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

/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
   Copyright (C) 1999-2014 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 <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 */
	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>.
d4697bc9	2	Copyright (C) 1999-2014 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
1ed0291c RH	20	#include <math.h>
1ed0291c RH	21	#include <math_private.h>
f964490f RM	22
	23	static const long double c[] = {
	24	#define ONE c[0]
	25	1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
	26
	27	/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
	28	x in <0,1/256> */
	29	#define SCOS1 c[1]
	30	#define SCOS2 c[2]
	31	#define SCOS3 c[3]
	32	#define SCOS4 c[4]
	33	#define SCOS5 c[5]
	34	-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
	35	4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
	36	-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
	37	2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
	38	-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
	39
	40	/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
	41	x in <0,0.1484375> */
	42	#define COS1 c[6]
	43	#define COS2 c[7]
	44	#define COS3 c[8]
	45	#define COS4 c[9]
	46	#define COS5 c[10]
	47	#define COS6 c[11]
	48	#define COS7 c[12]
	49	#define COS8 c[13]
	50	-4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */
	51	4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
	52	-1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
	53	2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
	54	-2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
	55	2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
	56	-1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
	57	4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
	58
	59	/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
	60	x in <0,1/256> */
	61	#define SSIN1 c[14]
	62	#define SSIN2 c[15]
	63	#define SSIN3 c[16]
	64	#define SSIN4 c[17]
	65	#define SSIN5 c[18]
	66	-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
	67	8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
	68	-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
	69	2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
	70	-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
	71
	72	/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
	73	x in <0,0.1484375> */
	74	#define SIN1 c[19]
	75	#define SIN2 c[20]
	76	#define SIN3 c[21]
	77	#define SIN4 c[22]
	78	#define SIN5 c[23]
	79	#define SIN6 c[24]
	80	#define SIN7 c[25]
	81	#define SIN8 c[26]
	82	-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
	83	8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
	84	-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
	85	2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
86	-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
87	1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
88	-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
89	2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
90	};
91
92	#define SINCOSL_COS_HI 0
93	#define SINCOSL_COS_LO 1
94	#define SINCOSL_SIN_HI 2
95	#define SINCOSL_SIN_LO 3
96	extern const long double __sincosl_table[];
97
98	void
99	__kernel_sincosl(long double x, long double y, long double sinx, long double cosx, int iy)
100	{
101	long double h, l, z, sin_l, cos_l_m1;
102	int64_t ix;
4ebd120c AM	103	uint32_t tix, hix, index;
	104	double xhi, hhi;
	105
	106	xhi = ldbl_high (x);
	107	EXTRACT_WORDS64 (ix, xhi);
	108	tix = ((uint64_t)ix) >> 32;
f964490f RM	109	tix &= ~0x80000000; /* tix = \|x\|'s high 32 bits */
	110	if (tix < 0x3fc30000) /* \|x\| < 0.1484375 */
	111	{
	112	/* Argument is small enough to approximate it by a Chebyshev
	113	polynomial of degree 16(17). */
	114	if (tix < 0x3c600000) /* \|x\| < 2^-57 */
	115	if (!((int)x)) /* generate inexact */
	116	{
	117	*sinx = x;
	118	*cosx = ONE;
	119	return;
	120	}
	121	z = x * x;
	122	sinx = x + (x (z(SIN1+z(SIN2+z(SIN3+z(SIN4+
	123	z(SIN5+z(SIN6+z(SIN7+zSIN8)))))))));
	124	cosx = ONE + (z(COS1+z(COS2+z(COS3+z*(COS4+
	125	z(COS5+z(COS6+z(COS7+zCOS8))))))));
	126	}
	127	else
	128	{
	129	/* So that we don't have to use too large polynomial, we find
	130	l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
	131	possible values for h. We look up cosl(h) and sinl(h) in
	132	pre-computed tables, compute cosl(l) and sinl(l) using a
	133	Chebyshev polynomial of degree 10(11) and compute
	134	sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and
	135	cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */
16f0eced RM	136	int six = tix;
	137	tix = ((six - 0x3ff00000) >> 4) + 0x3fff0000;
	138	index = 0x3ffe - (tix >> 16);
	139	hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
	140	x = fabsl (x);
	141	switch (index)
	142	{
	143	case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
	144	case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
	145	default:
	146	case 2: index = (hix - 0x3ffc3000) >> 10; break;
	147	}
	148	hix = (hix << 4) & 0x3fffffff;
	149	/*
	150	The following should work for double but generates the wrong index.
	151	For now the code above converts double to ieee extended to compute
9c84384c JM	152	the index back to double for the h value.
9c84384c JM	153
16f0eced	154
f964490f RM	155	index = 0x3fe - (tix >> 20);
f964490f RM	156	hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
c0df8e69 JM	157	if (signbit (x))
	158	{
	159	x = -x;
	160	y = -y;
	161	}
f964490f RM	162	switch (index)
	163	{
	164	case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
	165	case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
	166	default:
	167	case 2: index = (hix - 0x3fc30000) >> 14; break;
	168	}
16f0eced	169	*/
4ebd120c AM	170	INSERT_WORDS64 (hhi, ((uint64_t)hix) << 32);
4ebd120c AM	171	h = hhi;
f964490f RM	172	if (iy)
	173	l = y - (h - x);
	174	else
	175	l = x - h;
	176	z = l * l;
	177	sin_l = l(ONE+z(SSIN1+z(SSIN2+z(SSIN3+z(SSIN4+zSSIN5)))));
	178	cos_l_m1 = z(SCOS1+z(SCOS2+z(SCOS3+z(SCOS4+z*SCOS5))));
	179	z = __sincosl_table [index + SINCOSL_SIN_HI]
	180	+ (__sincosl_table [index + SINCOSL_SIN_LO]
	181	+ (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
	182	+ (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
	183	*sinx = (ix < 0) ? -z : z;
	184	*cosx = __sincosl_table [index + SINCOSL_COS_HI]
	185	+ (__sincosl_table [index + SINCOSL_COS_LO]
	186	- (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
	187	- __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
	188	}
	189	}