Commit Message
From 60e12f38145e4699cf231f7815cf1894d5e2d68d Mon Sep 17 00:00:00 2001
From: "Paul A. Clarke" <pc@us.ibm.com>
Date: Tue, 5 Dec 2017 09:32:56 -0600
Subject: [PATCH] New generic cosf
The same logic used in s_cosf.S version for x86 and powerpc
is used to create a generic s_cosf.c, so there is no performance
improvement in x86_64 and powerpc64.
-- 8< --
For s390, this is the improvement noted.
With patch:
"cosf": {
"": {
"duration": 1.00479e+10,
"iterations": 1.53856e+08,
"max": 900.645,
"min": 4.264,
"mean": 65.3074
}
}
Without patch:
"cosf": {
"": {
"duration": 9.93841e+09,
"iterations": 4.63972e+08,
"max": 1010.9,
"min": 6.593,
"mean": 21.4203
}
}
Tested on s390x, x86_64 and powerpc64le and powerpc32.
I include below a diff with recent generic s_sinf.c, as it is more
instructive than a diff with existing s_cosf.c. There are a fair number
of cosmetic changes, a few hard differences because it's a different
computation, and adoption of changes from recent patches deemed acceptable.
--
1c1
< /* Compute sine of argument.
---
> /* Compute cosine of argument.
24,25c24,25
< #ifndef SINF
< # define SINF_FUNC __sinf
---
> #ifndef COSF
> # define COSF_FUNC __cosf
27c27
< # define SINF_FUNC SINF
---
> # define COSF_FUNC COSF
44,46c44,46
< /* Chebyshev constants for sin, range 2^-27 - 2^-5. */
< static const double SS0 = -0x1.555555543d49dp-3;
< static const double SS1 = 0x1.110f475cec8c5p-7;
---
> /* Chebyshev constants for cos, range 2^-27 - 2^-5. */
> static const double CC0 = -0x1.fffffff5cc6fdp-2;
> static const double CC1 = 0x1.55514b178dac5p-5;
52d51
< static const double SMALL = 0x1p-50; /* 2^-50. */
78c77
< static const int ones[] = { +1, -1 };
---
> static const double ones[] = { +1, -1 };
80c79
< /* Compute the sine value using Chebyshev polynomials where
---
> /* Compute the cosine value using Chebyshev polynomials where
85,86c84
< SIGNBIT is used to add the correct sign after the Chebyshev
< polynomial is computed. */
---
> the sign of the result. */
88,89c86
< reduced (const double theta, const unsigned long int n,
< const unsigned long int signbit)
---
> reduced (double theta, unsigned int n)
91c88
< double sx;
---
> double sign, cx;
93,95c90
< /* We are operating on |x|, so we need to add back the original
< signbit for sinf. */
< int sign;
---
>
97c92,94
< sign = ones[((n >> 2) & 1) ^ signbit];
---
> n += 2;
> sign = ones[(n >> 2) & 1];
>
101c98
< /* Here sinf() is calculated using sin Chebyshev polynomial:
---
> /* Here cosf() is calculated using sin Chebyshev polynomial:
103,107c100,104
< sx = S3 + theta2 * S4; /* S3+x^2*S4. */
< sx = S2 + theta2 * sx; /* S2+x^2*(S3+x^2*S4). */
< sx = S1 + theta2 * sx; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */
< sx = S0 + theta2 * sx; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */
< sx = theta + theta * theta2 * sx;
---
> cx = S3 + theta2 * S4;
> cx = S2 + theta2 * cx;
> cx = S1 + theta2 * cx;
> cx = S0 + theta2 * cx;
> cx = theta + theta * theta2 * cx;
111c108
< /* Here sinf() is calculated using cos Chebyshev polynomial:
---
> /* Here cosf() is calculated using cos Chebyshev polynomial:
113,117c110,114
< sx = C3 + theta2 * C4; /* C3+x^2*C4. */
< sx = C2 + theta2 * sx; /* C2+x^2*(C3+x^2*C4). */
< sx = C1 + theta2 * sx; /* C1+x^2*(C2+x^2*(C3+x^2*C4)). */
< sx = C0 + theta2 * sx; /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))). */
< sx = 1.0 + theta2 * sx;
---
> cx = C3 + theta2 * C4;
> cx = C2 + theta2 * cx;
> cx = C1 + theta2 * cx;
> cx = C0 + theta2 * cx;
> cx = 1. + theta2 * cx;
119,121c116
<
< /* Add in the signbit and assign the result. */
