/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
- * Copyright (C) 2001-2014 Free Software Foundation, Inc.
+ * Copyright (C) 2001-2018 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
/* bsloww1 */
/* bsloww2 */
/* cslow2 */
-/* csloww */
-/* csloww1 */
-/* csloww2 */
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */
/* branred.c sincos32.c dosincos.c mpa.c */
/* sincos.tbl */
#include <errno.h>
+#include <float.h>
#include "endian.h"
#include "mydefs.h"
#include "usncs.h"
#include "MathLib.h"
+#include <math.h>
#include <math_private.h>
+#include <libm-alias-double.h>
#include <fenv.h>
/* Helper macros to compute sin of the input values. */
static double slow (double x);
static double slow1 (double x);
static double slow2 (double x);
-static double sloww (double x, double dx, double orig);
-static double sloww1 (double x, double dx, double orig, int m);
+static double sloww (double x, double dx, double orig, bool shift_quadrant);
+static double sloww1 (double x, double dx, double orig, bool shift_quadrant);
static double sloww2 (double x, double dx, double orig, int n);
static double bsloww (double x, double dx, double orig, int n);
static double bsloww1 (double x, double dx, double orig, int n);
static double bsloww2 (double x, double dx, double orig, int n);
int __branred (double x, double *a, double *aa);
static double cslow2 (double x);
-static double csloww (double x, double dx, double orig);
-static double csloww1 (double x, double dx, double orig, int m);
-static double csloww2 (double x, double dx, double orig, int n);
-
-/* Given a number partitioned into U and X such that U is an index into the
- sin/cos table, this macro computes the cosine of the number by combining
- the sin and cos of X (as computed by a variation of the Taylor series) with
- the values looked up from the sin/cos table to get the result in RES and a
- correction value in COR. */
-static double
-do_cos (mynumber u, double x, double *corp)
+
+/* Given a number partitioned into X and DX, this function computes the cosine
+ of the number by combining the sin and cos of X (as computed by a variation
+ of the Taylor series) with the values looked up from the sin/cos table to
+ get the result in RES and a correction value in COR. */
+static inline double
+__always_inline
+do_cos (double x, double dx, double *corp)
{
+ mynumber u;
+
+ if (x < 0)
+ dx = -dx;
+
+ u.x = big + fabs (x);
+ x = fabs (x) - (u.x - big) + dx;
+
double xx, s, sn, ssn, c, cs, ccs, res, cor;
xx = x * x;
s = x + x * xx * (sn3 + xx * sn5);
return res;
}
-/* A more precise variant of DO_COS where the number is partitioned into U, X
- and DX. EPS is the adjustment to the correction COR. */
-static double
-do_cos_slow (mynumber u, double x, double dx, double eps, double *corp)
+/* A more precise variant of DO_COS. EPS is the adjustment to the correction
+ COR. */
+static inline double
+__always_inline
+do_cos_slow (double x, double dx, double eps, double *corp)
{
+ mynumber u;
+
+ if (x <= 0)
+ dx = -dx;
+
+ u.x = big + fabs (x);
+ x = fabs (x) - (u.x - big);
+
double xx, y, x1, x2, e1, e2, res, cor;
double s, sn, ssn, c, cs, ccs;
xx = x * x;
cor = cor + ((cs - y) - e1 * x1);
res = y + cor;
cor = (y - res) + cor;
- if (cor > 0)
- cor = 1.0005 * cor + eps;
- else
- cor = 1.0005 * cor - eps;
+ cor = 1.0005 * cor + __copysign (eps, cor);
*corp = cor;
return res;
}
-/* Given a number partitioned into U and X and DX such that U is an index into
- the sin/cos table, this macro computes the sine of the number by combining
- the sin and cos of X (as computed by a variation of the Taylor series) with
- the values looked up from the sin/cos table to get the result in RES and a
- correction value in COR. */
-static double
-do_sin (mynumber u, double x, double dx, double *corp)
+/* Given a number partitioned into X and DX, this function computes the sine of
+ the number by combining the sin and cos of X (as computed by a variation of
+ the Taylor series) with the values looked up from the sin/cos table to get
+ the result in RES and a correction value in COR. */
+static inline double
+__always_inline
+do_sin (double x, double dx, double *corp)
{
+ mynumber u;
+
