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 <sys/cdefs.h>
  17 #if defined(LIBM_SCCS) && !defined(lint)
  18 __RCSID("$NetBSD: e_sqrtf.c,v 1.7 2002/05/26 22:01:53 wiz Exp $");
  19 #endif
  20
  21 #include "math.h"
  22 #include "math_private.h"
  23
  24 static  const float     one     = 1.0, tiny=1.0e-30;
  25
  26 float
  27 __ieee754_sqrtf(float x)
  28 {
  29         float z;
  30         int32_t sign = (int)0x80000000;
  31         int32_t ix,s,q,m,t,i;
  32         u_int32_t r;
  33
  34         GET_FLOAT_WORD(ix,x);
  35
  36     /* take care of Inf and NaN */
  37         if((ix&0x7f800000)==0x7f800000) {
  38             return x*x+x;               /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
  39                                            sqrt(-inf)=sNaN */
  40         }
  41     /* take care of zero */
  42         if(ix<=0) {
  43             if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */
  44             else if(ix<0)
  45                 return (x-x)/(x-x);             /* sqrt(-ve) = sNaN */
  46         }
  47     /* normalize x */
  48         m = (ix>>23);
  49         if(m==0) {                              /* subnormal x */
  50             for(i=0;(ix&0x00800000)==0;i++) ix<<=1;
  51             m -= i-1;
  52         }
  53         m -= 127;       /* unbias exponent */
  54         ix = (ix&0x007fffff)|0x00800000;
  55         if(m&1) /* odd m, double x to make it even */
  56             ix += ix;
  57         m >>= 1;        /* m = [m/2] */
  58
  59     /* generate sqrt(x) bit by bit */
  60         ix += ix;
  61         q = s = 0;              /* q = sqrt(x) */
  62         r = 0x01000000;         /* r = moving bit from right to left */
  63
  64         while(r!=0) {
  65             t = s+r;
  66             if(t<=ix) {
  67                 s    = t+r;
  68                 ix  -= t;
  69                 q   += r;
  70             }
  71             ix += ix;
  72             r>>=1;
  73         }
  74
  75     /* use floating add to find out rounding direction */
  76         if(ix!=0) {
  77             z = one-tiny; /* trigger inexact flag */
  78             if (z>=one) {
  79                 z = one+tiny;
  80                 if (z>one)
  81                     q += 2;
  82                 else
  83                     q += (q&1);
  84             }
  85         }
  86         ix = (q>>1)+0x3f000000;
  87         ix += (m <<23);
  88         SET_FLOAT_WORD(z,ix);
  89         return z;
  90 }