[thirdparty/glibc.git] / sysdeps / ieee754 / flt-32 / e_lgammaf_r.c

/* e_lgammaf_r.c -- float version of e_lgamma_r.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 <math.h>
#include <math_private.h>

static const float
two23=  8.3886080000e+06, /* 0x4b000000 */
half=  5.0000000000e-01, /* 0x3f000000 */
one =  1.0000000000e+00, /* 0x3f800000 */
pi  =  3.1415927410e+00, /* 0x40490fdb */
a0  =  7.7215664089e-02, /* 0x3d9e233f */
a1  =  3.2246702909e-01, /* 0x3ea51a66 */
a2  =  6.7352302372e-02, /* 0x3d89f001 */
a3  =  2.0580807701e-02, /* 0x3ca89915 */
a4  =  7.3855509982e-03, /* 0x3bf2027e */
a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
a7  =  5.1006977446e-04, /* 0x3a05b634 */
a8  =  2.2086278477e-04, /* 0x39679767 */
a9  =  1.0801156895e-04, /* 0x38e28445 */
a10 =  2.5214456400e-05, /* 0x37d383a2 */
a11 =  4.4864096708e-05, /* 0x383c2c75 */
tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
/* tt = -(tail of tf) */
tt  =  6.6971006518e-09, /* 0x31e61c52 */
t0  =  4.8383611441e-01, /* 0x3ef7b95e */
t1  = -1.4758771658e-01, /* 0xbe17213c */
t2  =  6.4624942839e-02, /* 0x3d845a15 */
t3  = -3.2788541168e-02, /* 0xbd064d47 */
t4  =  1.7970675603e-02, /* 0x3c93373d */
t5  = -1.0314224288e-02, /* 0xbc28fcfe */
t6  =  6.1005386524e-03, /* 0x3bc7e707 */
t7  = -3.6845202558e-03, /* 0xbb7177fe */
t8  =  2.2596477065e-03, /* 0x3b141699 */
t9  = -1.4034647029e-03, /* 0xbab7f476 */
t10 =  8.8108185446e-04, /* 0x3a66f867 */
t11 = -5.3859531181e-04, /* 0xba0d3085 */
t12 =  3.1563205994e-04, /* 0x39a57b6b */
t13 = -3.1275415677e-04, /* 0xb9a3f927 */
t14 =  3.3552918467e-04, /* 0x39afe9f7 */
u0  = -7.7215664089e-02, /* 0xbd9e233f */
u1  =  6.3282704353e-01, /* 0x3f2200f4 */
u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
u4  =  2.2896373272e-01, /* 0x3e6a7578 */
u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
v1  =  2.4559779167e+00, /* 0x401d2ebe */
v2  =  2.1284897327e+00, /* 0x4008392d */
v3  =  7.6928514242e-01, /* 0x3f44efdf */
v4  =  1.0422264785e-01, /* 0x3dd572af */
v5  =  3.2170924824e-03, /* 0x3b52d5db */
s0  = -7.7215664089e-02, /* 0xbd9e233f */
s1  =  2.1498242021e-01, /* 0x3e5c245a */
s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
s3  =  1.4635047317e-01, /* 0x3e15dce6 */
s4  =  2.6642270386e-02, /* 0x3cda40e4 */
s5  =  1.8402845599e-03, /* 0x3af135b4 */
s6  =  3.1947532989e-05, /* 0x3805ff67 */
r1  =  1.3920053244e+00, /* 0x3fb22d3b */
r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
r3  =  1.7193385959e-01, /* 0x3e300f6e */
r4  =  1.8645919859e-02, /* 0x3c98bf54 */
r5  =  7.7794247773e-04, /* 0x3a4beed6 */
r6  =  7.3266842264e-06, /* 0x36f5d7bd */
w0  =  4.1893854737e-01, /* 0x3ed67f1d */
w1  =  8.3333335817e-02, /* 0x3daaaaab */
w2  = -2.7777778450e-03, /* 0xbb360b61 */
w3  =  7.9365057172e-04, /* 0x3a500cfd */
w4  = -5.9518753551e-04, /* 0xba1c065c */
w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
w6  = -1.6309292987e-03; /* 0xbad5c4e8 */

static const float zero=  0.0000000000e+00;

static float
sin_pif(float x)
{
	float y,z;
	int n,ix;

