2.5-18.1

1 files changed, 146 insertions, 0 deletions

diff --git a/sysdeps/ieee754/ldbl-128ibm/k_cosl.c b/sysdeps/ieee754/ldbl-128ibm/k_cosl.c
new file mode 100644
index 0000000000..b442582b3f
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128ibm/k_cosl.c
@@ -0,0 +1,146 @@
+/* Quad-precision floating point cosine on <-pi/4,pi/4>.
+   Copyright (C) 1999,2004,2006 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, write to the Free
+   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
+   02111-1307 USA.  */
+
+#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 */
+};
+
+#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_cosl(long double x, long double y)
+{
+  long double h, l, z, sin_l, cos_l_m1;
+  int64_t ix;
+  u_int32_t tix, hix, index;
+  GET_LDOUBLE_MSW64 (ix, x);
+  tix = ((u_int64_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.  */
+      if (tix < 0x3c600000)		/* |x| < 2^-57 */
+	if (!((int)x)) return ONE;	/* generate inexact */
+      z = x * x;
+      return 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
+	 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 + (0x200 << index)) & (0xfffffc00 << 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;
+	}
+*/
+      SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0);
+      l = y - (h - x);
+      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))));
+      return __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));
+    }
+}