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Use fabs(x) instead of branching on signedness of input to sin and cos

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The sin and cos code is inconsistent about its use of fabs to get the
absolute value of X where in some places it conditionalizes the code
while in others it uses fabs.  fabs seems to be a better candidate in
most cases because it avoids a branch.  Similarly there is an attempt
to make it easier for the compiler to emit conditional assignment
instructions (like fcsel on aarch64) where it can, by isolating
conditional assignment constructs from the rest of the expression.

A further benefit of this change is to identify common constructs
across functions and consolidate them in future patches.

	* sysdeps/ieee754/dbl-64/s_sin.c (do_cos_slow): Use ternary
	instead of if/else.
	(do_sin_slow): Likewise.
	(do_sincos_1): Use fabs instead of if/else.
	(do_sincos_2): Likewise.
	(__sin): Likewise.
	(__cos): Likewise.
	(slow2): Likewise.
	(sloww): Likewise.
	(sloww1): Likewise.  Drop argument M.
	(sloww2): Use fabs instead of if/else.
	(bsloww): Likewise.
	(bsloww1): Likewise.
	(bsloww2): Likewise.
This commit is contained in:
Siddhesh Poyarekar 2016-08-30 13:01:59 +05:30
parent 1a822c6184
commit 9d84d0e51d
2 changed files with 100 additions and 148 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

15
ChangeLog
View File

@ -1,5 +1,20 @@
2016-08-30 Siddhesh Poyarekar <siddhesh@sourceware.org> 2016-08-30 Siddhesh Poyarekar <siddhesh@sourceware.org>
* sysdeps/ieee754/dbl-64/s_sin.c (do_cos_slow): Use ternary
instead of if/else.
(do_sin_slow): Likewise.
(do_sincos_1): Use fabs instead of if/else.
(do_sincos_2): Likewise.
(__sin): Likewise.
(__cos): Likewise.
(slow2): Likewise.
(sloww): Likewise.
(sloww1): Likewise. Drop argument M.
(sloww2): Use fabs instead of if/else.
(bsloww): Likewise.
(bsloww1): Likewise.
(bsloww2): Likewise.
* sysdeps/ieee754/dbl-64/s_sin.c (reduce_and_compute): Add * sysdeps/ieee754/dbl-64/s_sin.c (reduce_and_compute): Add
fall through comment. fall through comment.
(do_sincos_1): Likewise. (do_sincos_1): Likewise.

