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[PATCH 5/7] sin/cos slow paths: remove unused slowpath functions
Remove all unused slowpath functions. * sysdeps/ieee754/dbl-64/s_sin.c (TAYLOR_SLOW): Remove. (do_cos_slow): Likewise. (do_sin_slow): Likewise. (reduce_and_compute): Likewise. (slow): Likewise. (slow1): Likewise. (slow2): Likewise. (sloww): Likewise. (sloww1): Likewise. (sloww2): Likewise. (bslow): Likewise. (bslow1): Likewise. (bslow2): Likewise. (cslow2): Likewise.
This commit is contained in:
Wilco Dijkstra
parent
649095838b
commit
72f6e9a3e3
17
ChangeLog
17
ChangeLog
@ -1,3 +1,20 @@
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2018-04-03 Wilco Dijkstra <wdijkstr@arm.com>
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* sysdeps/ieee754/dbl-64/s_sin.c (TAYLOR_SLOW): Remove.
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(do_cos_slow): Likewise.
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(do_sin_slow): Likewise.
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(reduce_and_compute): Likewise.
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(slow): Likewise.
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(slow1): Likewise.
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(slow2): Likewise.
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(sloww): Likewise.
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(sloww1): Likewise.
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(sloww2): Likewise.
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(bslow): Likewise.
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(bslow1): Likewise.
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(bslow2): Likewise.
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(cslow2): Likewise.
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2018-04-03 Wilco Dijkstra <wdijkstr@arm.com>
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* sysdeps/ieee754/dbl-64/s_sin.c (TAYLOR_SIN): Remove cor parameter.
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@ -22,22 +22,11 @@
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/* */
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/* FUNCTIONS: usin */
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/* ucos */
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/* slow */
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/* slow1 */
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/* slow2 */
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/* sloww */
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/* sloww1 */
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/* sloww2 */
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/* bsloww */
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/* bsloww1 */
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/* bsloww2 */
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/* cslow2 */
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/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */
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/* branred.c sincos32.c dosincos.c mpa.c */
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/* sincos.tbl */
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/* branred.c sincos.tbl */
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/* */
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/* An ultimate sin and routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of sin(x) or cos(x) */
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/* An ultimate sin and cos routine. Given an IEEE double machine number x */
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/* it computes sin(x) or cos(x) with ~0.55 ULP. */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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@ -74,29 +63,6 @@
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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 * 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) * xx + 3.0 * aa * x1 * x2) \
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* (x0) + aa * 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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@ -123,23 +89,7 @@ static const double
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cs4 = -4.16666666666664434524222570944589E-02,
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cs6 = 1.38888874007937613028114285595617E-03;
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static const double t22 = 0x1.8p22;
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void __dubsin (double x, double dx, double w[]);
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void __docos (double x, double dx, double w[]);
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double __mpsin (double x, double dx, bool reduce_range);
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double __mpcos (double x, double dx, bool reduce_range);
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static double slow (double x);
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static double slow1 (double x);
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static double slow2 (double x);
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static double sloww (double x, double dx, double orig, bool shift_quadrant);
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static double sloww1 (double x, double dx, double orig, bool shift_quadrant);
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static double sloww2 (double x, double dx, double orig, int n);
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static double bsloww (double x, double dx, double orig, int n);
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static double bsloww1 (double x, double dx, double orig, int n);
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static double bsloww2 (double x, double dx, double orig, int n);
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int __branred (double x, double *a, double *aa);
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static double cslow2 (double x);
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/* Given a number partitioned into X and DX, this function computes the cosine
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of the number by combining the sin and cos of X (as computed by a variation
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@ -166,40 +116,6 @@ do_cos (double x, double dx)
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return cs + cor;
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}
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/* A more precise variant of DO_COS. EPS is the adjustment to the correction
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COR. */
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static inline double
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__always_inline
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do_cos_slow (double x, double dx, double eps, double *corp)
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{
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mynumber u;
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if (x <= 0)
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dx = -dx;
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u.x = big + fabs (x);
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x = fabs (x) - (u.x - big);
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double xx, y, x1, x2, e1, e2, res, cor;
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double s, sn, ssn, c, cs, ccs;
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xx = x * x;
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s = x * xx * (sn3 + xx * sn5);
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c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
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SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
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x1 = (x + t22) - t22;
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x2 = (x - x1) + dx;