+ if (x <= 0)
+ dx = -dx;
+ u.x = big + fabs (x);
+ x = fabs (x) - (u.x - big);
+
double xx, s, sn, ssn, c, cs, ccs, cor, res;
xx = x * x;
s = x + (dx + x * xx * (sn3 + xx * sn5));
return res;
}
-/* A more precise variant of res = do_sin where the number is partitioned into U, X
- and DX. EPS is the adjustment to the correction COR. */
-static double
-do_sin_slow (mynumber u, double x, double dx, double eps, double *corp)
+/* A more precise variant of DO_SIN. EPS is the adjustment to the correction
+ COR. */
+static inline double
+__always_inline
+do_sin_slow (double x, double dx, double eps, double *corp)
{
+ mynumber u;
+
+ if (x <= 0)
+ dx = -dx;
+ u.x = big + fabs (x);
+ x = fabs (x) - (u.x - big);
+
double xx, y, x1, x2, c1, c2, res, cor;
double s, sn, ssn, c, cs, ccs;
xx = x * x;
cor = cor + ((sn - y) + c1 * x1);
res = y + cor;
cor = (y - res) + cor;
- if (cor > 0)
- cor = 1.0005 * cor + eps;
- else
- cor = 1.0005 * cor - eps;
+ cor = 1.0005 * cor + __copysign (eps, cor);
*corp = cor;
return res;
}
-/* Reduce range of X and compute sin of a + da. K is the amount by which to
- rotate the quadrants. This allows us to use the same routine to compute cos
- by simply rotating the quadrants by 1. */
+/* Reduce range of X and compute sin of a + da. When SHIFT_QUADRANT is true,
+ the routine returns the cosine of a + da by rotating the quadrant once and
+ computing the sine of the result. */
static inline double
__always_inline
-reduce_and_compute (double x, unsigned int k)
+reduce_and_compute (double x, bool shift_quadrant)
{
double retval = 0, a, da;
unsigned int n = __branred (x, &a, &da);
- k = (n + k) % 4;
+ int4 k = (n + shift_quadrant) % 4;
switch (k)
{
- case 0:
- if (a * a < 0.01588)
- retval = bsloww (a, da, x, n);
- else
- retval = bsloww1 (a, da, x, n);
- break;
- case 2:
- if (a * a < 0.01588)
- retval = bsloww (-a, -da, x, n);
- else
- retval = bsloww1 (-a, -da, x, n);
- break;
-
- case 1:
- case 3:
- retval = bsloww2 (a, da, x, n);
- break;
+ case 2:
+ a = -a;
+ da = -da;
+ /* Fall through. */
+ case 0:
+ if (a * a < 0.01588)
+ retval = bsloww (a, da, x, n);
+ else
+ retval = bsloww1 (a, da, x, n);
+ break;
+
+ case 1:
+ case 3:
+ retval = bsloww2 (a, da, x, n);
+ break;
+ }
+ return retval;
+}
+
+static inline int4
+__always_inline
+reduce_sincos_1 (double x, double *a, double *da)
+{
+ mynumber v;
+
+ double t = (x * hpinv + toint);
+ double xn = t - toint;
+ v.x = t;
+ double y = (x - xn * mp1) - xn * mp2;
+ int4 n = v.i[LOW_HALF] & 3;
+ double db = xn * mp3;
+ double b = y - db;
+ db = (y - b) - db;
+
+ *a = b;
+ *da = db;
+
+ return n;
+}
+
+/* Compute sin (A + DA). cos can be computed by passing SHIFT_QUADRANT as
+ true, which results in shifting the quadrant N clockwise. */
+static double
+__always_inline
+do_sincos_1 (double a, double da, double x, int4 n, bool shift_quadrant)
+{
+ double xx, retval, res, cor;
+ double eps = fabs (x) * 1.2e-30;
+
+ int k1 = (n + shift_quadrant) & 3;
+ switch (k1)
+ { /* quarter of unit circle */
+ case 2:
+ a = -a;
+ da = -da;
+ /* Fall through. */
+ case 0:
+ xx = a * a;
+ if (xx < 0.01588)
+ {
+ /* Taylor series. */
+ res = TAYLOR_SIN (xx, a, da, cor);
+ cor = 1.02 * cor + __copysign (eps, cor);
+ retval = (res == res + cor) ? res : sloww (a, da, x, shift_quadrant);
+ }
+ else
+ {
+ res = do_sin (a, da, &cor);
+ cor = 1.035 * cor + __copysign (eps, cor);
+ retval = ((res == res + cor) ? __copysign (res, a)
+ : sloww1 (a, da, x, shift_quadrant));
+ }
+ break;
+
+ case 1:
+ case 3:
+ res = do_cos (a, da, &cor);
+ cor = 1.025 * cor + __copysign (eps, cor);
+ retval = ((res == res + cor) ? ((n & 2) ? -res : res)
+ : sloww2 (a, da, x, n));
+ break;
+ }
+
+ return retval;
+}
+
+static inline int4
+__always_inline
+reduce_sincos_2 (double x, double *a, double *da)
+{
+ mynumber v;
+
+ double t = (x * hpinv + toint);
+ double xn = t - toint;
+ v.x = t;
+ double xn1 = (xn + 8.0e22) - 8.0e22;
+ double xn2 = xn - xn1;
+ double y = ((((x - xn1 * mp1) - xn1 * mp2) - xn2 * mp1) - xn2 * mp2);
+ int4 n = v.i[LOW_HALF] & 3;
+ double db = xn1 * pp3;
+ t = y - db;
+ db = (y - t) - db;
+ db = (db - xn2 * pp3) - xn * pp4;
+ double b = t + db;
+ db = (t - b) + db;
+
+ *a = b;
+ *da = db;
