# optimization for Bessel function routines

Sun Feb 3 19:34:50 UTC 2019

```* src/e_j0.c:
. Replace calls to sin(x) and cos(x) with single call to sincos().

* src/e_j0f.c:
. Replace calls to sinf(x) and cosf(x) with single call to sincosf().

* src/e_j1.c:
. Replace calls to sin(x) and cos(x) with single call to sincos().

* src/e_j1f.c:
. Replace calls to sinf(x) and cosf(x) with single call to sincosf().

* src/e_jn.c:
. Replace calls to sin(x) and cos(x) with single call to sincos().

Index: src/e_j0.c
===================================================================
--- src/e_j0.c	(revision 343477)
+++ src/e_j0.c	(working copy)
@@ -93,8 +93,7 @@ __ieee754_j0(double x)
if(ix>=0x7ff00000) return one/(x*x);
x = fabs(x);
if(ix >= 0x40000000) {	/* |x| >= 2.0 */
-		s = sin(x);
-		c = cos(x);
+		sincos(x, &s, &c);
ss = s-c;
cc = s+c;
if(ix<0x7fe00000) {  /* Make sure x+x does not overflow. */
@@ -173,8 +172,7 @@ __ieee754_y0(double x)
*              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
-                s = sin(x);
-                c = cos(x);
+		sincos(x, &s, &c);
ss = s-c;
cc = s+c;
/*
Index: src/e_j0f.c
===================================================================
--- src/e_j0f.c	(revision 343477)
+++ src/e_j0f.c	(working copy)
@@ -55,8 +55,7 @@ __ieee754_j0f(float x)
if(ix>=0x7f800000) return one/(x*x);
x = fabsf(x);
if(ix >= 0x40000000) {	/* |x| >= 2.0 */
-		s = sinf(x);
-		c = cosf(x);
+		sincosf(x, &s, &c);
ss = s-c;
cc = s+c;
if(ix<0x7f000000) {  /* Make sure x+x does not overflow. */
@@ -128,8 +127,7 @@ __ieee754_y0f(float x)
*              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
-                s = sinf(x);
-                c = cosf(x);
+		sincosf(x, &s, &c);
ss = s-c;
cc = s+c;
/*
Index: src/e_j1.c
===================================================================
--- src/e_j1.c	(revision 343477)
+++ src/e_j1.c	(working copy)
@@ -94,8 +94,7 @@ __ieee754_j1(double x)
if(ix>=0x7ff00000) return one/x;
y = fabs(x);
if(ix >= 0x40000000) {	/* |x| >= 2.0 */
-		s = sin(y);
-		c = cos(y);
+		sincos(y, &s, &c);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) {  /* make sure y+y not overflow */
@@ -159,8 +158,7 @@ __ieee754_y1(double x)
/* y1(x<0) = NaN and raise invalid exception. */
if(hx<0) return vzero/vzero;
if(ix >= 0x40000000) {  /* |x| >= 2.0 */
-                s = sin(x);
-                c = cos(x);
+		sincos(x, &s, &c);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) {  /* make sure x+x not overflow */
Index: src/e_j1f.c
===================================================================
--- src/e_j1f.c	(revision 343477)
+++ src/e_j1f.c	(working copy)
@@ -56,8 +56,7 @@ __ieee754_j1f(float x)
if(ix>=0x7f800000) return one/x;
y = fabsf(x);
if(ix >= 0x40000000) {	/* |x| >= 2.0 */
-		s = sinf(y);
-		c = cosf(y);
+		sincosf(y, &s, &c);
ss = -s-c;
cc = s-c;
if(ix<0x7f000000) {  /* make sure y+y not overflow */
@@ -114,8 +113,7 @@ __ieee754_y1f(float x)
if(ix==0) return -one/vzero;
if(hx<0) return vzero/vzero;
if(ix >= 0x40000000) {  /* |x| >= 2.0 */
-                s = sinf(x);
-                c = cosf(x);
+		sincosf(x, &s, &c);
ss = -s-c;
cc = s-c;
if(ix<0x7f000000) {  /* make sure x+x not overflow */
Index: src/e_jn.c
===================================================================
--- src/e_jn.c	(revision 343477)
+++ src/e_jn.c	(working copy)
@@ -54,7 +54,7 @@ double
__ieee754_jn(int n, double x)
{
int32_t i,hx,ix,lx, sgn;
-	double a, b, temp, di;
+	double a, b, c, s, temp, di;
double z, w;

/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
@@ -91,11 +91,12 @@ __ieee754_jn(int n, double x)
*		   2	-s+c		-c-s
*		   3	 s+c		 c-s
*/
+		sincos(x, &s, &c);
switch(n&3) {
-		    case 0: temp =  cos(x)+sin(x); break;
-		    case 1: temp = -cos(x)+sin(x); break;
-		    case 2: temp = -cos(x)-sin(x); break;
-		    case 3: temp =  cos(x)-sin(x); break;
+		    case 0: temp =  c+s; break;
+		    case 1: temp = -c+s; break;
+		    case 2: temp = -c-s; break;
+		    case 3: temp =  c-s; break;
}
b = invsqrtpi*temp/sqrt(x);
} else {
@@ -216,7 +217,7 @@ __ieee754_yn(int n, double x)
{
int32_t i,hx,ix,lx;
int32_t sign;
-	double a, b, temp;
+	double a, b, c, s, temp;

EXTRACT_WORDS(hx,lx,x);
ix = 0x7fffffff&hx;
@@ -248,11 +249,12 @@ __ieee754_yn(int n, double x)
*		   2	-s+c		-c-s
*		   3	 s+c		 c-s
*/
+		sincos(x, &s, &c);
switch(n&3) {
-		    case 0: temp =  sin(x)-cos(x); break;
-		    case 1: temp = -sin(x)-cos(x); break;
-		    case 2: temp = -sin(x)+cos(x); break;
-		    case 3: temp =  sin(x)+cos(x); break;
+		    case 0: temp =  s-c; break;
+		    case 1: temp = -s-c; break;
+		    case 2: temp = -s+c; break;
+		    case 3: temp =  s+c; break;
}
b = invsqrtpi*temp/sqrt(x);
} else {
--
Steve
```