[PATCHv4] New generic sinf

Message ID 1509725611-9756-1-git-send-email-raji@linux.vnet.ibm.com
State New
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  • [PATCHv4] New generic sinf
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Commit Message

Rajalakshmi Srinivasaraghavan Nov. 3, 2017, 4:13 p.m.
Changes since version 3:

  - Added and corrected comments in reduced.
  - Removed the duplicate theta2 calculation in reduced.

---
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.

2017-11-03  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

Joseph Myers Nov. 23, 2017, 6:24 p.m. | #1
On Fri, 3 Nov 2017, Rajalakshmi Srinivasaraghavan wrote:

> +  /*  if |x|< Pi/4.  */

There should only be one space at the start of a comment, and it should 
start with a capital letter.

> +      if (abstheta < 9 * M_PI_4)        /* |x| < 9*Pi/4.  */
> +	{
> +	  unsigned long n = (abstheta * inv_PI_4) + 1;
> +	  theta = abstheta - pio2_table[n / 2];

Remark: this is only safe because abstheta is a value representable as 
float - specifically, because no double values that are below the 
FE_UPWARD value of 9 * M_PI_4, but still have the FE_UPWARD value of 
abstheta * inv_PI_4 being >= 9, are representable as float.  (There is 
exactly one such double value, 0x1.c463abeccb2bap+2.)  I think a comment 
to this effect, about why the conditional is sufficient to ensure that 
pio2_table[5] does not get accessed, is appropriate.

> +      else if (abstheta < INFINITY)

This would create spurious exceptions for quiet NaN arguments.  You need 
an unordered comparison using isless.  (You tested on exactly the 
architectures where GCC bugs mean unordered comparisons are wrongly used 
for ordered comparison operators and so this issue was hidden - bug 58684 
for powerpc, bug 52451 for x86_64/x86 before GCC 8, bug 77918 for s390.)

> +	      exponent = (exponent * (0x100000000 / 28 + 1)) >> 32;

It's the compiler's job to convert division into a multiplication if 
appropriate, depending on what's optimal for a given architecture.  You 
should write whatever division you mean.  If the compiler could reasonably 
simplify things (including using whatever range information it has for 
exponent) but does not, that should be filed as a compiler bug.  Only if 
the compiler can't reasonably determine how to express a given division as 
a multiplication should the C code in glibc maybe express it as a 
multiplication like this (and in that case a detailed comment explaining 
the issues should be present).

Patch

diff --git a/sysdeps/ieee754/flt-32/s_sinf.c b/sysdeps/ieee754/flt-32/s_sinf.c
index 3ec98f811d..739723b267 100644
--- a/sysdeps/ieee754/flt-32/s_sinf.c
+++ b/sysdeps/ieee754/flt-32/s_sinf.c
@@ -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 };
 
-    /* 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]);
+/* Compute the sine 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
+   SIGNBIT is used to add the correct sign after the Chebyshev
+   polynomial is computed.  */
+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;
+  /* Determine positive or negative primary interval.  */
+  sign = ones[((n >> 2) & 1) ^ signbit];
+  /* Are we in the primary interval of sin or cos?  */
+  if ((n & 2) == 0)
+    {
+      /* Here sinf() is calculated using sin Chebyshev polynomial:
+	x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */
+      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;
+    }
+  else
+    {
+     /* Here sinf() is calculated using cos Chebyshev polynomial:
+	1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).  */
+      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;
+    }
+
+  /* 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