+
+ return n;
+}
+
+/* Compute sin (A + DA). cos can be computed by passing SHIFT_QUADRANT as
+ true, which results in shifting the quadrant N clockwise. */
+static double
+__always_inline
+do_sincos_2 (double a, double da, double x, int4 n, bool shift_quadrant)
+{
+ double res, retval, cor, xx;
+
+ double eps = 1.0e-24;
+
+ int4 k = (n + shift_quadrant) & 3;
+
+ switch (k)
+ {
+ case 2:
+ a = -a;
+ da = -da;
+ /* Fall through. */
+ case 0:
+ xx = a * a;
+ if (xx < 0.01588)
+ {
+ /* Taylor series. */
+ res = TAYLOR_SIN (xx, a, da, cor);
+ cor = 1.02 * cor + __copysign (eps, cor);
+ retval = (res == res + cor) ? res : bsloww (a, da, x, n);
+ }
+ else
+ {
+ res = do_sin (a, da, &cor);
+ cor = 1.035 * cor + __copysign (eps, cor);
+ retval = ((res == res + cor) ? __copysign (res, a)
+ : bsloww1 (a, da, x, n));
+ }
+ break;
+
+ case 1:
+ case 3:
+ res = do_cos (a, da, &cor);
+ cor = 1.025 * cor + __copysign (eps, cor);
+ retval = ((res == res + cor) ? ((n & 2) ? -res : res)
+ : bsloww2 (a, da, x, n));
+ break;
}
+
return retval;
}
/* An ultimate sin routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of sin(x) */
/*******************************************************************/
+#ifdef IN_SINCOS
+static double
+#else
double
SECTION
+#endif
__sin (double x)
{
- double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs, xn, a, da, db, eps, xn1,
- xn2;
- mynumber u, v;
- int4 k, m, n;
+ double xx, res, t, cor;
+ mynumber u;
+ int4 k, m;
double retval = 0;
+#ifndef IN_SINCOS
SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
+#endif
u.x = x;
m = u.i[HIGH_HALF];
k = 0x7fffffff & m; /* no sign */
if (k < 0x3e500000) /* if x->0 =>sin(x)=x */
- retval = x;
+ {
+ math_check_force_underflow (x);
+ retval = x;
+ }
/*---------------------------- 2^-26 < |x|< 0.25 ----------------------*/
else if (k < 0x3fd00000)
{
/*---------------------------- 0.25<|x|< 0.855469---------------------- */
else if (k < 0x3feb6000)
{
- u.x = (m > 0) ? big + x : big - x;
- y = (m > 0) ? x - (u.x - big) : x + (u.x - big);
- xx = y * y;
- s = y + y * xx * (sn3 + xx * sn5);
- c = xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- if (m <= 0)
- {
- sn = -sn;
- ssn = -ssn;
- }
- cor = (ssn + s * ccs - sn * c) + cs * s;
- res = sn + cor;
- cor = (sn - res) + cor;
+ res = do_sin (x, 0, &cor);
retval = (res == res + 1.096 * cor) ? res : slow1 (x);
+ retval = __copysign (retval, x);
} /* else if (k < 0x3feb6000) */
/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/
else if (k < 0x400368fd)
{
- y = (m > 0) ? hp0 - x : hp0 + x;
- if (y >= 0)
- {
- u.x = big + y;
- y = (y - (u.x - big)) + hp1;
- }
- else
- {
- u.x = big - y;
- y = (-hp1) - (y + (u.x - big));
- }
- res = do_cos (u, y, &cor);
- retval = (res == res + 1.020 * cor) ? ((m > 0) ? res : -res) : slow2 (x);
+ t = hp0 - fabs (x);
+ res = do_cos (t, hp1, &cor);
+ retval = (res == res + 1.020 * cor) ? res : slow2 (x);
+ retval = __copysign (retval, x);
} /* else if (k < 0x400368fd) */
+#ifndef IN_SINCOS
/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/
else if (k < 0x419921FB)
{
- t = (x * hpinv + toint);
- xn = t - toint;
- v.x = t;
- y = (x - xn * mp1) - xn * mp2;
- n = v.i[LOW_HALF] & 3;
- da = xn * mp3;
- a = y - da;
- da = (y - a) - da;
- eps = ABS (x) * 1.2e-30;
-
- switch (n)
- { /* quarter of unit circle */
- case 0:
- case 2:
- xx = a * a;
- if (n)
- {
- a = -a;
- da = -da;
- }
- if (xx < 0.01588)
- {
- /* Taylor series. */
- res = TAYLOR_SIN (xx, a, da, cor);
- cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
- retval = (res == res + cor) ? res : sloww (a, da, x);
- }
- else
- {
- if (a > 0)
- m = 1;
- else
- {
- m = 0;
- a = -a;
- da = -da;
- }
- u.x = big + a;
- y = a - (u.x - big);
- res = do_sin (u, y, da, &cor);
- cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
- retval = ((res == res + cor) ? ((m) ? res : -res)
- : sloww1 (a, da, x, m));
- }
- break;
-
- case 1:
- case 3:
- if (a < 0)
- {
- a = -a;
- da = -da;
- }
- u.x = big + a;
- y = a - (u.x - big) + da;
- res = do_cos (u, y, &cor);
- cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
- retval = ((res == res + cor) ? ((n & 2) ? -res : res)
- : sloww2 (a, da, x, n));
- break;
- }
