libm/upstream-freebsd/lib/msun/src/s_tanl.c

/*-
 * Copyright (c) 2007 Steven G. Kargl
 * 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 unmodified, 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 ``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 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 <sys/cdefs.h>
__FBSDID("$FreeBSD$");

/*
 * Limited testing on pseudorandom numbers drawn within [0:4e8] shows
 * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million
 * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%).
 */

#include <float.h>
#ifdef __i386__
#include <ieeefp.h>
#endif

#include "math.h"
#include "math_private.h"
#if LDBL_MANT_DIG == 64
#include "../ld80/e_rem_pio2l.h"
#elif LDBL_MANT_DIG == 113
#include "../ld128/e_rem_pio2l.h"
#else
#error "Unsupported long double format"
#endif

long double
tanl(long double x)
{
	union IEEEl2bits z;
	int e0, s;
	long double y[2];
	long double hi, lo;

	z.e = x;
	s = z.bits.sign;
	z.bits.sign = 0;

	/* If x = +-0 or x is subnormal, then tan(x) = x. */
	if (z.bits.exp == 0)
		return (x);

	/* If x = NaN or Inf, then tan(x) = NaN. */
	if (z.bits.exp == 32767)
		return ((x - x) / (x - x));

	ENTERI();

	/* Optimize the case where x is already within range. */
	if (z.e < M_PI_4) {
		hi = __kernel_tanl(z.e, 0, 0);
		RETURNI(s ? -hi : hi);
	}

	e0 = __ieee754_rem_pio2l(x, y);
	hi = y[0];
	lo = y[1];

	switch (e0 & 3) {
	case 0:
	case 2:
	    hi = __kernel_tanl(hi, lo, 0);
	    break;
	case 1:
	case 3:
	    hi = __kernel_tanl(hi, lo, 1);
	    break;
	}

	RETURNI(hi);
}