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[PATCH][ppc] Merge power4+ overrides for mpa.c into a single place
- From: Siddhesh Poyarekar <siddhesh at redhat dot com>
- To: libc-alpha at sourceware dot org
- Cc: rsa at us dot ibm dot com
- Date: Wed, 27 Feb 2013 15:29:31 +0530
- Subject: [PATCH][ppc] Merge power4+ overrides for mpa.c into a single place
Hi,
This patch consolidates the mpa.c and Makefile in
sysdeps/powerpc/powerpc*/power4/fpu/ into a single place in
sysdeps/powerpc/power4. That way we avoid having redundant copies of
the files. Verified that the code generated is the same (except for
the debuginfo). I've not moved slowpow and slowexp since previous
patches I posted simply remove them.
OK to commit?
Siddhesh
* sysdeps/powerpc/powerpc32/power4/fpu/mpa.c: Move file...
* sysdeps/powerpc/power4/fpu/mpa.c: ... here.
* sysdeps/powerpc/powerpc32/power4/fpu/Makefile: Move file...
* sysdeps/powerpc/power4/fpu/Makefile: ... here.
* sysdeps/powerpc/powerpc64/power4/fpu/mpa.c: Remove.
* sysdeps/powerpc/powerpc64/power4/fpu/Makefile: Remove.
* sysdeps/powerpc/powerpc32/power4/Implies: New file.
* sysdeps/powerpc/powerpc64/power4/Implies: New file.
diff --git a/sysdeps/powerpc/power4/fpu/Makefile b/sysdeps/powerpc/power4/fpu/Makefile
new file mode 100644
index 0000000..f487ed6
--- /dev/null
+++ b/sysdeps/powerpc/power4/fpu/Makefile
@@ -0,0 +1,5 @@
+# Makefile fragment for POWER4/5/5+ with FPU.
+
+ifeq ($(subdir),math)
+CFLAGS-mpa.c += --param max-unroll-times=4 -funroll-loops -fpeel-loops
+endif
diff --git a/sysdeps/powerpc/power4/fpu/mpa.c b/sysdeps/powerpc/power4/fpu/mpa.c
new file mode 100644
index 0000000..f30d2cb
--- /dev/null
+++ b/sysdeps/powerpc/power4/fpu/mpa.c
@@ -0,0 +1,829 @@
+
+/*
+ * IBM Accurate Mathematical Library
+ * written by International Business Machines Corp.
+ * Copyright (C) 2001-2013 Free Software Foundation, Inc.
+ *
+ * This program 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.
+ *
+ * This program 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 this program; if not, see <http://www.gnu.org/licenses/>.
+ */
+/************************************************************************/
+/* MODULE_NAME: mpa.c */
+/* */
+/* FUNCTIONS: */
+/* mcr */
+/* acr */
+/* cpy */
+/* norm */
+/* denorm */
+/* mp_dbl */
+/* dbl_mp */
+/* add_magnitudes */
+/* sub_magnitudes */
+/* add */
+/* sub */
+/* mul */
+/* inv */
+/* dvd */
+/* */
+/* Arithmetic functions for multiple precision numbers. */
+/* Relative errors are bounded */
+/************************************************************************/
+
+
+#include "endian.h"
+#include "mpa.h"
+#include <sys/param.h>
+
+const mp_no mpone = {1, {1.0, 1.0}};
