Back to index

glibc  2.9
Functions | Variables
e_powf.c File Reference
#include "math.h"
#include "math_private.h"

Go to the source code of this file.

Functions

float __ieee754_powf (float x, float y)

Variables

static const float huge = 1.0e+30
static const float tiny = 1.0e-30
static float bp [] = {1.0, 1.5,}
static float dp_h [] = { 0.0, 5.84960938e-01,}
static float dp_l [] = { 0.0, 1.56322085e-06,}
static float zero = 0.0
static float one = 1.0
static float two = 2.0
static float two24 = 16777216.0
static float L1 = 6.0000002384e-01
static float L2 = 4.2857143283e-01
static float L3 = 3.3333334327e-01
static float L4 = 2.7272811532e-01
static float L5 = 2.3066075146e-01
static float L6 = 2.0697501302e-01
static float P1 = 1.6666667163e-01
static float P2 = -2.7777778450e-03
static float P3 = 6.6137559770e-05
static float P4 = -1.6533901999e-06
static float P5 = 4.1381369442e-08
static float lg2 = 6.9314718246e-01
static float lg2_h = 6.93145752e-01
static float lg2_l = 1.42860654e-06
static float ovt = 4.2995665694e-08
static float cp = 9.6179670095e-01
static float cp_h = 9.6179199219e-01
static float cp_l = 4.7017383622e-06
static float ivln2 = 1.4426950216e+00
static float ivln2_h = 1.4426879883e+00
static float ivln2_l = 7.0526075433e-06

Function Documentation

float __ieee754_powf ( float  x,
float  y 
)

Definition at line 63 of file e_powf.c.

{
       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;
}

Here is the call graph for this function:

Here is the caller graph for this function:


Variable Documentation

float bp[] = {1.0, 1.5,} [static]

Definition at line 30 of file e_powf.c.

float cp = 9.6179670095e-01 [static]

Definition at line 53 of file e_powf.c.

float cp_h = 9.6179199219e-01 [static]

Definition at line 54 of file e_powf.c.

float cp_l = 4.7017383622e-06 [static]

Definition at line 55 of file e_powf.c.

float dp_h[] = { 0.0, 5.84960938e-01,} [static]

Definition at line 31 of file e_powf.c.

float dp_l[] = { 0.0, 1.56322085e-06,} [static]

Definition at line 32 of file e_powf.c.

const float huge = 1.0e+30 [static]

Definition at line 23 of file e_powf.c.

float ivln2 = 1.4426950216e+00 [static]

Definition at line 56 of file e_powf.c.

float ivln2_h = 1.4426879883e+00 [static]

Definition at line 57 of file e_powf.c.

float ivln2_l = 7.0526075433e-06 [static]

Definition at line 58 of file e_powf.c.

float L1 = 6.0000002384e-01 [static]

Definition at line 38 of file e_powf.c.

float L2 = 4.2857143283e-01 [static]

Definition at line 39 of file e_powf.c.

float L3 = 3.3333334327e-01 [static]

Definition at line 40 of file e_powf.c.

float L4 = 2.7272811532e-01 [static]

Definition at line 41 of file e_powf.c.

float L5 = 2.3066075146e-01 [static]

Definition at line 42 of file e_powf.c.

float L6 = 2.0697501302e-01 [static]

Definition at line 43 of file e_powf.c.

float lg2 = 6.9314718246e-01 [static]

Definition at line 49 of file e_powf.c.

float lg2_h = 6.93145752e-01 [static]

Definition at line 50 of file e_powf.c.

float lg2_l = 1.42860654e-06 [static]

Definition at line 51 of file e_powf.c.

float one = 1.0 [static]

Definition at line 34 of file e_powf.c.

float ovt = 4.2995665694e-08 [static]

Definition at line 52 of file e_powf.c.

float P1 = 1.6666667163e-01 [static]

Definition at line 44 of file e_powf.c.

float P2 = -2.7777778450e-03 [static]

Definition at line 45 of file e_powf.c.

float P3 = 6.6137559770e-05 [static]

Definition at line 46 of file e_powf.c.

float P4 = -1.6533901999e-06 [static]

Definition at line 47 of file e_powf.c.

float P5 = 4.1381369442e-08 [static]

Definition at line 48 of file e_powf.c.

const float tiny = 1.0e-30 [static]

Definition at line 23 of file e_powf.c.

float two = 2.0 [static]

Definition at line 35 of file e_powf.c.

float two24 = 16777216.0 [static]

Definition at line 36 of file e_powf.c.

float zero = 0.0 [static]

Definition at line 33 of file e_powf.c.