path: root/src/math/e_sqrtf.c

/* 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;
        uint32_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;
}