+const mp_no mptwo = {1, {1.0, 2.0}};
+
+/* Compare mantissa of two multiple precision numbers regardless of the sign
+ and exponent of the numbers. */
+static int
+mcr (const mp_no *x, const mp_no *y, int p)
+{
+ long i;
+ long p2 = p;
+ for (i = 1; i <= p2; i++)
+ {
+ if (X[i] == Y[i])
+ continue;
+ else if (X[i] > Y[i])
+ return 1;
+ else
+ return -1;
+ }
+ return 0;
+}
+
+/* Compare the absolute values of two multiple precision numbers. */
+int
+__acr (const mp_no *x, const mp_no *y, int p)
+{
+ long i;
+
+ if (X[0] == ZERO)
+ {
+ if (Y[0] == ZERO)
+ i = 0;
+ else
+ i = -1;
+ }
+ else if (Y[0] == ZERO)
+ i = 1;
+ else
+ {
+ if (EX > EY)
+ i = 1;
+ else if (EX < EY)
+ i = -1;
+ else
+ i = mcr (x, y, p);
+ }
+
+ return i;
+}
+
+/* Copy multiple precision number X into Y. They could be the same
+ number. */
+void
+__cpy (const mp_no *x, mp_no *y, int p)
+{
+ long i;
+
+ EY = EX;
+ for (i = 0; i <= p; i++)
+ Y[i] = X[i];
+}
+
+/* Convert a multiple precision number *X into a double precision
+ number *Y, normalized case (|x| >= 2**(-1022))). */
+static void
+norm (const mp_no *x, double *y, int p)
+{
+#define R RADIXI
+ long i;
+ double a, c, u, v, z[5];
+ if (p < 5)
+ {
+ if (p == 1)
+ c = X[1];
+ else if (p == 2)
+ c = X[1] + R * X[2];
+ else if (p == 3)
+ c = X[1] + R * (X[2] + R * X[3]);
+ else if (p == 4)
+ c = (X[1] + R * X[2]) + R * R * (X[3] + R * X[4]);
+ }
+ else
+ {
+ for (a = ONE, z[1] = X[1]; z[1] < TWO23;)
+ {
+ a *= TWO;
+ z[1] *= TWO;
+ }
+
+ for (i = 2; i < 5; i++)
+ {
+ z[i] = X[i] * a;
+ u = (z[i] + CUTTER) - CUTTER;
+ if (u > z[i])
+ u -= RADIX;
+ z[i] -= u;
+ z[i - 1] += u * RADIXI;
+ }
+
+ u = (z[3] + TWO71) - TWO71;
+ if (u > z[3])
+ u -= TWO19;
+ v = z[3] - u;
+
+ if (v == TWO18)
+ {
+ if (z[4] == ZERO)
+ {
+ for (i = 5; i <= p; i++)
+ {
+ if (X[i] == ZERO)
+ continue;
+ else
+ {
+ z[3] += ONE;
+ break;
+ }
+ }
+ }
+ else
+ z[3] += ONE;
+ }
+
+ c = (z[1] + R * (z[2] + R * z[3])) / a;
+ }
+
+ c *= X[0];
+
+ for (i = 1; i < EX; i++)
+ c *= RADIX;
+ for (i = 1; i > EX; i--)
+ c *= RADIXI;
+
+ *y = c;
+#undef R
+}
+
+/* Convert a multiple precision number *X into a double precision
+ number *Y, Denormal case (|x| < 2**(-1022))). */
+static void
+denorm (const mp_no *x, double *y, int p)
+{
+ long i, k;
+ long p2 = p;
+ double c, u, z[5];
+
+#define R RADIXI
+ if (EX < -44 || (EX == -44 && X[1] < TWO5))
+ {
+ *y = ZERO;
+ return;
+ }
+
+ if (p2 == 1)
+ {
+ if (EX == -42)
+ {
+ z[1] = X[1] + TWO10;
+ z[2] = ZERO;
+ z[3] = ZERO;
+ k = 3;
+ }
+ else if (EX == -43)
+ {
+ z[1] = TWO10;
+ z[2] = X[1];
+ z[3] = ZERO;
+ k = 2;
+ }
+ else
+ {
+ z[1] = TWO10;
+ z[2] = ZERO;
+ z[3] = X[1];
+ k = 1;
+ }
+ }
+ else if (p2 == 2)
+ {
+ if (EX == -42)
+ {
