efficient sincos based on sin and cos

include/math.h

@@ -382,6 +382,10 @@ long double ynl(int, long double);
 double      scalb(double, double);
 float       scalbf(float, float);
 long double scalbl(long double, long double);
+
+void        sincos(double, double*, double*);
+void        sincosf(float, float*, float*);
+void        sincosl(long double, long double*, long double*);
 #endif
 
 #ifdef __cplusplus

src/linux/sincos.c

@@ -1,8 +0,0 @@
-#define _GNU_SOURCE
-#include <math.h>
-
-void sincos(double t, double *y, double *x)
-{
-	*y = sin(t);
-	*x = cos(t);
-}

src/math/sincos.c

@@ -0,0 +1,68 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */
+/*
+ * ====================================================
+ * 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"
+
+void sincos(double x, double *sin, double *cos)
+{
+	double y[2], s, c;
+	uint32_t n, ix;
+
+	GET_HIGH_WORD(ix, x);
+	ix &= 0x7fffffff;
+
+	/* |x| ~< pi/4 */
+	if (ix <= 0x3fe921fb) {
+		/* if |x| < 2**-27 * sqrt(2) */
+		if (ix < 0x3e46a09e) {
+			/* raise inexact if x != 0 */
+			if ((int)x == 0) {
+				*sin = x;
+				*cos = 1.0;
+			}
+			return;
+		}
+		*sin = __sin(x, 0.0, 0);
+		*cos = __cos(x, 0.0);
+		return;
+	}
+
+	/* sincos(Inf or NaN) is NaN */
+	if (ix >= 0x7ff00000) {
+		*sin = *cos = x - x;
+		return;
+	}
+
+	/* argument reduction needed */
+	n = __rem_pio2(x, y);
+	s = __sin(y[0], y[1], 1);
+	c = __cos(y[0], y[1]);
+	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;
+	}
+}

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;
+	}
+}

src/math/sincosl.c

@@ -0,0 +1,66 @@
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+void sincosl(long double x, long double *sin, long double *cos)
+{
+	double s, c;
+	sincos(x, &s, &c);
+	*sin = s;
+	*cos = c;
+}
+#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+#include "__rem_pio2l.h"
+
+void sincosl(long double x, long double *sin, long double *cos)
+{
+	union IEEEl2bits u;
+	int n;
+	long double y[2], s, c;
+
+	u.e = x;
+	u.bits.sign = 0;
+
+	/* x = +-0 or subnormal */
+	if (!u.bits.exp) {
+		*sin = x;
+		*cos = 1.0;
+		return;
+	}
+
+	/* x = nan or inf */
+	if (u.bits.exp == 0x7fff) {
+		*sin = *cos = x - x;
+		return;
+	}
+
+	/* |x| < pi/4 */
+	if (u.e < M_PI_4) {
+		*sin = __sinl(x, 0, 0);
+		*cos = __cosl(x, 0);
+		return;
+	}
+
+	n = __rem_pio2l(x, y);
+	s = __sinl(y[0], y[1], 1);
+	c = __cosl(y[0], y[1]);
+	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;
+	}
+}
+#endif