From 1678be70260358c5919e90bfa2aef497ac227925 Mon Sep 17 00:00:00 2001
From: "H.J. Lu" <hjl.tools@gmail.com>
Date: Mon, 22 Oct 2018 16:09:57 -0700
Subject: [PATCH] Use generic vector computations in s_sincosf.h
Use generic vector computations in s_sincosf.h to support vectorized
s_sincosf. Update __sincosf_table for vectorized s_sincosf. On
Broadwell, bench-sincosf shows:
Before After Improvement
max 160.273 114.198 40%
min 6.25 5.625 11%
mean 13.0325 10.6462 22%
Vectorized sincosf_poly shows
Before After Improvement
max 138.653 114.198 21%
min 5.004 5.625 -11%
mean 11.5934 10.6462 9%
Tested on x86-64 and i686 as well as with build-many-glibcs.py.
* sysdeps/ieee754/flt-32/s_sincosf.h (v2df_t): New.
Include <v2df_to_sf.h>.
(sincos_t): Use v2df_t for generic vector computations.
(sincosf_poly): Use generic vector computations.
(sinf_poly): Updated for generic vector computations.
* sysdeps/ieee754/flt-32/s_sincosf_data.c (__sincosf_table):
Rearranged for generic vector computations.
* sysdeps/ieee754/flt-32/v2df_to_sf.h: New file.
* sysdeps/x86/fpu/v2df_to_sf.h: Likewise.
* sysdeps/powerpc/Makefile (CFLAGS-s_sincosf.c): New.
* sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c: Just include
<sysdeps/ieee754/flt-32/s_sincosf.c>.
---
sysdeps/ieee754/flt-32/s_sincosf.h | 51 ++--
sysdeps/ieee754/flt-32/s_sincosf_data.c | 18 +-
sysdeps/ieee754/flt-32/v2df_to_sf.h | 24 ++
sysdeps/powerpc/Makefile | 4 +
sysdeps/x86/fpu/v2df_to_sf.h | 31 +++
sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c | 271 +------------------
6 files changed, 95 insertions(+), 304 deletions(-)
create mode 100644 sysdeps/ieee754/flt-32/v2df_to_sf.h
create mode 100644 sysdeps/x86/fpu/v2df_to_sf.h
@@ -20,6 +20,10 @@
#include <math.h>
#include "math_config.h"
+typedef double v2df_t __attribute__ ((vector_size (2 * sizeof (double))));
+
+#include <v2df_to_sf.h>
+
/* 2PI * 2^-64. */
static const double pi63 = 0x1.921FB54442D18p-62;
/* PI / 4. */
@@ -31,8 +35,10 @@ typedef struct
double sign[4]; /* Sign of sine in quadrants 0..3. */
double hpi_inv; /* 2 / PI ( * 2^24 if !TOINT_INTRINSICS). */
double hpi; /* PI / 2. */
- double c0, c1, c2, c3, c4; /* Cosine polynomial. */
- double s1, s2, s3; /* Sine polynomial. */
+ /* Cosine polynomial: c0, c1, c2, c3, c4.
+ Sine polynomial: s1, s2, s3. */
+ double c0, c1;
+ v2df_t s1c2, s2c3, s3c4;
} sincos_t;
/* Polynomial data (the cosine polynomial is negated in the 2nd entry). */
@@ -55,27 +61,28 @@ static inline void
sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp,
float *cosp)
{
- double x3, x4, x5, x6, s, c, c1, c2, s1;
+ v2df_t vx2x2 = { x2, x2 };
+ v2df_t vxx2 = { x, x2 };
+ v2df_t vx3x4, vs1c2;
- x4 = x2 * x2;
- x3 = x2 * x;
- c2 = p->c3 + x2 * p->c4;
- s1 = p->s2 + x2 * p->s3;
+ vx3x4 = vx2x2 * vxx2;
+ vs1c2 = p->s2c3 + vx2x2 * p->s3c4;
/* Swap sin/cos result based on quadrant. */
- float *tmp = (n & 1 ? cosp : sinp);
- cosp = (n & 1 ? sinp : cosp);
- sinp = tmp;
-
- c1 = p->c0 + x2 * p->c1;
- x5 = x3 * x2;
- x6 = x4 * x2;
+ if (n & 1)
+ {
+ float *tmp = cosp;
+ cosp = sinp;
+ sinp = tmp;
+ }
- s = x + x3 * p->s1;
- c = c1 + x4 * p->c2;
+ double c1 = p->c0 + x2 * p->c1;
+ v2df_t vxc1 = { x, c1 };
+ v2df_t vx5x6 = vx3x4 * vx2x2;
- *sinp = s + x5 * s1;
- *cosp = c + x6 * c2;
+ v2df_t vsincos = vxc1 + vx3x4 * p->s1c2;
+ vsincos = vsincos + vx5x6 * vs1c2;
+ v2df_to_sf (vsincos, sinp, cosp);
}
/* Return the sine of inputs X and X2 (X squared) using the polynomial P.