+ double a, da;
+ int4 n = reduce_sincos_1 (x, &a, &da);
+ retval = do_sincos_1 (a, da, x, n, false);
} /* else if (k < 0x419921FB ) */
/*---------------------105414350 <|x|< 281474976710656 --------------------*/
else if (k < 0x42F00000)
{
- t = (x * hpinv + toint);
- xn = t - toint;
- v.x = t;
- xn1 = (xn + 8.0e22) - 8.0e22;
- xn2 = xn - xn1;
- y = ((((x - xn1 * mp1) - xn1 * mp2) - xn2 * mp1) - xn2 * mp2);
- n = v.i[LOW_HALF] & 3;
- da = xn1 * pp3;
- t = y - da;
- da = (y - t) - da;
- da = (da - xn2 * pp3) - xn * pp4;
- a = t + da;
- da = (t - a) + da;
- eps = 1.0e-24;
-
- switch (n)
- {
- case 0:
- case 2:
- xx = a * a;
- if (n)
- {
- a = -a;
- da = -da;
- }
- if (xx < 0.01588)
- {
- /* Taylor series. */
- res = TAYLOR_SIN (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);
- }
- else
- {
- double t;
- if (a > 0)
- {
- m = 1;
- t = a;
- db = da;
- }
- else
- {
- m = 0;
- t = -a;
- db = -da;
- }
- u.x = big + t;
- y = t - (u.x - big);
- res = do_sin (u, y, db, &cor);
- cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
- retval = ((res == res + cor) ? ((m) ? res : -res)
- : bsloww1 (a, da, x, n));
- }
- break;
-
- case 1:
- case 3:
- if (a < 0)
- {
- a = -a;
- da = -da;
- }
- u.x = big + a;
- y = a - (u.x - big) + da;
- res = do_cos (u, y, &cor);
- cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
- retval = ((res == res + cor) ? ((n & 2) ? -res : res)
- : bsloww2 (a, da, x, n));
- break;
- }
+ double a, da;
+
+ int4 n = reduce_sincos_2 (x, &a, &da);
+ retval = do_sincos_2 (a, da, x, n, false);
} /* else if (k < 0x42F00000 ) */
/* -----------------281474976710656 <|x| <2^1024----------------------------*/
else if (k < 0x7ff00000)
- retval = reduce_and_compute (x, 0);
+ retval = reduce_and_compute (x, false);
/*--------------------- |x| > 2^1024 ----------------------------------*/
else
__set_errno (EDOM);
retval = x / x;
}
+#endif
return retval;
}
/* it computes the correctly rounded (to nearest) value of cos(x) */
/*******************************************************************/
+#ifdef IN_SINCOS
+static double
+#else
double
SECTION
+#endif
__cos (double x)
{
- double y, xx, res, t, cor, xn, a, da, db, eps, xn1,
- xn2;
- mynumber u, v;
- int4 k, m, n;
+ double y, xx, res, cor, a, da;
+ mynumber u;
+ int4 k, m;
double retval = 0;
+#ifndef IN_SINCOS
SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
+#endif
u.x = x;
m = u.i[HIGH_HALF];
else if (k < 0x3feb6000)
{ /* 2^-27 < |x| < 0.855469 */
- y = ABS (x);
- u.x = big + y;
- y = y - (u.x - big);
- res = do_cos (u, y, &cor);
+ res = do_cos (x, 0, &cor);
retval = (res == res + 1.020 * cor) ? res : cslow2 (x);
} /* else if (k < 0x3feb6000) */
else if (k < 0x400368fd)
{ /* 0.855469 <|x|<2.426265 */ ;
- y = hp0 - ABS (x);
+ y = hp0 - fabs (x);
a = y + hp1;
da = (y - a) + hp1;
xx = a * a;
if (xx < 0.01588)
{
res = TAYLOR_SIN (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);
+ cor = 1.02 * cor + __copysign (1.0e-31, cor);
+ retval = (res == res + cor) ? res : sloww (a, da, x, true);
}
else
{
- if (a > 0)
- {
- m = 1;
- }
- else
- {
- m = 0;
- a = -a;
- da = -da;
- }
- u.x = big + a;
- y = a - (u.x - big);
- res = do_sin (u, y, da, &cor);
- cor = (cor > 0) ? 1.035 * cor + 1.0e-31 : 1.035 * cor - 1.0e-31;
- retval = ((res == res + cor) ? ((m) ? res : -res)
- : csloww1 (a, da, x, m));
+ res = do_sin (a, da, &cor);
+ cor = 1.035 * cor + __copysign (1.0e-31, cor);
+ retval = ((res == res + cor) ? __copysign (res, a)
+ : sloww1 (a, da, x, true));
}
} /* else if (k < 0x400368fd) */
+#ifndef IN_SINCOS
else if (k < 0x419921FB)
{ /* 2.426265<|x|< 105414350 */
- t = (x * hpinv + toint);
- xn = t - toint;
- v.x = t;
- y = (x - xn * mp1) - xn * mp2;
- n = v.i[LOW_HALF] & 3;
- da = xn * mp3;
- a = y - da;
- da = (y - a) - da;
- eps = ABS (x) * 1.2e-30;
-
- switch (n)
- {
- case 1:
- case 3:
- xx = a * a;
- if (n == 1)
- {
- a = -a;
- da = -da;
- }
- if (xx < 0.01588)
- {
- res = TAYLOR_SIN (xx, a, da, cor);
- cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
- retval = (res == res + cor) ? res : csloww (a, da, x);
- }
- else
- {
- if (a > 0)
- {
- m = 1;
- }
- else
- {
- m = 0;
- a = -a;
- da = -da;
- }
- u.x = big + a;
- y = a - (u.x - big);