233
sysdeps/ieee754/dbl-64/s_sin.c
View File

@ -133,7 +133,7 @@ static double slow (double x);
static double slow1 (double x); static double slow1 (double x);
static double slow2 (double x); static double slow2 (double x);
static double sloww (double x, double dx, double orig, int n); static double sloww (double x, double dx, double orig, int n);
static double sloww1 (double x, double dx, double orig, int m, int n); static double sloww1 (double x, double dx, double orig, int n);
static double sloww2 (double x, double dx, double orig, int n); static double sloww2 (double x, double dx, double orig, int n);
static double bsloww (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 bsloww1 (double x, double dx, double orig, int n);
@ -181,10 +181,7 @@ do_cos_slow (mynumber u, double x, double dx, double eps, double *corp)
cor = cor + ((cs - y) - e1 * x1); cor = cor + ((cs - y) - e1 * x1);
res = y + cor; res = y + cor;
cor = (y - res) + cor; cor = (y - res) + cor;
if (cor > 0) cor = 1.0005 * cor + ((cor > 0) ? eps : -eps);
cor = 1.0005 * cor + eps;
else
cor = 1.0005 * cor - eps;
*corp = cor; *corp = cor;
return res; return res;
} }
@ -229,10 +226,7 @@ do_sin_slow (mynumber u, double x, double dx, double eps, double *corp)
cor = cor + ((sn - y) + c1 * x1); cor = cor + ((sn - y) + c1 * x1);
res = y + cor; res = y + cor;
cor = (y - res) + cor; cor = (y - res) + cor;
if (cor > 0) cor = 1.0005 * cor + ((cor > 0) ? eps : -eps);
cor = 1.0005 * cor + eps;
else
cor = 1.0005 * cor - eps;
*corp = cor; *corp = cor;
return res; return res;
} }
@ -297,7 +291,6 @@ do_sincos_1 (double a, double da, double x, int4 n, int4 k)
{ {
double xx, retval, res, cor, y; double xx, retval, res, cor, y;
mynumber u; mynumber u;
int m;
double eps = fabs (x) * 1.2e-30; double eps = fabs (x) * 1.2e-30;
int k1 = (n + k) & 3; int k1 = (n + k) & 3;
@ -318,37 +311,28 @@ do_sincos_1 (double a, double da, double x, int4 n, int4 k)
} }
else else
{ {
if (a > 0) double db = (a > 0 ? da : -da);
m = 1; u.x = big + fabs (a);
else y = fabs (a) - (u.x - big);
{ res = do_sin (u, y, db, &cor);
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; cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
retval = ((res == res + cor) ? ((m) ? res : -res) retval = ((res == res + cor) ? ((a > 0) ? res : -res)
: sloww1 (a, da, x, m, k)); : sloww1 (a, da, x, k));
} }
break; break;
case 1: case 1:
case 3: case 3:
if (a < 0)
{ {
a = -a; double db = (a > 0 ? da : -da);
da = -da; u.x = big + fabs (a);
y = fabs (a) - (u.x - big) + db;
res = do_cos (u, y, &cor);
cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
retval = ((res == res + cor) ? ((k1 & 2) ? -res : res)
: sloww2 (a, da, x, n));
break;
} }
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) ? ((k1 & 2) ? -res : res)
: sloww2 (a, da, x, n));
break;
} }
return retval; return retval;
@ -410,43 +394,28 @@ do_sincos_2 (double a, double da, double x, int4 n, int4 k)
} }
else else
{ {
double t, db, y; double db = (a > 0 ? da : -da);
int m; u.x = big + fabs (a);
if (a > 0) double y = fabs (a) - (u.x - big);
{
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); res = do_sin (u, y, db, &cor);
cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps; cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
retval = ((res == res + cor) ? ((m) ? res : -res) retval = ((res == res + cor) ? ((a > 0) ? res : -res)
: bsloww1 (a, da, x, n)); : bsloww1 (a, da, x, n));
} }
break; break;
case 1: case 1:
case 3: case 3:
if (a < 0)
{ {
a = -a; double db = (a > 0 ? da : -da);
da = -da; u.x = big + fabs (a);
double y = fabs (a) - (u.x - big) + db;