@@ -88,21 +95,21 @@ sinf_poly (double x, double x2, const sincos_t *p, int n)
if ((n & 1) == 0)
{
x3 = x * x2;
- s1 = p->s2 + x2 * p->s3;
+ s1 = p->s2c3[0] + x2 * p->s3c4[0];
x7 = x3 * x2;
- s = x + x3 * p->s1;
+ s = x + x3 * p->s1c2[0];
return s + x7 * s1;
}
else
{
x4 = x2 * x2;
- c2 = p->c3 + x2 * p->c4;
+ c2 = p->s2c3[1] + x2 * p->s3c4[1];
c1 = p->c0 + x2 * p->c1;
x6 = x4 * x2;
- c = c1 + x4 * p->c2;
+ c = c1 + x4 * p->s1c2[1];
return c + x6 * c2;
}
@@ -35,12 +35,9 @@ const sincos_t __sincosf_table[2] =
0x1.921FB54442D18p0,
0x1p0,
-0x1.ffffffd0c621cp-2,
- 0x1.55553e1068f19p-5,
- -0x1.6c087e89a359dp-10,
- 0x1.99343027bf8c3p-16,
- -0x1.555545995a603p-3,
- 0x1.1107605230bc4p-7,
- -0x1.994eb3774cf24p-13
+ { -0x1.555545995a603p-3, 0x1.55553e1068f19p-5 },
+ { 0x1.1107605230bc4p-7, -0x1.6c087e89a359dp-10 },
+ { -0x1.994eb3774cf24p-13, 0x1.99343027bf8c3p-16 }
},
{
{ 1.0, -1.0, -1.0, 1.0 },
@@ -52,12 +49,9 @@ const sincos_t __sincosf_table[2] =
0x1.921FB54442D18p0,
-0x1p0,
0x1.ffffffd0c621cp-2,
- -0x1.55553e1068f19p-5,
- 0x1.6c087e89a359dp-10,
- -0x1.99343027bf8c3p-16,
- -0x1.555545995a603p-3,
- 0x1.1107605230bc4p-7,
- -0x1.994eb3774cf24p-13
+ { -0x1.555545995a603p-3, -0x1.55553e1068f19p-5 },
+ { 0x1.1107605230bc4p-7, 0x1.6c087e89a359dp-10 },
+ { -0x1.994eb3774cf24p-13, -0x1.99343027bf8c3p-16 }
}
};
new file mode 100644
@@ -0,0 +1,24 @@
+/* Convert V2DF to SF. Generic version.
+ Copyright (C) 2018 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+static inline void
+v2df_to_sf (v2df_t v2df, float *f0p, float *f1p)
+{
+ *f0p = (float) v2df[0];
+ *f1p = (float) v2df[1];
+}
@@ -50,3 +50,7 @@ endif
ifneq (,$(filter %le,$(config-machine)))
abilist-pattern = %-le.abilist
endif
+
+ifeq ($(subdir),math)
+CFLAGS-s_sincosf.c += -Wno-psabi
+endif
new file mode 100644
@@ -0,0 +1,31 @@
+/* Convert V2DF to SF. x86 version.
+ Copyright (C) 2018 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#ifdef __SSE2_MATH__
+typedef float v4sf_t __attribute__ ((vector_size (4 * sizeof (float))));
+
+static inline void
+v2df_to_sf (v2df_t v2df, float *f0p, float *f1p)
+{
+ v4sf_t v4sf = __builtin_ia32_cvtpd2ps (v2df);
+ *f0p = v4sf[0];
+ *f1p = v4sf[1];
+}
+#else
+# include <sysdeps/ieee754/flt-32/v2df_to_sf.h>
+#endif
@@ -1,271 +1,2 @@
-/* Compute sine and cosine of argument optimized with vector.
- Copyright (C) 2017 Free Software Foundation, Inc.
- This file is part of the GNU C Library.
-
- The GNU C Library is free software; you can redistribute it and/or
- modify it under the terms of the GNU Lesser General Public
- License as published by the Free Software Foundation; either
- version 2.1 of the License, or (at your option) any later version.
-
- The GNU C Library is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- Lesser General Public License for more details.
