cosmopolitan/libc/tinymath/log1pf.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 │
╚──────────────────────────────────────────────────────────────────────────────╝
│                                                                              │
│ Copyright (c) 1992-2024 The FreeBSD Project                                  │
│ Copyright (c) 1993 Sun Microsystems, Inc.                                    │
│ All rights reserved.                                                         │
│                                                                              │
│ 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.                                                                 │
│                                                                              │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/tinymath/freebsd.internal.h"
__static_yoink("freebsd_libm_notice");
__static_yoink("fdlibm_notice");

/* s_log1pf.c -- float version of s_log1p.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

static const float
ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
two25 =    3.355443200e+07,	/* 0x4c000000 */
Lp1 = 6.6666668653e-01,	/* 3F2AAAAB */
Lp2 = 4.0000000596e-01,	/* 3ECCCCCD */
Lp3 = 2.8571429849e-01, /* 3E924925 */
Lp4 = 2.2222198546e-01, /* 3E638E29 */
Lp5 = 1.8183572590e-01, /* 3E3A3325 */
Lp6 = 1.5313838422e-01, /* 3E1CD04F */
Lp7 = 1.4798198640e-01; /* 3E178897 */

static const float zero = 0.0;
static volatile float vzero = 0.0;

/**
 * Returns log(1 + x).
 */
float
log1pf(float x)
{
	float hfsq,f,c,s,z,R,u;
	int32_t k,hx,hu,ax;

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

	k = 1;
	if (hx < 0x3ed413d0) {			/* 1+x < sqrt(2)+  */
	    if(ax>=0x3f800000) {		/* x <= -1.0 */
		if(x==(float)-1.0) return -two25/vzero; /* log1p(-1)=+inf */
		else return (x-x)/(x-x);	/* log1p(x<-1)=NaN */
	    }
	    if(ax<0x38000000) {			/* |x| < 2**-15 */
		if(two25+x>zero			/* raise inexact */
	            &&ax<0x33800000) 		/* |x| < 2**-24 */
		    return x;
		else
		    return x - x*x*(float)0.5;
	    }
	    if(hx>0||hx<=((int32_t)0xbe95f619)) {
		k=0;f=x;hu=1;}		/* sqrt(2)/2- <= 1+x < sqrt(2)+ */
	}
	if (hx >= 0x7f800000) return x+x;
	if(k!=0) {
	    if(hx<0x5a000000) {
		STRICT_ASSIGN(float,u,(float)1.0+x);
		GET_FLOAT_WORD(hu,u);
	        k  = (hu>>23)-127;
		/* correction term */
	        c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
		c /= u;
	    } else {
		u  = x;
		GET_FLOAT_WORD(hu,u);
	        k  = (hu>>23)-127;
		c  = 0;
	    }
	    hu &= 0x007fffff;
	    /*
	     * The approximation to sqrt(2) used in thresholds is not
	     * critical.  However, the ones used above must give less
	     * strict bounds than the one here so that the k==0 case is
	     * never reached from here, since here we have committed to
	     * using the correction term but don't use it if k==0.
	     */
	    if(hu<0x3504f4) {			/* u < sqrt(2) */
	        SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
	    } else {
	        k += 1;
		SET_FLOAT_WORD(u,hu|0x3f000000);	/* normalize u/2 */
	        hu = (0x00800000-hu)>>2;
	    }
	    f = u-(float)1.0;
	}
	hfsq=(float)0.5*f*f;
	if(hu==0) {	/* |f| < 2**-20 */
	    if(f==zero) {
		if(k==0) {
		    return zero;
		} else {
		    c += k*ln2_lo;
		    return k*ln2_hi+c;
		}
	    }
	    R = hfsq*((float)1.0-(float)0.66666666666666666*f);
	    if(k==0) return f-R; else
	    	     return k*ln2_hi-((R-(k*ln2_lo+c))-f);
	}
 	s = f/((float)2.0+f);
	z = s*s;
	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
	if(k==0) return f-(hfsq-s*(hfsq+R)); else
		 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
}