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  * $NetBSD: e_sqrtf.c,v 1.7 2002/05/26 22:01:53 wiz Exp $
  16  * $DragonFly: src/lib/libm/src/e_sqrtf.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  17  */
  18
  19 #include <math.h>
  20 #include "math_private.h"
  21
  22 static  const float     one     = 1.0, tiny=1.0e-30;
  23
  24 float
  25 sqrtf(float x)
  26 {
  27         float z;
  28         int32_t sign = (int)0x80000000;
  29         int32_t ix,s,q,m,t,i;
  30         u_int32_t r;
  31
  32         GET_FLOAT_WORD(ix,x);
  33
  34     /* take care of Inf and NaN */
  35         if((ix&0x7f800000)==0x7f800000) {
  36             return x*x+x;               /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
  37                                            sqrt(-inf)=sNaN */
  38         }
  39     /* take care of zero */
  40         if(ix<=0) {
  41             if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */
  42             else if(ix<0)
  43                 return (x-x)/(x-x);             /* sqrt(-ve) = sNaN */
  44         }
  45     /* normalize x */
  46         m = (ix>>23);
  47         if(m==0) {                              /* subnormal x */
  48             for(i=0;(ix&0x00800000)==0;i++) ix<<=1;
  49             m -= i-1;
  50         }
  51         m -= 127;       /* unbias exponent */
  52         ix = (ix&0x007fffff)|0x00800000;
  53         if(m&1) /* odd m, double x to make it even */
  54             ix += ix;
  55         m >>= 1;        /* m = [m/2] */
  56
  57     /* generate sqrt(x) bit by bit */
  58         ix += ix;
  59         q = s = 0;              /* q = sqrt(x) */
  60         r = 0x01000000;         /* r = moving bit from right to left */
  61
  62         while(r!=0) {
  63             t = s+r;
  64             if(t<=ix) {
  65                 s    = t+r;
  66                 ix  -= t;
  67                 q   += r;
  68             }
  69             ix += ix;
  70             r>>=1;
  71         }
  72
  73     /* use floating add to find out rounding direction */
  74         if(ix!=0) {
  75             z = one-tiny; /* trigger inexact flag */
  76             if (z>=one) {
  77                 z = one+tiny;
  78                 if (z>one)
  79                     q += 2;
  80                 else
  81                     q += (q&1);
  82             }
  83         }
  84         ix = (q>>1)+0x3f000000;
  85         ix += (m <<23);
  86         SET_FLOAT_WORD(z,ix);
  87         return z;
  88 }