Trigonometric optimizations for POWER

1 files changed, 274 insertions, 0 deletions

diff --git a/sysdeps/powerpc/fpu/k_rem_pio2f.c b/sysdeps/powerpc/fpu/k_rem_pio2f.c
new file mode 100644
index 0000000000..9635340219
--- /dev/null
+++ b/sysdeps/powerpc/fpu/k_rem_pio2f.c
@@ -0,0 +1,274 @@
+/* k_rem_pio2f.c -- float version of e_rem_pio2.c
+   Copyright (C) 2011 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Library General Public License as
+   published by the Free Software Foundation; either version 2 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
+   Library General Public License for more details.
+
+   You should have received a copy of the GNU Library General Public
+   License along with the GNU C Library; see the file COPYING.LIB.  If not,
+   write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+   Boston, MA 02111-1307, USA.  */
+
+#include <math.h>
+
+#include "math_private.h"
+#include "s_float_bitwise.h"
+
+
+static const float two_over_pi[] = {
+  1.62000000e+02, 2.49000000e+02, 1.31000000e+02, 1.10000000e+02,
+  7.80000000e+01, 6.80000000e+01, 2.10000000e+01, 4.10000000e+01,
+  2.52000000e+02, 3.90000000e+01, 8.70000000e+01, 2.09000000e+02,
+  2.45000000e+02, 5.20000000e+01, 2.21000000e+02, 1.92000000e+02,
+  2.19000000e+02, 9.80000000e+01, 1.49000000e+02, 1.53000000e+02,
+  6.00000000e+01, 6.70000000e+01, 1.44000000e+02, 6.50000000e+01,
+  2.54000000e+02, 8.10000000e+01, 9.90000000e+01, 1.71000000e+02,
+  2.22000000e+02, 1.87000000e+02, 1.97000000e+02, 9.70000000e+01,
+  1.83000000e+02, 3.60000000e+01, 1.10000000e+02, 5.80000000e+01,
+  6.60000000e+01, 7.70000000e+01, 2.10000000e+02, 2.24000000e+02,
+  6.00000000e+00, 7.30000000e+01, 4.60000000e+01, 2.34000000e+02,
+  9.00000000e+00, 2.09000000e+02, 1.46000000e+02, 2.80000000e+01,
+  2.54000000e+02, 2.90000000e+01, 2.35000000e+02, 2.80000000e+01,
+  1.77000000e+02, 4.10000000e+01, 1.67000000e+02, 6.20000000e+01,
+  2.32000000e+02, 1.30000000e+02, 5.30000000e+01, 2.45000000e+02,
+  4.60000000e+01, 1.87000000e+02, 6.80000000e+01, 1.32000000e+02,
+  2.33000000e+02, 1.56000000e+02, 1.12000000e+02, 3.80000000e+01,
+  1.80000000e+02, 9.50000000e+01, 1.26000000e+02, 6.50000000e+01,
+  5.70000000e+01, 1.45000000e+02, 2.14000000e+02, 5.70000000e+01,
+  1.31000000e+02, 8.30000000e+01, 5.70000000e+01, 2.44000000e+02,
+  1.56000000e+02, 1.32000000e+02, 9.50000000e+01, 1.39000000e+02,
+  1.89000000e+02, 2.49000000e+02, 4.00000000e+01, 5.90000000e+01,
+  3.10000000e+01, 2.48000000e+02, 1.51000000e+02, 2.55000000e+02,
+  2.22000000e+02, 5.00000000e+00, 1.52000000e+02, 1.50000000e+01,
+  2.39000000e+02, 4.70000000e+01, 1.70000000e+01, 1.39000000e+02,
+  9.00000000e+01, 1.00000000e+01, 1.09000000e+02, 3.10000000e+01,
+  1.09000000e+02, 5.40000000e+01, 1.26000000e+02, 2.07000000e+02,
+  3.90000000e+01, 2.03000000e+02, 9.00000000e+00, 1.83000000e+02,