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e1 = (sn + t22) - t22;
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e2 = (sn - e1) + ssn;
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cor = (ccs - cs * c - e1 * x2 - e2 * x) - sn * s;
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y = cs - e1 * x1;
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cor = cor + ((cs - y) - e1 * x1);
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res = y + cor;
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cor = (y - res) + cor;
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cor = 1.0005 * cor + __copysign (eps, cor);
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*corp = cor;
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return res;
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}
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/* Given a number partitioned into X and DX, this function computes the sine of
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the number by combining the sin and cos of X (as computed by a variation of
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the Taylor series) with the values looked up from the sin/cos table to get
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@ -224,70 +140,6 @@ do_sin (double x, double dx)
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return sn + cor;
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}
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/* A more precise variant of DO_SIN. EPS is the adjustment to the correction
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COR. */
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static inline double
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__always_inline
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do_sin_slow (double x, double dx, double eps, double *corp)
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{
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mynumber u;
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if (x <= 0)
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dx = -dx;
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u.x = big + fabs (x);
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x = fabs (x) - (u.x - big);
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double xx, y, x1, x2, c1, c2, res, cor;
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double s, sn, ssn, c, cs, ccs;
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xx = x * x;
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s = x * xx * (sn3 + xx * sn5);
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c = xx * (cs2 + xx * (cs4 + xx * cs6));
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SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
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x1 = (x + t22) - t22;
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x2 = (x - x1) + dx;
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c1 = (cs + t22) - t22;
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c2 = (cs - c1) + ccs;
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cor = (ssn + s * ccs + cs * s + c2 * x + c1 * x2 - sn * x * dx) - sn * c;
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y = sn + c1 * x1;
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cor = cor + ((sn - y) + c1 * x1);
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res = y + cor;
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cor = (y - res) + cor;
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cor = 1.0005 * cor + __copysign (eps, cor);
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*corp = cor;
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return res;
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}
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/* Reduce range of X and compute sin of a + da. When SHIFT_QUADRANT is true,
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the routine returns the cosine of a + da by rotating the quadrant once and
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computing the sine of the result. */
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static inline double
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__always_inline
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reduce_and_compute (double x, bool shift_quadrant)
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{
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double retval = 0, a, da;
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unsigned int n = __branred (x, &a, &da);
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int4 k = (n + shift_quadrant) % 4;
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switch (k)
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{
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case 2:
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a = -a;
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da = -da;
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/* Fall through. */
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case 0:
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if (a * a < 0.01588)
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retval = bsloww (a, da, x, n);
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else
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retval = bsloww1 (a, da, x, n);
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break;
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case 1:
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case 3:
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retval = bsloww2 (a, da, x, n);
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break;
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}
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return retval;
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}
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/* Reduce range of x to within PI/2 with abs (x) < 105414350. The high part
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is written to *a, the low part to *da. Range reduction is accurate to 136
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bits so that when x is large and *a very close to zero, all 53 bits of *a
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@ -508,299 +360,6 @@ __cos (double x)
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return retval;
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}
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/************************************************************************/
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/* Routine compute sin(x) for 2^-26 < |x|< 0.25 by Taylor with more */
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/* precision and if still doesn't accurate enough by mpsin or dubsin */
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/************************************************************************/
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static inline double
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__always_inline
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slow (double x)
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{
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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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__dubsin (fabs (x), 0, w);
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if (w[0] == w[0] + 1.000000001 * w[1])
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return __copysign (w[0], x);
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return __copysign (__mpsin (fabs (x), 0, false), x);
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}
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/*******************************************************************************/
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/* Routine compute sin(x) for 0.25<|x|< 0.855469 by __sincostab.tbl and Taylor */
