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

/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
   Copyright (C) 1999-2016 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
   <http://www.gnu.org/licenses/>.  */

#include <float.h>
#include <math.h>
#include <math_private.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 */

/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
   x in <0,0.1484375>  */
#define COS1 c[6]
#define COS2 c[7]
#define COS3 c[8]
#define COS4 c[9]
#define COS5 c[10]
#define COS6 c[11]
#define COS7 c[12]
#define COS8 c[13]
-4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */
 4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
-1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
 2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
-2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
 2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
-1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
 4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */

/* 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 */

/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
   x in <0,0.1484375>  */
#define SIN1 c[19]
#define SIN2 c[20]
#define SIN3 c[21]
#define SIN4 c[22]
#define SIN5 c[23]
#define SIN6 c[24]
#define SIN7 c[25]
#define SIN8 c[26]
-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 */
};

#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[];

void
__kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, 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 16(17).  */
      if (tix < 0x3c600000)		/* |x| < 2^-57 */
	{
	  math_check_force_underflow (x);
	  if (!((int)x))			/* generate inexact */
	    {
	      *sinx = x;
	      *cosx = ONE;
	      return;
	    }
	}
      z = x * x;
      *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
			z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
      *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
		     z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
    }
  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) and
	 cosl(h+l) = cosl(h)cosl(l) - sinl(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);
      if (signbit (x))
	{
	  x = -x;
	  y = -y;
	}
      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 = 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));
      *sinx = (ix < 0) ? -z : z;
      *cosx = __sincosl_table [index + SINCOSL_COS_HI]
	      + (__sincosl_table [index + SINCOSL_COS_LO]
		 - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
		    - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
    }
}
Commit	Line	Data
f964490f	1	/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
f7a9f785	2	Copyright (C) 1999-2016 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 PE	17	License along with the GNU C Library; if not, see
59ba27a6 PE	18	<http://www.gnu.org/licenses/>. */
f964490f	19
ad39cce0	20	#include <float.h>
1ed0291c RH	21	#include <math.h>
1ed0291c RH	22	#include <math_private.h>
f964490f RM	23
	24	static const long double c[] = {
	25	#define ONE c[0]
	26	1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
	27
	28	/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
	29	x in <0,1/256> */
	30	#define SCOS1 c[1]
	31	#define SCOS2 c[2]
	32	#define SCOS3 c[3]
	33	#define SCOS4 c[4]
	34	#define SCOS5 c[5]
	35	-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
	36	4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
	37	-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
	38	2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
	39	-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
	40
	41	/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
	42	x in <0,0.1484375> */
	43	#define COS1 c[6]
	44	#define COS2 c[7]
	45	#define COS3 c[8]
	46	#define COS4 c[9]
	47	#define COS5 c[10]
	48	#define COS6 c[11]
	49	#define COS7 c[12]
	50	#define COS8 c[13]
	51	-4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */
	52	4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
	53	-1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
	54	2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
	55	-2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
	56	2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
	57	-1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
	58	4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
	59
	60	/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
	61	x in <0,1/256> */
	62	#define SSIN1 c[14]
	63	#define SSIN2 c[15]
	64	#define SSIN3 c[16]
	65	#define SSIN4 c[17]
	66	#define SSIN5 c[18]