-
- You should have received a copy of the GNU Lesser General Public
- License along with the GNU C Library; if not, see
- <http://www.gnu.org/licenses/>. */
-
-#include <errno.h>
-#include <math.h>
-#include <math_private.h>
-#include <x86intrin.h>
-#include <libm-alias-float.h>
-
#define SINCOSF __sincosf_fma
-
-#ifndef SINCOSF
-# define SINCOSF_FUNC __sincosf
-#else
-# define SINCOSF_FUNC SINCOSF
-#endif
-
-/* PI/2 with 98 bits of accuracy. */
-static const double PI_2_hi = 0x1.921fb544p+0;
-static const double PI_2_lo = 0x1.0b4611a626332p-34;
-
-static const double SMALL = 0x1p-50; /* 2^-50. */
-static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */
-
-#define FLOAT_EXPONENT_SHIFT 23
-#define FLOAT_EXPONENT_BIAS 127
-
-static const double pio2_table[] = {
- 0 * M_PI_2,
- 1 * M_PI_2,
- 2 * M_PI_2,
- 3 * M_PI_2,
- 4 * M_PI_2,
- 5 * M_PI_2
-};
-
-static const double invpio4_table[] = {
- 0x0p+0,
- 0x1.45f306cp+0,
- 0x1.c9c882ap-28,
- 0x1.4fe13a8p-58,
- 0x1.f47d4dp-85,
- 0x1.bb81b6cp-112,
- 0x1.4acc9ep-142,
- 0x1.0e4107cp-169
-};
-
-static const double ones[] = { 1.0, -1.0 };
-
-/* Chebyshev constants for sin and cos, range -PI/4 - PI/4. */
-static const __v2df V0 = { -0x1.5555555551cd9p-3, -0x1.ffffffffe98aep-2};
-static const __v2df V1 = { 0x1.1111110c2688bp-7, 0x1.55555545c50c7p-5 };
-static const __v2df V2 = { -0x1.a019f8b4bd1f9p-13, -0x1.6c16b348b6874p-10 };
-static const __v2df V3 = { 0x1.71d7264e6b5b4p-19, 0x1.a00eb9ac43ccp-16 };
-static const __v2df V4 = { -0x1.a947e1674b58ap-26, -0x1.23c97dd8844d7p-22 };
-
-/* Chebyshev constants for sin and cos, range 2^-27 - 2^-5. */
-static const __v2df VC0 = { -0x1.555555543d49dp-3, -0x1.fffffff5cc6fdp-2 };
-static const __v2df VC1 = { 0x1.110f475cec8c5p-7, 0x1.55514b178dac5p-5 };
-
-static const __v2df v2ones = { 1.0, 1.0 };
-
-/* Compute the sine and cosine values using Chebyshev polynomials where
- THETA is the range reduced absolute value of the input
- and it is less than Pi/4,
- N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
- whether a sine or cosine approximation is more accurate and
- SIGNBIT is used to add the correct sign after the Chebyshev
- polynomial is computed. */
-static void
-reduced_sincos (const double theta, const unsigned int n,
- const unsigned int signbit, float *sinx, float *cosx)
-{
- __v2df v2x, v2sx, v2cx;
- const __v2df v2theta = { theta, theta };
- const __v2df v2theta2 = v2theta * v2theta;
- /* Here sinf() and cosf() are calculated using sin Chebyshev polynomial:
- x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
- v2x = V3 + v2theta2 * V4; /* S3+x^2*S4. */
- v2x = V2 + v2theta2 * v2x; /* S2+x^2*(S3+x^2*S4). */
- v2x = V1 + v2theta2 * v2x; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */
- v2x = V0 + v2theta2 * v2x; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */
- v2x = v2theta2 * v2x;
- v2cx = v2ones + v2x;
- v2sx = v2theta + v2theta * v2x;
- /* We are operating on |x|, so we need to add back the original
- signbit for sinf. */
- /* Determine positive or negative primary interval. */
- /* Are we in the primary interval of sin or cos? */
- if ((n & 2) == 0)
- {
- const __v2df v2sign =
- {
- ones[((n >> 2) & 1) ^ signbit],
- ones[((n + 2) >> 2) & 1]
- };
- v2cx[0] = v2sx[0];
- v2cx *= v2sign;
- __v4sf v4sx = _mm_cvtpd_ps (v2cx);
- *sinx = v4sx[0];
- *cosx = v4sx[1];
- }
- else
- {
- const __v2df v2sign =
- {