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

	if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
	y = -x;		/* x is assume negative */

    /*
     * argument reduction, make sure inexact flag not raised if input
     * is an integer
     */
	z = __floorf(y);
	if(z!=y) {				/* inexact anyway */
	    y  *= (float)0.5;
	    y   = (float)2.0*(y - __floorf(y));	/* y = |x| mod 2.0 */
	    n   = (int) (y*(float)4.0);
	} else {
	    if(ix>=0x4b800000) {
		y = zero; n = 0;                 /* y must be even */
	    } else {
		if(ix<0x4b000000) z = y+two23;	/* exact */
		GET_FLOAT_WORD(n,z);
		n &= 1;
		y  = n;
		n<<= 2;
	    }
	}
	switch (n) {
	    case 0:   y =  __kernel_sinf(pi*y,zero,0); break;
	    case 1:
	    case 2:   y =  __kernel_cosf(pi*((float)0.5-y),zero); break;
	    case 3:
	    case 4:   y =  __kernel_sinf(pi*(one-y),zero,0); break;
	    case 5:
	    case 6:   y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
	    default:  y =  __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
	    }
	return -y;
}


float
__ieee754_lgammaf_r(float x, int *signgamp)
{
	float t,y,z,nadj,p,p1,p2,p3,q,r,w;
	int i,hx,ix;

	GET_FLOAT_WORD(hx,x);

    /* purge off +-inf, NaN, +-0, and negative arguments */
	*signgamp = 1;
	ix = hx&0x7fffffff;
	if(__builtin_expect(ix>=0x7f800000, 0)) return x*x;
	if(__builtin_expect(ix==0, 0))
	  {
	    if (hx < 0)
	      *signgamp = -1;
	    return one/fabsf(x);
	  }
	if(__builtin_expect(ix<0x30800000, 0)) {
	    /* |x|<2**-30, return -log(|x|) */
	    if(hx<0) {
		*signgamp = -1;
		return -__ieee754_logf(-x);
	    } else return -__ieee754_logf(x);
	}
	if(hx<0) {
	    if(ix>=0x4b000000)	/* |x|>=2**23, must be -integer */
		return x/zero;
	    t = sin_pif(x);
	    if(t==zero) return one/fabsf(t); /* -integer */
	    nadj = __ieee754_logf(pi/fabsf(t*x));
	    if(t<zero) *signgamp = -1;
	    x = -x;
	}

