Implement ldbl-96 sinl / cosl / sincosl (bug 13851).

1 files changed, 123 insertions, 0 deletions

diff --git a/sysdeps/ieee754/ldbl-96/k_cosl.c b/sysdeps/ieee754/ldbl-96/k_cosl.c
new file mode 100644
index 0000000000..9e8f33a283
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/k_cosl.c
@@ -0,0 +1,123 @@
+/* Extended-precision floating point cosine on <-pi/4,pi/4>.
+   Copyright (C) 1999-2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Based on quad-precision cosine 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>
+
+/* The polynomials have not been optimized for extended-precision and
+   may contain more terms than needed.  */
+
+static const long double c[] = {
+#define ONE c[0]
+ 1.00000000000000000000000000000000000E+00L,
+
+/* 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,
+ 4.16666666666666666666666666556146073E-02L,
+-1.38888888888888888888309442601939728E-03L,
+ 2.48015873015862382987049502531095061E-05L,
+-2.75573112601362126593516899592158083E-07L,
+
+/* 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,
+ 4.16666666666666666666666666651287795E-02L,
+-1.38888888888888888888888742314300284E-03L,
+ 2.48015873015873015867694002851118210E-05L,
+-2.75573192239858811636614709689300351E-07L,
+ 2.08767569877762248667431926878073669E-09L,
+-1.14707451049343817400420280514614892E-11L,
+ 4.77810092804389587579843296923533297E-14L,
+
+/* 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,
+ 8.33333333333333333333333333146298442E-03L,
+-1.98412698412698412697726277416810661E-04L,
+ 2.75573192239848624174178393552189149E-06L,
+-2.50521016467996193495359189395805639E-08L,
+};
+
+#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;
+  int index;
+
+  if (signbit (x))
+    {
+      x = -x;
+      y = -y;
+    }
+  if (x < 0.1484375L)
+    {
+      /* Argument is small enough to approximate it by a Chebyshev
+	 polynomial of degree 16.  */
+      if (x < 0x1p-33L)
+	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).  */
+      index = (int) (128 * (x - (0.1484375L - 1.0L / 256.0L)));
+      h = 0.1484375L + index / 128.0;
+      index *= 4;
+      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));
+    }
+}