efficient sincos based on sin and cos

src/math/sincosf.c

@@ -0,0 +1,113 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_sinf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+#include "libm.h"
+
+/* Small multiples of pi/2 rounded to double precision. */
+static const double
+s1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
+s2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
+s3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
+s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
+
+void sincosf(float x, float *sin, float *cos)
+{
+	double y, s, c;
+	uint32_t n, hx, ix;
+
+	GET_FLOAT_WORD(hx, x);
+	ix = hx & 0x7fffffff;
+
+	/* |x| ~<= pi/4 */
+	if (ix <= 0x3f490fda) {
+		/* |x| < 2**-12 */
+		if (ix < 0x39800000) {
+			/* raise inexact if x != 0 */
+			if((int)x == 0) {
+				*sin = x;
+				*cos = 1.0f;
+			}
+			return;
+		}
+		*sin = __sindf(x);
+		*cos = __cosdf(x);
+		return;
+	}
+
+	/* |x| ~<= 5*pi/4 */
+	if (ix <= 0x407b53d1) {  
+		if (ix <= 0x4016cbe3) {  /* |x| ~<= 3pi/4 */
+			if (hx < 0x80000000) {
+				*sin = __cosdf(x - s1pio2);
+				*cos = __sindf(s1pio2 - x);
+			} else {
+				*sin = -__cosdf(x + s1pio2);
+				*cos = __sindf(x + s1pio2);
+			}
+			return;
+		}
+		*sin = __sindf(hx < 0x80000000 ? s2pio2 - x : -s2pio2 - x);
+		*cos = -__cosdf(hx < 0x80000000 ? x - s2pio2 : x + s2pio2);
+		return;
+	}
+
+	/* |x| ~<= 9*pi/4 */
+	if (ix <= 0x40e231d5) {
+		if (ix <= 0x40afeddf) {  /* |x| ~<= 7*pi/4 */
+			if (hx < 0x80000000) {
+				*sin = -__cosdf(x - s3pio2);
+				*cos = __sindf(x - s3pio2);
+			} else {
+				*sin = __cosdf(x + s3pio2);
+				*cos = __sindf(-s3pio2 - x);
+			}
+			return;
+		}
+		*sin = __sindf(hx < 0x80000000 ? x - s4pio2 : x + s4pio2);
+		*cos = __cosdf(hx < 0x80000000 ? x - s4pio2 : x + s4pio2);
+		return;
+	}
+
+	/* sin(Inf or NaN) is NaN */
+	if (ix >= 0x7f800000) {
+		*sin = *cos = x - x;
+		return;
+	}
+
+	/* general argument reduction needed */
+	n = __rem_pio2f(x, &y);
+	s = __sindf(y);
+	c = __cosdf(y);
+	switch (n&3) {
+	case 0:
+		*sin = s;
+		*cos = c;
+		break;
+	case 1:
+		*sin = c;
+		*cos = -s;
+		break;
+	case 2:
+		*sin = -s;
+		*cos = -c;
+		break;
+	case 3:
+	default:
+		*sin = -c;
+		*cos = s;
+		break;
+	}
+}