libm: Add a proper sincos() implementation
Add a proper sincos() implementation that unifies the common
calculations for sin and cos instead of running them twice.
This should cause a speedup even in code not using that
(fairly uncommon) function because gcc can optimize separate
sin() and cos() calls into sincos() calls.
Signed-off-by: Bernhard Rosenkraenzer <Bernhard.Rosenkranzer@linaro.org>
Change-Id: I644578ab443506c7404d2638d6d4917ff6c96f20
diff --git a/libm/sincos.c b/libm/sincos.c
index e9f6dcc..0259bde 100644
--- a/libm/sincos.c
+++ b/libm/sincos.c
@@ -26,25 +26,143 @@
*/
#define _GNU_SOURCE 1
#include <math.h>
+#define INLINE_KERNEL_COSDF
+#define INLINE_KERNEL_SINDF
+#include "src/math_private.h"
+#include "src/k_cosf.c"
+#include "src/k_sinf.c"
-// Disable sincos optimization for all functions in this file,
-// otherwise gcc would generate infinite calls.
-// Refer to gcc PR46926.
-// -fno-builtin-sin or -fno-builtin-cos can disable sincos optimization,
-// but these two options do not work inside optimize pragma in-file.
-// Thus we just enforce -O0 when compiling this file.
-#pragma GCC optimize ("O0")
+/* 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 */
+/* For implementation details, see src/s_sin.c, src/s_cos.c */
void sincos(double x, double *psin, double *pcos)
{
- *psin = sin(x);
- *pcos = cos(x);
+ double y[2], z=0.0;
+ int32_t n, ix;
+
+ /* High word of x. */
+ GET_HIGH_WORD(ix, x);
+
+ /* |x| ~< pi/4 */
+ ix &= 0x7fffffff;
+ if(ix <= 0x3fe921fb) {
+ if(ix < 0x3e400000) { /* \x\ < 2**-27 */
+ if((int)x==0) { /* generate inexact */
+ *psin = x;
+ *pcos = 1.0;
+ return;
+ }
+ }
+ *psin = __kernel_sin(x, z, 0);
+ *pcos = __kernel_cos(x, z);
+ return;
+ } else if(ix>=0x7ff00000) { /* sin(Inf or NaN) and cos(Inf or NaN) is NaN */
+ *psin = *pcos = x-x;
+ return;
+ } else {
+ n = __ieee754_rem_pio2(x, y);
+ switch(n&3) {
+ case 0:
+ *psin = __kernel_sin(y[0],y[1],1);
+ *pcos = __kernel_cos(y[0],y[1]);
+ return;
+ case 1:
+ *psin = __kernel_cos(y[0],y[1]);
+ *pcos = -__kernel_sin(y[0],y[1],1);
+ return;
+ case 2:
+ *psin = -__kernel_sin(y[0],y[1],1);
+ *pcos = -__kernel_cos(y[0],y[1]);
+ return;
+ default:
+ *psin = -__kernel_cos(y[0],y[1]);
+ *pcos = __kernel_sin(y[0],y[1],1);
+ return;
+ }
+ }
}
+/* For implementation details, see src/s_sinf.c, src/s_cosf.c */
void sincosf(float x, float *psin, float *pcos)
{
- *psin = sinf(x);
- *pcos = cosf(x);
+ float y[2];
+ int32_t n, hx, ix;
+
+ GET_FLOAT_WORD(hx, x);
+ ix = hx & 0x7fffffff;
+
+ if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
+ if(ix < 0x39800000) { /* |x| < 2**-12 */
+ if(((int)x)==0) { /* x with inexact if x != 0 */
+ *psin = x;
+ *pcos = 1.0;
+ return;
+ }
+ }
+ *psin = __kernel_sindf(x);
+ *pcos = __kernel_cosdf(x);
+ return;
+ } else if(ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */
+ if(ix <= 0x4016cbe3) { /* |x| ~<= 3pi/4 */
+ if(hx>0) {
+ *psin = __kernel_cosdf(x - s1pio2);
+ *pcos = __kernel_sindf(s1pio2 - x);
+ return;
+ } else {
+ *psin = -__kernel_cosdf(x + s1pio2);
+ *pcos = __kernel_sindf(x + s1pio2);
+ return;
+ }
+ } else {
+ *psin = __kernel_sindf((hx > 0 ? s2pio2 : -s2pio2) - x);
+ *pcos = -__kernel_cosdf(x + (hx > 0 ? -s2pio2 : s2pio2));
+ return;
+ }
+ } else if(ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */
+ if(ix <= 0x40afeddf) { /* |x| ~<= 7*pi/4 */
+ if(hx>0) {
+ *psin = -__kernel_cosdf(x - s3pio2);
+ *pcos = __kernel_sindf(x - s3pio2);
+ return;
+ } else {
+ *psin = __kernel_cosdf(x + s3pio2);
+ *pcos = __kernel_sindf(-s3pio2 - x);
+ return;
+ }
+ } else {
+ *psin = __kernel_sindf(x + (hx > 0 ? -s4pio2 : s4pio2));
+ *pcos = __kernel_cosdf(x + (hx > 0 ? -s4pio2 : s4pio2));
+ return;
+ }
+ } else if(ix>=0x7f800000) { /* sin and cos (Inf or NaN) is NaN */
+ *psin = *pcos = x-x;
+ return;
+ } else {
+ n = __ieee754_rem_pio2f(x,y);
+ switch(n&3) {
+ case 0:
+ *psin = __kernel_sindf((double)y[0]+y[1]);
+ *pcos = __kernel_cosdf((double)y[0]+y[1]);
+ return;
+ case 1:
+ *psin = __kernel_cosdf((double)y[0]+y[1]);
+ *pcos = __kernel_sindf(-(double)y[0]-y[1]);
+ return;
+ case 2:
+ *psin = __kernel_sindf(-(double)y[0]-y[1]);
+ *pcos = -__kernel_cosdf((double)y[0]+y[1]);
+ return;
+ default:
+ *psin = -__kernel_cosdf((double)y[0]+y[1]);
+ *pcos = __kernel_sindf((double)y[0]+y[1]);
+ return;
+ }
+ }
}
void sincosl(long double x, long double *psin, long double *pcos)