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-rw-r--r--sysdeps/ieee754/dbl-64/s_sin.c136
1 files changed, 62 insertions, 74 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
index 6c1475b..2be8fe3 100644
--- a/sysdeps/ieee754/dbl-64/s_sin.c
+++ b/sysdeps/ieee754/dbl-64/s_sin.c
@@ -55,6 +55,50 @@
#include <math_private.h>
#include <fenv.h>
+/* Helper macros to compute sin of the input values. */
+#define POLYNOMIAL2(xx) ((((s5.x * (xx) + s4.x) * (xx) + s3.x) * (xx) + s2.x) \
+ * (xx))
+
+#define POLYNOMIAL(xx) (POLYNOMIAL2 (xx) + s1.x)
+
+/* The computed polynomial is a variation of the Taylor series expansion for
+ sin(a):
+
+ a - a^3/3! + a^5/5! - a^7/7! + a^9/9! + (1 - a^2) * da / 2
+
+ The constants s1, s2, s3, etc. are pre-computed values of 1/3!, 1/5! and so
+ on. The result is returned to LHS and correction in COR. */
+#define TAYLOR_SINCOS(xx, a, da, cor) \
+({ \
+ double t = ((POLYNOMIAL (xx) * (a) - 0.5 * (da)) * (xx) + (da)); \
+ double res = (a) + t; \
+ (cor) = ((a) - res) + t; \
+ res; \
+})
+
+/* This is again a variation of the Taylor series expansion with the term
+ x^3/3! expanded into the following for better accuracy:
+
+ bb * x ^ 3 + 3 * aa * x * x1 * x2 + aa * x1 ^ 3 + aa * x2 ^ 3
+
+ The correction term is dx and bb + aa = -1/3!
+ */
+#define TAYLOR_SLOW(x0, dx, cor) \
+({ \
+ static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ \
+ double xx = (x0) * (x0); \
+ double x1 = ((x0) + th2_36) - th2_36; \
+ double y = aa.x * x1 * x1 * x1; \
+ double r = (x0) + y; \
+ double x2 = ((x0) - x1) + (dx); \
+ double t = (((POLYNOMIAL2 (xx) + bb.x) * xx + 3.0 * aa.x * x1 * x2) \
+ * (x0) + aa.x * x2 * x2 * x2 + (dx)); \
+ t = (((x0) - r) + y) + t; \
+ double res = r + t; \
+ (cor) = (r - res) + t; \
+ res; \
+})
+
#define SINCOS_TABLE_LOOKUP(u, sn, ssn, cs, ccs) \
({ \
int4 k = u.i[LOW_HALF] << 2; \
@@ -160,9 +204,8 @@ __sin (double x)
else if (k < 0x3fd00000)
{
xx = x * x;
- /*Taylor series. */
- t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + s1.x)
- * (xx * x));
+ /* Taylor series. */
+ t = POLYNOMIAL (xx) * (xx * x);
res = x + t;
cor = (x - res) + t;
retval = (res == res + 1.07 * cor) ? res : slow (x);
@@ -237,11 +280,8 @@ __sin (double x)
}
if (xx < 0.01588)
{
- /*Taylor series */
- t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
- + s1.x) * a - 0.5 * da) * xx + da;
- res = a + t;
- cor = (a - res) + t;
+ /* Taylor series. */
+ res = TAYLOR_SINCOS (xx, a, da, cor);
cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
retval = (res == res + cor) ? res : sloww (a, da, x);
}
@@ -327,11 +367,8 @@ __sin (double x)
}
if (xx < 0.01588)
{
- /* Taylor series */
- t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
- + s1.x) * a - 0.5 * da) * xx + da;
- res = a + t;
- cor = (a - res) + t;
+ /* Taylor series. */
+ res = TAYLOR_SINCOS (xx, a, da, cor);
cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
retval = (res == res + cor) ? res : bsloww (a, da, x, n);
}
@@ -452,10 +489,7 @@ __cos (double x)
xx = a * a;
if (xx < 0.01588)
{
- t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + s1.x)
- * a - 0.5 * da) * xx + da;
- res = a + t;
- cor = (a - res) + t;
+ res = TAYLOR_SINCOS (xx, a, da, cor);
cor = (cor > 0) ? 1.02 * cor + 1.0e-31 : 1.02 * cor - 1.0e-31;
retval = (res == res + cor) ? res : csloww (a, da, x);
}