+ z[1] = X[1] + TWO10;
+ z[2] = X[2];
+ z[3] = ZERO;
+ k = 3;
+ }
+ else if (EX == -43)
+ {
+ z[1] = TWO10;
+ z[2] = X[1];
+ z[3] = X[2];
+ k = 2;
+ }
+ else
+ {
+ z[1] = TWO10;
+ z[2] = ZERO;
+ z[3] = X[1];
+ k = 1;
+ }
+ }
+ else
+ {
+ if (EX == -42)
+ {
+ z[1] = X[1] + TWO10;
+ z[2] = X[2];
+ k = 3;
+ }
+ else if (EX == -43)
+ {
+ z[1] = TWO10;
+ z[2] = X[1];
+ k = 2;
+ }
+ else
+ {
+ z[1] = TWO10;
+ z[2] = ZERO;
+ k = 1;
+ }
+ z[3] = X[k];
+ }
+
+ u = (z[3] + TWO57) - TWO57;
+ if (u > z[3])
+ u -= TWO5;
+
+ if (u == z[3])
+ {
+ for (i = k + 1; i <= p2; i++)
+ {
+ if (X[i] == ZERO)
+ continue;
+ else
+ {
+ z[3] += ONE;
+ break;
+ }
+ }
+ }
+
+ c = X[0] * ((z[1] + R * (z[2] + R * z[3])) - TWO10);
+
+ *y = c * TWOM1032;
+#undef R
+}
+
+/* Convert multiple precision number *X into double precision number *Y. The
+ result is correctly rounded to the nearest/even. */
+void
+__mp_dbl (const mp_no *x, double *y, int p)
+{
+ if (X[0] == ZERO)
+ {
+ *y = ZERO;
+ return;
+ }
+
+ if (__glibc_likely (EX > -42 || (EX == -42 && X[1] >= TWO10)))
+ norm (x, y, p);
+ else
+ denorm (x, y, p);
+}
+
+/* Get the multiple precision equivalent of X into *Y. If the precision is too
+ small, the result is truncated. */
+void
+__dbl_mp (double x, mp_no *y, int p)
+{
+ long i, n;
+ long p2 = p;
+ double u;
+
+ /* Sign. */
+ if (x == ZERO)
+ {
+ Y[0] = ZERO;
+ return;
+ }
+ else if (x > ZERO)
+ Y[0] = ONE;
+ else
+ {
+ Y[0] = MONE;
+ x = -x;
+ }
+
+ /* Exponent. */
+ for (EY = ONE; x >= RADIX; EY += ONE)
+ x *= RADIXI;
+ for (; x < ONE; EY -= ONE)
+ x *= RADIX;
+
+ /* Digits. */
+ n = MIN (p2, 4);
+ for (i = 1; i <= n; i++)
+ {
+ u = (x + TWO52) - TWO52;
+ if (u > x)
+ u -= ONE;
+ Y[i] = u;
+ x -= u;
+ x *= RADIX;
+ }
+ for (; i <= p2; i++)
+ Y[i] = ZERO;
+}
+
+/* Add magnitudes of *X and *Y assuming that abs (*X) >= abs (*Y) > 0. The
+ sign of the sum *Z is not changed. X and Y may overlap but not X and Z or
+ Y and Z. No guard digit is used. The result equals the exact sum,
+ truncated. */
+static void
+add_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
+{
+ long i, j, k;
+ long p2 = p;
+
+ EZ = EX;
+
+ i = p2;
+ j = p2 + EY - EX;
+ k = p2 + 1;
+
+ if (j < 1)
+ {
+ __cpy (x, z, p);
+ return;
+ }
+ else
+ Z[k] = ZERO;
+
+ for (; j > 0; i--, j--)
+ {
+ Z[k] += X[i] + Y[j];
+ if (Z[k] >= RADIX)
+ {
+ Z[k] -= RADIX;
+ Z[--k] = ONE;
+ }
+ else
+ Z[--k] = ZERO;
+ }
+
+ for (; i > 0; i--)
+ {
+ Z[k] += X[i];
+ if (Z[k] >= RADIX)
+ {
+ Z[k] -= RADIX;
+ Z[--k] = ONE;
+ }
+ else
+ Z[--k] = ZERO;
+ }
+
+ if (Z[1] == ZERO)
+ {
+ for (i = 1; i <= p2; i++)
+ Z[i] = Z[i + 1];
+ }
+ else
+ EZ += ONE;
+}
+
+/* Subtract the magnitudes of *X and *Y assuming that abs (*x) > abs (*y) > 0.
