source: azure_iot_hub/trunk/musl-1.1.18/src/math/sqrtf.c@ 389

/* origin: FreeBSD /usr/src/lib/msun/src/e_sqrtf.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 "libm.h"

static const float 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 */
                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 = 1.0f - tiny; /* raise inexact flag */
                if (z >= 1.0f) {
                        z = 1.0f + tiny;
                        if (z > 1.0f)
                                q += 2;
                        else
                                q += q & 1;
                }
        }
        ix = (q>>1) + 0x3f000000;
        ix += m << 23;
        SET_FLOAT_WORD(z, ix);
        return z;
}