non-int) is NaN */ |
| if((n|yisint)==0) return (x-x)/(x-x); |
| |
| s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ |
| if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ |
| |
| /* |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)? huge*huge:tiny*tiny; |
| if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; |
| } |
| /* over/underflow if x is not close to one */ |
| if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny; |
| if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*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-one; /* t has 20 trailing zeros */ |
| w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); |
| u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ |
| v = t*ivln2_l-w*ivln2; |
| t1 = u+v; |
| SET_LOW_WORD(t1,0); |
| t2 = v-(t1-u); |
| } else { |
| double ss,s2,s_h,s_l,t_h,t_l; |
| n = 0; |
| /* take care subnormal number */ |
| if(ix<0x00100000) |
| {ax *= two53; 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 ss = 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 = one/(ax+bp[k]); |
| ss = u*v; |
| s_h = ss; |
| SET_LOW_WORD(s_h,0); |
| /* t_h=ax+bp[k] High */ |
| t_h = zero; |
| 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 = ss*ss; |
| r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); |
| r += s_l*(s_h+ss); |
| 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 = ss*(1+...) */ |
| u = s_h*t_h; |
| v = s_l*t_h+t_l*ss; |
| /* 2/(3log2)*(ss+...) */ |
| p_h = u+v; |
| SET_LOW_WORD(p_h,0); |
| 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) = (ss+..)*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); |
| } |
| |
| /* 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*huge*huge; /* overflow */ |
| else { |
| if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ |
| } |
| } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ |
| if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ |
| return s*tiny*tiny; /* underflow */ |
| else { |
| if(p_l<=z-p_h) return s*tiny*tiny; /* 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 = zero; |
| 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*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-two)-(w+z*w); |
| z = one-(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; |
| } |