+ The sign of the difference *Z is not changed. X and Y may overlap but not X
+ and Z or Y and Z. One guard digit is used. The error is less than one
+ ULP. */
+static void
+sub_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
+{
+ long i, j, k;
+ long p2 = p;
+
+ EZ = EX;
+
+ if (EX == EY)
+ {
+ i = j = k = p2;
+ Z[k] = Z[k + 1] = ZERO;
+ }
+ else
+ {
+ j = EX - EY;
+ if (j > p2)
+ {
+ __cpy (x, z, p);
+ return;
+ }
+ else
+ {
+ i = p2;
+ j = p2 + 1 - j;
+ k = p2;
+ if (Y[j] > ZERO)
+ {
+ Z[k + 1] = RADIX - Y[j--];
+ Z[k] = MONE;
+ }
+ else
+ {
+ Z[k + 1] = ZERO;
+ Z[k] = ZERO;
+ j--;
+ }
+ }
+ }
+
+ for (; j > 0; i--, j--)
+ {
+ Z[k] += (X[i] - Y[j]);
+ if (Z[k] < ZERO)
+ {
+ Z[k] += RADIX;
+ Z[--k] = MONE;
+ }
+ else
+ Z[--k] = ZERO;
+ }
+
+ for (; i > 0; i--)
+ {
+ Z[k] += X[i];
+ if (Z[k] < ZERO)
+ {
+ Z[k] += RADIX;
+ Z[--k] = MONE;
+ }
+ else
+ Z[--k] = ZERO;
+ }
+
+ for (i = 1; Z[i] == ZERO; i++);
+ EZ = EZ - i + 1;
+ for (k = 1; i <= p2 + 1;)
+ Z[k++] = Z[i++];
+ for (; k <= p2;)
+ Z[k++] = ZERO;
+}
+
+/* Add *X and *Y and store the result in *Z. X and Y may overlap, but not X
+ and Z or Y and Z. One guard digit is used. The error is less than one
+ ULP. */
+void
+__add (const mp_no *x, const mp_no *y, mp_no *z, int p)
+{
+ int n;
+
+ if (X[0] == ZERO)
+ {
+ __cpy (y, z, p);
+ return;
+ }
+ else if (Y[0] == ZERO)
+ {
+ __cpy (x, z, p);
+ return;
+ }
+
+ if (X[0] == Y[0])
+ {
+ if (__acr (x, y, p) > 0)
+ {
+ add_magnitudes (x, y, z, p);
+ Z[0] = X[0];
+ }
+ else
+ {
+ add_magnitudes (y, x, z, p);
+ Z[0] = Y[0];
+ }
+ }
+ else
+ {
+ if ((n = __acr (x, y, p)) == 1)
+ {
+ sub_magnitudes (x, y, z, p);
+ Z[0] = X[0];
+ }
+ else if (n == -1)
+ {
+ sub_magnitudes (y, x, z, p);
+ Z[0] = Y[0];
+ }
+ else
+ Z[0] = ZERO;
+ }
+}
+
+/* Subtract *Y from *X and return the result in *Z. X and Y may overlap but
+ not X and Z or Y and Z. One guard digit is used. The error is less than
+ one ULP. */
+void
+__sub (const mp_no *x, const mp_no *y, mp_no *z, int p)
+{
+ int n;
+
+ if (X[0] == ZERO)
+ {
+ __cpy (y, z, p);
+ Z[0] = -Z[0];
+ return;
+ }
+ else if (Y[0] == ZERO)
+ {
+ __cpy (x, z, p);
+ return;
+ }
+
+ if (X[0] != Y[0])
+ {
+ if (__acr (x, y, p) > 0)
+ {
+ add_magnitudes (x, y, z, p);
+ Z[0] = X[0];
+ }
+ else
+ {
+ add_magnitudes (y, x, z, p);
+ Z[0] = -Y[0];
+ }
+ }
+ else
+ {
+ if ((n = __acr (x, y, p)) == 1)
+ {
+ sub_magnitudes (x, y, z, p);
+ Z[0] = X[0];
+ }
+ else if (n == -1)
+ {
+ sub_magnitudes (y, x, z, p);
+ Z[0] = -Y[0];
+ }
+ else
+ Z[0] = ZERO;
+ }
+}
+
+/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X
+ and Z or Y and Z. For P in [1, 2, 3], the exact result is truncated to P