	67	-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
	68	8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
	69	-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
	70	2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
	71	-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
	72
	73	/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
	74	x in <0,0.1484375> */
	75	#define SIN1 c[19]
	76	#define SIN2 c[20]
	77	#define SIN3 c[21]
	78	#define SIN4 c[22]
	79	#define SIN5 c[23]
	80	#define SIN6 c[24]
	81	#define SIN7 c[25]
	82	#define SIN8 c[26]
	83	-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
	84	8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
	85	-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
	86	2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
87	-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
88	1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
89	-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
90	2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
91	};
92
93	#define SINCOSL_COS_HI 0
94	#define SINCOSL_COS_LO 1
95	#define SINCOSL_SIN_HI 2
96	#define SINCOSL_SIN_LO 3
97	extern const long double __sincosl_table[];
98
99	void
100	__kernel_sincosl(long double x, long double y, long double sinx, long double cosx, int iy)
101	{
102	long double h, l, z, sin_l, cos_l_m1;
103	int64_t ix;
4ebd120c AM	104	uint32_t tix, hix, index;
	105	double xhi, hhi;
	106
	107	xhi = ldbl_high (x);
	108	EXTRACT_WORDS64 (ix, xhi);
	109	tix = ((uint64_t)ix) >> 32;
f964490f RM	110	tix &= ~0x80000000; /* tix = \|x\|'s high 32 bits */
	111	if (tix < 0x3fc30000) /* \|x\| < 0.1484375 */
	112	{
	113	/* Argument is small enough to approximate it by a Chebyshev
	114	polynomial of degree 16(17). */
	115	if (tix < 0x3c600000) /* \|x\| < 2^-57 */
ad39cce0	116	{
d96164c3	117	math_check_force_underflow (x);
ad39cce0 JM	118	if (!((int)x)) /* generate inexact */
	119	{
	120	*sinx = x;
	121	*cosx = ONE;
	122	return;
	123	}
	124	}
f964490f RM	125	z = x * x;
	126	sinx = x + (x (z(SIN1+z(SIN2+z(SIN3+z(SIN4+
	127	z(SIN5+z(SIN6+z(SIN7+zSIN8)))))))));
	128	cosx = ONE + (z(COS1+z(COS2+z(COS3+z*(COS4+
	129	z(COS5+z(COS6+z(COS7+zCOS8))))))));
	130	}
	131	else
	132	{
	133	/* So that we don't have to use too large polynomial, we find
	134	l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
	135	possible values for h. We look up cosl(h) and sinl(h) in
	136	pre-computed tables, compute cosl(l) and sinl(l) using a
	137	Chebyshev polynomial of degree 10(11) and compute
	138	sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and
	139	cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */
16f0eced RM	140	int six = tix;
	141	tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
	142	index = 0x3ffe - (tix >> 16);
	143	hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
	144	x = fabsl (x);
	145	switch (index)
	146	{
	147	case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
	148	case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
	149	default:
	150	case 2: index = (hix - 0x3ffc3000) >> 10; break;
	151	}
	152	hix = (hix << 4) & 0x3fffffff;
	153	/*
	154	The following should work for double but generates the wrong index.
	155	For now the code above converts double to ieee extended to compute
9c84384c JM	156	the index back to double for the h value.
9c84384c JM	157
16f0eced	158
f964490f RM	159	index = 0x3fe - (tix >> 20);
f964490f RM	160	hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
c0df8e69 JM	161	if (signbit (x))
	162	{
	163	x = -x;
	164	y = -y;
	165	}
f964490f RM	166	switch (index)
	167	{
	168	case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
	169	case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
	170	default:
	171	case 2: index = (hix - 0x3fc30000) >> 14; break;
	172	}
16f0eced	173	*/
4ebd120c AM	174	INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32);
4ebd120c AM	175	h = hhi;
f964490f RM	176	if (iy)
	177	l = y - (h - x);
	178	else
	179	l = x - h;
	180	z = l * l;
	181	sin_l = l(ONE+z(SSIN1+z(SSIN2+z(SSIN3+z(SSIN4+zSSIN5)))));
	182	cos_l_m1 = z(SCOS1+z(SCOS2+z(SCOS3+z(SCOS4+z*SCOS5))));
	183	z = __sincosl_table [index + SINCOSL_SIN_HI]
	184	+ (__sincosl_table [index + SINCOSL_SIN_LO]
	185	+ (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
	186	+ (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
	187	*sinx = (ix < 0) ? -z : z;
	188	*cosx = __sincosl_table [index + SINCOSL_COS_HI]
	189	+ (__sincosl_table [index + SINCOSL_COS_LO]
	190	- (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
	191	- __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
	192	}
	193	}