[thirdparty/glibc.git] / sysdeps / ieee754 / ldbl-128ibm / k_sinl.c

/* Quad-precision floating point sine on <-pi/4,pi/4>.
   Copyright (C) 1999-2019 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Jakub Jelinek <jj@ultra.linux.cz>

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <https://www.gnu.org/licenses/>.  */

#include <float.h>
#include <math.h>
#include <math_private.h>
#include <math-underflow.h>

static const long double c[] = {
#define ONE c[0]
 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */

/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
   x in <0,1/256>  */
#define SCOS1 c[1]
#define SCOS2 c[2]
#define SCOS3 c[3]
#define SCOS4 c[4]
#define SCOS5 c[5]
-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */

/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
   x in <0,0.1484375>  */
#define SIN1 c[6]
#define SIN2 c[7]
#define SIN3 c[8]
#define SIN4 c[9]
#define SIN5 c[10]
#define SIN6 c[11]
#define SIN7 c[12]
#define SIN8 c[13]
-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */

/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
   x in <0,1/256>  */
#define SSIN1 c[14]
#define SSIN2 c[15]
#define SSIN3 c[16]
#define SSIN4 c[17]
#define SSIN5 c[18]
-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
};

#define SINCOSL_COS_HI 0
#define SINCOSL_COS_LO 1
#define SINCOSL_SIN_HI 2
#define SINCOSL_SIN_LO 3
extern const long double __sincosl_table[];

long double
__kernel_sinl(long double x, long double y, int iy)
{
  long double h, l, z, sin_l, cos_l_m1;
  int64_t ix;
  uint32_t tix, hix, index;
  double xhi, hhi;

  xhi = ldbl_high (x);
  EXTRACT_WORDS64 (ix, xhi);
  tix = ((uint64_t)ix) >> 32;
  tix &= ~0x80000000;			/* tix = |x|'s high 32 bits */
  if (tix < 0x3fc30000)			/* |x| < 0.1484375 */
    {
      /* Argument is small enough to approximate it by a Chebyshev
	 polynomial of degree 17.  */
      if (tix < 0x3c600000)		/* |x| < 2^-57 */
	{
	  math_check_force_underflow (x);
	  if (!((int)x)) return x;	/* generate inexact */
	}
      z = x * x;
      return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
		       z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
    }
  else
    {
      /* So that we don't have to use too large polynomial,  we find
	 l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
	 possible values for h.  We look up cosl(h) and sinl(h) in
	 pre-computed tables,  compute cosl(l) and sinl(l) using a
	 Chebyshev polynomial of degree 10(11) and compute
	 sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l).  */
      int six = tix;
      tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
      index = 0x3ffe - (tix >> 16);
      hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
      x = fabsl (x);
      switch (index)
	{
	case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
	case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
	default:
	case 2: index = (hix - 0x3ffc3000) >> 10; break;
	}
      hix = (hix << 4) & 0x3fffffff;
/*
    The following should work for double but generates the wrong index.
    For now the code above converts double to ieee extended to compute
    the index back to double for the h value.