+ digits. In case P > 3 the error is bounded by 1.001 ULP. */
+void
+__mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
+{
+ long i, i1, i2, j, k, k2;
+ long p2 = p;
+ double u, zk, zk2;
+
+ /* Is z=0? */
+ if (__glibc_unlikely (X[0] * Y[0] == ZERO))
+ {
+ Z[0] = ZERO;
+ return;
+ }
+
+ /* Multiply, add and carry */
+ k2 = (p2 < 3) ? p2 + p2 : p2 + 3;
+ zk = Z[k2] = ZERO;
+ for (k = k2; k > 1;)
+ {
+ if (k > p2)
+ {
+ i1 = k - p2;
+ i2 = p2 + 1;
+ }
+ else
+ {
+ i1 = 1;
+ i2 = k;
+ }
+#if 1
+ /* Rearrange this inner loop to allow the fmadd instructions to be
+ independent and execute in parallel on processors that have
+ dual symmetrical FP pipelines. */
+ if (i1 < (i2 - 1))
+ {
+ /* Make sure we have at least 2 iterations. */
+ if (((i2 - i1) & 1L) == 1L)
+ {
+ /* Handle the odd iterations case. */
+ zk2 = x->d[i2 - 1] * y->d[i1];
+ }
+ else
+ zk2 = 0.0;
+ /* Do two multiply/adds per loop iteration, using independent
+ accumulators; zk and zk2. */
+ for (i = i1, j = i2 - 1; i < i2 - 1; i += 2, j -= 2)
+ {
+ zk += x->d[i] * y->d[j];
+ zk2 += x->d[i + 1] * y->d[j - 1];
+ }
+ zk += zk2; /* Final sum. */
+ }
+ else
+ {
+ /* Special case when iterations is 1. */
+ zk += x->d[i1] * y->d[i1];
+ }
+#else
+ /* The original code. */
+ for (i = i1, j = i2 - 1; i < i2; i++, j--)
+ zk += X[i] * Y[j];
+#endif
+
+ u = (zk + CUTTER) - CUTTER;
+ if (u > zk)
+ u -= RADIX;
+ Z[k] = zk - u;
+ zk = u * RADIXI;
+ --k;
+ }
+ Z[k] = zk;
+
+ /* Is there a carry beyond the most significant digit? */
+ if (Z[1] == ZERO)
+ {
+ for (i = 1; i <= p2; i++)
+ Z[i] = Z[i + 1];
+ EZ = EX + EY - 1;
+ }
+ else
+ EZ = EX + EY;
+
+ Z[0] = X[0] * Y[0];
+}
+
+/* Square *X and store result in *Y. X and Y may not overlap. For P in
+ [1, 2, 3], the exact result is truncated to P digits. In case P > 3 the
+ error is bounded by 1.001 ULP. This is a faster special case of
+ multiplication. */
+void
+__sqr (const mp_no *x, mp_no *y, int p)
+{
+ long i, j, k, ip;
+ double u, yk;
+
+ /* Is z=0? */
+ if (__glibc_unlikely (X[0] == ZERO))
+ {
+ Y[0] = ZERO;
+ return;
+ }
+
+ /* We need not iterate through all X's since it's pointless to
+ multiply zeroes. */
+ for (ip = p; ip > 0; ip--)
+ if (X[ip] != ZERO)
+ break;
+
+ k = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
+
+ while (k > 2 * ip + 1)
+ Y[k--] = ZERO;
+
+ yk = ZERO;
+
+ while (k > p)
+ {
+ double yk2 = 0.0;
+ long lim = k / 2;
+
+ if (k % 2 == 0)
+ {
+ yk += X[lim] * X[lim];
+ lim--;
+ }
+
+ /* In __mul, this loop (and the one within the next while loop) run
+ between a range to calculate the mantissa as follows:
+
+ Z[k] = X[k] * Y[n] + X[k+1] * Y[n-1] ... + X[n-1] * Y[k+1]
