micropython/lib/libm/ef_sqrt.c

/*
 * This file is part of the MicroPython project, http://micropython.org/
 *
 * These math functions are taken from newlib-nano-2, the newlib/libm/math
 * directory, available from https://github.com/32bitmicro/newlib-nano-2.
 *
 * Appropriate copyright headers are reproduced below.
 */

/* ef_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 "fdlibm.h"

#ifdef __STDC__
static	const float	one	= 1.0f, tiny=1.0e-30f;
#else
static	float	one	= 1.0f, tiny=1.0e-30f;
#endif

// sqrtf is exactly __ieee754_sqrtf when _IEEE_LIBM defined
float sqrtf(float x)
/*
#ifdef __STDC__
	float __ieee754_sqrtf(float x)
#else
	float __ieee754_sqrtf(x)
	float x;
#endif
*/
{
	float z;
	__uint32_t r,hx;
	__int32_t ix,s,q,m,t,i;

	GET_FLOAT_WORD(ix,x);
	hx = ix&0x7fffffff;

    /* take care of Inf and NaN */
	if(!FLT_UWORD_IS_FINITE(hx))
	    return x*x+x;		/* sqrt(NaN)=NaN, sqrt(+inf)=+inf
					   sqrt(-inf)=sNaN */
    /* take care of zero and -ves */
	if(FLT_UWORD_IS_ZERO(hx)) return x;/* sqrt(+-0) = +-0 */
	if(ix<0) return (x-x)/(x-x);		/* sqrt(-ve) = sNaN */

    /* normalize x */
	m = (ix>>23);
	if(FLT_UWORD_IS_SUBNORMAL(hx)) {		/* subnormal x */
	    for(i=0;(ix&0x00800000L)==0;i++) ix<<=1;
	    m -= i-1;
	}
	m -= 127;	/* unbias exponent */
	ix = (ix&0x007fffffL)|0x00800000L;
	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 = 0x01000000L;		/* 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)+0x3f000000L;
	ix += (m <<23);
	SET_FLOAT_WORD(z,ix);
	return z;
}