[PATCHv3] New generic sinf
Commit Message
Changes since version 2:
- Added code comments.
- Added BZ in Changelog.
- Spacing correction.
- Added const to theta2 variable.
- Change in some constant representation.
---
Changes since version 1:
- Removed sccs id.
---
The same logic used in s_sinf.S version of x86 and powerpc
is moved as generic s_sinf.c, so there is no performance
improvement in x86_64 and powerpc64.
For s390, this is the improvement noted.
With patch:
benchtests/bench-sinf
"": {
"duration": 9.91026e+09,
"iterations": 4.6512e+08,
"max": 130.26,
"min": 7.027,
"mean": 21.3069
}
Without patch:
"": {
"duration": 1.00656e+10,
"iterations": 1.65699e+08,
"max": 1740.57,
"min": 4.729,
"mean": 60.7461
}
Also addressed comments from Joseph on generic sincosf version
Ref:https://sourceware.org/ml/libc-alpha/2017-10/msg00367.html
---
This implementation is based on optimized sinf assembly versions
of x86_64 and powerpc.
Tested on s390, x86_64 and powerpc64le.
2017-11-02 Rajalakshmi Srinivasaraghavan <raji@linux.vnet.ibm.com>
[BZ #5997]
* sysdeps/ieee754/flt-32/s_sinf.c: New implementation.
---
sysdeps/ieee754/flt-32/s_sinf.c | 262 +++++++++++++++++++++++++++++++++-------
1 file changed, 221 insertions(+), 41 deletions(-)
Comments
On 11/2/2017 4:50 PM, Rajalakshmi Srinivasaraghavan wrote:
> +static inline float
> +reduced (const double theta, const unsigned long n,
> + const unsigned long signbit)
> +{
> + double sx;
> + const double theta2 = theta * theta;
> + /* We are operating on|x|, so we need to add back the original
> + * signbit for sinf. */
> + int sign;
> + sign = ones[((n >> 2) & 1) ^ signbit];
> + theta2 = theta * theta;
Isn't the above a duplication?
> + /* Chebyshev polynomial of the form for sin:
> + * x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).
Isn't the following an expansion for cos?
> + * 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
On Thu, 2 Nov 2017, Rajalakshmi Srinivasaraghavan wrote:
> +/* reduced (theta, n, signbit):
> + * Compute sine (n * theta) using Chebyshev polynomials, where
> + * - -Pi/4 <= theta < Pi/4
> + * - n thus indicates the actual quadrant in which n*theta resides.
> + * n is used to decide whether a sine or cosine approximation is
> + * more accurate and the sign of the result. */
GNU standard does not have the leading '*' on each line of the comment,
and does not repeat the function name / prototype in the comment; the
values of arguments should be referred to in uppercase in the comment.
And this function certainly isn't computing sin (n * theta), there's no
multiplication by n involved. I think it might actually be something like
sin (((-1)**SIGNBIT) * (THETA + (N >> 1)*PI/2)), but the comment needs to
state this, or whatever the actual function calculated is, explicitly
(along with the constraint on the range for THETA).
@@ -1,21 +1,20 @@
-/* s_sinf.c -- float version of s_sin.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_sinf.c,v 1.4 1995/05/10 20:48:16 jtc Exp $";
-#endif
+/* Compute sine of argument.
+ Copyright (C) 2017 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
#include <errno.h>
#include <math.h>
@@ -28,35 +27,216 @@ static char rcsid[] = "$NetBSD: s_sinf.c,v 1.4 1995/05/10 20:48:16 jtc Exp $";
# define SINF_FUNC SINF
#endif
-float SINF_FUNC(float x)
-{
- float y[2],z=0.0;
- int32_t n, ix;
+/* 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;
- GET_FLOAT_WORD(ix,x);
+/* 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;
- /* |x| ~< pi/4 */
- ix &= 0x7fffffff;
- if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0);
+/* Chebyshev constants for sin, range 2^-27 - 2^-5. */
+static const double SS0 = -0x1.555555543d49dp-3;
+static const double SS1 = 0x1.110f475cec8c5p-7;
- /* sin(Inf or NaN) is NaN */
- else if (ix>=0x7f800000) {
- if (ix == 0x7f800000)
- __set_errno (EDOM);
- return x-x;
- }
+/* 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
+};
+
+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 int ones[] = { +1, -1 };
+
+/* reduced (theta, n, signbit):
+ * Compute sine (n * theta) using Chebyshev polynomials, where
+ * - -Pi/4 <= theta < Pi/4
+ * - n thus indicates the actual quadrant in which n*theta resides.
