/*-
* 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.
*/

#include <stdint.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);
}

static volatile const double vzero = 0;

long double
tanpil(long double x)
{
       long double ax, hi, lo, odd, t;
       uint64_t lx;
       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);
}