Author: kargl
Date: Sun Aug 31 21:38:03 2014
New Revision: 270893
URL: http://svnweb.freebsd.org/changeset/base/270893
Log:
Compute sin(pi*x) without actually doing the pi*x multiplication.
sin_pi(x) is only called for x < 0 and |x| < 2**(p-1) where p is
the precision of x. The new argument reduction is an optimization
compared to the old code, and it removes a chunk of dead code.
Accuracy tests in the intervals (-21,-20), (-20,-19), ... (-1,0)
show no differences between the old and new code.
Obtained from: bde
Modified:
head/lib/msun/src/e_lgamma_r.c
head/lib/msun/src/e_lgammaf_r.c
Modified: head/lib/msun/src/e_lgamma_r.c
==============================================================================
--- head/lib/msun/src/e_lgamma_r.c Sun Aug 31 21:18:23 2014
(r270892)
+++ head/lib/msun/src/e_lgamma_r.c Sun Aug 31 21:38:03 2014
(r270893)
@@ -156,37 +156,35 @@ w6 = -1.63092934096575273989e-03; /* 0x
static const double zero= 0.00000000000000000000e+00;
- static double sin_pi(double x)
+/*
+ * Compute sin(pi*x) without actually doing the pi*x multiplication.
+ * sin_pi(x) is only called for x < 0 and |x| < 2**(p-1) where p is
+ * the precision of x.
+ */
+static double
+sin_pi(double x)
{
+ volatile double vz;
double y,z;
- int n,ix;
+ int n;
- GET_HIGH_WORD(ix,x);
- ix &= 0x7fffffff;
+ y = -x;
- if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0);
- y = -x; /* x is assume negative */
+ vz = y+0x1p52; /* depend on 0 <= y < 0x1p52 */
+ z = vz-0x1p52; /* rint(y) for the above range */
+ if (z == y)
+ return (zero);
+
+ vz = y+0x1p50;
+ GET_LOW_WORD(n,vz); /* bits for rounded y (units 0.25) */
+ z = vz-0x1p50; /* y rounded to a multiple of 0.25 */
+ if (z > y) {
+ z -= 0.25; /* adjust to round down */
+ n--;
+ }
+ n &= 7; /* octant of y mod 2 */
+ y = y - z + n * 0.25; /* y mod 2 */
- /*
- * argument reduction, make sure inexact flag not raised if input
- * is an integer
- */
- z = floor(y);
- if(z!=y) { /* inexact anyway */
- y *= 0.5;
- y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */
- n = (int) (y*4.0);
- } else {
- if(ix>=0x43400000) {
- y = zero; n = 0; /* y must be even */
- } else {
- if(ix<0x43300000) z = y+two52; /* exact */
- GET_LOW_WORD(n,z);
- n &= 1;
- y = n;
- n<<= 2;
- }
- }
switch (n) {
case 0: y = __kernel_sin(pi*y,zero,0); break;
case 1:
Modified: head/lib/msun/src/e_lgammaf_r.c
==============================================================================
--- head/lib/msun/src/e_lgammaf_r.c Sun Aug 31 21:18:23 2014
(r270892)
+++ head/lib/msun/src/e_lgammaf_r.c Sun Aug 31 21:38:03 2014
(r270893)
@@ -89,37 +89,35 @@ w6 = -1.6309292987e-03; /* 0xbad5c4e8 *
static const float zero= 0.0000000000e+00;
- static float sin_pif(float x)
+/*
+ * Compute sin(pi*x) without actually doing the pi*x multiplication.
+ * sin_pi(x) is only called for x < 0 and |x| < 2**(p-1) where p is
+ * the precision of x.
+ */
+static float
+sin_pi(float x)
{
+ volatile float vz;
float y,z;
- int n,ix;
+ int n;
- GET_FLOAT_WORD(ix,x);
- ix &= 0x7fffffff;
+ y = -x;
- if(ix<0x3e800000) return __kernel_sindf(pi*x);
- y = -x; /* x is assume negative */
+ vz = y+0x1p23F; /* depend on 0 <= y < 0x1p23 */
+ z = vz-0x1p23F; /* rintf(y) for the above range */
+ if (z == y)
+ return (zero);
+
+ vz = y+0x1p21F;
+ GET_FLOAT_WORD(n,vz); /* bits for rounded y (units 0.25) */
+ z = vz-0x1p21F; /* y rounded to a multiple of 0.25 */
+ if (z > y) {
+ z -= 0.25F; /* adjust to round down */
+ n--;
+ }
+ n &= 7; /* octant of y mod 2 */
+ y = y - z + n * 0.25F; /* y mod 2 */
- /*
- * argument reduction, make sure inexact flag not raised if input
- * is an integer
- */
- z = floorf(y);
- if(z!=y) { /* inexact anyway */
- y *= (float)0.5;
- y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */
- n = (int) (y*(float)4.0);
- } else {
- if(ix>=0x4b800000) {
- y = zero; n = 0; /* y must be even */
- } else {
- if(ix<0x4b000000) z = y+two23; /* exact */
- GET_FLOAT_WORD(n,z);
- n &= 1;
- y = n;
- n<<= 2;
- }
- }
switch (n) {
case 0: y = __kernel_sindf(pi*y); break;
case 1:
@@ -157,7 +155,7 @@ __ieee754_lgammaf_r(float x, int *signga
if(hx<0) {
if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */
return one/zero;
- t = sin_pif(x);
+ t = sin_pi(x);
if(t==zero) return one/zero; /* -integer */
nadj = __ieee754_logf(pi/fabsf(t*x));
if(t<zero) *signgamp = -1;
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