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e_powf.c

/* 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.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_powf.c,v 1.7 1996/04/08 15:43:44 phil Exp $";
#endif

#include "math.h"
#include "math_private.h"

static const float huge = 1.0e+30, tiny = 1.0e-30;

#ifdef __STDC__
static const float
#else
static float
#endif
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
zero    =  0.0,
one   =  1.0,
two   =  2.0,
two24 =  16777216.0,    /* 0x4b800000 */
      /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1  =  6.0000002384e-01, /* 0x3f19999a */
L2  =  4.2857143283e-01, /* 0x3edb6db7 */
L3  =  3.3333334327e-01, /* 0x3eaaaaab */
L4  =  2.7272811532e-01, /* 0x3e8ba305 */
L5  =  2.3066075146e-01, /* 0x3e6c3255 */
L6  =  2.0697501302e-01, /* 0x3e53f142 */
P1   =  1.6666667163e-01, /* 0x3e2aaaab */
P2   = -2.7777778450e-03, /* 0xbb360b61 */
P3   =  6.6137559770e-05, /* 0x388ab355 */
P4   = -1.6533901999e-06, /* 0xb5ddea0e */
P5   =  4.1381369442e-08, /* 0x3331bb4c */
lg2  =  6.9314718246e-01, /* 0x3f317218 */
lg2_h  =  6.93145752e-01, /* 0x3f317200 */
lg2_l  =  1.42860654e-06, /* 0x35bfbe8c */
ovt =  4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
cp    =  9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
cp_h  =  9.6179199219e-01, /* 0x3f763800 =head of cp */
cp_l  =  4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
ivln2    =  1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
ivln2_h  =  1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/

#ifdef __STDC__
      float __ieee754_powf(float x, float y)
#else
      float __ieee754_powf(x,y)
      float x, y;
#endif
{
      float z,ax,z_h,z_l,p_h,p_l;
      float y1,t1,t2,r,s,t,u,v,w;
      int32_t i,j,k,yisint,n;
      int32_t hx,hy,ix,iy,is;

      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 */
      if(x == 1.0) return one;
      if(x == -1.0 && isinf(y)) return one;

    /* +-NaN return x+y */
      if(ix > 0x7f800000 ||
         iy > 0x7f800000)
            return 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 */
          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);

      /* 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 */
          SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(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 = (float)3.0+s2+r;
          GET_FLOAT_WORD(is,t_h);
          SET_FLOAT_WORD(t_h,is&0xfffff000);
          t_l = r-((t_h-(float)3.0)-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 = (float)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);
      }

      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;
}

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