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/* and if result still doesn't accurate enough by mpsin or dubsin */
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/*******************************************************************************/
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static inline double
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__always_inline
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slow1 (double x)
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{
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double w[2], cor, res;
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res = do_sin_slow (x, 0, 0, &cor);
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if (res == res + cor)
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return res;
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__dubsin (fabs (x), 0, w);
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if (w[0] == w[0] + 1.000000005 * w[1])
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return w[0];
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return __mpsin (fabs (x), 0, false);
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}
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/**************************************************************************/
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/* Routine compute sin(x) for 0.855469 <|x|<2.426265 by __sincostab.tbl */
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/* and if result still doesn't accurate enough by mpsin or dubsin */
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/**************************************************************************/
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static inline double
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__always_inline
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slow2 (double x)
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{
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double w[2], y, y1, y2, cor, res;
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double t = hp0 - fabs (x);
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res = do_cos_slow (t, hp1, 0, &cor);
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if (res == res + cor)
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return res;
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y = fabs (x) - hp0;
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y1 = y - hp1;
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y2 = (y - y1) - hp1;
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__docos (y1, y2, w);
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if (w[0] == w[0] + 1.000000005 * w[1])
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return w[0];
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return __mpsin (fabs (x), 0, false);
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}
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/* Compute sin(x + dx) where X is small enough to use Taylor series around zero
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and (x + dx) in the first or third quarter of the unit circle. ORIG is the
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original value of X for computing error of the result. If the result is not
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accurate enough, the routine calls mpsin or dubsin. SHIFT_QUADRANT rotates
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the unit circle by 1 to compute the cosine instead of sine. */
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static inline double
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__always_inline
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sloww (double x, double dx, double orig, bool shift_quadrant)
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{
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double y, t, res, cor, w[2], a, da, xn;
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mynumber v;
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int4 n;
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res = TAYLOR_SLOW (x, dx, cor);
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double eps = fabs (orig) * 3.1e-30;
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cor = 1.0005 * cor + __copysign (eps, cor);
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if (res == res + cor)
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return res;
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a = fabs (x);
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da = (x > 0) ? dx : -dx;
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__dubsin (a, da, w);
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eps = fabs (orig) * 1.1e-30;
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cor = 1.000000001 * w[1] + __copysign (eps, w[1]);
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if (w[0] == w[0] + cor)
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return __copysign (w[0], x);
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t = (orig * hpinv + toint);
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xn = t - toint;
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v.x = t;
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y = (orig - xn * mp1) - xn * mp2;
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n = (v.i[LOW_HALF] + shift_quadrant) & 3;
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da = xn * pp3;
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t = y - da;
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da = (y - t) - da;
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y = xn * pp4;
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a = t - y;
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da = ((t - a) - y) + da;
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if (n & 2)
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{
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a = -a;
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da = -da;
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}
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x = fabs (a);
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dx = (a > 0) ? da : -da;
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__dubsin (x, dx, w);
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eps = fabs (orig) * 1.1e-40;
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cor = 1.000000001 * w[1] + __copysign (eps, w[1]);
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if (w[0] == w[0] + cor)
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return __copysign (w[0], a);
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return shift_quadrant ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
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}
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/* Compute sin(x + dx) where X is in the first or third quarter of the unit
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circle. ORIG is the original value of X for computing error of the result.
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If the result is not accurate enough, the routine calls mpsin or dubsin.
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SHIFT_QUADRANT rotates the unit circle by 1 to compute the cosine instead of
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sine. */
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static inline double
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__always_inline
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sloww1 (double x, double dx, double orig, bool shift_quadrant)
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{
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double w[2], cor, res;
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res = do_sin_slow (x, dx, 3.1e-30 * fabs (orig), &cor);
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if (res == res + cor)
