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      1 /*-
      2  * Copyright (c) 2017-2023 Steven G. Kargl
      3  * All rights reserved.
      4  *
      5  * Redistribution and use in source and binary forms, with or without
      6  * modification, are permitted provided that the following conditions
      7  * are met:
      8  * 1. Redistributions of source code must retain the above copyright
      9  *    notice unmodified, this list of conditions, and the following
     10  *    disclaimer.
     11  * 2. Redistributions in binary form must reproduce the above copyright
     12  *    notice, this list of conditions and the following disclaimer in the
     13  *    documentation and/or other materials provided with the distribution.
     14  *
     15  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
     16  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
     17  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
     18  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
     19  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
     20  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
     21  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
     22  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
     23  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
     24  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
     25  */
     26 
     27 /*
     28  * See ../src/s_tanpi.c for implementation details.
     29  */
     30 
     31 #include "math.h"
     32 #include "math_private.h"
     33 
     34 /*
     35  * pi_hi contains the leading 56 bits of a 169 bit approximation for pi.
     36  */
     37 static const long double
     38 pi_hi = 3.14159265358979322702026593105983920e+00L,
     39 pi_lo = 1.14423774522196636802434264184180742e-17L;
     40 
     41 static inline long double
     42 __kernel_tanpil(long double x)
     43 {
     44 	long double hi, lo, t;
     45 
     46 	if (x < 0.25) {
     47 		hi = (double)x;
     48 		lo = x - hi;
     49 		lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
     50 		hi *= pi_hi;
     51 		_2sumF(hi, lo);
     52 		t = __kernel_tanl(hi, lo, -1);
     53 	} else if (x > 0.25) {
     54 		x = 0.5 - x;
     55 		hi = (double)x;
     56 		lo = x - hi;
     57 		lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
     58 		hi *= pi_hi;
     59 		_2sumF(hi, lo);
     60 		t = - __kernel_tanl(hi, lo, 1);
     61 	} else
     62 		t = 1;
     63 
     64 	return (t);
     65 }
     66 
     67 static volatile const double vzero = 0;
     68 
     69 long double
     70 tanpil(long double x)
     71 {
     72 	long double ai, ar, ax, hi, lo, t;
     73 	double odd;
     74 
     75 	ax = fabsl(x);
     76 
     77 	if (ax < 1) {
     78 		if (ax < 0.5) {
     79 			if (ax < 0x1p-60) {
     80 				if (x == 0)
     81 					return (x);
     82 				hi = (double)x;
     83 				hi *= 0x1p113L;
     84 				lo = x * 0x1p113L - hi;
     85 				t = (pi_lo + pi_hi) * lo + pi_lo * lo +
     86 				    pi_hi * hi;
     87 				return (t * 0x1p-113L);
     88 			}
     89 			t = __kernel_tanpil(ax);
     90 		} else if (ax == 0.5)
     91 			t = 1 / vzero;
     92 		else
     93 			t = -__kernel_tanpil(1 - ax);
     94 		return (x < 0 ? -t : t);
     95 	}
     96 
     97 	if (ax < 0x1p112) {
     98 		/* Split ax = ai + ar with 0 <= ar < 1. */
     99 		FFLOORL128(ax, ai, ar);
    100 		odd = fmodl(ai, 2.L) == 0 ? 1 : -1;
    101 		if (ar < 0.5)
    102 			t = ar == 0 ? copysign(0., odd) : __kernel_tanpil(ar);
    103 		else if (ar == 0.5)
    104 			t = odd / vzero;
    105 		else
    106 			t = -__kernel_tanpil(1 - ar);
    107 		return (x < 0 ? -t : t);
    108 	}
    109 
    110 	/* x = +-inf or nan. */
    111 	if (isinf(x) || isnan(x))
    112 		return (vzero / vzero);
    113 
    114 	/*
    115 	 * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even
    116 	 * or odd integer to set t = +0 or -0.
    117 	 * For |x| >= 0x1p113, it is always an even integer, so t = 0.
    118 	 */
    119 	t = fmodl(ax,2.L) == 0  ? 0 : copysign(0., -1.);
    120 	return (copysignl(t, x));
    121 }
    122