e_sqrtf.c

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/* e_sqrtf.c -- float version of e_sqrt.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.
 * ====================================================
 */

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

static  const float one = 1.0, tiny=1.0e-30;

float
sqrtf(float x)
{
    float z;
    int32_t sign = (int)0x80000000; 
    int32_t ix,s,q,m,t,i;
    u_int32_t r;

    GET_FLOAT_WORD(ix,x);

    /* take care of Inf and NaN */
    if((ix&0x7f800000)==0x7f800000) {           
        return x*x+x;       /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
                       sqrt(-inf)=sNaN */
    } 
    /* take care of zero */
    if(ix<=0) {
        if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */
        else if(ix<0)
        return (x-x)/(x-x);     /* sqrt(-ve) = sNaN */
    }
    /* normalize x */
    m = (ix>>23);
    if(m==0) {              /* subnormal x */
        for(i=0;(ix&0x00800000)==0;i++) ix<<=1;
        m -= i-1;
    }
    m -= 127;   /* unbias exponent */
    ix = (ix&0x007fffff)|0x00800000;
    if(m&1) /* odd m, double x to make it even */
        ix += ix;
    m >>= 1;    /* m = [m/2] */

    /* generate sqrt(x) bit by bit */
    ix += ix;
    q = s = 0;      /* q = sqrt(x) */
    r = 0x01000000;     /* r = moving bit from right to left */

    while(r!=0) {
        t = s+r; 
        if(t<=ix) { 
        s    = t+r; 
        ix  -= t; 
        q   += r; 
        } 
        ix += ix;
        r>>=1;
    }

    /* use floating add to find out rounding direction */
    if(ix!=0) {
        z = one-tiny; /* trigger inexact flag */
        if (z>=one) {
            z = one+tiny;
        if (z>one)
            q += 2;
        else
            q += (q&1);
        }
    }
    ix = (q>>1)+0x3f000000;
    ix += (m <<23);
    SET_FLOAT_WORD(z,ix);
    return z;
}