- ones[((n + 2) >> 2) & 1],
- ones[((n >> 2) & 1) ^ signbit]
- };
- v2cx[0] = v2sx[0];
- v2cx *= v2sign;
- __v4sf v4sx = _mm_cvtpd_ps (v2cx);
- *sinx = v4sx[1];
- *cosx = v4sx[0];
- }
-}
-
-void
-SINCOSF_FUNC (float x, float *sinx, float *cosx)
-{
- double theta = x;
- double abstheta = fabs (theta);
- uint32_t ix, xi;
- GET_FLOAT_WORD (xi, x);
- /* |x| */
- ix = xi & 0x7fffffff;
- /* If |x|< Pi/4. */
- if (ix < 0x3f490fdb)
- {
- if (ix >= 0x3d000000) /* |x| >= 2^-5. */
- {
- __v2df v2x, v2sx, v2cx;
- const __v2df v2theta = { theta, theta };
- const __v2df v2theta2 = v2theta * v2theta;
- /* Chebyshev polynomial of the form for sin and cos. */
- v2x = V3 + v2theta2 * V4;
- v2x = V2 + v2theta2 * v2x;
- v2x = V1 + v2theta2 * v2x;
- v2x = V0 + v2theta2 * v2x;
- v2x = v2theta2 * v2x;
- v2cx = v2ones + v2x;
- v2sx = v2theta + v2theta * v2x;
- v2cx[0] = v2sx[0];
- __v4sf v4sx = _mm_cvtpd_ps (v2cx);
- *sinx = v4sx[0];
- *cosx = v4sx[1];
- }
- else if (ix >= 0x32000000) /* |x| >= 2^-27. */
- {
- /* A simpler Chebyshev approximation is close enough for this range:
- for sin: x+x^3*(SS0+x^2*SS1)
- for cos: 1.0+x^2*(CC0+x^3*CC1). */
- __v2df v2x, v2sx, v2cx;
- const __v2df v2theta = { theta, theta };
- const __v2df v2theta2 = v2theta * v2theta;
- v2x = VC0 + v2theta * v2theta2 * VC1;
- v2x = v2theta2 * v2x;
- v2cx = v2ones + v2x;
- v2sx = v2theta + v2theta * v2x;
- v2cx[0] = v2sx[0];
- __v4sf v4sx = _mm_cvtpd_ps (v2cx);
- *sinx = v4sx[0];
- *cosx = v4sx[1];
- }
- else
- {
- /* Handle some special cases. */
- if (ix)
- *sinx = theta - (theta * SMALL);
- else
- *sinx = theta;
- *cosx = 1.0 - abstheta;
- }
- }
- else /* |x| >= Pi/4. */
- {
- unsigned int signbit = xi >> 31;
- if (ix < 0x40e231d6) /* |x| < 9*Pi/4. */
- {
- /* There are cases where FE_UPWARD rounding mode can
- produce a result of abstheta * inv_PI_4 == 9,
- where abstheta < 9pi/4, so the domain for
- pio2_table must go to 5 (9 / 2 + 1). */
- unsigned int n = (abstheta * inv_PI_4) + 1;
- theta = abstheta - pio2_table[n / 2];
- reduced_sincos (theta, n, signbit, sinx, cosx);
- }
- else if (ix < 0x7f800000)
- {
- if (ix < 0x4b000000) /* |x| < 2^23. */
- {
- unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
- double x = n / 2;
- theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
- /* Argument reduction needed. */
- reduced_sincos (theta, n, signbit, sinx, cosx);
- }
- else /* |x| >= 2^23. */
- {
- x = fabsf (x);
- int exponent
- = (ix >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
- exponent += 3;
- exponent /= 28;
- double a = invpio4_table[exponent] * x;
- double b = invpio4_table[exponent + 1] * x;
- double c = invpio4_table[exponent + 2] * x;
- double d = invpio4_table[exponent + 3] * x;
- uint64_t l = a;
- l &= ~0x7;
- a -= l;
- double e = a + b;
- l = e;
- e = a - l;
- if (l & 1)
- {
- e -= 1.0;
- e += b;
- e += c;
- e += d;
- e *= M_PI_4;
- reduced_sincos (e, l + 1, signbit, sinx, cosx);
- }
- else
- {
- e += b;
- e += c;
- e += d;
- if (e <= 1.0)
- {
- e *= M_PI_4;
- reduced_sincos (e, l + 1, signbit, sinx, cosx);
- }
- else
- {
- l++;
- e -= 2.0;
- e *= M_PI_4;
- reduced_sincos (e, l + 1, signbit, sinx, cosx);
- }
- }
- }
- }
- else
- {
- if (ix == 0x7f800000)
- __set_errno (EDOM);
- /* sin/cos(Inf or NaN) is NaN. */
- *sinx = *cosx = x - x;
- }
- }
-}
-
-#ifndef SINCOSF
-libm_alias_float (__sincos, sincos)
-#endif
+#include <sysdeps/ieee754/flt-32/s_sincosf.c>
--
2.19.2