    /* purge off 1 and 2 */
	if (ix==0x3f800000||ix==0x40000000) r = 0;
    /* for x < 2.0 */
	else if(ix<0x40000000) {
	    if(ix<=0x3f666666) {	/* lgamma(x) = lgamma(x+1)-log(x) */
		r = -__ieee754_logf(x);
		if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
		else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
		else {y = x; i=2;}
	    } else {
		r = zero;
		if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
		else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
		else {y=x-one;i=2;}
	    }
	    switch(i) {
	      case 0:
		z = y*y;
		p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
		p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
		p  = y*p1+p2;
		r  += (p-(float)0.5*y); break;
	      case 1:
		z = y*y;
		w = z*y;
		p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));	/* parallel comp */
		p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
		p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
		p  = z*p1-(tt-w*(p2+y*p3));
		r += (tf + p); break;
	      case 2:
		p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
		p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
		r += (-(float)0.5*y + p1/p2);
	    }
	}
	else if(ix<0x41000000) {			/* x < 8.0 */
	    i = (int)x;
	    t = zero;
	    y = x-(float)i;
	    p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
	    q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
	    r = half*y+p/q;
	    z = one;	/* lgamma(1+s) = log(s) + lgamma(s) */
	    switch(i) {
	    case 7: z *= (y+(float)6.0);	/* FALLTHRU */
	    case 6: z *= (y+(float)5.0);	/* FALLTHRU */
	    case 5: z *= (y+(float)4.0);	/* FALLTHRU */
	    case 4: z *= (y+(float)3.0);	/* FALLTHRU */
	    case 3: z *= (y+(float)2.0);	/* FALLTHRU */
		    r += __ieee754_logf(z); break;
	    }
    /* 8.0 <= x < 2**26 */
	} else if (ix < 0x4c800000) {
	    t = __ieee754_logf(x);
	    z = one/x;
	    y = z*z;
	    w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
	    r = (x-half)*(t-one)+w;
	} else
    /* 2**26 <= x <= inf */
	    r =  x*(__ieee754_logf(x)-one);
	if(hx<0) r = nadj - r;
	return r;
}
strong_alias (__ieee754_lgammaf_r, __lgammaf_r_finite)
Commit	Line	Data
f7eac6eb RM	1	/* e_lgammaf_r.c -- float version of e_lgamma_r.c.
	2	* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
	3	*/
	4
	5	/*
	6	* ====================================================
	7	* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
	8	*
	9	* Developed at SunPro, a Sun Microsystems, Inc. business.
	10	* Permission to use, copy, modify, and distribute this
d705269e	11	* software is freely granted, provided that this notice
f7eac6eb RM	12	* is preserved.
	13	* ====================================================
	14	*/
	15
1ed0291c RH	16	#include <math.h>
1ed0291c RH	17	#include <math_private.h>
f7eac6eb	18
d705269e	19	static const float
f7eac6eb RM	20	two23= 8.3886080000e+06, /* 0x4b000000 */
	21	half= 5.0000000000e-01, /* 0x3f000000 */
	22	one = 1.0000000000e+00, /* 0x3f800000 */
	23	pi = 3.1415927410e+00, /* 0x40490fdb */
	24	a0 = 7.7215664089e-02, /* 0x3d9e233f */
	25	a1 = 3.2246702909e-01, /* 0x3ea51a66 */
	26	a2 = 6.7352302372e-02, /* 0x3d89f001 */
	27	a3 = 2.0580807701e-02, /* 0x3ca89915 */
	28	a4 = 7.3855509982e-03, /* 0x3bf2027e */
	29	a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
	30	a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
	31	a7 = 5.1006977446e-04, /* 0x3a05b634 */
	32	a8 = 2.2086278477e-04, /* 0x39679767 */
	33	a9 = 1.0801156895e-04, /* 0x38e28445 */
	34	a10 = 2.5214456400e-05, /* 0x37d383a2 */