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;
} }
u.x = big + a;
double 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;
} }
return retval; return retval;
@ -494,8 +463,10 @@ __sin (double x)
/*---------------------------- 0.25<|x|< 0.855469---------------------- */ /*---------------------------- 0.25<|x|< 0.855469---------------------- */
else if (k < 0x3feb6000) else if (k < 0x3feb6000)
{ {
u.x = (m > 0) ? big + x : big - x; u.x = big + fabs (x);
y = (m > 0) ? x - (u.x - big) : x + (u.x - big); y = fabs (x) - (u.x - big);
y = (x > 0 ? y : -y);
xx = y * y; xx = y * y;
s = y + y * xx * (sn3 + xx * sn5); s = y + y * xx * (sn3 + xx * sn5);
c = xx * (cs2 + xx * (cs4 + xx * cs6)); c = xx * (cs2 + xx * (cs4 + xx * cs6));
@ -515,17 +486,11 @@ __sin (double x)
else if (k < 0x400368fd) else if (k < 0x400368fd)
{ {
y = (m > 0) ? hp0 - x : hp0 + x; t = hp0 - fabs (x);
if (y >= 0) u.x = big + fabs (t);
{ y = fabs (t) - (u.x - big);
u.x = big + y; y = ((t >= 0) ? hp1 : -hp1) + y;
y = (y - (u.x - big)) + hp1;
}
else
{
u.x = big - y;
y = (-hp1) - (y + (u.x - big));
}
res = do_cos (u, y, &cor); res = do_cos (u, y, &cor);
retval = (res == res + 1.020 * cor) ? ((m > 0) ? res : -res) : slow2 (x); retval = (res == res + 1.020 * cor) ? ((m > 0) ? res : -res) : slow2 (x);
} /* else if (k < 0x400368fd) */ } /* else if (k < 0x400368fd) */
@ -619,22 +584,13 @@ __cos (double x)
} }
else else
{ {
if (a > 0) double db = (a > 0 ? da : -da);
{ u.x = big + fabs (a);
m = 1; y = fabs (a) - (u.x - big);
} res = do_sin (u, y, db, &cor);
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; cor = (cor > 0) ? 1.035 * cor + 1.0e-31 : 1.035 * cor - 1.0e-31;
retval = ((res == res + cor) ? ((m) ? res : -res) retval = ((res == res + cor) ? ((a > 0) ? res : -res)
: sloww1 (a, da, x, m, 1)); : sloww1 (a, da, x, 1));
} }
} /* else if (k < 0x400368fd) */ } /* else if (k < 0x400368fd) */
@ -728,20 +684,11 @@ slow2 (double x)
mynumber u; mynumber u;
double w[2], y, y1, y2, cor, res, del; double w[2], y, y1, y2, cor, res, del;
y = fabs (x); double t = hp0 - fabs (x);
y = hp0 - y; u.x = big + fabs (t);
if (y >= 0) y = fabs (t) - (u.x - big);
{ del = (t >= 0) ? hp1 : -hp1;
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); res = do_cos_slow (u, y, del, 0, &cor);
if (res == res + cor) if (res == res + cor)
return (x > 0) ? res : -res; return (x > 0) ? res : -res;
@ -773,19 +720,18 @@ sloww (double x, double dx, double orig, int k)
int4 n; int4 n;
res = TAYLOR_SLOW (x, dx, cor); res = TAYLOR_SLOW (x, dx, cor);
if (cor > 0) double eps = fabs (orig) * 3.1e-30;
cor = 1.0005 * cor + fabs (orig) * 3.1e-30;
else cor = 1.0005 * cor + ((cor > 0) ? eps : -eps);
cor = 1.0005 * cor - fabs (orig) * 3.1e-30;
if (res == res + cor) if (res == res + cor)
return res; return res;
(x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w); a = fabs (x);
if (w[1] > 0) da = (x > 0) ? dx : -dx;
cor = 1.000000001 * w[1] + fabs (orig) * 1.1e-30; __dubsin (a, da, w);
else eps = fabs (orig) * 1.1e-30;
cor = 1.000000001 * w[1] - fabs (orig) * 1.1e-30; cor = 1.000000001 * w[1] + ((w[1] > 0) ? eps : -eps);
if (w[0] == w[0] + cor) if (w[0] == w[0] + cor)
return (x > 0) ? w[0] : -w[0]; return (x > 0) ? w[0] : -w[0];
@ -807,11 +753,11 @@ sloww (double x, double dx, double orig, int k)
a = -a; a = -a;
da = -da; da = -da;
} }
(a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w); x = fabs (a);
if (w[1] > 0) dx = (a > 0) ? da : -da;
cor = 1.000000001 * w[1] + fabs (orig) * 1.1e-40; __dubsin (x, dx, w);
else eps = fabs (orig) * 1.1e-40;
cor = 1.000000001 * w[1] - fabs (orig) * 1.1e-40; cor = 1.000000001 * w[1] + ((w[1] > 0) ? eps : -eps);
