/*      $OpenBSD: s_tanl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $     */
/*-
 * 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.
 */

/*
 * Compute tan(x) for x where x is reduced to y = x - k * pi / 2.
 * 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 <sys/types.h>
#include <machine/ieee.h>
#include <float.h>
#include <math.h>

#include "math_private.h"

#if LDBL_MANT_DIG == 64
#define NX      3
#define PREC    2
#elif LDBL_MANT_DIG == 113
#define NX      5
#define PREC    3
#else
#error "Unsupported long double format"
#endif

static const long double two24 = 1.67772160000000000000e+07L;

long double
tanl(long double x)
{
        union {
                long double e;
                struct ieee_ext bits;
        } z;
        int i, e0, s;
        double xd[NX], yd[PREC];
        long double hi, lo;

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

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

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

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

        /* Split z.e into a 24-bit representation. */
        e0 = ilogbl(z.e) - 23;
        z.e = scalbnl(z.e, -e0);
        for (i = 0; i < NX; i++) {
                xd[i] = (double)((int32_t)z.e);
                z.e = (z.e - xd[i]) * two24;
        }
        
        /* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */
        e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC);

#if PREC == 2
        hi = (long double)yd[0] + yd[1];
        lo = yd[1] - (hi - yd[0]);
#else /* PREC == 3 */
        long double t;
        t = (long double)yd[2] + yd[1];
        hi = t + yd[0];
        lo = yd[0] - (hi - t);
#endif

        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;
        }

        return (s ? -hi : hi);
}