	35	a11 = 4.4864096708e-05, /* 0x383c2c75 */
	36	tc = 1.4616321325e+00, /* 0x3fbb16c3 */
	37	tf = -1.2148628384e-01, /* 0xbdf8cdcd */
	38	/* tt = -(tail of tf) */
	39	tt = 6.6971006518e-09, /* 0x31e61c52 */
	40	t0 = 4.8383611441e-01, /* 0x3ef7b95e */
	41	t1 = -1.4758771658e-01, /* 0xbe17213c */
	42	t2 = 6.4624942839e-02, /* 0x3d845a15 */
	43	t3 = -3.2788541168e-02, /* 0xbd064d47 */
	44	t4 = 1.7970675603e-02, /* 0x3c93373d */
	45	t5 = -1.0314224288e-02, /* 0xbc28fcfe */
	46	t6 = 6.1005386524e-03, /* 0x3bc7e707 */
	47	t7 = -3.6845202558e-03, /* 0xbb7177fe */
	48	t8 = 2.2596477065e-03, /* 0x3b141699 */
	49	t9 = -1.4034647029e-03, /* 0xbab7f476 */
	50	t10 = 8.8108185446e-04, /* 0x3a66f867 */
	51	t11 = -5.3859531181e-04, /* 0xba0d3085 */
	52	t12 = 3.1563205994e-04, /* 0x39a57b6b */
	53	t13 = -3.1275415677e-04, /* 0xb9a3f927 */
	54	t14 = 3.3552918467e-04, /* 0x39afe9f7 */
	55	u0 = -7.7215664089e-02, /* 0xbd9e233f */
	56	u1 = 6.3282704353e-01, /* 0x3f2200f4 */
	57	u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
	58	u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
	59	u4 = 2.2896373272e-01, /* 0x3e6a7578 */
	60	u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
	61	v1 = 2.4559779167e+00, /* 0x401d2ebe */
	62	v2 = 2.1284897327e+00, /* 0x4008392d */
	63	v3 = 7.6928514242e-01, /* 0x3f44efdf */
	64	v4 = 1.0422264785e-01, /* 0x3dd572af */
	65	v5 = 3.2170924824e-03, /* 0x3b52d5db */
	66	s0 = -7.7215664089e-02, /* 0xbd9e233f */
	67	s1 = 2.1498242021e-01, /* 0x3e5c245a */
	68	s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
	69	s3 = 1.4635047317e-01, /* 0x3e15dce6 */
	70	s4 = 2.6642270386e-02, /* 0x3cda40e4 */
	71	s5 = 1.8402845599e-03, /* 0x3af135b4 */
	72	s6 = 3.1947532989e-05, /* 0x3805ff67 */
	73	r1 = 1.3920053244e+00, /* 0x3fb22d3b */
	74	r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
	75	r3 = 1.7193385959e-01, /* 0x3e300f6e */
	76	r4 = 1.8645919859e-02, /* 0x3c98bf54 */
	77	r5 = 7.7794247773e-04, /* 0x3a4beed6 */
	78	r6 = 7.3266842264e-06, /* 0x36f5d7bd */
	79	w0 = 4.1893854737e-01, /* 0x3ed67f1d */
	80	w1 = 8.3333335817e-02, /* 0x3daaaaab */
	81	w2 = -2.7777778450e-03, /* 0xbb360b61 */
	82	w3 = 7.9365057172e-04, /* 0x3a500cfd */
	83	w4 = -5.9518753551e-04, /* 0xba1c065c */
84	w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
85	w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
86
f7eac6eb	87	static const float zero= 0.0000000000e+00;
f7eac6eb	88
0ac5ae23 UD	89	static float
0ac5ae23 UD	90	sin_pif(float x)
f7eac6eb RM	91	{
	92	float y,z;
	93	int n,ix;
	94
	95	GET_FLOAT_WORD(ix,x);
	96	ix &= 0x7fffffff;
	97
	98	if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
	99	y = -x; /* x is assume negative */
	100
	101	/*
	102	* argument reduction, make sure inexact flag not raised if input
	103	* is an integer
	104	*/
	105	z = __floorf(y);
	106	if(z!=y) { /* inexact anyway */
	107	y *= (float)0.5;
	108	y = (float)2.0(y - __floorf(y)); / y = \|x\| mod 2.0 */
	109	n = (int) (y*(float)4.0);
	110	} else {
0ac5ae23 UD	111	if(ix>=0x4b800000) {
	112	y = zero; n = 0; /* y must be even */
	113	} else {
	114	if(ix<0x4b000000) z = y+two23; /* exact */
f7eac6eb RM	115	GET_FLOAT_WORD(n,z);
f7eac6eb RM	116	n &= 1;
0ac5ae23 UD	117	y = n;
	118	n<<= 2;
	119	}
	120	}
f7eac6eb RM	121	switch (n) {
f7eac6eb RM	122	case 0: y = __kernel_sinf(pi*y,zero,0); break;
d705269e	123	case 1:
f7eac6eb	124	case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break;
d705269e	125	case 3:
f7eac6eb RM	126	case 4: y = __kernel_sinf(pi*(one-y),zero,0); break;