+ * n is used to decide whether a sine or cosine approximation is
+ * more accurate and the sign of the result. */
- /* argument reduction needed */
- else {
- n = __ieee754_rem_pio2f(x,y);
- switch(n&3) {
- case 0: return __kernel_sinf(y[0],y[1],1);
- case 1: return __kernel_cosf(y[0],y[1]);
- case 2: return -__kernel_sinf(y[0],y[1],1);
- default:
- return -__kernel_cosf(y[0],y[1]);
+static inline float
+reduced (const double theta, const unsigned long n,
+ const unsigned long signbit)
+{
+ double sx;
+ const double theta2 = theta * theta;
+ /* We are operating on |x|, so we need to add back the original
+ * signbit for sinf. */
+ int sign;
+ sign = ones[((n >> 2) & 1) ^ signbit];
+ theta2 = theta * theta;
+ /* Chebyshev polynomial of the form for sin:
+ * x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).
+ * 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
+ if ((n & 2) == 0)
+ {
+ 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))). */
+ /* x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
+ sx = theta + theta * theta2 * sx;
+ }
+ else
+ {
+ 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))). */
+ /* 1.0 + x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
+ sx = 1.0 + theta2 * sx;
+ }
+
+ /* Add in the signbit and assign the result. */
+ return sign * sx;
+}
+
+float
+SINF_FUNC (float x)
+{
+ double cx;
+ double theta = x;
+ double abstheta = fabs (theta);
+ /* if |x|< Pi/4. */
+ if (abstheta < M_PI_4)
+ {
+ if (abstheta >= 0x1p-5) /* |x| >= 2^-5. */
+ {
+ const double theta2 = theta * theta;
+ /* 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;
+ return cx;
+ }
+ else if (abstheta >= 0x1p-27) /* |x| >= 2^-27. */
+ {
+ /* A simpler Chebyshev approximation is close enough for this range:
+ * for sin: x+x^3*(SS0+x^2*SS1). */
+ const double theta2 = theta * theta;
+ cx = SS0 + theta2 * SS1;
+ cx = theta + theta * theta2 * cx;
+ return cx;
+ }
+ else
+ {
+ /* Handle some special cases. */
+ if (theta)
+ return theta - (theta * SMALL);
+ else
+ return theta;
+ }
+ }
+ else /* |x| >= Pi/4. */
+ {
+ unsigned long signbit = (x < 0);
+ if (abstheta < 9 * M_PI_4) /* |x| < 9*Pi/4. */
+ {
+ unsigned long n = (abstheta * inv_PI_4) + 1;
+ theta = abstheta - pio2_table[n / 2];
+ return reduced (theta, n, signbit);
+ }
+ else if (abstheta < INFINITY)
+ {
+ if (abstheta < 0x1p+23) /* |x| < 2^23. */
+ {
+ unsigned long n = floor (abstheta * inv_PI_4) + 1.0;
+ double x = floor (n / 2.0);
+ theta = x * PI_2_lo + (x * PI_2_hi + abstheta);
+ /* Argument reduction needed. */
+ return reduced (theta, n, signbit);
+ }
+ else /* |x| >= 2^23. */
+ {
+ x = fabs (x);
+ int exponent;
+ GET_FLOAT_WORD (exponent, x);
+ exponent =
+ (exponent >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
+ exponent += 3;
+ exponent = (exponent * (0x100000000 / 28 + 1)) >> 32;
+ 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;
+ unsigned long 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, signbit);
+ }
+ else
+ {
+ e += b;
+ e += c;
+ e += d;
+ if (e <= 1.0)
+ {
+ e *= M_PI_4;
+ return reduced (e, l + 1, signbit);
+ }
+ else
+ {
+ l++;
+ e -= 2.0;
+ e *= M_PI_4;
+ return reduced (e, l + 1, signbit);
+ }
+ }
}
}
+ else
+ {
+ int32_t ix;
+ /* High word of x. */
+ GET_FLOAT_WORD (ix, abstheta);
+ /* sin(Inf or NaN) is NaN. */
+ if (ix == 0x7f800000)
+ __set_errno (EDOM);
+ return x - x;
+ }
+ }
}
#ifndef SINF