      index = 0x3fe - (tix >> 20);
      hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
      x = fabsl (x);
      switch (index)
	{
	case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
	case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
	default:
	case 2: index = (hix - 0x3fc30000) >> 14; break;
	}
*/
      INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32);
      h = hhi;
      if (iy)
	l = (ix < 0 ? -y : y) - (h - x);
      else
	l = x - h;
      z = l * l;
      sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
      cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
      z = __sincosl_table [index + SINCOSL_SIN_HI]
	  + (__sincosl_table [index + SINCOSL_SIN_LO]
	     + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
	     + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
      return (ix < 0) ? -z : z;
    }
}
Commit	Line	Data
f964490f	1	/* Quad-precision floating point sine on <-pi/4,pi/4>.
04277e02	2	Copyright (C) 1999-2019 Free Software Foundation, Inc.
f964490f RM	3	This file is part of the GNU C Library.
	4	Contributed by Jakub Jelinek <jj@ultra.linux.cz>
	5
	6	The GNU C Library is free software; you can redistribute it and/or
	7	modify it under the terms of the GNU Lesser General Public
	8	License as published by the Free Software Foundation; either
	9	version 2.1 of the License, or (at your option) any later version.
	10
	11	The GNU C Library is distributed in the hope that it will be useful,
	12	but WITHOUT ANY WARRANTY; without even the implied warranty of
	13	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
	14	Lesser General Public License for more details.
	15
	16	You should have received a copy of the GNU Lesser General Public
59ba27a6	17	License along with the GNU C Library; if not, see
5a82c748	18	<https://www.gnu.org/licenses/>. */
f964490f	19
ad39cce0	20	#include <float.h>
1ed0291c RH	21	#include <math.h>
1ed0291c RH	22	#include <math_private.h>
8f5b00d3	23	#include <math-underflow.h>
f964490f RM	24
	25	static const long double c[] = {
	26	#define ONE c[0]
	27	1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
	28
	29	/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
	30	x in <0,1/256> */
	31	#define SCOS1 c[1]
	32	#define SCOS2 c[2]
	33	#define SCOS3 c[3]
	34	#define SCOS4 c[4]
	35	#define SCOS5 c[5]
	36	-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
	37	4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
	38	-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
	39	2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
	40	-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
	41
	42	/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
	43	x in <0,0.1484375> */
	44	#define SIN1 c[6]
	45	#define SIN2 c[7]
	46	#define SIN3 c[8]
	47	#define SIN4 c[9]
	48	#define SIN5 c[10]
	49	#define SIN6 c[11]
	50	#define SIN7 c[12]
	51	#define SIN8 c[13]
	52	-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
	53	8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
	54	-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
	55	2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
	56	-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
	57	1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
	58	-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
	59	2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
	60
	61	/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
	62	x in <0,1/256> */
	63	#define SSIN1 c[14]
	64	#define SSIN2 c[15]
	65	#define SSIN3 c[16]
	66	#define SSIN4 c[17]
	67	#define SSIN5 c[18]
	68	-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
	69	8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
	70	-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
	71	2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
	72	-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
	73	};
	74
	75	#define SINCOSL_COS_HI 0
	76	#define SINCOSL_COS_LO 1
	77	#define SINCOSL_SIN_HI 2
	78	#define SINCOSL_SIN_LO 3
	79	extern const long double __sincosl_table[];
	80
	81	long double
	82	__kernel_sinl(long double x, long double y, int iy)
	83	{
	84	long double h, l, z, sin_l, cos_l_m1;
	85	int64_t ix;
24ab7723	86	uint32_t tix, hix, index;
4ebd120c AM	87	double xhi, hhi;
	88
	89	xhi = ldbl_high (x);
	90	EXTRACT_WORDS64 (ix, xhi);
24ab7723	91	tix = ((uint64_t)ix) >> 32;
f964490f RM	92	tix &= ~0x80000000; /* tix = \|x\|'s high 32 bits */
	93	if (tix < 0x3fc30000) /* \|x\| < 0.1484375 */
	94	{
	95	/* Argument is small enough to approximate it by a Chebyshev
	96	polynomial of degree 17. */
	97	if (tix < 0x3c600000) /* \|x\| < 2^-57 */
ad39cce0	98	{
d96164c3	99	math_check_force_underflow (x);
ad39cce0 JM	100	if (!((int)x)) return x; /* generate inexact */
ad39cce0 JM	101	}
f964490f RM	102	z = x * x;
	103	return x + (x * (z(SIN1+z(SIN2+z(SIN3+z(SIN4+
	104	z(SIN5+z(SIN6+z(SIN7+zSIN8)))))))));
	105	}
	106	else
	107	{
	108	/* So that we don't have to use too large polynomial, we find
	109	l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
	110	possible values for h. We look up cosl(h) and sinl(h) in
	111	pre-computed tables, compute cosl(l) and sinl(l) using a
	112	Chebyshev polynomial of degree 10(11) and compute
	113	sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */
16f0eced RM	114	int six = tix;
	115	tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
	116	index = 0x3ffe - (tix >> 16);
	117	hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
	118	x = fabsl (x);
	119	switch (index)
	120	{
	121	case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
	122	case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
	123	default:
	124	case 2: index = (hix - 0x3ffc3000) >> 10; break;
	125	}
	126	hix = (hix << 4) & 0x3fffffff;
	127	/*
	128	The following should work for double but generates the wrong index.
	129	For now the code above converts double to ieee extended to compute
9c84384c JM	130	the index back to double for the h value.
9c84384c JM	131
f964490f RM	132	index = 0x3fe - (tix >> 20);
	133	hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
	134	x = fabsl (x);
	135	switch (index)
	136	{
	137	case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
	138	case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
	139	default:
	140	case 2: index = (hix - 0x3fc30000) >> 14; break;
	141	}
16f0eced	142	*/
4ebd120c AM	143	INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32);
4ebd120c AM	144	h = hhi;
f964490f	145	if (iy)
c0df8e69	146	l = (ix < 0 ? -y : y) - (h - x);
f964490f RM	147	else
	148	l = x - h;
	149	z = l * l;
	150	sin_l = l(ONE+z(SSIN1+z(SSIN2+z(SSIN3+z(SSIN4+zSSIN5)))));
	151	cos_l_m1 = z(SCOS1+z(SCOS2+z(SCOS3+z(SCOS4+z*SCOS5))));
	152	z = __sincosl_table [index + SINCOSL_SIN_HI]
	153	+ (__sincosl_table [index + SINCOSL_SIN_LO]
	154	+ (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
	155	+ (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
	156	return (ix < 0) ? -z : z;
	157	}
	158	}