- res = do_sin (u, y, da, &cor);
- cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
- retval = ((res == res + cor) ? ((m) ? res : -res)
- : csloww1 (a, da, x, m));
- }
- break;
-
- case 0:
- case 2:
- if (a < 0)
- {
- a = -a;
- da = -da;
- }
- u.x = big + a;
- y = a - (u.x - big) + da;
- res = do_cos (u, y, &cor);
- cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
- retval = ((res == res + cor) ? ((n) ? -res : res)
- : csloww2 (a, da, x, n));
- break;
- }
+ double a, da;
+ int4 n = reduce_sincos_1 (x, &a, &da);
+ retval = do_sincos_1 (a, da, x, n, true);
} /* else if (k < 0x419921FB ) */
else if (k < 0x42F00000)
{
- t = (x * hpinv + toint);
- xn = t - toint;
- v.x = t;
- xn1 = (xn + 8.0e22) - 8.0e22;
- xn2 = xn - xn1;
- y = ((((x - xn1 * mp1) - xn1 * mp2) - xn2 * mp1) - xn2 * mp2);
- n = v.i[LOW_HALF] & 3;
- da = xn1 * pp3;
- t = y - da;
- da = (y - t) - da;
- da = (da - xn2 * pp3) - xn * pp4;
- a = t + da;
- da = (t - a) + da;
- eps = 1.0e-24;
-
- switch (n)
- {
- case 1:
- case 3:
- xx = a * a;
- if (n == 1)
- {
- a = -a;
- da = -da;
- }
- if (xx < 0.01588)
- {
- res = TAYLOR_SIN (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);
- }
- else
- {
- double t;
- if (a > 0)
- {
- m = 1;
- t = a;
- db = da;
- }
- else
- {
- m = 0;
- t = -a;
- db = -da;
- }
- u.x = big + t;
- y = t - (u.x - big);
- res = do_sin (u, y, db, &cor);
- cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
- retval = ((res == res + cor) ? ((m) ? res : -res)
- : bsloww1 (a, da, x, n));
- }
- break;
-
- case 0:
- case 2:
- if (a < 0)
- {
- a = -a;
- da = -da;
- }
- u.x = big + a;
- y = a - (u.x - big) + da;
- res = do_cos (u, y, &cor);
- cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
- retval = ((res == res + cor) ? ((n) ? -res : res)
- : bsloww2 (a, da, x, n));
- break;
- }
+ double a, da;
+
+ int4 n = reduce_sincos_2 (x, &a, &da);
+ retval = do_sincos_2 (a, da, x, n, true);
} /* else if (k < 0x42F00000 ) */
/* 281474976710656 <|x| <2^1024 */
else if (k < 0x7ff00000)
- retval = reduce_and_compute (x, 1);
+ retval = reduce_and_compute (x, true);
else
{
__set_errno (EDOM);
retval = x / x; /* |x| > 2^1024 */
}
+#endif
return retval;
}
/* precision and if still doesn't accurate enough by mpsin or dubsin */
/************************************************************************/
-static double
-SECTION
+static inline double
+__always_inline
slow (double x)
{
double res, cor, w[2];
res = TAYLOR_SLOW (x, 0, cor);
if (res == res + 1.0007 * cor)
return res;
- else
- {
- __dubsin (ABS (x), 0, w);
- if (w[0] == w[0] + 1.000000001 * w[1])
- return (x > 0) ? w[0] : -w[0];
- else
- return (x > 0) ? __mpsin (x, 0, false) : -__mpsin (-x, 0, false);
- }
+
+ __dubsin (fabs (x), 0, w);
+ if (w[0] == w[0] + 1.000000001 * w[1])
+ return __copysign (w[0], x);
+
+ return __copysign (__mpsin (fabs (x), 0, false), x);
}
/*******************************************************************************/
/* and if result still doesn't accurate enough by mpsin or dubsin */
/*******************************************************************************/
-static double
-SECTION
+static inline double
+__always_inline
slow1 (double x)
{
- mynumber u;
- double w[2], y, cor, res;
- y = ABS (x);
- u.x = big + y;
- y = y - (u.x - big);
- res = do_sin_slow (u, y, 0, 0, &cor);
+ double w[2], cor, res;
+
+ res = do_sin_slow (x, 0, 0, &cor);
if (res == res + cor)
- return (x > 0) ? res : -res;
- else
- {
- __dubsin (ABS (x), 0, w);
- if (w[0] == w[0] + 1.000000005 * w[1])
- return (x > 0) ? w[0] : -w[0];
- else
- return (x > 0) ? __mpsin (x, 0, false) : -__mpsin (-x, 0, false);
- }
+ return res;
+
+ __dubsin (fabs (x), 0, w);
+ if (w[0] == w[0] + 1.000000005 * w[1])
+ return w[0];
+
+ return __mpsin (fabs (x), 0, false);
}
/**************************************************************************/
/* Routine compute sin(x) for 0.855469 <|x|<2.426265 by __sincostab.tbl */
/* and if result still doesn't accurate enough by mpsin or dubsin */
/**************************************************************************/
-static double
-SECTION
+static inline double
+__always_inline
slow2 (double x)
{
- mynumber u;
- double w[2], y, y1, y2, cor, res, del;
