gonzui

    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: #include "math.h"
   17: #include "math_private.h"
   18: 
   19: static const volatile float huge = 1.0e+30, tiny = 1.0e-30;
   20: 
   21: static const float
   22: bp[] = {1.0, 1.5,},
   23: dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
   24: dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
   25: zero    =  0.0,
   26: one     =  1.0,
   27: two     =  2.0,
   28: two24   =  16777216.0,    /* 0x4b800000 */
   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
   53: powf(float x, float y)
   54: {
   55:         float z,ax,z_h,z_l,p_h,p_l;
   56:         float yy1,t1,t2,r,s,t,u,v,w;
   57:         int32_t i,j,k,yisint,n;
   58:         int32_t hx,hy,ix,iy,is;
   59: 
   60:         GET_FLOAT_WORD(hx,x);
   61:         GET_FLOAT_WORD(hy,y);
   62:         ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
   63: 
   64:     /* y==zero: x**0 = 1 */
   65:         if(iy==0) return one;  
   66: 
   67:     /* +-NaN return x+y */
   68:         if(ix > 0x7f800000 ||
   69:            iy > 0x7f800000)
   70:                 return x+y;   
   71: 
   72:     /* determine if y is an odd int when x < 0
   73:      * yisint = 0       ... y is not an integer
   74:      * yisint = 1       ... y is an odd int
   75:      * yisint = 2       ... y is an even int
   76:      */
   77:         yisint  = 0;
   78:         if(hx<0) {     
   79:             if(iy>=0x4b800000) yisint = 2; /* even integer y */
   80:             else if(iy>=0x3f800000) {
   81:                 k = (iy>>23)-0x7f;       /* exponent */
   82:                 j = iy>>(23-k);
   83:                 if((j<<(23-k))==iy) yisint = 2-(j&1);
   84:             }          
   85:         } 
   86: 
   87:     /* special value of y */
   88:         if (iy==0x7f800000) {  /* y is +-inf */
   89:             if (ix==0x3f800000)
   90:                 return  y - y; /* inf**+-1 is NaN */
   91:             else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
   92:                 return (hy>=0)? y: zero;
   93:             else                       /* (|x|<1)**-,+inf = inf,0 */
   94:                 return (hy<0)?-y: zero;
   95:         } 
   96:         if(iy==0x3f800000) {   /* y is  +-1 */
   97:             if(hy<0) return one/x; else return x;
   98:         }
   99:         if(hy==0x40000000) return x*x; /* y is  2 */
  100:         if(hy==0x3f000000) {   /* y is  0.5 */
  101:             if(hx>=0)  /* x >= +0 */
  102:             return sqrtf(x);   
  103:         }
  104: 
  105:         ax   = fabsf(x);
  106:     /* special value of x */
  107:         if(ix==0x7f800000||ix==0||ix==0x3f800000){
  108:             z = ax;                    /*x is +-0,+-inf,+-1*/
  109:             if(hy<0) z = one/z;        /* z = (1/|x|) */
  110:             if(hx<0) {
  111:                 if(((ix-0x3f800000)|yisint)==0) {
  112:                     z = (z-z)/(z-z); /* (-1)**non-int is NaN */
  113:                 } else if(yisint==1) 
  114:                     z = -z;           /* (x<0)**odd = -(|x|**odd) */
  115:             }
  116:             return z;
  117:         }
  118:     
  119:     /* (x<0)**(non-int) is NaN */
  120:         if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
  121: 
  122:     /* |y| is huge */
  123:         if(iy>0x4d000000) { /* if |y| > 2**27 */
  124:         /* over/underflow if x is not close to one */
  125:             if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
  126:             if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
  127:         /* now |1-x| is tiny <= 2**-20, suffice to compute 
  128:            log(x) by x-x^2/2+x^3/3-x^4/4 */
  129:             t = ax-one;                /* t has 20 trailing zeros */
  130:             w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
  131:             u = ivln2_h*t;     /* ivln2_h has 16 sig. bits */
  132:             v = t*ivln2_l-w*ivln2;
