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[PATCH 2/7] sin/cos slow paths: remove large range reduction

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This patch removes the large range reduction code and defers to the huge range
reduction code.  The first level range reducer supports inputs up to 2^27,
which is way too large given that inputs for sin/cos are typically small
(< 10), and optimizing for a smaller range would give a significant speedup.

Input values above 2^27 are practically never used, so there is no reason for
supporting range reduction between 2^27 and 2^48.  Removing it significantly
simplifies code and enables further speedups.  There is about a 2.3x slowdown
in this range due to __branred being extremely slow  (a better algorithm could
easily more than double performance).

	* sysdeps/ieee754/dbl-64/s_sin.c (reduce_sincos_2): Remove function.
	(do_sincos_2): Likewise.
	(__sin): Remove middle range reduction case.
	(__cos): Likewise.
	* sysdeps/ieee754/dbl-64/s_sincos.c (__sincos): Remove middle range
	reduction case.
This commit is contained in:
Wilco Dijkstra 2018-04-03 16:28:03 +01:00
parent 19a8b9a300
commit 7a5640f23a
3 changed files with 11 additions and 103 deletions
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9
ChangeLog
View File

@ -1,3 +1,12 @@
2018-04-03 Wilco Dijkstra <wdijkstr@arm.com>
* sysdeps/ieee754/dbl-64/s_sin.c (reduce_sincos_2): Remove function.
(do_sincos_2): Likewise.
(__sin): Remove middle range reduction case.
(__cos): Likewise.
* sysdeps/ieee754/dbl-64/s_sincos.c (__sincos): Remove middle range
reduction case.
2018-04-03 Wilco Dijkstra <wdijkstr@arm.com>
* sysdeps/aarch64/libm-test-ulps: Update ULP for sin, cos, sincos.

95
sysdeps/ieee754/dbl-64/s_sin.c
View File

@ -362,80 +362,6 @@ do_sincos_1 (double a, double da, double x, int4 n, bool shift_quadrant)
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) */
@ -498,16 +424,7 @@ __sin (double x)
retval = do_sincos_1 (a, da, x, n, false);
} /* else if (k < 0x419921FB ) */
/*---------------------105414350 <|x|< 281474976710656 --------------------*/
else if (k < 0x42F00000)
{
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----------------------------*/
/* --------------------105414350 <|x| <2^1024------------------------------*/
else if (k < 0x7ff00000)
retval = reduce_and_compute (x, false);
@ -584,15 +501,7 @@ __cos (double x)
retval = do_sincos_1 (a, da, x, n, true);
} /* else if (k < 0x419921FB ) */
else if (k < 0x42F00000)
{
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 */
/* 105414350 <|x| <2^1024 */
else if (k < 0x7ff00000)
retval = reduce_and_compute (x, true);

10
sysdeps/ieee754/dbl-64/s_sincos.c
View File

@ -84,16 +84,6 @@ __sincos (double x, double *sinx, double *cosx)
*sinx = do_sincos_1 (a, da, x, n, false);
*cosx = do_sincos_1 (a, da, x, n, true);
return;
}
if (k < 0x42F00000)
{
double a, da;
int4 n = reduce_sincos_2 (x, &a, &da);
*sinx = do_sincos_2 (a, da, x, n, false);
*cosx = do_sincos_2 (a, da, x, n, true);
return;
}
if (k < 0x7ff00000)