+ double w[2], y, y1, y2, cor, res;
- y = ABS (x);
- y = hp0 - y;
- if (y >= 0)
- {
- u.x = big + y;
- y = y - (u.x - big);
- del = hp1;
- }
- else
- {
- u.x = big - y;
- y = -(y + (u.x - big));
- del = -hp1;
- }
- res = do_cos_slow (u, y, del, 0, &cor);
+ double t = hp0 - fabs (x);
+ res = do_cos_slow (t, hp1, 0, &cor);
if (res == res + cor)
- return (x > 0) ? res : -res;
- else
- {
- y = ABS (x) - hp0;
- y1 = y - hp1;
- y2 = (y - y1) - hp1;
- __docos (y1, y2, w);
- if (w[0] == w[0] + 1.000000005 * w[1])
- return (x > 0) ? w[0] : -w[0];
- else
- return (x > 0) ? __mpsin (x, 0, false) : -__mpsin (-x, 0, false);
- }
-}
+ return res;
-/***************************************************************************/
-/* Routine compute sin(x+dx) (Double-Length number) where x is small enough*/
-/* to use Taylor series around zero and (x+dx) */
-/* 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 mpsin1 or dubsin */
-/***************************************************************************/
+ y = fabs (x) - hp0;
+ y1 = y - hp1;
+ y2 = (y - y1) - hp1;
+ __docos (y1, y2, w);
+ if (w[0] == w[0] + 1.000000005 * w[1])
+ return w[0];
-static double
-SECTION
-sloww (double x, double dx, double orig)
+ return __mpsin (fabs (x), 0, false);
+}
+
+/* Compute sin(x + dx) where X is small enough to use Taylor series around zero
+ and (x + dx) in the first or third quarter of the unit circle. ORIG is the
+ original value of X for computing error of the result. If the result is not
+ accurate enough, the routine calls mpsin or dubsin. SHIFT_QUADRANT rotates
+ the unit circle by 1 to compute the cosine instead of sine. */
+static inline double
+__always_inline
+sloww (double x, double dx, double orig, bool shift_quadrant)
{
double y, t, res, cor, w[2], a, da, xn;
mynumber v;
int4 n;
res = TAYLOR_SLOW (x, dx, cor);
- if (cor > 0)
- cor = 1.0005 * cor + ABS (orig) * 3.1e-30;
- else
- cor = 1.0005 * cor - ABS (orig) * 3.1e-30;
+
+ double eps = fabs (orig) * 3.1e-30;
+
+ cor = 1.0005 * cor + __copysign (eps, cor);
if (res == res + cor)
return res;
- else
- {
- (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
- if (w[1] > 0)
- cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-30;
- else
- cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-30;
- if (w[0] == w[0] + cor)
- return (x > 0) ? w[0] : -w[0];
- else
- {
- t = (orig * hpinv + toint);
- xn = t - toint;
- v.x = t;
- y = (orig - xn * mp1) - xn * mp2;
- n = v.i[LOW_HALF] & 3;
- da = xn * pp3;
- t = y - da;
- da = (y - t) - da;
- y = xn * pp4;
- a = t - y;
- da = ((t - a) - y) + da;
- if (n & 2)
- {
- a = -a;
- da = -da;
- }
- (a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w);
- if (w[1] > 0)
- cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-40;
- else
- cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-40;
-
- if (w[0] == w[0] + cor)
- return (a > 0) ? w[0] : -w[0];
- else
- return __mpsin (orig, 0, true);
- }
+ a = fabs (x);
+ da = (x > 0) ? dx : -dx;
+ __dubsin (a, da, w);
+ eps = fabs (orig) * 1.1e-30;
+ cor = 1.000000001 * w[1] + __copysign (eps, w[1]);
+
+ if (w[0] == w[0] + cor)
+ return __copysign (w[0], x);
+
+ t = (orig * hpinv + toint);
+ xn = t - toint;
+ v.x = t;
+ y = (orig - xn * mp1) - xn * mp2;
+ n = (v.i[LOW_HALF] + shift_quadrant) & 3;
+ da = xn * pp3;
+ t = y - da;
+ da = (y - t) - da;
+ y = xn * pp4;
+ a = t - y;
+ da = ((t - a) - y) + da;
+
+ if (n & 2)
+ {
+ a = -a;
+ da = -da;
}
-}
+ x = fabs (a);
+ dx = (a > 0) ? da : -da;
+ __dubsin (x, dx, w);
+ eps = fabs (orig) * 1.1e-40;
+ cor = 1.000000001 * w[1] + __copysign (eps, w[1]);
-/***************************************************************************/
-/* Routine compute sin(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 mpsin1 or dubsin */
-/***************************************************************************/
+ if (w[0] == w[0] + cor)
+ return __copysign (w[0], a);
-static double
-SECTION
-sloww1 (double x, double dx, double orig, int m)
+ return shift_quadrant ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
+}
+
+/* Compute sin(x + dx) where X is in the first or third quarter of the unit
+ circle. ORIG is the original value of X for computing error of the result.
