[picodrive.git] / platform / gp2x / code940 / uClibc / e_log.c

/* @(#)e_log.c 5.1 93/09/24 */
/*
 * ====================================================
 * 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.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";
#endif

/* __ieee754_log(x)
 * Return the logrithm of x
 *
 * Method :
 *   1. Argument Reduction: find k and f such that
 *			x = 2^k * (1+f),
 *	   where  sqrt(2)/2 < 1+f < sqrt(2) .
 *
 *   2. Approximation of log(1+f).
 *	Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
 *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
 *	     	 = 2s + s*R
 *      We use a special Reme algorithm on [0,0.1716] to generate
 * 	a polynomial of degree 14 to approximate R The maximum error
 *	of this polynomial approximation is bounded by 2**-58.45. In
 *	other words,
 *		        2      4      6      8      10      12      14
 *	    R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
 *  	(the values of Lg1 to Lg7 are listed in the program)
 *	and
 *	    |      2          14          |     -58.45
 *	    | Lg1*s +...+Lg7*s    -  R(z) | <= 2
 *	    |                             |
 *	Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
 *	In order to guarantee error in log below 1ulp, we compute log
 *	by
 *		log(1+f) = f - s*(f - R)	(if f is not too large)
 *		log(1+f) = f - (hfsq - s*(hfsq+R)).	(better accuracy)
 *
 *	3. Finally,  log(x) = k*ln2 + log(1+f).
 *			    = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
 *	   Here ln2 is split into two floating point number:
 *			ln2_hi + ln2_lo,
 *	   where n*ln2_hi is always exact for |n| < 2000.
 *
 * Special cases:
 *	log(x) is NaN with signal if x < 0 (including -INF) ;
 *	log(+INF) is +INF; log(0) is -INF with signal;
 *	log(NaN) is that NaN with no signal.
 *
 * Accuracy:
 *	according to an error analysis, the error is always less than
 *	1 ulp (unit in the last place).
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following
 * constants. The decimal values may be used, provided that the
 * compiler will convert from decimal to binary accurately enough
 * to produce the hexadecimal values shown.
 */

#include "math.h"
#include "math_private.h"

#ifdef __STDC__
static const double
#else
static double
#endif
ln2_hi  =  6.93147180369123816490e-01,	/* 3fe62e42 fee00000 */
ln2_lo  =  1.90821492927058770002e-10,	/* 3dea39ef 35793c76 */
two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */

#ifdef __STDC__
static const double zero   =  0.0;
#else
static double zero   =  0.0;
#endif

#ifdef __STDC__
	double __ieee754_log(double x)
#else
	double __ieee754_log(x)
	double x;
#endif
{
	double hfsq,f,s,z,R,w,t1,t2,dk;
	int32_t k,hx,i,j;
	u_int32_t lx;

	EXTRACT_WORDS(hx,lx,x);

