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authormrb0nk500 <b0nk@b0nk.xyz>2023-02-02 17:29:19 -0400
committermrb0nk500 <b0nk@b0nk.xyz>2023-02-03 13:27:06 -0400
commitf2eabdb6257c09cf2890dac5e9737912728542af (patch)
tree3b46f6787185d65605651a0f48776dc9779ce648 /src/MSL_C.PPCEABI.bare.H/k_cos.c
parenteef1dd840b7cecac28c2e6b0574707b90a37d4e7 (diff)
global: Add rest of Dolphin SDK proper, add MSL, and MetroTRK
Finally, it links properly.
Diffstat (limited to 'src/MSL_C.PPCEABI.bare.H/k_cos.c')
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1 files changed, 92 insertions, 0 deletions
diff --git a/src/MSL_C.PPCEABI.bare.H/k_cos.c b/src/MSL_C.PPCEABI.bare.H/k_cos.c
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+/* @(#)k_cos.c 1.2 95/01/04 */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/*
+ * __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 "fdlibm.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;
+ int ix;
+ ix = __HI(x) & 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 {
+ __HI(qx) = ix - 0x00200000; /* x/4 */
+ __LO(qx) = 0;
+ }
+ hz = 0.5 * z - qx;
+ a = one - qx;
+ return a - (hz - (z * r - x * y));
+ }
+}