+ If the result is not accurate enough, the routine calls mpsin or dubsin.
+ SHIFT_QUADRANT rotates the unit circle by 1 to compute the cosine instead of
+ sine. */
+static inline double
+__always_inline
+sloww1 (double x, double dx, double orig, bool shift_quadrant)
{
- mynumber u;
- double w[2], y, cor, res;
+ double w[2], cor, res;
- u.x = big + x;
- y = x - (u.x - big);
- res = do_sin_slow (u, y, dx, 3.1e-30 * ABS (orig), &cor);
+ res = do_sin_slow (x, dx, 3.1e-30 * fabs (orig), &cor);
if (res == res + cor)
- return (m > 0) ? res : -res;
- else
- {
- __dubsin (x, dx, w);
+ return __copysign (res, x);
- if (w[1] > 0)
- cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
- else
- cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+ dx = (x > 0 ? dx : -dx);
+ __dubsin (fabs (x), dx, w);
- if (w[0] == w[0] + cor)
- return (m > 0) ? w[0] : -w[0];
- else
- return __mpsin (orig, 0, true);
- }
+ double eps = 1.1e-30 * fabs (orig);
+ cor = 1.000000005 * w[1] + __copysign (eps, w[1]);
+
+ if (w[0] == w[0] + cor)
+ return __copysign (w[0], x);
+
+ return shift_quadrant ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
}
/***************************************************************************/
/* accurate enough routine calls mpsin1 or dubsin */
/***************************************************************************/
-static double
-SECTION
+static inline double
+__always_inline
sloww2 (double x, double dx, double orig, int n)
{
- mynumber u;
- double w[2], y, cor, res;
+ double w[2], cor, res;
- u.x = big + x;
- y = x - (u.x - big);
- res = do_cos_slow (u, y, dx, 3.1e-30 * ABS (orig), &cor);
+ res = do_cos_slow (x, dx, 3.1e-30 * fabs (orig), &cor);
if (res == res + cor)
return (n & 2) ? -res : res;
- else
- {
- __docos (x, dx, w);
- if (w[1] > 0)
- cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
- else
- cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+ dx = x > 0 ? dx : -dx;
+ __docos (fabs (x), dx, w);
- if (w[0] == w[0] + cor)
- return (n & 2) ? -w[0] : w[0];
- else
- return __mpsin (orig, 0, true);
- }
+ double eps = 1.1e-30 * fabs (orig);
+ cor = 1.000000005 * w[1] + __copysign (eps, 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);
}
/***************************************************************************/
/* result.And if result not accurate enough routine calls other routines */
/***************************************************************************/
-static double
-SECTION
+static inline double
+__always_inline
bsloww (double x, double dx, double orig, int n)
{
- double res, cor, w[2];
+ double res, cor, w[2], a, da;
res = TAYLOR_SLOW (x, dx, cor);
- cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+ cor = 1.0005 * cor + __copysign (1.1e-24, cor);
if (res == res + cor)
return res;
- else
- {
- (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
- if (w[1] > 0)
- cor = 1.000000001 * w[1] + 1.1e-24;
- else
- cor = 1.000000001 * w[1] - 1.1e-24;
- if (w[0] == w[0] + cor)
- return (x > 0) ? w[0] : -w[0];
- else
- return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
- }
+
+ a = fabs (x);
+ da = (x > 0) ? dx : -dx;
+ __dubsin (a, da, w);
+ cor = 1.000000001 * 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);
}
/***************************************************************************/
/* And if result not accurate enough routine calls other routines */
/***************************************************************************/
-static double
-SECTION
+static inline double
+__always_inline
bsloww1 (double x, double dx, double orig, int n)
{
- mynumber u;
- double w[2], y, cor, res;
+ double w[2], cor, res;
- y = ABS (x);
- u.x = big + y;
- y = y - (u.x - big);
- dx = (x > 0) ? dx : -dx;
- res = do_sin_slow (u, y, dx, 1.1e-24, &cor);
+ res = do_sin_slow (x, dx, 1.1e-24, &cor);
if (res == res + cor)
return (x > 0) ? res : -res;
- else
- {
- __dubsin (ABS (x), dx, w);
- if (w[1] > 0)
- cor = 1.000000005 * w[1] + 1.1e-24;
- else
- cor = 1.000000005 * w[1] - 1.1e-24;
+ dx = (x > 0) ? dx : -dx;
+ __dubsin (fabs (x), dx, w);
- if (w[0] == w[0] + cor)
- return (x > 0) ? w[0] : -w[0];
- else
- return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
- }
+ 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);
}
/***************************************************************************/
/* And if result not accurate enough routine calls other routines */
/***************************************************************************/
-static double
-SECTION
+static inline double
+__always_inline
bsloww2 (double x, double dx, double orig, int n)
{
- mynumber u;
- double w[2], y, cor, res;
+ double w[2], cor, res;
- y = ABS (x);