+ + X[n] * Y[k]
+
+ For X == Y, we can get away with summing halfway and doubling the
+ result. For cases where the range size is even, the mid-point needs
+ to be added separately (above). */
+ for (i = k - p, j = p; i <= lim; i++, j--)
+ yk2 += X[i] * X[j];
+
+ yk += 2.0 * yk2;
+
+ u = (yk + CUTTER) - CUTTER;
+ if (u > yk)
+ u -= RADIX;
+ Y[k--] = yk - u;
+ yk = u * RADIXI;
+ }
+
+ while (k > 1)
+ {
+ double yk2 = 0.0;
+ long lim = k / 2;
+
+ if (k % 2 == 0)
+ {
+ yk += X[lim] * X[lim];
+ lim--;
+ }
+
+ /* Likewise for this loop. */
+ for (i = 1, j = k - 1; i <= lim; i++, j--)
+ yk2 += X[i] * X[j];
+
+ yk += 2.0 * yk2;
+
+ u = (yk + CUTTER) - CUTTER;
+ if (u > yk)
+ u -= RADIX;
+ Y[k--] = yk - u;
+ yk = u * RADIXI;
+ }
+ Y[k] = yk;
+
+ /* Squares are always positive. */
+ Y[0] = 1.0;
+
+ EY = 2 * EX;
+ /* Is there a carry beyond the most significant digit? */
+ if (__glibc_unlikely (Y[1] == ZERO))
+ {
+ for (i = 1; i <= p; i++)
+ Y[i] = Y[i + 1];
+ EY--;
+ }
+}
+
+/* Invert *X and store in *Y. Relative error bound:
+ - For P = 2: 1.001 * R ^ (1 - P)
+ - For P = 3: 1.063 * R ^ (1 - P)
+ - For P > 3: 2.001 * R ^ (1 - P)
+
+ *X = 0 is not permissible. */
+static void
+__inv (const mp_no *x, mp_no *y, int p)
+{
+ long i;
+ double t;
+ mp_no z, w;
+ static const int np1[] =
+ { 0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3,
+ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
+ };
+
+ __cpy (x, &z, p);
+ z.e = 0;
+ __mp_dbl (&z, &t, p);
+ t = ONE / t;
+ __dbl_mp (t, y, p);
+ EY -= EX;
+
+ for (i = 0; i < np1[p]; i++)
+ {
+ __cpy (y, &w, p);
+ __mul (x, &w, y, p);
+ __sub (&mptwo, y, &z, p);
+ __mul (&w, &z, y, p);
+ }
+}
+
+/* Divide *X by *Y and store result in *Z. X and Y may overlap but not X and Z
+ or Y and Z. Relative error bound:
+ - For P = 2: 2.001 * R ^ (1 - P)
+ - For P = 3: 2.063 * R ^ (1 - P)
+ - For P > 3: 3.001 * R ^ (1 - P)
+
+ *X = 0 is not permissible. */
+void
+__dvd (const mp_no *x, const mp_no *y, mp_no *z, int p)
+{
+ mp_no w;
+
+ if (X[0] == ZERO)
+ Z[0] = ZERO;
+ else
+ {
+ __inv (y, &w, p);
+ __mul (x, &w, z, p);
+ }
+}
diff --git a/sysdeps/powerpc/powerpc32/power4/Implies b/sysdeps/powerpc/powerpc32/power4/Implies
new file mode 100644
index 0000000..a372141
--- /dev/null
+++ b/sysdeps/powerpc/powerpc32/power4/Implies
@@ -0,0 +1,2 @@
+powerpc/power4/fpu
+powerpc/power4
diff --git a/sysdeps/powerpc/powerpc32/power4/fpu/Makefile b/sysdeps/powerpc/powerpc32/power4/fpu/Makefile
deleted file mode 100644
index f487ed6..0000000
--- a/sysdeps/powerpc/powerpc32/power4/fpu/Makefile
+++ /dev/null
@@ -1,5 +0,0 @@
-# Makefile fragment for POWER4/5/5+ with FPU.