< return sign * sx;
---
> return sign * cx;
125c120
< SINF_FUNC (float x)
---
> COSF_FUNC (float x)
127d121
< double cx;
130,131c124
< /* If |x|< Pi/4. */
< if (abstheta < M_PI_4)
---
> if (isless (abstheta, M_PI_4))
133c126,127
< if (abstheta >= 0x1p-5) /* |x| >= 2^-5. */
---
> double cx;
> if (abstheta >= 0x1p-5)
136,142c130,136
< /* Chebyshev polynomial of the form for sin
< x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
< cx = S3 + theta2 * S4;
< cx = S2 + theta2 * cx;
< cx = S1 + theta2 * cx;
< cx = S0 + theta2 * cx;
< cx = theta + theta * theta2 * cx;
---
> /* Chebyshev polynomial of the form for cos:
> * 1 + x^2 (C0 + x^2 (C1 + x^2 (C2 + x^2 (C3 + x^2 * C4)))). */
> cx = C3 + theta2 * C4;
> cx = C2 + theta2 * cx;
> cx = C1 + theta2 * cx;
> cx = C0 + theta2 * cx;
> cx = 1. + theta2 * cx;
145c139
< else if (abstheta >= 0x1p-27) /* |x| >= 2^-27. */
---
> else if (abstheta >= 0x1p-27)
148c142
< for sin: x+x^3*(SS0+x^2*SS1). */
---
> * 1 + x^2 (CC0 + x^3 * CC1). */
150,151c144,145
< cx = SS0 + theta2 * SS1;
< cx = theta + theta * theta2 * cx;
---
> cx = CC0 + theta * theta2 * CC1;
> cx = 1.0 + theta2 * cx;
156,160c150,151
< /* Handle some special cases. */
< if (theta)
< return theta - (theta * SMALL);
< else
< return theta;
---
> /* For small enough |theta|, this is close enough. */
> return 1.0 - abstheta;
163c154
< else /* |x| >= Pi/4. */
---
> else /* |theta| >= Pi/4. */
165,166c156
< unsigned long int signbit = (x < 0);
< if (abstheta < 9 * M_PI_4) /* |x| < 9*Pi/4. */
---
> if (isless (abstheta, 9 * M_PI_4))
172c162
< unsigned long int n = (abstheta * inv_PI_4) + 1;
---
> unsigned int n = (abstheta * inv_PI_4) + 1;
174c164
< return reduced (theta, n, signbit);
---
> return reduced (theta, n);
178c168
< if (abstheta < 0x1p+23) /* |x| < 2^23. */
---
> if (abstheta < 0x1p+23)
180,181c170,171
< unsigned long int n = __floor (abstheta * inv_PI_4) + 1.0;
< double x = __floor (n / 2.0);
---
> unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1.0;
> double x = n / 2.0;
184c174
< return reduced (theta, n, signbit);
---
> return reduced (theta, n);
186c176
< else /* |x| >= 2^23. */
---
> else /* |theta| >= 2^23. */
191,192c181,182
< exponent
< = (exponent >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
---
> exponent = (exponent >> FLOAT_EXPONENT_SHIFT)
> - FLOAT_EXPONENT_BIAS;
212c202
< return reduced (e, l + 1, signbit);
---
> return reduced (e, l + 1);
222c212
< return reduced (e, l + 1, signbit);
---
> return reduced (e, l + 1);
229c219
< return reduced (e, l + 1, signbit);
---
> return reduced (e, l + 1);
237d226
< /* High word of x. */
239,240c228,229
< /* Sin(Inf or NaN) is NaN. */
< if (ix == 0x7f800000)
---
> /* cos(Inf or NaN) is NaN. */
> if (ix == 0x7f800000) /* Inf. */
247,248c236,237
< #ifndef SINF
< libm_alias_float (__sin, sin)
---
> #ifndef COSF
> libm_alias_float (__cos, cos)
-- 8< --
2017-12-05 Paul A. Clarke <pc@us.ibm.com>
* sysdeps/ieee754/flt-32/s_cosf.c: New implementation.
---
sysdeps/ieee754/flt-32/s_cosf.c | 254 +++++++++++++++++++++++++++++++++-------
1 file changed, 214 insertions(+), 40 deletions(-)
Comments
On Tue, Dec 5, 2017 at 12:45 PM, Paul Clarke <pc@us.ibm.com> wrote:
> From 60e12f38145e4699cf231f7815cf1894d5e2d68d Mon Sep 17 00:00:00 2001
> From: "Paul A. Clarke" <pc@us.ibm.com>
> Date: Tue, 5 Dec 2017 09:32:56 -0600
> Subject: [PATCH] New generic cosf
>
> The same logic used in s_cosf.S version for x86 and powerpc
> is used to create a generic s_cosf.c, so there is no performance
> improvement in x86_64 and powerpc64.
>
> -- 8< --
> For s390, this is the improvement noted.