- u.x = big + y;
- y = y - (u.x - big);
- dx = (x > 0) ? dx : -dx;
- res = do_cos_slow (u, y, dx, 1.1e-24, &cor);
+ res = do_cos_slow (x, dx, 1.1e-24, &cor);
if (res == res + cor)
return (n & 2) ? -res : res;
- else
- {
- __docos (ABS (x), dx, w);
- if (w[1] > 0)
- cor = 1.000000005 * w[1] + 1.1e-24;
- else
- cor = 1.000000005 * w[1] - 1.1e-24;
+ dx = (x > 0) ? dx : -dx;
+ __docos (fabs (x), dx, w);
- if (w[0] == w[0] + cor)
- return (n & 2) ? -w[0] : w[0];
- else
- return (n & 1) ? __mpsin (orig, 0, true) : __mpcos (orig, 0, true);
- }
+ 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);
}
/************************************************************************/
/* precision and if still doesn't accurate enough by mpcos or docos */
/************************************************************************/
-static double
-SECTION
+static inline double
+__always_inline
cslow2 (double x)
{
- mynumber u;
- double w[2], y, cor, res;
-
- y = ABS (x);
- u.x = big + y;
- y = y - (u.x - big);
- res = do_cos_slow (u, y, 0, 0, &cor);
- if (res == res + cor)
- return res;
- else
- {
- y = ABS (x);
- __docos (y, 0, w);
- if (w[0] == w[0] + 1.000000005 * w[1])
- return w[0];
- else
- return __mpcos (x, 0, false);
- }
-}
-
-/***************************************************************************/
-/* Routine compute cos(x+dx) (Double-Length number) where x is small enough*/
-/* to use Taylor series around zero and (x+dx) .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 double
-SECTION
-csloww (double x, double dx, double orig)
-{
- double y, t, res, cor, w[2], a, da, xn;
- mynumber v;
- int4 n;
-
- /* Taylor series */
- res = TAYLOR_SLOW (x, dx, cor);
-
- if (cor > 0)
- cor = 1.0005 * cor + ABS (orig) * 3.1e-30;
- else
- cor = 1.0005 * cor - ABS (orig) * 3.1e-30;
+ double w[2], cor, res;
+ res = do_cos_slow (x, 0, 0, &cor);
if (res == res + cor)
return res;
- else
- {
- (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
- if (w[1] > 0)
- cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-30;
- else
- cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-30;
+ __docos (fabs (x), 0, w);
+ if (w[0] == w[0] + 1.000000005 * w[1])
+ return w[0];
- if (w[0] == w[0] + cor)
- return (x > 0) ? w[0] : -w[0];
- else
- {
- t = (orig * hpinv + toint);
- xn = t - toint;
- v.x = t;
- y = (orig - xn * mp1) - xn * mp2;
- n = v.i[LOW_HALF] & 3;
- da = xn * pp3;
- t = y - da;
- da = (y - t) - da;
- y = xn * pp4;
- a = t - y;
- da = ((t - a) - y) + da;
- if (n == 1)
- {
- a = -a;
- da = -da;
- }
- (a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w);
-
- if (w[1] > 0)
- cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-40;
- else
- cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-40;
-
- if (w[0] == w[0] + cor)
- return (a > 0) ? w[0] : -w[0];
- else
- return __mpcos (orig, 0, true);
- }
- }
-}
-
-/***************************************************************************/
-/* Routine compute sin(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 double
-SECTION
-csloww1 (double x, double dx, double orig, int m)
-{
- mynumber u;
- double w[2], y, cor, res;
-
- u.x = big + x;
- y = x - (u.x - big);
- res = do_sin_slow (u, y, dx, 3.1e-30 * ABS (orig), &cor);
-
- if (res == res + cor)
- return (m > 0) ? res : -res;
- else
- {
- __dubsin (x, dx, w);
- if (w[1] > 0)
- cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
- else
- cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
- if (w[0] == w[0] + cor)
- return (m > 0) ? w[0] : -w[0];
- else
- return __mpcos (orig, 0, true);
- }
-}
-
-
-/***************************************************************************/
-/* Routine compute sin(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 double
-SECTION
-csloww2 (double x, double dx, double orig, int n)
-{
- mynumber u;
- double w[2], y, cor, res;
-
- u.x = big + x;
- y = x - (u.x - big);
- res = do_cos_slow (u, y, dx, 3.1e-30 * ABS (orig), &cor);
-
- if (res == res + cor)
- return (n) ? -res : res;
- else
- {
- __docos (x, dx, w);
- if (w[1] > 0)
- cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
- else
- cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
- if (w[0] == w[0] + cor)
- return (n) ? -w[0] : w[0];
- else
- return __mpcos (orig, 0, true);
- }
+ return __mpcos (x, 0, false);
}
#ifndef __cos
-weak_alias (__cos, cos)
-# ifdef NO_LONG_DOUBLE
-strong_alias (__cos, __cosl)
-weak_alias (__cos, cosl)
-# endif
+libm_alias_double (__cos, cos)
#endif
#ifndef __sin
-weak_alias (__sin, sin)
-# ifdef NO_LONG_DOUBLE
-strong_alias (__sin, __sinl)
-weak_alias (__sin, sinl)
-# endif
+libm_alias_double (__sin, sin)
#endif
projects / thirdparty / glibc.git / blobdiff