root/lib/math/ef_pow.c

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DEFINITIONS

This source file includes following definitions.
  1. powf

   1 /* ef_pow.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 #include "fdlibm.h"
  17 #include "stdlib.h"
  18 
  19 static const float
  20 bp[] = {1.0, 1.5,},
  21 dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
  22 dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
  23 zero    =  0.0,
  24 one     =  1.0,
  25 two     =  2.0,
  26 two24   =  16777216.0,  /* 0x4b800000 */
  27 huge    =  1.0e30,
  28 tiny    =  1.0e-30,
  29         /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
  30 L1  =  6.0000002384e-01, /* 0x3f19999a */
  31 L2  =  4.2857143283e-01, /* 0x3edb6db7 */
  32 L3  =  3.3333334327e-01, /* 0x3eaaaaab */
  33 L4  =  2.7272811532e-01, /* 0x3e8ba305 */
  34 L5  =  2.3066075146e-01, /* 0x3e6c3255 */
  35 L6  =  2.0697501302e-01, /* 0x3e53f142 */
  36 P1   =  1.6666667163e-01, /* 0x3e2aaaab */
  37 P2   = -2.7777778450e-03, /* 0xbb360b61 */
  38 P3   =  6.6137559770e-05, /* 0x388ab355 */
  39 P4   = -1.6533901999e-06, /* 0xb5ddea0e */
  40 P5   =  4.1381369442e-08, /* 0x3331bb4c */
  41 lg2  =  6.9314718246e-01, /* 0x3f317218 */
  42 lg2_h  =  6.93145752e-01, /* 0x3f317200 */
  43 lg2_l  =  1.42860654e-06, /* 0x35bfbe8c */
  44 ovt =  4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
  45 cp    =  9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
  46 cp_h  =  9.6179199219e-01, /* 0x3f763800 =head of cp */
  47 cp_l  =  4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
  48 ivln2    =  1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
  49 ivln2_h  =  1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
  50 ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
  51 
  52 float powf(float x, float y)
  53 {
  54         float z,ax,z_h,z_l,p_h,p_l;
  55         float y1,t1,t2,r,s,t,u,v,w;
  56         int i,j,k,yisint,n;
  57         int hx,hy,ix,iy,is;
  58 
  59         GET_FLOAT_WORD(hx,x);
  60         GET_FLOAT_WORD(hy,y);
  61         ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
  62 
  63     /* y==zero: x**0 = 1 */
  64         if(FLT_UWORD_IS_ZERO(iy)) return one;   
  65 
  66     /* +-NaN return x+y */
  67         if(FLT_UWORD_IS_NAN(ix) ||
  68            FLT_UWORD_IS_NAN(iy))
  69                 return x+y;     
  70 
  71     /* determine if y is an odd int when x < 0
  72      * yisint = 0       ... y is not an integer
  73      * yisint = 1       ... y is an odd int
  74      * yisint = 2       ... y is an even int
  75      */
  76         yisint  = 0;
  77         if(hx<0) {      
  78             if(iy>=0x4b800000) yisint = 2; /* even integer y */
  79             else if(iy>=0x3f800000) {
  80                 k = (iy>>23)-0x7f;         /* exponent */
  81                 j = iy>>(23-k);
  82                 if((j<<(23-k))==iy) yisint = 2-(j&1);
  83             }           
  84         } 
  85 
  86     /* special value of y */
  87         if (FLT_UWORD_IS_INFINITE(iy)) {        /* y is +-inf */
  88             if (ix==0x3f800000)
  89                 return  y - y;  /* inf**+-1 is NaN */
  90             else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
  91                 return (hy>=0)? y: zero;
  92             else                        /* (|x|<1)**-,+inf = inf,0 */
  93                 return (hy<0)?-y: zero;
  94         } 
  95         if(iy==0x3f800000) {    /* y is  +-1 */
  96             if(hy<0) return one/x; else return x;
  97         }
  98         if(hy==0x40000000) return x*x; /* y is  2 */
  99         if(hy==0x3f000000) {    /* y is  0.5 */
 100             if(hx>=0)   /* x >= +0 */
 101             return sqrtf(x);    
 102         }
 103 
 104         ax   = fabsf(x);
 105     /* special value of x */
 106         if(FLT_UWORD_IS_INFINITE(ix)||FLT_UWORD_IS_ZERO(ix)||ix==0x3f800000){
 107             z = ax;                     /*x is +-0,+-inf,+-1*/
 108             if(hy<0) z = one/z; /* z = (1/|x|) */
 109             if(hx<0) {
 110                 if(((ix-0x3f800000)|yisint)==0) {
 111                     z = (z-z)/(z-z); /* (-1)**non-int is NaN */
 112                 } else if(yisint==1) 
 113                     z = -z;             /* (x<0)**odd = -(|x|**odd) */
 114             }
 115             return z;
 116         }
 117     
 118     /* (x<0)**(non-int) is NaN */
 119         if(((((unsigned int)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
 120 
 121     /* |y| is huge */
 122         if(iy>0x4d000000) { /* if |y| > 2**27 */
 123         /* over/underflow if x is not close to one */
 124             if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
 125             if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
 126         /* now |1-x| is tiny <= 2**-20, suffice to compute 
 127            log(x) by x-x^2/2+x^3/3-x^4/4 */
