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Consolidate common code into macros
Consolidated common Taylor series polynomials into macros in s_sin.c to make it a bit cleaner.
This commit is contained in:
Siddhesh Poyarekar
parent
d84f25c7d8
commit
4aafb73cb2
13
ChangeLog
13
ChangeLog
@ -1,3 +1,16 @@
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2013-09-19 Siddhesh Poyarekar <siddhesh@redhat.com>
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* sysdeps/ieee754/dbl-64/s_sin.c (POLYNOMIAL2): New macro.
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(POLYNOMIAL): Likewise.
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(TAYLOR_SINCOS): Likewise.
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(TAYLOR_SLOW): Likewise.
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(__sin): Use TAYLOR_SINCOS.
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(__cos): Likewise.
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(slow): Use TAYLOR_SLOW.
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(sloww): Likewise.
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(bsloww): Likewise.
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(csloww): Likewise.
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2013-09-19 Liubov Dmitrieva <liubov.dmitrieva@intel.com>
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* stdlib/strtod_l.c: Fix buffer overrun.
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@ -55,6 +55,50 @@
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#include <math_private.h>
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#include <fenv.h>
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/* Helper macros to compute sin of the input values. */
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#define POLYNOMIAL2(xx) ((((s5.x * (xx) + s4.x) * (xx) + s3.x) * (xx) + s2.x) \
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* (xx))
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#define POLYNOMIAL(xx) (POLYNOMIAL2 (xx) + s1.x)
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/* The computed polynomial is a variation of the Taylor series expansion for
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sin(a):
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a - a^3/3! + a^5/5! - a^7/7! + a^9/9! + (1 - a^2) * da / 2
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The constants s1, s2, s3, etc. are pre-computed values of 1/3!, 1/5! and so
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on. The result is returned to LHS and correction in COR. */
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#define TAYLOR_SINCOS(xx, a, da, cor) \
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({ \
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double t = ((POLYNOMIAL (xx) * (a) - 0.5 * (da)) * (xx) + (da)); \
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double res = (a) + t; \
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(cor) = ((a) - res) + t; \
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res; \
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})
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/* This is again a variation of the Taylor series expansion with the term
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x^3/3! expanded into the following for better accuracy:
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bb * x ^ 3 + 3 * aa * x * x1 * x2 + aa * x1 ^ 3 + aa * x2 ^ 3
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The correction term is dx and bb + aa = -1/3!
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*/
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#define TAYLOR_SLOW(x0, dx, cor) \
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({ \
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static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ \
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double xx = (x0) * (x0); \
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double x1 = ((x0) + th2_36) - th2_36; \
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double y = aa.x * x1 * x1 * x1; \
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double r = (x0) + y; \
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double x2 = ((x0) - x1) + (dx); \
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double t = (((POLYNOMIAL2 (xx) + bb.x) * xx + 3.0 * aa.x * x1 * x2) \
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* (x0) + aa.x * x2 * x2 * x2 + (dx)); \
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t = (((x0) - r) + y) + t; \
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double res = r + t; \
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(cor) = (r - res) + t; \
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res; \
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})
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#define SINCOS_TABLE_LOOKUP(u, sn, ssn, cs, ccs) \
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({ \
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int4 k = u.i[LOW_HALF] << 2; \
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@ -160,9 +204,8 @@ __sin (double x)
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else if (k < 0x3fd00000)
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{
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xx = x * x;
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/*Taylor series. */
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t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + s1.x)
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* (xx * x));
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/* Taylor series. */
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t = POLYNOMIAL (xx) * (xx * x);
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res = x + t;
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cor = (x - res) + t;
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retval = (res == res + 1.07 * cor) ? res : slow (x);
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@ -237,11 +280,8 @@ __sin (double x)
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}
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if (xx < 0.01588)
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{
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/*Taylor series */
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t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
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+ s1.x) * a - 0.5 * da) * xx + da;
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res = a + t;
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cor = (a - res) + t;
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/* Taylor series. */
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res = TAYLOR_SINCOS (xx, a, da, cor);
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cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
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retval = (res == res + cor) ? res : sloww (a, da, x);
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}
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@ -327,11 +367,8 @@ __sin (double x)
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}
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if (xx < 0.01588)
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{
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/* Taylor series */
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t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
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+ s1.x) * a - 0.5 * da) * xx + da;
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res = a + t;
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cor = (a - res) + t;
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/* Taylor series. */
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res = TAYLOR_SINCOS (xx, a, da, cor);
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cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
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retval = (res == res + cor) ? res : bsloww (a, da, x, n);
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}
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@ -452,10 +489,7 @@ __cos (double x)
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xx = a * a;
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if (xx < 0.01588)
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{
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t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + s1.x)
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* a - 0.5 * da) * xx + da;
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res = a + t;
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cor = (a - res) + t;
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res = TAYLOR_SINCOS (xx, a, da, cor);
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cor = (cor > 0) ? 1.02 * cor + 1.0e-31 : 1.02 * cor - 1.0e-31;
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retval = (res == res + cor) ? res : csloww (a, da, x);
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}
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@ -514,10 +548,7 @@ __cos (double x)
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}
