| /* |
| * ==================================================== |
| * 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 "bsd_privatef.h" |
| |
| float bsd__ieee754_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; |
| |
| /* y==zero: x**0 = 1 */ |
| if(iy==0) return one; |
| |
| /* x==1: 1**y = 1, even if y is NaN */ |
| if (hx==0x3f800000) return one; |
| |
| /* y!=zero: result is NaN if either arg is NaN */ |
| if(ix > 0x7f800000 || |
| iy > 0x7f800000) |
| return (x+0.0F)+(y+0.0F); |
| |
| /* 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) |
| return one; /* (-1)**+-inf is NaN */ |
| else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */ |
| return (hy>=0)? y: zero; |
| else /* (|x|<1)**-,+inf = inf,0 */ |
| return (hy<0)?-y: zero; |
| } |
| if(iy==0x3f800000) { /* y is +-1 */ |
| if(hy<0) return one/x; else return x; |
| } |
| if(hy==0x40000000) return x*x; /* y is 2 */ |
| 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){ |
| z = ax; /*x is +-0,+-inf,+-1*/ |
| if(hy<0) z = one/z; /* z = (1/|x|) */ |
| 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; |
| } |
| |
| n = ((u_int32_t)hx>>31)-1; |
| |
| /* (x<0)**(non-int) is NaN */ |
| if((n|yisint)==0) return (x-x)/(x-x); |
| |
| sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */ |
| if((n|(yisint-1))==0) sn = -one; /* (-ve)**(odd int) */ |
| |
| /* |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)*((float)0.5-t*((float)0.333333333333-t*(float)0.25)); |
| 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) k=0; /* |x|<sqrt(3/2) */ |
| else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */ |
| 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 = one/(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 = (float)3.0+s2+r; |
| GET_FLOAT_WORD(is,t_h); |
| SET_FLOAT_WORD(t_h,is&0xfffff000); |
| t_l = r-((t_h-(float)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; |
| 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 */ |
| return sn*tiny*tiny; /* underflow */ |
| else if ((j&0xffffffff)==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-two)-(w+z*w); |
| z = one-(r-z); |
| GET_FLOAT_WORD(j,z); |
| j += (n<<23); |
| if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */ |
| else SET_FLOAT_WORD(z,j); |
| return sn*z; |
| } |
