|
|
@@ -0,0 +1,151 @@
|
|
|
+/* @(#)s_sincos.c 5.1 13/07/15 */
|
|
|
+/*
|
|
|
+ * ====================================================
|
|
|
+ * Copyright (C) 2013 Elliot Saba. All rights reserved.
|
|
|
+ *
|
|
|
+ * Developed at the University of Washington.
|
|
|
+ * Permission to use, copy, modify, and distribute this
|
|
|
+ * software is freely granted, provided that this notice
|
|
|
+ * is preserved.
|
|
|
+ * ====================================================
|
|
|
+ */
|
|
|
+ #include "cdefs-compat.h"
|
|
|
+
|
|
|
+/* sincos(x, s, c)
|
|
|
+ * Several applications need sine and cosine of the same
|
|
|
+ * angle x. This function computes both at the same time,
|
|
|
+ * and stores the results in *sin and *cos.
|
|
|
+ *
|
|
|
+ * kernel function:
|
|
|
+ * __kernel_sin ... sine function on [-pi/4,pi/4]
|
|
|
+ * __kernel_cos ... cose function on [-pi/4,pi/4]
|
|
|
+ * __ieee754_rem_pio2 ... argument reduction routine
|
|
|
+ *
|
|
|
+ * Method.
|
|
|
+ * Borrow liberally from s_sin.c and s_cos.c, merging
|
|
|
+ * efforts where applicable and returning their values in
|
|
|
+ * appropriate variables, thereby slightly reducing the
|
|
|
+ * amount of work relative to just calling sin/cos(x)
|
|
|
+ * separately
|
|
|
+ *
|
|
|
+ * Special cases:
|
|
|
+ * Let trig be any of sin, cos, or tan.
|
|
|
+ * sincos(+-INF, s, c) is NaN, with signals;
|
|
|
+ * sincos(NaN, s, c) is that NaN;
|
|
|
+ */
|
|
|
+
|
|
|
+#include <float.h>
|
|
|
+
|
|
|
+#include "openlibm.h"
|
|
|
+//#define INLINE_REM_PIO2
|
|
|
+#include "math_private.h"
|
|
|
+//#include "e_rem_pio2.c"
|
|
|
+
|
|
|
+/* Constants used in polynomial approximation of sin/cos */
|
|
|
+static const double
|
|
|
+one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
|
|
+half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
|
|
+S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
|
|
|
+S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
|
|
|
+S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
|
|
|
+S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
|
|
|
+S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
|
|
|
+S6 = 1.58969099521155010221e-10, /* 0x3DE5D93A, 0x5ACFD57C */
|
|
|
+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 */
|
|
|
+
|
|
|
+void
|
|
|
+__kernel_sincos( double x, double y, int iy, double * k_s, double * k_c )
|
|
|
+{
|
|
|
+ /* Inline calculation of sin/cos, as we can save
|
|
|
+ some work, and we will always need to calculate
|
|
|
+ both values, no matter the result of switch */
|
|
|
+ double z, w, r, v, hz;
|
|
|
+ z = x*x;
|
|
|
+ w = z*z;
|
|
|
+
|
|
|
+ /* cos-specific computation; equivalent to calling
|
|
|
+ __kernel_cos(x,y) and storing in k_c*/
|
|
|
+ r = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6));
|
|
|
+ hz = 0.5*z;
|
|
|
+ v = one-hz;
|
|
|
+
|
|
|
+ *k_c = v + (((one-v)-hz) + (z*r-x*y));
|
|
|
+
|
|
|
+ /* sin-specific computation; equivalent to calling
|
|
|
+ __kernel_sin(x,y,1) and storing in k_s*/
|
|
|
+ r = S2+z*(S3+z*S4) + z*w*(S5+z*S6);
|
|
|
+ v = z*x;
|
|
|
+ if(iy == 0)
|
|
|
+ *k_s = x+v*(S1+z*r);
|
|
|
+ else
|
|
|
+ *k_s = x-((z*(half*y-v*r)-y)-v*S1);
|
|
|
+}
|
|
|
+
|
|
|
+void
|
|
|
+sincos(double x, double * s, double * c)
|
|
|
+{
|
|
|
+ double y[2];
|
|
|
+ int32_t ix;
|
|
|
+
|
|
|
+ /* Store high word of x in ix */
|
|
|
+ GET_HIGH_WORD(ix,x);
|
|
|
+
|
|
|
+ /* |x| ~< pi/4 */
|
|
|
+ ix &= 0x7fffffff;
|
|
|
+ if(ix <= 0x3fe921fb) {
|
|
|
+ /* Check for small x for sin and cos */
|
|
|
+ if(ix<0x3e46a09e) {
|
|
|
+ /* Check for exact zero */
|
|
|
+ if( (int)x==0 ) {
|
|
|
+ *s = x;
|
|
|
+ *c = 1.0;
|
|
|
+ return;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ /* Call kernel function with 0 extra */
|
|
|
+ __kernel_sincos(x,0.0,0, s, c);
|
|
|
+ } else if( ix >= 0x7ff00000 ) {
|
|
|
+ /* sincos(Inf or NaN) is NaN */
|
|
|
+ *s = x-x;
|
|
|
+ *c = x-x;
|
|
|
+ }
|
|
|
+
|
|
|
+ /*argument reduction needed*/
|
|
|
+ else {
|
|
|
+ double k_c, k_s;
|
|
|
+ printf( "bleh?\n");
|
|
|
+
|
|
|
+ /* Calculate remainer, then sub out to kernel */
|
|
|
+ int32_t n = __ieee754_rem_pio2(x,y);
|
|
|
+ __kernel_sincos( y[0], y[1], 1, &k_s, &k_c );
|
|
|
+
|
|
|
+ /* Figure out permutation of sin/cos outputs to true outputs */
|
|
|
+ switch(n&3) {
|
|
|
+ case 0:
|
|
|
+ *c = k_c;
|
|
|
+ *s = k_s;
|
|
|
+ break;
|
|
|
+ case 1:
|
|
|
+ *c = -k_s;
|
|
|
+ *s = k_c;
|
|
|
+ break;
|
|
|
+ case 2:
|
|
|
+ *c = -k_c;
|
|
|
+ *s = -k_s;
|
|
|
+ break;
|
|
|
+ default:
|
|
|
+ *c = k_s;
|
|
|
+ *s = -k_c;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+#if (LDBL_MANT_DIG == 53)
|
|
|
+__weak_reference(sincos, sincosl);
|
|
|
+#endif
|
Elliot Saba