  133:             t1 = u+v;
  134:             GET_FLOAT_WORD(is,t1);
  135:             SET_FLOAT_WORD(t1,is&0xfffff000);
  136:             t2 = v-(t1-u);
  137:         } else {
  138:             float s2,s_h,s_l,t_h,t_l;
  139:             n = 0;
  140:         /* take care subnormal number */
  141:             if(ix<0x00800000)
  142:                 {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
  143:             n  += ((ix)>>23)-0x7f;
  144:             j  = ix&0x007fffff;
  145:         /* determine interval */
  146:             ix = j|0x3f800000;         /* normalize ix */
  147:             if(j<=0x1cc471) k=0;       /* |x|<sqrt(3/2) */
  148:             else if(j<0x5db3d7) k=1;   /* |x|<sqrt(3)   */
  149:             else {k=0;n+=1;ix -= 0x00800000;}
  150:             SET_FLOAT_WORD(ax,ix);
  151: 
  152:         /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
  153:             u = ax-bp[k];              /* bp[0]=1.0, bp[1]=1.5 */
  154:             v = one/(ax+bp[k]);
  155:             s = u*v;
  156:             s_h = s;
  157:             GET_FLOAT_WORD(is,s_h);
  158:             SET_FLOAT_WORD(s_h,is&0xfffff000);
  159:         /* t_h=ax+bp[k] High */
  160:             SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
  161:             t_l = ax - (t_h-bp[k]);
  162:             s_l = v*((u-s_h*t_h)-s_h*t_l);
  163:         /* compute log(ax) */
  164:             s2 = s*s;
  165:             r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
  166:             r += s_l*(s_h+s);
  167:             s2  = s_h*s_h;
  168:             t_h = (float)3.0+s2+r;
  169:             GET_FLOAT_WORD(is,t_h);
  170:             SET_FLOAT_WORD(t_h,is&0xfffff000);
  171:             t_l = r-((t_h-(float)3.0)-s2);
  172:         /* u+v = s*(1+...) */
  173:             u = s_h*t_h;
  174:             v = s_l*t_h+t_l*s;
  175:         /* 2/(3log2)*(s+...) */
  176:             p_h = u+v;
  177:             GET_FLOAT_WORD(is,p_h);
  178:             SET_FLOAT_WORD(p_h,is&0xfffff000);
  179:             p_l = v-(p_h-u);
  180:             z_h = cp_h*p_h;            /* cp_h+cp_l = 2/(3*log2) */
  181:             z_l = cp_l*p_h+p_l*cp+dp_l[k];
  182:         /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
  183:             t = (float)n;
  184:             t1 = (((z_h+z_l)+dp_h[k])+t);
  185:             GET_FLOAT_WORD(is,t1);
  186:             SET_FLOAT_WORD(t1,is&0xfffff000);
  187:             t2 = z_l-(((t1-t)-dp_h[k])-z_h);
  188:         }
  189: 
  190:         s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
  191:         if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
  192:             s = -one;  /* (-ve)**(odd int) */
  193: 
  194:     /* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */
  195:         GET_FLOAT_WORD(is,y);
  196:         SET_FLOAT_WORD(yy1,is&0xfffff000);
  197:         p_l = (y-yy1)*t1+y*t2;
  198:         p_h = yy1*t1;
  199:         z = p_l+p_h;
  200:         GET_FLOAT_WORD(j,z);
  201:         if (j>0x43000000)                              /* if z > 128 */
  202:             return s*huge*huge;                                /* overflow */
  203:         else if (j==0x43000000) {                      /* if z == 128 */
  204:             if(p_l+ovt>z-p_h) return s*huge*huge;      /* overflow */
  205:         }
  206:         else if ((j&0x7fffffff)>0x43160000)            /* z <= -150 */
  207:             return s*tiny*tiny;                                /* underflow */
  208:         else if (j==0xc3160000){                       /* z == -150 */
  209:             if(p_l<=z-p_h) return s*tiny*tiny;         /* underflow */
  210:         }
  211:     /*
  212:      * compute 2**(p_h+p_l)
  213:      */
  214:         i = j&0x7fffffff;
  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,n);       /* subnormal output */
  239:         else SET_FLOAT_WORD(z,j);
  240:         return s*z;
  241: }