lib/libm/src/e_sqrtf.c

   1 /* e_sqrtf.c -- float version of e_sqrt.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 float     one     = 1.0, tiny=1.0e-30;
  20
  21 float
  22 sqrtf(float x)
  23 {
  24         float z;
  25         int32_t sign = (int)0x80000000;
  26         int32_t ix,s,q,m,t,i;
  27         u_int32_t r;
  28
  29         GET_FLOAT_WORD(ix,x);
  30
  31     /* take care of Inf and NaN */
  32         if((ix&0x7f800000)==0x7f800000) {
  33             return x*x+x;               /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
  34                                            sqrt(-inf)=sNaN */
  35         }
  36     /* take care of zero */
  37         if(ix<=0) {
  38             if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */
  39             else if(ix<0)
  40                 return (x-x)/(x-x);             /* sqrt(-ve) = sNaN */
  41         }
  42     /* normalize x */
  43         m = (ix>>23);
  44         if(m==0) {                              /* subnormal x */
  45             for(i=0;(ix&0x00800000)==0;i++) ix<<=1;
  46             m -= i-1;
  47         }
  48         m -= 127;       /* unbias exponent */
  49         ix = (ix&0x007fffff)|0x00800000;
  50         if(m&1) /* odd m, double x to make it even */
  51             ix += ix;
  52         m >>= 1;        /* m = [m/2] */
  53
  54     /* generate sqrt(x) bit by bit */
  55         ix += ix;
  56         q = s = 0;              /* q = sqrt(x) */
  57         r = 0x01000000;         /* r = moving bit from right to left */
  58
  59         while(r!=0) {
  60             t = s+r;
  61             if(t<=ix) {
  62                 s    = t+r;
  63                 ix  -= t;
  64                 q   += r;
  65             }
  66             ix += ix;
  67             r>>=1;
  68         }
  69
  70     /* use floating add to find out rounding direction */
  71         if(ix!=0) {
  72             z = one-tiny; /* trigger inexact flag */
  73             if (z>=one) {
  74                 z = one+tiny;
  75                 if (z>one)
  76                     q += 2;
  77                 else
  78                     q += (q&1);
  79             }
  80         }
  81         ix = (q>>1)+0x3f000000;
  82         ix += (m <<23);
  83         SET_FLOAT_WORD(z,ix);
  84         return z;
  85 }