/* e_powf.c -- float version of e_pow.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. * ==================================================== */
/* 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 y - y;/* inf**+-1 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 __ieee754_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; }
/* (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>0x4d000000) { /* if |y| > 2**27 */ /* over/underflow if x is not close to one */ if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny; if(ix>0x3f800007) return (hy>0)? huge*huge: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 = x-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);
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
/* 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 s*huge*huge;/* overflow */ else if (j==0x43000000) {/* if z == 128 */ if(p_l+ovt>z-p_h) return s*huge*huge;/* overflow */ } else if ((j&0x7fffffff)>0x43160000)/* z <= -150 */ return s*tiny*tiny;/* underflow */ else if ((u_int32_t) j==0xc3160000){/* z == -150 */ if(p_l<=z-p_h) return s*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&0xfffff000); 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 s*z; }
