compiler/stdc/math/e_powf.c

   1 /* e_powf.c -- float version of e_pow.c.
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 #ifndef lint
  17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_powf.c,v 1.12 2004/06/01 19:33:30 bde Exp $";
  18 #endif
  19
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 static const float
  24 bp[] = {1.0, 1.5,},
  25 dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
  26 dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
  27 zero    =  0.0,
  28 one     =  1.0,
  29 two     =  2.0,
  30 two24   =  16777216.0,  /* 0x4b800000 */
  31 huge    =  1.0e30,
  32 tiny    =  1.0e-30,
  33         /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
  34 L1  =  6.0000002384e-01, /* 0x3f19999a */
  35 L2  =  4.2857143283e-01, /* 0x3edb6db7 */
  36 L3  =  3.3333334327e-01, /* 0x3eaaaaab */
  37 L4  =  2.7272811532e-01, /* 0x3e8ba305 */
  38 L5  =  2.3066075146e-01, /* 0x3e6c3255 */
  39 L6  =  2.0697501302e-01, /* 0x3e53f142 */
  40 P1   =  1.6666667163e-01, /* 0x3e2aaaab */
  41 P2   = -2.7777778450e-03, /* 0xbb360b61 */
  42 P3   =  6.6137559770e-05, /* 0x388ab355 */
  43 P4   = -1.6533901999e-06, /* 0xb5ddea0e */
  44 P5   =  4.1381369442e-08, /* 0x3331bb4c */
  45 lg2  =  6.9314718246e-01, /* 0x3f317218 */
  46 lg2_h  =  6.93145752e-01, /* 0x3f317200 */
  47 lg2_l  =  1.42860654e-06, /* 0x35bfbe8c */
  48 ovt =  4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
  49 cp    =  9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
  50 cp_h  =  9.6179199219e-01, /* 0x3f763800 =head of cp */
  51 cp_l  =  4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
  52 ivln2    =  1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
  53 ivln2_h  =  1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
  54 ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
  55
  56 float
  57 __ieee754_powf(float x, float y)
  58 {
  59         float z,ax,z_h,z_l,p_h,p_l;
  60         float y1,t1,t2,r,s,sn,t,u,v,w;
  61         int32_t i,j,k,yisint,n;
  62         int32_t hx,hy,ix,iy,is;
  63
  64         GET_FLOAT_WORD(hx,x);
  65         GET_FLOAT_WORD(hy,y);
  66         ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
  67
  68     /* y==zero: x**0 = 1 */
  69         if(iy==0) return one;
  70
  71     /* +-NaN return x+y */
  72         if(ix > 0x7f800000 ||
  73            iy > 0x7f800000)
  74                 return x+y;
  75
  76     /* determine if y is an odd int when x < 0
  77      * yisint = 0       ... y is not an integer
  78      * yisint = 1       ... y is an odd int
  79      * yisint = 2       ... y is an even int
  80      */
  81         yisint  = 0;
  82         if(hx<0) {
  83             if(iy>=0x4b800000) yisint = 2; /* even integer y */
  84             else if(iy>=0x3f800000) {
  85                 k = (iy>>23)-0x7f;         /* exponent */
  86                 j = iy>>(23-k);
  87                 if((j<<(23-k))==iy) yisint = 2-(j&1);
  88             }
  89         }
  90
  91     /* special value of y */
  92         if (iy==0x7f800000) {   /* y is +-inf */
  93             if (ix==0x3f800000)
  94                 return  y - y;  /* inf**+-1 is NaN */
  95             else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
  96                 return (hy>=0)? y: zero;
  97             else                        /* (|x|<1)**-,+inf = inf,0 */
  98                 return (hy<0)?-y: zero;
  99         }
 100         if(iy==0x3f800000) {    /* y is  +-1 */
 101             if(hy<0) return one/x; else return x;
 102         }
 103         if(hy==0x40000000) return x*x; /* y is  2 */
 104         if(hy==0x3f000000) {    /* y is  0.5 */
 105             if(hx>=0)   /* x >= +0 */
 106             return __ieee754_sqrtf(x);
 107         }
 108
 109         ax   = fabsf(x);
 110     /* special value of x */
 111         if(ix==0x7f800000||ix==0||ix==0x3f800000){
 112             z = ax;                     /*x is +-0,+-inf,+-1*/
 113             if(hy<0) z = one/z; /* z = (1/|x|) */
 114             if(hx<0) {
 115                 if(((ix-0x3f800000)|yisint)==0) {
 116                     z = (z-z)/(z-z); /* (-1)**non-int is NaN */
 117                 } else if(yisint==1)
 118                     z = -z;             /* (x<0)**odd = -(|x|**odd) */
 119             }
 120             return z;
 121         }
 122
 123         n = ((uint32_t)hx>>31)-1;
 124
 125     /* (x<0)**(non-int) is NaN */
 126         if((n|yisint)==0) return (x-x)/(x-x);
 127
 128         sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
 129         if((n|(yisint-1))==0) sn = -one;/* (-ve)**(odd int) */
 130
 131     /* |y| is huge */
 132         if(iy>0x4d000000) { /* if |y| > 2**27 */
 133         /* over/underflow if x is not close to one */
 134             if(ix<0x3f7ffff8) return (hy<0)? sn*huge*huge:sn*tiny*tiny;
 135             if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*tiny*tiny;