>
> With patch:
> "cosf": {
> "": {
> "duration": 1.00479e+10,
> "iterations": 1.53856e+08,
> "max": 900.645,
> "min": 4.264,
> "mean": 65.3074
> }
> }
> Without patch:
> "cosf": {
> "": {
> "duration": 9.93841e+09,
> "iterations": 4.63972e+08,
> "max": 1010.9,
> "min": 6.593,
> "mean": 21.4203
> }
> }
>
> Tested on s390x, x86_64 and powerpc64le and powerpc32.
>
> I include below a diff with recent generic s_sinf.c, as it is more
> instructive than a diff with existing s_cosf.c. There are a fair number
> of cosmetic changes, a few hard differences because it's a different
> computation, and adoption of changes from recent patches deemed acceptable.
1. Please use the current s_sinf.c.
2. Please use "diff -up".
On Tue, 5 Dec 2017, Paul Clarke wrote:
> + unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1.0;
> + double x = n / 2.0;
I'd expect adding integer 1 and dividing by integer 2, as in the current
sinf version, unless there's some reason that's incorrect in this case.
On Tue, Dec 5, 2017 at 12:45 PM, Paul Clarke <pc@us.ibm.com> wrote:
> From 60e12f38145e4699cf231f7815cf1894d5e2d68d Mon Sep 17 00:00:00 2001
> From: "Paul A. Clarke" <pc@us.ibm.com>
> Date: Tue, 5 Dec 2017 09:32:56 -0600
> Subject: [PATCH] New generic cosf
>
> The same logic used in s_cosf.S version for x86 and powerpc
> is used to create a generic s_cosf.c, so there is no performance
> improvement in x86_64 and powerpc64.
>
> -- 8< --
> For s390, this is the improvement noted.
>
> With patch:
> "cosf": {
> "": {
> "duration": 1.00479e+10,
> "iterations": 1.53856e+08,
> "max": 900.645,
> "min": 4.264,
> "mean": 65.3074
> }
> }
> Without patch:
> "cosf": {
> "": {
> "duration": 9.93841e+09,
> "iterations": 4.63972e+08,
> "max": 1010.9,
> "min": 6.593,
> "mean": 21.4203
> }
> }
Did I misunderstand, or did the mean time increase with the patch?
On 12/05/2017 07:11 PM, Matt Turner wrote:
> On Tue, Dec 5, 2017 at 12:45 PM, Paul Clarke <pc@us.ibm.com> wrote:
>> The same logic used in s_cosf.S version for x86 and powerpc
>> is used to create a generic s_cosf.c, so there is no performance
>> improvement in x86_64 and powerpc64.
>>
>> -- 8< --
>> For s390, this is the improvement noted.
>>
>> With patch:
>> "cosf": {
>> "": {
>> "duration": 1.00479e+10,
>> "iterations": 1.53856e+08,
>> "max": 900.645,
>> "min": 4.264,
>> "mean": 65.3074
>> }
>> }
>> Without patch:
>> "cosf": {
>> "": {
>> "duration": 9.93841e+09,
>> "iterations": 4.63972e+08,
>> "max": 1010.9,
>> "min": 6.593,
>> "mean": 21.4203
>> }
>> }
>
> Did I misunderstand, or did the mean time increase with the patch?
Sigh. It's not you. I was trying to mimic Raji's patch, but confused her "with/without" with what I'd normally use "before/after". I'll rectify in V2.
PC
@@ -1,21 +1,20 @@
-/* s_cosf.c -- float version of s_cos.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: s_cosf.c,v 1.4 1995/05/10 20:47:03 jtc Exp $";
-#endif
+/* Compute cosine of argument.