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return __copysign (res, x);
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dx = (x > 0 ? dx : -dx);
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__dubsin (fabs (x), dx, w);
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double eps = 1.1e-30 * fabs (orig);
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cor = 1.000000005 * w[1] + __copysign (eps, w[1]);
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if (w[0] == w[0] + cor)
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return __copysign (w[0], x);
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return shift_quadrant ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
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}
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/***************************************************************************/
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/* Routine compute sin(x+dx) (Double-Length number) where x in second or */
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/* fourth quarter of unit circle.Routine receive also the original value */
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/* and quarter(n= 1or 3)of x for computing error of result.And if result not*/
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/* accurate enough routine calls mpsin1 or dubsin */
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/***************************************************************************/
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static inline double
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__always_inline
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sloww2 (double x, double dx, double orig, int n)
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{
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double w[2], cor, res;
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res = do_cos_slow (x, dx, 3.1e-30 * fabs (orig), &cor);
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if (res == res + cor)
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return (n & 2) ? -res : res;
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dx = x > 0 ? dx : -dx;
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__docos (fabs (x), dx, w);
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double eps = 1.1e-30 * fabs (orig);
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cor = 1.000000005 * w[1] + __copysign (eps, w[1]);
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if (w[0] == w[0] + cor)
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return (n & 2) ? -w[0] : w[0];
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return (n & 1) ? __mpsin (orig, 0, true) : __mpcos (orig, 0, true);
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}
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/***************************************************************************/
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/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */
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/* is small enough to use Taylor series around zero and (x+dx) */
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/* in first or third quarter of unit circle.Routine receive also */
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/* (right argument) the original value of x for computing error of */
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/* result.And if result not accurate enough routine calls other routines */
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/***************************************************************************/
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static inline double
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__always_inline
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bsloww (double x, double dx, double orig, int n)
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{
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double res, cor, w[2], a, da;
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res = TAYLOR_SLOW (x, dx, cor);
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cor = 1.0005 * cor + __copysign (1.1e-24, cor);
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if (res == res + cor)
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return res;
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a = fabs (x);
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da = (x > 0) ? dx : -dx;
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__dubsin (a, da, w);
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cor = 1.000000001 * w[1] + __copysign (1.1e-24, w[1]);
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if (w[0] == w[0] + cor)
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return __copysign (w[0], x);
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return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
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}
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/***************************************************************************/
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/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */
|
||||
/* in first or third quarter of unit circle.Routine receive also */
|
||||
/* (right argument) the original value of x for computing error of result.*/
|
||||
/* And if result not accurate enough routine calls other routines */
|
||||
/***************************************************************************/
|
||||
|
||||
static inline double
|
||||
__always_inline
|
||||
bsloww1 (double x, double dx, double orig, int n)
|
||||
{
|
||||
double w[2], cor, res;
|
||||
|
||||
res = do_sin_slow (x, dx, 1.1e-24, &cor);
|
||||
if (res == res + cor)
|
||||
return (x > 0) ? res : -res;
|
||||
|
||||
dx = (x > 0) ? dx : -dx;
|
||||
__dubsin (fabs (x), dx, w);
|
||||
|
||||
cor = 1.000000005 * w[1] + __copysign (1.1e-24, w[1]);
|
||||
|
||||
if (w[0] == w[0] + cor)
|
||||
return __copysign (w[0], x);
|
||||
|
||||
return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
|
||||
}
|
||||
|
||||
/***************************************************************************/
|
||||
/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */
|
||||
/* in second or fourth quarter of unit circle.Routine receive also the */
|
||||
/* original value and quarter(n= 1or 3)of x for computing error of result. */
|
||||
/* And if result not accurate enough routine calls other routines */
|
||||
/***************************************************************************/
|
||||
|
||||
static inline double
|
||||
__always_inline
|
||||
bsloww2 (double x, double dx, double orig, int n)
|
||||
{
|
||||
double w[2], cor, res;
|
||||
|
||||
res = do_cos_slow (x, dx, 1.1e-24, &cor);
|
||||
if (res == res + cor)
|
||||
return (n & 2) ? -res : res;
|
||||
|
||||
dx = (x > 0) ? dx : -dx;
|
||||
__docos (fabs (x), dx, w);
|
||||
|
||||
cor = 1.000000005 * w[1] + __copysign (1.1e-24, w[1]);
|
||||
|
||||
if (w[0] == w[0] + cor)
|
||||
return (n & 2) ? -w[0] : w[0];
|
||||
|
||||
return (n & 1) ? __mpsin (orig, 0, true) : __mpcos (orig, 0, true);
|
||||
}
|
||||
|
||||
/************************************************************************/
|
||||
/* Routine compute cos(x) for 2^-27 < |x|< 0.25 by Taylor with more */
|
||||
/* precision and if still doesn't accurate enough by mpcos or docos */
|
||||
/************************************************************************/
|
||||
|
||||
static inline double
|
||||
__always_inline
|
||||
cslow2 (double x)
|
||||
{
|
||||
double w[2], cor, res;
|
||||
|
||||
res = do_cos_slow (x, 0, 0, &cor);
|
||||
if (res == res + cor)
|
||||
return res;
|
||||
|
||||
__docos (fabs (x), 0, w);
|
||||
if (w[0] == w[0] + 1.000000005 * w[1])
|
||||
return w[0];
|
||||
|
||||
return __mpcos (x, 0, false);
|
||||
}
|
||||
|
||||
#ifndef __cos
|
||||
libm_alias_double (__cos, cos)
|
||||
#endif
|
||||
|
||||
Loading…
Reference in New Issue
Block a user