	k=0;
	if (hx < 0x00100000) {			/* x < 2**-1022  */
	    if (((hx&0x7fffffff)|lx)==0)
		return -two54/zero;		/* log(+-0)=-inf */
	    if (hx<0) return (x-x)/zero;	/* log(-#) = NaN */
	    k -= 54; x *= two54; /* subnormal number, scale up x */
	    GET_HIGH_WORD(hx,x);
	}
	if (hx >= 0x7ff00000) return x+x;
	k += (hx>>20)-1023;
	hx &= 0x000fffff;
	i = (hx+0x95f64)&0x100000;
	SET_HIGH_WORD(x,hx|(i^0x3ff00000));	/* normalize x or x/2 */
	k += (i>>20);
	f = x-1.0;
	if((0x000fffff&(2+hx))<3) {	/* |f| < 2**-20 */
	    if(f==zero) {if(k==0) return zero;  else {dk=(double)k;
				 return dk*ln2_hi+dk*ln2_lo;}
	    }
	    R = f*f*(0.5-0.33333333333333333*f);
	    if(k==0) return f-R; else {dk=(double)k;
	    	     return dk*ln2_hi-((R-dk*ln2_lo)-f);}
	}
 	s = f/(2.0+f);
	dk = (double)k;
	z = s*s;
	i = hx-0x6147a;
	w = z*z;
	j = 0x6b851-hx;
	t1= w*(Lg2+w*(Lg4+w*Lg6));
	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
	i |= j;
	R = t2+t1;
	if(i>0) {
	    hfsq=0.5*f*f;
	    if(k==0) return f-(hfsq-s*(hfsq+R)); else
		     return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
	} else {
	    if(k==0) return f-s*(f-R); else
		     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
	}
}
Commit	Line	Data
	1	/* @(#)e_log.c 5.1 93/09/24 */
	2	/*
	3	* ====================================================
	4	* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
	5	*
	6	* Developed at SunPro, a Sun Microsystems, Inc. business.
	7	* Permission to use, copy, modify, and distribute this
	8	* software is freely granted, provided that this notice
	9	* is preserved.
	10	* ====================================================
	11	*/
	12
	13	#if defined(LIBM_SCCS) && !defined(lint)
	14	static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";
	15	#endif
	16
	17	/* __ieee754_log(x)
	18	* Return the logrithm of x
	19	*
	20	* Method :
	21	* 1. Argument Reduction: find k and f such that
	22	* x = 2^k * (1+f),
	23	* where sqrt(2)/2 < 1+f < sqrt(2) .
	24	*
	25	* 2. Approximation of log(1+f).
	26	* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
	27	* = 2s + 2/3 s3 + 2/5 s5 + .....,
	28	* = 2s + s*R
	29	* We use a special Reme algorithm on [0,0.1716] to generate
	30	* a polynomial of degree 14 to approximate R The maximum error
	31	* of this polynomial approximation is bounded by 2**-58.45. In
	32	* other words,
	33	* 2 4 6 8 10 12 14
	34	* R(z) ~ Lg1s +Lg2s +Lg3s +Lg4s +Lg5s +Lg6s +Lg7*s
	35	* (the values of Lg1 to Lg7 are listed in the program)
	36	* and
	37	* \| 2 14 \| -58.45
	38	* \| Lg1s +...+Lg7s - R(z) \| <= 2
	39	* \| \|
	40	* Note that 2s = f - sf = f - hfsq + shfsq, where hfsq = f*f/2.
	41	* In order to guarantee error in log below 1ulp, we compute log
	42	* by
	43	* log(1+f) = f - s*(f - R) (if f is not too large)
	44	* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
	45	*
	46	* 3. Finally, log(x) = k*ln2 + log(1+f).
	47	* = kln2_hi+(f-(hfsq-(s(hfsq+R)+k*ln2_lo)))
	48	* Here ln2 is split into two floating point number:
	49	* ln2_hi + ln2_lo,
	50	* where n*ln2_hi is always exact for \|n\| < 2000.
	51	*
	52	* Special cases:
	53	* log(x) is NaN with signal if x < 0 (including -INF) ;
	54	* log(+INF) is +INF; log(0) is -INF with signal;
	55	* log(NaN) is that NaN with no signal.
	56	*
	57	* Accuracy:
	58	* according to an error analysis, the error is always less than
	59	* 1 ulp (unit in the last place).
	60	*
	61	* Constants:
	62	* The hexadecimal values are the intended ones for the following
	63	* constants. The decimal values may be used, provided that the
	64	* compiler will convert from decimal to binary accurately enough
	65	* to produce the hexadecimal values shown.
	66	*/
	67
	68	#include "math.h"
	69	#include "math_private.h"
	70
	71	#ifdef __STDC__
	72	static const double
	73	#else
	74	static double
	75	#endif
	76	ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
	77	ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
	78	two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
	79	Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
	80	Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
	81	Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
	82	Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
	83	Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
	84	Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
	85	Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
	86
	87	#ifdef __STDC__
	88	static const double zero = 0.0;
	89	#else
	90	static double zero = 0.0;
	91	#endif
	92
	93	#ifdef __STDC__
	94	double __ieee754_log(double x)
	95	#else
	96	double __ieee754_log(x)
	97	double x;
	98	#endif
	99	{
	100	double hfsq,f,s,z,R,w,t1,t2,dk;
	101	int32_t k,hx,i,j;
	102	u_int32_t lx;
	103
	104	EXTRACT_WORDS(hx,lx,x);
	105
	106	k=0;
	107	if (hx < 0x00100000) { /* x < 2*-1022 /
	108	if (((hx&0x7fffffff)\|lx)==0)
	109	return -two54/zero; /* log(+-0)=-inf */
	110	if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
	111	k -= 54; x = two54; / subnormal number, scale up x */
	112	GET_HIGH_WORD(hx,x);
	113	}
	114	if (hx >= 0x7ff00000) return x+x;
	115	k += (hx>>20)-1023;
	116	hx &= 0x000fffff;
	117	i = (hx+0x95f64)&0x100000;
	118	SET_HIGH_WORD(x,hx\|(i^0x3ff00000)); /* normalize x or x/2 */
	119	k += (i>>20);
	120	f = x-1.0;
	121	if((0x000fffff&(2+hx))<3) { /* \|f\| < 2*-20 /
	122	if(f==zero) {if(k==0) return zero; else {dk=(double)k;
	123	return dkln2_hi+dkln2_lo;}
	124	}
	125	R = ff(0.5-0.33333333333333333*f);
	126	if(k==0) return f-R; else {dk=(double)k;
	127	return dkln2_hi-((R-dkln2_lo)-f);}
	128	}
	129	s = f/(2.0+f);
	130	dk = (double)k;
	131	z = s*s;
	132	i = hx-0x6147a;
	133	w = z*z;
	134	j = 0x6b851-hx;
	135	t1= w(Lg2+w(Lg4+w*Lg6));
	136	t2= z(Lg1+w(Lg3+w(Lg5+wLg7)));
	137	i \|= j;
	138	R = t2+t1;
	139	if(i>0) {
	140	hfsq=0.5ff;
	141	if(k==0) return f-(hfsq-s*(hfsq+R)); else
	142	return dkln2_hi-((hfsq-(s(hfsq+R)+dk*ln2_lo))-f);
	143	} else {
	144	if(k==0) return f-s*(f-R); else
	145	return dkln2_hi-((s(f-R)-dk*ln2_lo)-f);
	146	}
	147	}