/* 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. * ====================================================
*/
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 nan_mix(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>=0x4b800000) yisint = 2; /* even integer y */ elseif(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 */ elseif (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; elsereturn 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 */
} elseif(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<0x3f7ffff6) 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)*(half-t*(thrd-t*qrtr));
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) */ elseif(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 = 3+s2+r;
GET_FLOAT_WORD(is,t_h);
SET_FLOAT_WORD(t_h,is&0xfffff000);
t_l = r-((t_h-3)-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 = 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 */ elseif (j==0x43000000) { /* if z == 128 */ if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
} elseif ((j&0x7fffffff)>0x43160000) /* z <= -150 */ return sn*tiny*tiny; /* underflow */ elseif (j==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;
}
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