+ Copyright (C) 2017 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
#include <errno.h>
#include <math.h>
@@ -28,35 +27,210 @@ static char rcsid[] = "$NetBSD: s_cosf.c,v 1.4 1995/05/10 20:47:03 jtc Exp $";
# define COSF_FUNC COSF
#endif
-float COSF_FUNC(float x)
+/* Chebyshev constants for cos, range -PI/4 - PI/4. */
+static const double C0 = -0x1.ffffffffe98aep-2;
+static const double C1 = 0x1.55555545c50c7p-5;
+static const double C2 = -0x1.6c16b348b6874p-10;
+static const double C3 = 0x1.a00eb9ac43ccp-16;
+static const double C4 = -0x1.23c97dd8844d7p-22;
+
+/* Chebyshev constants for sin, range -PI/4 - PI/4. */
+static const double S0 = -0x1.5555555551cd9p-3;
+static const double S1 = 0x1.1111110c2688bp-7;
+static const double S2 = -0x1.a019f8b4bd1f9p-13;
+static const double S3 = 0x1.71d7264e6b5b4p-19;
+static const double S4 = -0x1.a947e1674b58ap-26;
+
+/* Chebyshev constants for cos, range 2^-27 - 2^-5. */
+static const double CC0 = -0x1.fffffff5cc6fdp-2;
+static const double CC1 = 0x1.55514b178dac5p-5;
+
+/* 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 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, -1 };
+
+/* Compute the cosine value 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
+ the sign of the result. */
+static inline float
+reduced (double theta, unsigned int n)
{
- float y[2],z=0.0;
- int32_t n,ix;
+ double sign, cx;
+ const double theta2 = theta * theta;
- GET_FLOAT_WORD(ix,x);
+ /* Determine positive or negative primary interval. */
+ n += 2;
+ sign = ones[(n >> 2) & 1];
- /* |x| ~< pi/4 */
- ix &= 0x7fffffff;
- if(ix <= 0x3f490fd8) return __kernel_cosf(x,z);
+ /* Are we in the primary interval of sin or cos? */
+ if ((n & 2) == 0)
+ {
+ /* Here cosf() is calculated using sin Chebyshev polynomial:
+ x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
+ cx = S3 + theta2 * S4;
+ cx = S2 + theta2 * cx;
+ cx = S1 + theta2 * cx;
+ cx = S0 + theta2 * cx;
+ cx = theta + theta * theta2 * cx;
+ }
+ else
+ {
+ /* Here cosf() is calculated using cos Chebyshev polynomial:
+ 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
+ cx = C3 + theta2 * C4;
+ cx = C2 + theta2 * cx;
+ cx = C1 + theta2 * cx;
+ cx = C0 + theta2 * cx;
+ cx = 1. + theta2 * cx;
+ }
+ return sign * cx;
+}
- /* cos(Inf or NaN) is NaN */
- else if (ix>=0x7f800000) {
- if (ix == 0x7f800000)
- __set_errno (EDOM);
- return x-x;
+float
+COSF_FUNC (float x)
+{
+ double theta = x;
+ double abstheta = fabs (theta);
+ if (isless (abstheta, M_PI_4))
+ {
+ double cx;
+ if (abstheta >= 0x1p-5)
+ {
+ const double theta2 = theta * theta;
+ /* Chebyshev polynomial of the form for cos:
+ * 1 + x^2 (C0 + x^2 (C1 + x^2 (C2 + x^2 (C3 + x^2 * C4)))). */
+ cx = C3 + theta2 * C4;
+ cx = C2 + theta2 * cx;
+ cx = C1 + theta2 * cx;
+ cx = C0 + theta2 * cx;
+ cx = 1. + theta2 * cx;
+ return cx;
}
-
- /* argument reduction needed */
- else {
- n = __ieee754_rem_pio2f(x,y);
- switch(n&3) {
- case 0: return __kernel_cosf(y[0],y[1]);
- case 1: return -__kernel_sinf(y[0],y[1],1);
- case 2: return -__kernel_cosf(y[0],y[1]);
- default:
- return __kernel_sinf(y[0],y[1],1);
+ else if (abstheta >= 0x1p-27)
+ {
+ /* A simpler Chebyshev approximation is close enough for this range:
+ * 1 + x^2 (CC0 + x^3 * CC1). */
+ const double theta2 = theta * theta;
+ cx = CC0 + theta * theta2 * CC1;
+ cx = 1.0 + theta2 * cx;
+ return cx;
+ }
+ else
+ {
+ /* For small enough |theta|, this is close enough. */
+ return 1.0 - abstheta;
+ }
+ }
+ else /* |theta| >= Pi/4. */
+ {
+ if (isless (abstheta, 9 * M_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];
+ return reduced (theta, n);
+ }
+ else if (isless (abstheta, INFINITY))
+ {
+ if (abstheta < 0x1p+23)
+ {
+ unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1.0;
+ double x = n / 2.0;
+ theta = x * PI_2_lo + (x * PI_2_hi + abstheta);
+ /* Argument reduction needed. */
+ return reduced (theta, n);
+ }
+ else /* |theta| >= 2^23. */
+ {
+ x = fabsf (x);
+ int exponent;
+ GET_FLOAT_WORD (exponent, x);
+ exponent = (exponent >> 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;
+ return reduced (e, l + 1);
+ }
+ else
+ {
+ e += b;
+ e += c;
+ e += d;
+ if (e <= 1.0)
+ {
+ e *= M_PI_4;
+ return reduced (e, l + 1);
+ }
+ else
+ {
+ l++;
+ e -= 2.0;
+ e *= M_PI_4;
+ return reduced (e, l + 1);
+ }
+ }
}
}
+ else
+ {
+ int32_t ix;
+ GET_FLOAT_WORD (ix, abstheta);
+ /* cos(Inf or NaN) is NaN. */
+ if (ix == 0x7f800000) /* Inf. */
+ __set_errno (EDOM);
+ return x - x;
+ }
+ }
}
#ifndef COSF