atanl.c

/* origin: FreeBSD /usr/src/lib/msun/src/s_atanl.c */
/*
 * ====================================================
 * 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.
 * ====================================================
 */
/*
 * See comments in atan.c.
 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
 */

#include "libm.h"

#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double atanl(long double x)
{
	return atan(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"

#define ATAN_CONST      (BIAS + 65)     /* 2**65 */
#define ATAN_LINEAR     (BIAS - 32)     /* 2**-32 */
static const long double huge = 1.0e300;

static const long double atanhi[] = {
	 4.63647609000806116202e-01L,
	 7.85398163397448309628e-01L,
	 9.82793723247329067960e-01L,
	 1.57079632679489661926e+00L,
};

static const long double atanlo[] = {
	 1.18469937025062860669e-20L,
	-1.25413940316708300586e-20L,
	 2.55232234165405176172e-20L,
	-2.50827880633416601173e-20L,
};

static const long double aT[] = {
	 3.33333333333333333017e-01L,
	-1.99999999999999632011e-01L,
	 1.42857142857046531280e-01L,
	-1.11111111100562372733e-01L,
	 9.09090902935647302252e-02L,
	-7.69230552476207730353e-02L,
	 6.66661718042406260546e-02L,
	-5.88158892835030888692e-02L,
	 5.25499891539726639379e-02L,
	-4.70119845393155721494e-02L,
	 4.03539201366454414072e-02L,
	-2.91303858419364158725e-02L,
	 1.24822046299269234080e-02L,
};

static long double T_even(long double x)
{
	return aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] +
		x * (aT[8] + x * (aT[10] + x * aT[12])))));
}

static long double T_odd(long double x)
{
	return aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] +
		x * (aT[9] + x * aT[11]))));
}

long double atanl(long double x)
{
	union IEEEl2bits u;
	long double w,s1,s2,z;
	int id;
	int16_t expsign, expt;
	int32_t expman;

	u.e = x;
	expsign = u.xbits.expsign;
	expt = expsign & 0x7fff;
	if (expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */
		if (expt == BIAS + LDBL_MAX_EXP &&
		    ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0)  /* NaN */
			return x+x;
		if (expsign > 0)
			return  atanhi[3]+atanlo[3];
		else
			return -atanhi[3]-atanlo[3];
	}
	/* Extract the exponent and the first few bits of the mantissa. */
	/* XXX There should be a more convenient way to do this. */
	expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
	if (expman < ((BIAS - 2) << 8) + 0xc0) {  /* |x| < 0.4375 */
		if (expt < ATAN_LINEAR) {   /* if |x| is small, atanl(x)~=x */
			/* raise inexact */
			if (huge+x > 1.0)
				return x;
		}
		id = -1;
	} else {
		x = fabsl(x);
		if (expman < (BIAS << 8) + 0x30) {  /* |x| < 1.1875 */
			if (expman < ((BIAS - 1) << 8) + 0x60) { /*  7/16 <= |x| < 11/16 */
				id = 0;
				x = (2.0*x-1.0)/(2.0+x);
			} else {                                 /* 11/16 <= |x| < 19/16 */
				id = 1;
				x = (x-1.0)/(x+1.0);
			}
		} else {
			if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */
				id = 2;
				x = (x-1.5)/(1.0+1.5*x);
			} else {                                 /* 2.4375 <= |x| < 2^ATAN_CONST */
				id = 3;
				x = -1.0/x;
			}
		}
	}
	/* end of argument reduction */
	z = x*x;
	w = z*z;
	/* break sum aT[i]z**(i+1) into odd and even poly */
	s1 = z*T_even(w);
	s2 = w*T_odd(w);
	if (id < 0)
		return x - x*(s1+s2);
	z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
	return expsign < 0 ? -z : z;
}
#endif