cosmopolitan/libc/tinymath/hypotf2.c

/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-│
│ vi: set noet ft=c ts=8 sw=8 fenc=utf-8                                   :vi │
╚──────────────────────────────────────────────────────────────────────────────╝
│                                                                              │
│ FreeBSD lib/msun/src/e_hypotf.c                                              │
│ Copyright (c) 1992-2023 The FreeBSD Project.                                 │
│                                                                              │
│ Redistribution and use in source and binary forms, with or without           │
│ modification, are permitted provided that the following conditions           │
│ are met:                                                                     │
│ 1. Redistributions of source code must retain the above copyright            │
│    notice, this list of conditions and the following disclaimer.             │
│ 2. Redistributions in binary form must reproduce the above copyright         │
│    notice, this list of conditions and the following disclaimer in the       │
│    documentation and/or other materials provided with the distribution.      │
│                                                                              │
│ THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND       │
│ ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE        │
│ IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE   │
│ ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE      │
│ FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL   │
│ DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS      │
│ OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)        │
│ HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT   │
│ LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY    │
│ OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF       │
│ SUCH DAMAGE.                                                                 │
│                                                                              │
│ 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 "libc/tinymath/freebsd.internal.h"
__static_yoink("freebsd_libm_notice");
__static_yoink("fdlibm_notice");

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

float
sqrtf2(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 += ((uint32_t)m <<23);
	SET_FLOAT_WORD(z,ix);
	return z;
}

/**
 * Returns euclidean distance.
 *
 * Error is less than 1 ULP.
 */
float
hypotf2(float x, float y)
{
	float a,b,t1,t2,y1,y2,w;
	int32_t j,k,ha,hb;

	GET_FLOAT_WORD(ha,x);
	ha &= 0x7fffffff;
	GET_FLOAT_WORD(hb,y);
	hb &= 0x7fffffff;
	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
	a = fabsf(a);
	b = fabsf(b);
	if((ha-hb)>0xf000000) {return a+b;} /* x/y > 2**30 */
	k=0;
	if(ha > 0x58800000) {	/* a>2**50 */
	   if(ha >= 0x7f800000) {	/* Inf or NaN */
	       /* Use original arg order iff result is NaN; quieten sNaNs. */
	       w = fabsl(x+0.0L)-fabsf(y+0);
	       if(ha == 0x7f800000) w = a;
	       if(hb == 0x7f800000) w = b;
	       return w;
	   }
	   /* scale a and b by 2**-68 */
	   ha -= 0x22000000; hb -= 0x22000000;	k += 68;
	   SET_FLOAT_WORD(a,ha);
	   SET_FLOAT_WORD(b,hb);
	}
	if(hb < 0x26800000) {	/* b < 2**-50 */
	    if(hb <= 0x007fffff) {	/* subnormal b or 0 */
	        if(hb==0) return a;
		SET_FLOAT_WORD(t1,0x7e800000);	/* t1=2^126 */
		b *= t1;
		a *= t1;
		k -= 126;
	    } else {		/* scale a and b by 2^68 */
	        ha += 0x22000000; 	/* a *= 2^68 */
		hb += 0x22000000;	/* b *= 2^68 */
		k -= 68;
		SET_FLOAT_WORD(a,ha);
		SET_FLOAT_WORD(b,hb);
	    }
	}
    /* medium size a and b */
	w = a-b;
	if (w>b) {
	    SET_FLOAT_WORD(t1,ha&0xfffff000);
	    t2 = a-t1;
	    w  = sqrtf2(t1*t1-(b*(-b)-t2*(a+t1)));
	} else {
	    a  = a+a;
	    SET_FLOAT_WORD(y1,hb&0xfffff000);
	    y2 = b - y1;
	    SET_FLOAT_WORD(t1,(ha+0x00800000)&0xfffff000);
	    t2 = a - t1;
	    w  = sqrtf2(t1*y1-(w*(-w)-(t1*y2+t2*b)));
	}
	if(k!=0) {
	    SET_FLOAT_WORD(t1,(127+k)<<23);
	    return t1*w;
	} else return w;
}