 136         /* now |1-x| is tiny <= 2**-20, suffice to compute
 137            log(x) by x-x^2/2+x^3/3-x^4/4 */
 138             t = ax-1;           /* t has 20 trailing zeros */
 139             w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
 140             u = ivln2_h*t;      /* ivln2_h has 16 sig. bits */
 141             v = t*ivln2_l-w*ivln2;
 142             t1 = u+v;
 143             GET_FLOAT_WORD(is,t1);
 144             SET_FLOAT_WORD(t1,is&0xfffff000);
 145             t2 = v-(t1-u);
 146         } else {
 147             float s2,s_h,s_l,t_h,t_l;
 148             n = 0;
 149         /* take care subnormal number */
 150             if(ix<0x00800000)
 151                 {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
 152             n  += ((ix)>>23)-0x7f;
 153             j  = ix&0x007fffff;
 154         /* determine interval */
 155             ix = j|0x3f800000;          /* normalize ix */
 156             if(j<=0x1cc471) k=0;        /* |x|<sqrt(3/2) */
 157             else if(j<0x5db3d7) k=1;    /* |x|<sqrt(3)   */
 158             else {k=0;n+=1;ix -= 0x00800000;}
 159             SET_FLOAT_WORD(ax,ix);
 160
 161         /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
 162             u = ax-bp[k];               /* bp[0]=1.0, bp[1]=1.5 */
 163             v = one/(ax+bp[k]);
 164             s = u*v;
 165             s_h = s;
 166             GET_FLOAT_WORD(is,s_h);
 167             SET_FLOAT_WORD(s_h,is&0xfffff000);
 168         /* t_h=ax+bp[k] High */
 169             is = ((ix>>1)&0xfffff000)|0x20000000;
 170             SET_FLOAT_WORD(t_h,is+0x00400000+(k<<21));
 171             t_l = ax - (t_h-bp[k]);
 172             s_l = v*((u-s_h*t_h)-s_h*t_l);
 173         /* compute log(ax) */
 174             s2 = s*s;
 175             r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
 176             r += s_l*(s_h+s);
 177             s2  = s_h*s_h;
 178             t_h = (float)3.0+s2+r;
 179             GET_FLOAT_WORD(is,t_h);
 180             SET_FLOAT_WORD(t_h,is&0xfffff000);
 181             t_l = r-((t_h-(float)3.0)-s2);
 182         /* u+v = s*(1+...) */
 183             u = s_h*t_h;
 184             v = s_l*t_h+t_l*s;
 185         /* 2/(3log2)*(s+...) */
 186             p_h = u+v;
 187             GET_FLOAT_WORD(is,p_h);
 188             SET_FLOAT_WORD(p_h,is&0xfffff000);
 189             p_l = v-(p_h-u);
 190             z_h = cp_h*p_h;             /* cp_h+cp_l = 2/(3*log2) */
 191             z_l = cp_l*p_h+p_l*cp+dp_l[k];
 192         /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
 193             t = (float)n;
 194             t1 = (((z_h+z_l)+dp_h[k])+t);
 195             GET_FLOAT_WORD(is,t1);
 196             SET_FLOAT_WORD(t1,is&0xfffff000);
 197             t2 = z_l-(((t1-t)-dp_h[k])-z_h);
 198         }
 199
 200     /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
 201         GET_FLOAT_WORD(is,y);
 202         SET_FLOAT_WORD(y1,is&0xfffff000);
 203         p_l = (y-y1)*t1+y*t2;
 204         p_h = y1*t1;
 205         z = p_l+p_h;
 206         GET_FLOAT_WORD(j,z);
 207         if (j>0x43000000)                               /* if z > 128 */
 208             return sn*huge*huge;                        /* overflow */
 209         else if (j==0x43000000) {                       /* if z == 128 */
 210             if(p_l+ovt>z-p_h) return sn*huge*huge;      /* overflow */
 211         }
 212         else if ((j&0x7fffffff)>0x43160000)             /* z <= -150 */
 213             return sn*tiny*tiny;                        /* underflow */
 214         else if (j==0xc3160000){                        /* z == -150 */
 215             if(p_l<=z-p_h) return sn*tiny*tiny;         /* underflow */
 216         }
 217     /*
 218      * compute 2**(p_h+p_l)
 219      */
 220         i = j&0x7fffffff;
 221         k = (i>>23)-0x7f;
 222         n = 0;
 223         if(i>0x3f000000) {              /* if |z| > 0.5, set n = [z+0.5] */
 224             n = j+(0x00800000>>(k+1));
 225             k = ((n&0x7fffffff)>>23)-0x7f;      /* new k for n */
 226             SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
 227             n = ((n&0x007fffff)|0x00800000)>>(23-k);
 228             if(j<0) n = -n;
 229             p_h -= t;
 230         }
 231         t = p_l+p_h;
 232         GET_FLOAT_WORD(is,t);
 233         SET_FLOAT_WORD(t,is&0xffff8000);
 234         u = t*lg2_h;
 235         v = (p_l-(t-p_h))*lg2+t*lg2_l;
 236         z = u+v;
 237         w = v-(z-u);
 238         t  = z*z;
 239         t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
 240         r  = (z*t1)/(t1-two)-(w+z*w);
 241         z  = one-(r-z);
 242         GET_FLOAT_WORD(j,z);
 243         j += (n<<23);
 244         if((j>>23)<=0) z = scalbnf(z,n);        /* subnormal output */
 245         else SET_FLOAT_WORD(z,j);
 246         return sn*z;
 247 }