initial import

[picodrive.git] / platform / gp2x / uClibc / k_cos.c

diff --git a/platform/gp2x/uClibc/k_cos.c b/platform/gp2x/uClibc/k_cos.c
new file mode 100644 (file)
index 0000000..03c208a
--- /dev/null
+++ b/platform/gp2x/uClibc/k_cos.c
@@ -0,0 +1,96 @@
+/* @(#)k_cos.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $";
+#endif
+
+/*
+ * __kernel_cos( x,  y )
+ * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ *
+ * Algorithm
+ *     1. Since cos(-x) = cos(x), we need only to consider positive x.
+ *     2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
+ *     3. cos(x) is approximated by a polynomial of degree 14 on
+ *        [0,pi/4]
+ *                                      4            14
+ *             cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
+ *        where the remez error is
+ *
+ *     |              2     4     6     8     10    12     14 |     -58
+ *     |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
+ *     |                                                      |
+ *
+ *                    4     6     8     10    12     14
+ *     4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
+ *            cos(x) = 1 - x*x/2 + r
+ *        since cos(x+y) ~ cos(x) - sin(x)*y
+ *                       ~ cos(x) - x*y,
+ *        a correction term is necessary in cos(x) and hence
+ *             cos(x+y) = 1 - (x*x/2 - (r - x*y))
+ *        For better accuracy when x > 0.3, let qx = |x|/4 with
+ *        the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
+ *        Then
+ *             cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
+ *        Note that 1-qx and (x*x/2-qx) is EXACT here, and the
+ *        magnitude of the latter is at least a quarter of x*x/2,
+ *        thus, reducing the rounding error in the subtraction.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
+C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
+C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
+C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
+C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
+C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
+
+#ifdef __STDC__
+       double __kernel_cos(double x, double y)
+#else
+       double __kernel_cos(x, y)
+       double x,y;
+#endif
+{
+       double a,hz,z,r,qx;
+       int32_t ix;
+       GET_HIGH_WORD(ix,x);
+       ix &= 0x7fffffff;                       /* ix = |x|'s high word*/
+       if(ix<0x3e400000) {                     /* if x < 2**27 */
+           if(((int)x)==0) return one;         /* generate inexact */
+       }
+       z  = x*x;
+       r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
+       if(ix < 0x3FD33333)                     /* if |x| < 0.3 */
+           return one - (0.5*z - (z*r - x*y));
+       else {
+           if(ix > 0x3fe90000) {               /* x > 0.78125 */
+               qx = 0.28125;
+           } else {
+               INSERT_WORDS(qx,ix-0x00200000,0);       /* x/4 */
+           }
+           hz = 0.5*z-qx;
+           a  = one-qx;
+           return a - (hz - (z*r-x*y));
+       }
+}