if (w[0] == w[0] + cor) if (w[0] == w[0] + cor)
return (a > 0) ? w[0] : -w[0]; return (a > 0) ? w[0] : -w[0];
@ -828,27 +774,26 @@ sloww (double x, double dx, double orig, int k)
static double static double
SECTION SECTION
sloww1 (double x, double dx, double orig, int m, int k) sloww1 (double x, double dx, double orig, int k)
{ {
mynumber u; mynumber u;
double w[2], y, cor, res; double w[2], y, cor, res;
u.x = big + x; u.x = big + fabs (x);
y = x - (u.x - big); y = fabs (x) - (u.x - big);
dx = (x > 0 ? dx : -dx);
res = do_sin_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor); res = do_sin_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor);
if (res == res + cor) if (res == res + cor)
return (m > 0) ? res : -res; return (x > 0) ? res : -res;
__dubsin (x, dx, w); __dubsin (fabs (x), dx, w);
if (w[1] > 0) double eps = 1.1e-30 * fabs (orig);
cor = 1.000000005 * w[1] + 1.1e-30 * fabs (orig); cor = 1.000000005 * w[1] + ((w[1] > 0) ? eps : -eps);
else
cor = 1.000000005 * w[1] - 1.1e-30 * fabs (orig);
if (w[0] == w[0] + cor) if (w[0] == w[0] + cor)
return (m > 0) ? w[0] : -w[0]; return (x > 0) ? w[0] : -w[0];
return (k == 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); return (k == 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
} }
@ -867,19 +812,18 @@ sloww2 (double x, double dx, double orig, int n)
mynumber u; mynumber u;
double w[2], y, cor, res; double w[2], y, cor, res;
u.x = big + x; u.x = big + fabs (x);
y = x - (u.x - big); y = fabs (x) - (u.x - big);
dx = (x > 0 ? dx : -dx);
res = do_cos_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor); res = do_cos_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor);
if (res == res + cor) if (res == res + cor)
return (n & 2) ? -res : res; return (n & 2) ? -res : res;
__docos (x, dx, w); __docos (fabs (x), dx, w);
if (w[1] > 0) double eps = 1.1e-30 * fabs (orig);
cor = 1.000000005 * w[1] + 1.1e-30 * fabs (orig); cor = 1.000000005 * w[1] + ((w[1] > 0) ? eps : -eps);
else
cor = 1.000000005 * w[1] - 1.1e-30 * fabs (orig);
if (w[0] == w[0] + cor) if (w[0] == w[0] + cor)
return (n & 2) ? -w[0] : w[0]; return (n & 2) ? -w[0] : w[0];
@ -899,18 +843,17 @@ static double
SECTION SECTION
bsloww (double x, double dx, double orig, int n) 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); 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 + ((cor > 0) ? 1.1e-24 : -1.1e-24);
if (res == res + cor) if (res == res + cor)
return res; return res;
(x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w); a = fabs (x);
if (w[1] > 0) da = (x > 0) ? dx : -dx;
cor = 1.000000001 * w[1] + 1.1e-24; __dubsin (a, da, w);
else cor = 1.000000001 * w[1] + ((w[1] > 0) ? 1.1e-24 : -1.1e-24);
cor = 1.000000001 * w[1] - 1.1e-24;
if (w[0] == w[0] + cor) if (w[0] == w[0] + cor)
return (x > 0) ? w[0] : -w[0]; return (x > 0) ? w[0] : -w[0];
@ -942,10 +885,7 @@ bsloww1 (double x, double dx, double orig, int n)
__dubsin (fabs (x), dx, w); __dubsin (fabs (x), dx, w);
if (w[1] > 0) cor = 1.000000005 * w[1] + ((w[1] > 0) ? 1.1e-24 : -1.1e-24);
cor = 1.000000005 * w[1] + 1.1e-24;
else
cor = 1.000000005 * w[1] - 1.1e-24;
if (w[0] == w[0] + cor) if (w[0] == w[0] + cor)
return (x > 0) ? w[0] : -w[0]; return (x > 0) ? w[0] : -w[0];
@ -977,10 +917,7 @@ bsloww2 (double x, double dx, double orig, int n)
__docos (fabs (x), dx, w); __docos (fabs (x), dx, w);
if (w[1] > 0) cor = 1.000000005 * w[1] + ((w[1] > 0) ? 1.1e-24 : -1.1e-24);
cor = 1.000000005 * w[1] + 1.1e-24;
else
cor = 1.000000005 * w[1] - 1.1e-24;
if (w[0] == w[0] + cor) if (w[0] == w[0] + cor)
return (n & 2) ? -w[0] : w[0]; return (n & 2) ? -w[0] : w[0];