	127	case 5:
	128	case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
	129	default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
	130	}
	131	return -y;
	132	}
	133
	134
0ac5ae23 UD	135	float
0ac5ae23 UD	136	__ieee754_lgammaf_r(float x, int *signgamp)
f7eac6eb RM	137	{
	138	float t,y,z,nadj,p,p1,p2,p3,q,r,w;
	139	int i,hx,ix;
	140
	141	GET_FLOAT_WORD(hx,x);
	142
	143	/* purge off +-inf, NaN, +-0, and negative arguments */
	144	*signgamp = 1;
	145	ix = hx&0x7fffffff;
0ac5ae23 UD	146	if(__builtin_expect(ix>=0x7f800000, 0)) return x*x;
0ac5ae23 UD	147	if(__builtin_expect(ix==0, 0))
c039eedd UD	148	{
	149	if (hx < 0)
	150	*signgamp = -1;
	151	return one/fabsf(x);
	152	}
ffa3cd7f JM	153	if(__builtin_expect(ix<0x30800000, 0)) {
ffa3cd7f JM	154	/* \|x\|<2*-30, return -log(\|x\|) /
f7eac6eb	155	if(hx<0) {
0ac5ae23 UD	156	*signgamp = -1;
0ac5ae23 UD	157	return -__ieee754_logf(-x);
f7eac6eb RM	158	} else return -__ieee754_logf(x);
	159	}
	160	if(hx<0) {
0ac5ae23	161	if(ix>=0x4b000000) /* \|x\|>=2*23, must be -integer /
d705269e	162	return x/zero;
f7eac6eb	163	t = sin_pif(x);
d705269e	164	if(t==zero) return one/fabsf(t); /* -integer */
f7eac6eb RM	165	nadj = __ieee754_logf(pi/fabsf(t*x));
	166	if(t<zero) *signgamp = -1;
	167	x = -x;
	168	}
	169
	170	/* purge off 1 and 2 */
	171	if (ix==0x3f800000\|\|ix==0x40000000) r = 0;
	172	/* for x < 2.0 */
	173	else if(ix<0x40000000) {
0ac5ae23	174	if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
f7eac6eb RM	175	r = -__ieee754_logf(x);
	176	if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
	177	else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
0ac5ae23	178	else {y = x; i=2;}
f7eac6eb	179	} else {
0ac5ae23 UD	180	r = zero;
	181	if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
	182	else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
f7eac6eb RM	183	else {y=x-one;i=2;}
	184	}
	185	switch(i) {
	186	case 0:
	187	z = y*y;
	188	p1 = a0+z(a2+z(a4+z(a6+z(a8+z*a10))));
	189	p2 = z(a1+z(a3+z(a5+z(a7+z(a9+za11)))));
	190	p = y*p1+p2;
	191	r += (p-(float)0.5*y); break;
	192	case 1:
	193	z = y*y;
	194	w = z*y;
	195	p1 = t0+w(t3+w(t6+w(t9 +wt12))); /* parallel comp */
	196	p2 = t1+w(t4+w(t7+w(t10+wt13)));
	197	p3 = t2+w(t5+w(t8+w(t11+wt14)));
	198	p = zp1-(tt-w(p2+y*p3));
	199	r += (tf + p); break;
d705269e	200	case 2:
f7eac6eb RM	201	p1 = y(u0+y(u1+y(u2+y(u3+y(u4+yu5)))));
	202	p2 = one+y(v1+y(v2+y(v3+y(v4+y*v5))));
	203	r += (-(float)0.5*y + p1/p2);
	204	}
	205	}
0ac5ae23	206	else if(ix<0x41000000) { /* x < 8.0 */
f7eac6eb RM	207	i = (int)x;
	208	t = zero;
	209	y = x-(float)i;
	210	p = y(s0+y(s1+y(s2+y(s3+y(s4+y(s5+y*s6))))));
	211	q = one+y(r1+y(r2+y(r3+y(r4+y(r5+yr6)))));
	212	r = half*y+p/q;
	213	z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
	214	switch(i) {
	215	case 7: z = (y+(float)6.0); / FALLTHRU */
	216	case 6: z = (y+(float)5.0); / FALLTHRU */
	217	case 5: z = (y+(float)4.0); / FALLTHRU */
	218	case 4: z = (y+(float)3.0); / FALLTHRU */
	219	case 3: z = (y+(float)2.0); / FALLTHRU */
	220	r += __ieee754_logf(z); break;
	221	}
ff069f02 JM	222	/* 8.0 <= x < 2*26 /
ff069f02 JM	223	} else if (ix < 0x4c800000) {
f7eac6eb RM	224	t = __ieee754_logf(x);
	225	z = one/x;
	226	y = z*z;
	227	w = w0+z(w1+y(w2+y(w3+y(w4+y(w5+yw6)))));
	228	r = (x-half)*(t-one)+w;
d705269e	229	} else
ff069f02	230	/* 2*26 <= x <= inf /
f7eac6eb RM	231	r = x*(__ieee754_logf(x)-one);
	232	if(hx<0) r = nadj - r;
	233	return r;
	234	}
0ac5ae23	235	strong_alias (__ieee754_lgammaf_r, __lgammaf_r_finite)