From d05653dd8d0244e66016339a2d2ffa330e56baeb 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%

	* sysdeps/ieee754/flt-32/math_config.h (V2DF_TO_V4SF_INTRINSIC):
	New.
	* sysdeps/ieee754/flt-32/s_sincosf.h (v2df_t): New.
	(v4sf_t): Likewise.
	(sincos_t): Rearranged to support vectorized load.
	(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/x86/fpu/math_private.h: New file.
	* sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c: Just include
	<sysdeps/ieee754/flt-32/s_sincosf.c>.
---
 sysdeps/ieee754/flt-32/math_config.h         |   5 +
 sysdeps/ieee754/flt-32/s_sincosf.h           |  52 ++--
 sysdeps/ieee754/flt-32/s_sincosf_data.c      |  18 +-
 sysdeps/x86/fpu/math_private.h               |  28 ++
 sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c | 271 +------------------
 5 files changed, 70 insertions(+), 304 deletions(-)
 create mode 100644 sysdeps/x86/fpu/math_private.h

diff --git a/sysdeps/ieee754/flt-32/math_config.h b/sysdeps/ieee754/flt-32/math_config.h
index 8ca7532686..819fe8a0d2 100644
--- a/sysdeps/ieee754/flt-32/math_config.h
+++ b/sysdeps/ieee754/flt-32/math_config.h
@@ -57,6 +57,11 @@ static inline int32_t
 converttoint (double_t x);
 #endif
 
+#ifndef V2DF_TO_V4SF_INTRINSIC
+# define V2DF_TO_V4SF_INTRINSIC(v2df) \
+  { (float) v2df[0], (float) v2df[1] };
+#endif
+
 static inline uint32_t
 asuint (float f)
 {
diff --git a/sysdeps/ieee754/flt-32/s_sincosf.h b/sysdeps/ieee754/flt-32/s_sincosf.h
index 1dcb04f235..412bd6ac1b 100644
--- a/sysdeps/ieee754/flt-32/s_sincosf.h
+++ b/sysdeps/ieee754/flt-32/s_sincosf.h
@@ -25,14 +25,19 @@ static const double pi63 = 0x1.921FB54442D18p-62;
 /* PI / 4.  */
 static const double pio4 = 0x1.921FB54442D18p-1;
 
+typedef double v2df_t __attribute__ ((vector_size (2 * sizeof (double))));
+typedef float v4sf_t __attribute__ ((vector_size (4 * sizeof (float))));
+
 /* The constants and polynomials for sine and cosine.  */
 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 +60,30 @@ 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;
+  v4sf_t v4sf = V2DF_TO_V4SF_INTRINSIC (vsincos);
+  *sinp = v4sf[0];
+  *cosp = v4sf[1];
 }
 
 /* Return the sine of inputs X and X2 (X squared) using the polynomial P.
@@ -88,21 +96,21 @@ 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;
     }
diff --git a/sysdeps/ieee754/flt-32/s_sincosf_data.c b/sysdeps/ieee754/flt-32/s_sincosf_data.c
index 21fc2b60f9..6d3ed77d4c 100644
--- a/sysdeps/ieee754/flt-32/s_sincosf_data.c
+++ b/sysdeps/ieee754/flt-32/s_sincosf_data.c
@@ -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 }
   }
 };
 
diff --git a/sysdeps/x86/fpu/math_private.h b/sysdeps/x86/fpu/math_private.h
new file mode 100644
index 0000000000..3052683a4f
--- /dev/null
+++ b/sysdeps/x86/fpu/math_private.h
@@ -0,0 +1,28 @@
+/* Configure optimized libm functions.  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/>.  */
+
+#ifndef X86_MATH_PRIVATE_H
+#define X86_MATH_PRIVATE_H 1
+
+#ifdef __SSE2_MATH__
+# define V2DF_TO_V4SF_INTRINSIC(v2df) __builtin_ia32_cvtpd2ps (v2df)
+#endif
+
+#include_next <math_private.h>
+
+#endif
diff --git a/sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c b/sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c
index 0b80c4fe0d..253dab15d8 100644
--- a/sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c
+++ b/sysdeps/x86_64/fpu/multiarch/s_sincosf-fma.c
@@ -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