 128             t = x-1;            /* t has 20 trailing zeros */
 129             w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
 130             u = ivln2_h*t;      /* ivln2_h has 16 sig. bits */
 131             v = t*ivln2_l-w*ivln2;
 132             t1 = u+v;
 133             GET_FLOAT_WORD(is,t1);
 134             SET_FLOAT_WORD(t1,is&0xfffff000);
 135             t2 = v-(t1-u);
 136         } else {
 137             float s2,s_h,s_l,t_h,t_l;
 138             n = 0;
 139         /* take care subnormal number */
 140             if(FLT_UWORD_IS_SUBNORMAL(ix))
 141                 {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
 142             n  += ((ix)>>23)-0x7f;
 143             j  = ix&0x007fffff;
 144         /* determine interval */
 145             ix = j|0x3f800000;          /* normalize ix */
 146             if(j<=0x1cc471) k=0;        /* |x|<sqrt(3/2) */
 147             else if(j<0x5db3d7) k=1;    /* |x|<sqrt(3)   */
 148             else {k=0;n+=1;ix -= 0x00800000;}
 149             SET_FLOAT_WORD(ax,ix);
 150 
 151         /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
 152             u = ax-bp[k];               /* bp[0]=1.0, bp[1]=1.5 */
 153             v = one/(ax+bp[k]);
 154             s = u*v;
 155             s_h = s;
 156             GET_FLOAT_WORD(is,s_h);
 157             SET_FLOAT_WORD(s_h,is&0xfffff000);
 158         /* t_h=ax+bp[k] High */
 159             SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
 160             t_l = ax - (t_h-bp[k]);
 161             s_l = v*((u-s_h*t_h)-s_h*t_l);
 162         /* compute log(ax) */
 163             s2 = s*s;
 164             r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
 165             r += s_l*(s_h+s);
 166             s2  = s_h*s_h;
 167             t_h = (float)3.0+s2+r;
 168             GET_FLOAT_WORD(is,t_h);
 169             SET_FLOAT_WORD(t_h,is&0xfffff000);
 170             t_l = r-((t_h-(float)3.0)-s2);
 171         /* u+v = s*(1+...) */
 172             u = s_h*t_h;
 173             v = s_l*t_h+t_l*s;
 174         /* 2/(3log2)*(s+...) */
 175             p_h = u+v;
 176             GET_FLOAT_WORD(is,p_h);
 177             SET_FLOAT_WORD(p_h,is&0xfffff000);
 178             p_l = v-(p_h-u);
 179             z_h = cp_h*p_h;             /* cp_h+cp_l = 2/(3*log2) */
 180             z_l = cp_l*p_h+p_l*cp+dp_l[k];
 181         /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
 182             t = (float)n;
 183             t1 = (((z_h+z_l)+dp_h[k])+t);
 184             GET_FLOAT_WORD(is,t1);
 185             SET_FLOAT_WORD(t1,is&0xfffff000);
 186             t2 = z_l-(((t1-t)-dp_h[k])-z_h);
 187         }
 188 
 189         s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
 190         if(((((unsigned int)hx>>31)-1)|(yisint-1))==0)
 191             s = -one;   /* (-ve)**(odd int) */
 192 
 193     /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
 194         GET_FLOAT_WORD(is,y);
 195         SET_FLOAT_WORD(y1,is&0xfffff000);
 196         p_l = (y-y1)*t1+y*t2;
 197         p_h = y1*t1;
 198         z = p_l+p_h;
 199         GET_FLOAT_WORD(j,z);
 200         i = j&0x7fffffff;
 201         if (j>0) {
 202             if (i>FLT_UWORD_EXP_MAX)
 203                 return s*huge*huge;                     /* overflow */
 204             else if (i==FLT_UWORD_EXP_MAX)
 205                 if(p_l+ovt>z-p_h) return s*huge*huge;   /* overflow */
 206         } else {
 207             if (i>FLT_UWORD_EXP_MIN)
 208                 return s*tiny*tiny;                     /* underflow */
 209             else if (i==FLT_UWORD_EXP_MIN)
 210                 if(p_l<=z-p_h) return s*tiny*tiny;      /* underflow */
 211         }
 212     /*
 213      * compute 2**(p_h+p_l)
 214      */
 215         k = (i>>23)-0x7f;
 216         n = 0;
 217         if(i>0x3f000000) {              /* if |z| > 0.5, set n = [z+0.5] */
 218             n = j+(0x00800000>>(k+1));
 219             k = ((n&0x7fffffff)>>23)-0x7f;      /* new k for n */
 220             SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
 221             n = ((n&0x007fffff)|0x00800000)>>(23-k);
 222             if(j<0) n = -n;
 223             p_h -= t;
 224         } 
 225         t = p_l+p_h;
 226         GET_FLOAT_WORD(is,t);
 227         SET_FLOAT_WORD(t,is&0xfffff000);
 228         u = t*lg2_h;
 229         v = (p_l-(t-p_h))*lg2+t*lg2_l;
 230         z = u+v;
 231         w = v-(z-u);
 232         t  = z*z;
 233         t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
 234         r  = (z*t1)/(t1-two)-(w+z*w);
 235         z  = one-(r-z);
 236         GET_FLOAT_WORD(j,z);
 237         j += (n<<23);
 238         if((j>>23)<=0) z = scalbnf(z,(int)n);   /* subnormal output */
 239         else SET_FLOAT_WORD(z,j);
 240         return s*z;
 241 }

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