/*-
 * Copyright (c) 2017, 2023 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.
 */

/*
 * See ../src/s_tanpi.c for implementation details.
 */

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

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

static const double
pi_hi =  3.1415926814079285e+00,        /* 0x400921fb 0x58000000 */
pi_lo = -2.7818135228334233e-08;        /* 0xbe5dde97 0x3dcb3b3a */

static inline long double
__kernel_tanpil(long double x)
{
        long double hi, lo, t;

        if (x < 0.25) {
                hi = (float)x;
                lo = x - hi;
                lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
                hi *= pi_hi;
                _2sumF(hi, lo);
                t = __kernel_tanl(hi, lo, -1);
        } else if (x > 0.25) {
                x = 0.5 - x;
                hi = (float)x;
                lo = x - hi;
                lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
                hi *= pi_hi;
                _2sumF(hi, lo);
                t = - __kernel_tanl(hi, lo, 1);
        } else
                t = 1;

        return (t);
}

volatile static const double vzero = 0;

long double
tanpil(long double x)
{
        long double ax, hi, lo, odd, t;
        uint64_t lx, m;
        uint32_t j0;
        uint16_t hx, ix;

        EXTRACT_LDBL80_WORDS(hx, lx, x);
        ix = hx & 0x7fff;
        INSERT_LDBL80_WORDS(ax, ix, lx);

        ENTERI();

        if (ix < 0x3fff) {                      /* |x| < 1 */
                if (ix < 0x3ffe) {              /* |x| < 0.5 */
                        if (ix < 0x3fdd) {      /* |x| < 0x1p-34 */
                                if (x == 0)
                                        RETURNI(x);
                                INSERT_LDBL80_WORDS(hi, hx,
                                    lx & 0xffffffff00000000ull);
                                hi *= 0x1p63L;
                                lo = x * 0x1p63L - hi;
                                t = (pi_lo + pi_hi) * lo + pi_lo * hi +
                                    pi_hi * hi;
                                RETURNI(t * 0x1p-63L);
                        }
                        t = __kernel_tanpil(ax);
                } else if (ax == 0.5)
                        t = 1 / vzero;
                else
                        t = -__kernel_tanpil(1 - ax);
                RETURNI((hx & 0x8000) ? -t : t);
        }

        if (ix < 0x403e) {                      /* 1 <= |x| < 0x1p63 */
                FFLOORL80(x, j0, ix, lx);       /* Integer part of ax. */
                odd = (uint64_t)x & 1 ? -1 : 1;
                ax -= x;
                EXTRACT_LDBL80_WORDS(ix, lx, ax);

                if (ix < 0x3ffe)                /* |x| < 0.5 */
                        t = ix == 0 ? copysignl(0, odd) : __kernel_tanpil(ax);
                else if (ax == 0.5L)
                        t = odd / vzero;
                else
                        t = -__kernel_tanpil(1 - ax);
                RETURNI((hx & 0x8000) ? -t : t);
        }

        /* x = +-inf or nan. */
        if (ix >= 0x7fff)
                RETURNI(vzero / vzero);

        /*
         * For 0x1p63 <= |x| < 0x1p64 need to determine if x is an even
         * or odd integer to set t = +0 or -0.
         * For |x| >= 0x1p64, it is always an even integer, so t = 0.
         */
        t = ix >= 0x403f ? 0 : (copysignl(0, (lx & 1) ? -1 : 1));
        RETURNI((hx & 0x8000) ? -t : t);
}