@@ -514,10 +548,7 @@ __cos (double x)
}
if (xx < 0.01588)
{
- t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
- + s1.x) * a - 0.5 * da) * xx + da;
- res = a + t;
- cor = (a - res) + t;
+ res = TAYLOR_SINCOS (xx, a, da, cor);
cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
retval = (res == res + cor) ? res : csloww (a, da, x);
}
@@ -602,10 +633,7 @@ __cos (double x)
}
if (xx < 0.01588)
{
- t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
- + s1.x) * a - 0.5 * da) * xx + da;
- res = a + t;
- cor = (a - res) + t;
+ res = TAYLOR_SINCOS (xx, a, da, cor);
cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
retval = (res == res + cor) ? res : bsloww (a, da, x, n);
}
@@ -684,18 +712,8 @@ static double
SECTION
slow (double x)
{
- static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
- double y, x1, x2, xx, r, t, res, cor, w[2];
- x1 = (x + th2_36) - th2_36;
- y = aa.x * x1 * x1 * x1;
- r = x + y;
- x2 = x - x1;
- xx = x * x;
- t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
- + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2;
- t = ((x - r) + y) + t;
- res = r + t;
- cor = (r - res) + t;
+ double res, cor, w[2];
+ res = TAYLOR_SLOW (x, 0, cor);
if (res == res + 1.0007 * cor)
return res;
else
@@ -813,24 +831,14 @@ static double
SECTION
sloww (double x, double dx, double orig)
{
- static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
- double y, x1, x2, xx, r, t, res, cor, w[2], a, da, xn;
+ double y, t, res, cor, w[2], a, da, xn;
union
{
int4 i[2];
double x;
} v;
int4 n;
- x1 = (x + th2_36) - th2_36;
- y = aa.x * x1 * x1 * x1;
- r = x + y;
- x2 = (x - x1) + dx;
- xx = x * x;
- t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
- + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
- t = ((x - r) + y) + t;
- res = r + t;
- cor = (r - res) + t;
+ res = TAYLOR_SLOW (x, dx, cor);
cor =
(cor >
0) ? 1.0005 * cor + ABS (orig) * 3.1e-30 : 1.0005 * cor -
@@ -1004,19 +1012,9 @@ static double
SECTION
bsloww (double x, double dx, double orig, int n)
{
- static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
- double y, x1, x2, xx, r, t, res, cor, w[2];
-
- x1 = (x + th2_36) - th2_36;
- y = aa.x * x1 * x1 * x1;
- r = x + y;
- x2 = (x - x1) + dx;
- xx = x * x;
- t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
- + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
- t = ((x - r) + y) + t;
- res = r + t;
- cor = (r - res) + t;
+ double res, cor, w[2];
+
+ res = TAYLOR_SLOW (x, dx, cor);
cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
if (res == res + cor)
return res;
@@ -1191,8 +1189,7 @@ static double
SECTION
csloww (double x, double dx, double orig)
{
- static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
- double y, x1, x2, xx, r, t, res, cor, w[2], a, da, xn;
+ double y, t, res, cor, w[2], a, da, xn;
union
{
int4 i[2];
@@ -1200,17 +1197,8 @@ csloww (double x, double dx, double orig)
} v;
int4 n;
- x1 = (x + th2_36) - th2_36;
- y = aa.x * x1 * x1 * x1;
- r = x + y;
- x2 = (x - x1) + dx;
- xx = x * x;
/* Taylor series */
- t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
- + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
- t = ((x - r) + y) + t;
- res = r + t;
- cor = (r - res) + t;
+ t = TAYLOR_SLOW (x, dx, cor);
if (cor > 0)
cor = 1.0005 * cor + ABS (orig) * 3.1e-30;
generated by cgit v1.1 at 2024-11-21 23:59:44 +0000