efficient sincos based on sin and cos

diff --git a/include/math.h b/include/math.h
index f320b8e..b9139b0 100644 (file)
--- a/include/math.h
+++ b/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);
 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
 #endif
 
 #ifdef __cplusplus

diff --git a/src/linux/sincos.c b/src/linux/sincos.c
deleted file mode 100644 (file)
index b69ffce..0000000
--- a/src/linux/sincos.c
+++ /dev/null
@@ -1,8 +0,0 @@
-#define _GNU_SOURCE
-#include <math.h>
-
-void sincos(double t, double *y, double *x)
-{
-       *y = sin(t);
-       *x = cos(t);
-}

diff --git a/src/math/sincos.c b/src/math/sincos.c
new file mode 100644 (file)
index 0000000..442e285
--- /dev/null
+++ b/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;
+       }
+}

diff --git a/src/math/sincosf.c b/src/math/sincosf.c
new file mode 100644 (file)
index 0000000..fede5f2
--- /dev/null
+++ b/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;
+       }
+}

diff --git a/src/math/sincosl.c b/src/math/sincosl.c
new file mode 100644 (file)
index 0000000..378dc97
--- /dev/null
+++ b/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