+  7.90000000e+01, 7.00000000e+01, 6.30000000e+01, 1.02000000e+02,
+  1.58000000e+02, 9.50000000e+01, 2.34000000e+02, 4.50000000e+01,
+  1.17000000e+02, 3.90000000e+01, 1.86000000e+02, 1.99000000e+02,
+  2.35000000e+02, 2.29000000e+02, 2.41000000e+02, 1.23000000e+02,
+  6.10000000e+01, 7.00000000e+00, 5.70000000e+01, 2.47000000e+02,
+  1.38000000e+02, 8.20000000e+01, 1.46000000e+02, 2.34000000e+02,
+  1.07000000e+02, 2.51000000e+02, 9.50000000e+01, 1.77000000e+02,
+  3.10000000e+01, 1.41000000e+02, 9.30000000e+01, 8.00000000e+00,
+  8.60000000e+01, 3.00000000e+00, 4.80000000e+01, 7.00000000e+01,
+  2.52000000e+02, 1.23000000e+02, 1.07000000e+02, 1.71000000e+02,
+  2.40000000e+02, 2.07000000e+02, 1.88000000e+02, 3.20000000e+01,
+  1.54000000e+02, 2.44000000e+02, 5.40000000e+01, 2.90000000e+01,
+  1.69000000e+02, 2.27000000e+02, 1.45000000e+02, 9.70000000e+01,
+  9.40000000e+01, 2.30000000e+02, 2.70000000e+01, 8.00000000e+00,
+  1.01000000e+02, 1.53000000e+02, 1.33000000e+02, 9.50000000e+01,
+  2.00000000e+01, 1.60000000e+02, 1.04000000e+02, 6.40000000e+01,
+  1.41000000e+02, 2.55000000e+02, 2.16000000e+02, 1.28000000e+02,
+  7.70000000e+01, 1.15000000e+02, 3.90000000e+01, 4.90000000e+01,
+  6.00000000e+00, 6.00000000e+00, 2.10000000e+01, 8.60000000e+01,
+  2.02000000e+02, 1.15000000e+02, 1.68000000e+02, 2.01000000e+02,
+  9.60000000e+01, 2.26000000e+02, 1.23000000e+02, 1.92000000e+02,
+  1.40000000e+02, 1.07000000e+02
+};
+
+
+static const float PIo2[] = {
+  1.5703125000e+00,		/* 0x3fc90000 */
+  4.5776367188e-04,		/* 0x39f00000 */
+  2.5987625122e-05,		/* 0x37da0000 */
+  7.5437128544e-08,		/* 0x33a20000 */
+  6.0026650317e-11,		/* 0x2e840000 */
+  7.3896444519e-13,		/* 0x2b500000 */
+  5.3845816694e-15,		/* 0x27c20000 */
+  5.6378512969e-18,		/* 0x22d00000 */
+  8.3009228831e-20,		/* 0x1fc40000 */
+  3.2756352257e-22,		/* 0x1bc60000 */
+  6.3331015649e-25,		/* 0x17440000 */
+};
+
+
+static const float zero  = 0.0000000000e+00;
+static const float one   = 1.0000000000;
+static const float twon8 = 3.9062500000e-03;
+static const float two8  = 2.5600000000e+02;
+
+
+int32_t
+__fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx)
+{
+  int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih, exp;
+  float z, fw, f[20], fq[20], q[20];
+
+  /* initialize jk */
+  jp = jk = 9;
+
+  /* determine jx,jv,q0, note that 3>q0 */
+  jx = nx - 1;
+  exp = __float_get_exp (e0) - 127;
+  jv = (exp - 3) / 8;
+  if (jv < 0)
+    jv = 0;
+  q0 = exp - 8 * (jv + 1);
+
+  /* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */
+  j = jv - jx;
+  m = jx + jk;
+  for (i = 0; i <= m; i++, j++)
+    f[i] = (j < 0) ? zero : two_over_pi[j];
+
+  /* compute q[0],q[1],...q[jk] */
+  for (i = 0; i <= jk; i++)
+    {
+      for (j = 0, fw = 0.0; j <= jx; j++)
+	fw += x[j] * f[jx + i - j];
+      q[i] = fw;
+    }
+
+  jz = jk;
+recompute:
+  /* distill q[] into iq[] reversingly */
+  for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--)
+    {
+      fw = truncf (twon8 * z);
+      iq[i] = (int32_t) (z - two8 * fw);
+      z = q[j - 1] + fw;
+    }
+
+  /* compute n */
+  z = __scalbnf (z, q0);	/* actual value of z */
+  z -= 8.0 * floorf (z * 0.125);	/* trim off integer >= 8 */
+  n = (int32_t) z;
+  z -= truncf (z);
+  ih = 0;
+  if (q0 > 0)
+    {				/* need iq[jz-1] to determine n */
+      i = (iq[jz - 1] >> (8 - q0));
+      n += i;
+      iq[jz - 1] -= i << (8 - q0);
+      ih = iq[jz - 1] >> (7 - q0);
+    }
+  else if (q0 == 0)
+    ih = iq[jz - 1] >> 8;
+  else if (z >= 0.5)
+    ih = 2;
+
+  if (ih > 0)
+    {				/* q > 0.5 */
+      n += 1;
+      carry = 0;
+      for (i = 0; i < jz; i++)
+	{			/* compute 1-q */
+	  j = iq[i];
+	  if (carry == 0)
+	    {
+	      if (j != 0)
+		{
+		  carry = 1;
+		  iq[i] = 0x100 - j;
+		}
+	    }
+	  else
+	    iq[i] = 0xff - j;
+	}
+      if (q0 > 0)
+	{			/* rare case: chance is 1 in 12 */
+	  switch (q0)
+	    {
+	    case 1:
+	      iq[jz - 1] &= 0x7f;
+	      break;
+	    case 2:
+	      iq[jz - 1] &= 0x3f;
+	      break;
+	    }
+	}
+      if (ih == 2)
+	{
+	  z = one - z;
+	  if (carry != 0)
+	    z -= __scalbnf (one, q0);
+	}
+    }
+
+  /* check if recomputation is needed */
+  if (z == zero)
+    {
+      j = 0;
+      for (i = jz - 1; i >= jk; i--)
+	j |= iq[i];
+      if (j == 0)
+	{			/* need recomputation */
+	  for (k = 1; iq[jk - k] == 0; k++);	/* k = no. of terms needed */
+
+	  for (i = jz + 1; i <= jz + k; i++)
+	    {			/* add q[jz+1] to q[jz+k] */
+	      f[jx + i] = two_over_pi[jv + i];
+	      for (j = 0, fw = 0.0; j <= jx; j++)
+		fw += x[j] * f[jx + i - j];
+	      q[i] = fw;
+	    }
+	  jz += k;
+	  goto recompute;
+	}
+    }
+
+  /* chop off zero terms */
+  if (z == 0.0)
+    {
+      jz -= 1;
+      q0 -= 8;
+      while (iq[jz] == 0)
+	{
+	  jz--;
+	  q0 -= 8;
+	}
+    }
+  else
+    {				/* break z into 8-bit if necessary */
+      z = __scalbnf (z, -q0);
+      if (z >= two8)
+	{
+	  fw = truncf (twon8 * z);
+	  iq[jz] = (int32_t) (z - two8 * fw);
+	  jz += 1;
+	  q0 += 8;
+	  iq[jz] = (int32_t) fw;
+	}
+      else
+	iq[jz] = (int32_t) z;
+    }
+
+  /* convert integer "bit" chunk to floating-point value */
+  fw = __scalbnf (one, q0);
+  for (i = jz; i >= 0; i--)
+    {
+      q[i] = fw * (float) iq[i];
+      fw *= twon8;
+    }
+
+  /* compute PIo2[0,...,jp]*q[jz,...,0] */
+  for (i = jz; i >= 0; i--)
+    {
+      for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++)
+	fw += PIo2[k] * q[i + k];
+      fq[jz - i] = fw;
+    }
+
+  /* compress fq[] into y[] */
+  fw = 0.0;
+  for (i = jz; i >= 0; i--)
+    fw += fq[i];
+  y[0] = (ih == 0) ? fw : -fw;
+  fw = fq[0] - fw;
+  for (i = 1; i <= jz; i++)
+    fw += fq[i];
+  y[1] = (ih == 0) ? fw : -fw;
+
+  return n & 7;
+}