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if (xx < 0.01588)
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{
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t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
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+ s1.x) * a - 0.5 * da) * xx + da;
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res = a + t;
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cor = (a - res) + t;
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res = TAYLOR_SINCOS (xx, a, da, cor);
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cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
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retval = (res == res + cor) ? res : csloww (a, da, x);
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}
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@ -602,10 +633,7 @@ __cos (double x)
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}
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if (xx < 0.01588)
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{
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t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
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+ s1.x) * a - 0.5 * da) * xx + da;
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res = a + t;
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cor = (a - res) + t;
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res = TAYLOR_SINCOS (xx, a, da, cor);
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cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
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retval = (res == res + cor) ? res : bsloww (a, da, x, n);
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}
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@ -684,18 +712,8 @@ static double
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SECTION
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slow (double x)
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{
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static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
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double y, x1, x2, xx, r, t, res, cor, w[2];
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x1 = (x + th2_36) - th2_36;
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y = aa.x * x1 * x1 * x1;
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r = x + y;
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x2 = x - x1;
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xx = x * x;
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t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
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+ 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2;
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t = ((x - r) + y) + t;
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res = r + t;
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cor = (r - res) + t;
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double res, cor, w[2];
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res = TAYLOR_SLOW (x, 0, cor);
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if (res == res + 1.0007 * cor)
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return res;
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else
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@ -813,24 +831,14 @@ static double
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SECTION
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sloww (double x, double dx, double orig)
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{
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static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
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double y, x1, x2, xx, r, t, res, cor, w[2], a, da, xn;
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double y, t, res, cor, w[2], a, da, xn;
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union
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{
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int4 i[2];
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double x;
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} v;
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int4 n;
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x1 = (x + th2_36) - th2_36;
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y = aa.x * x1 * x1 * x1;
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r = x + y;
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x2 = (x - x1) + dx;
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xx = x * x;
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t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
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+ 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
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t = ((x - r) + y) + t;
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res = r + t;
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cor = (r - res) + t;
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res = TAYLOR_SLOW (x, dx, cor);
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cor =
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(cor >
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0) ? 1.0005 * cor + ABS (orig) * 3.1e-30 : 1.0005 * cor -
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@ -1004,19 +1012,9 @@ static double
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SECTION
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bsloww (double x, double dx, double orig, int n)
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{
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static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
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double y, x1, x2, xx, r, t, res, cor, w[2];
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double res, cor, w[2];
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x1 = (x + th2_36) - th2_36;
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y = aa.x * x1 * x1 * x1;
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r = x + y;
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x2 = (x - x1) + dx;
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xx = x * x;
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t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
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+ 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
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t = ((x - r) + y) + t;
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res = r + t;
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cor = (r - res) + t;
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res = TAYLOR_SLOW (x, dx, cor);
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cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
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if (res == res + cor)
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return res;
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@ -1191,8 +1189,7 @@ static double
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SECTION
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csloww (double x, double dx, double orig)
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{
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static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
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double y, x1, x2, xx, r, t, res, cor, w[2], a, da, xn;
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double y, t, res, cor, w[2], a, da, xn;
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union
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{
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int4 i[2];
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@ -1200,17 +1197,8 @@ csloww (double x, double dx, double orig)
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} v;
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int4 n;
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x1 = (x + th2_36) - th2_36;
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y = aa.x * x1 * x1 * x1;
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r = x + y;
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x2 = (x - x1) + dx;
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xx = x * x;
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/* Taylor series */
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t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
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+ 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
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t = ((x - r) + y) + t;
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res = r + t;
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cor = (r - res) + t;
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t = TAYLOR_SLOW (x, dx, cor);
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if (cor > 0)
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cor = 1.0005 * cor + ABS (orig) * 3.1e-30;
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