-
-ifeq ($(subdir),math)
-CFLAGS-mpa.c += --param max-unroll-times=4 -funroll-loops -fpeel-loops
-endif
diff --git a/sysdeps/powerpc/powerpc32/power4/fpu/mpa.c b/sysdeps/powerpc/powerpc32/power4/fpu/mpa.c
deleted file mode 100644
index f30d2cb..0000000
--- a/sysdeps/powerpc/powerpc32/power4/fpu/mpa.c
+++ /dev/null
@@ -1,829 +0,0 @@
-
-/*
- * IBM Accurate Mathematical Library
- * written by International Business Machines Corp.
- * Copyright (C) 2001-2013 Free Software Foundation, Inc.
- *
- * This program 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.
- *
- * This program 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 this program; if not, see <http://www.gnu.org/licenses/>.
- */
-/************************************************************************/
-/* MODULE_NAME: mpa.c */
-/* */
-/* FUNCTIONS: */
-/* mcr */
-/* acr */
-/* cpy */
-/* norm */
-/* denorm */
-/* mp_dbl */
-/* dbl_mp */
-/* add_magnitudes */
-/* sub_magnitudes */
-/* add */
-/* sub */
-/* mul */
-/* inv */
-/* dvd */
-/* */
-/* Arithmetic functions for multiple precision numbers. */
-/* Relative errors are bounded */
-/************************************************************************/
-
-
-#include "endian.h"
-#include "mpa.h"
-#include <sys/param.h>
-
-const mp_no mpone = {1, {1.0, 1.0}};
-const mp_no mptwo = {1, {1.0, 2.0}};
-
-/* Compare mantissa of two multiple precision numbers regardless of the sign
- and exponent of the numbers. */
-static int
-mcr (const mp_no *x, const mp_no *y, int p)
-{
- long i;
- long p2 = p;
- for (i = 1; i <= p2; i++)
- {
- if (X[i] == Y[i])
- continue;
- else if (X[i] > Y[i])
- return 1;
- else
- return -1;
- }
- return 0;
-}
-
-/* Compare the absolute values of two multiple precision numbers. */
-int
-__acr (const mp_no *x, const mp_no *y, int p)
-{
- long i;
-
- if (X[0] == ZERO)
- {
- if (Y[0] == ZERO)
- i = 0;
- else
- i = -1;
- }
- else if (Y[0] == ZERO)
- i = 1;
- else
- {
- if (EX > EY)
- i = 1;
- else if (EX < EY)
- i = -1;
- else
- i = mcr (x, y, p);
- }
-
- return i;
-}
-
-/* Copy multiple precision number X into Y. They could be the same
- number. */
-void
-__cpy (const mp_no *x, mp_no *y, int p)
-{
- long i;
-
- EY = EX;
- for (i = 0; i <= p; i++)
- Y[i] = X[i];
-}
-
-/* Convert a multiple precision number *X into a double precision
- number *Y, normalized case (|x| >= 2**(-1022))). */
-static void
-norm (const mp_no *x, double *y, int p)
-{
-#define R RADIXI
- long i;
- double a, c, u, v, z[5];
- if (p < 5)
- {
- if (p == 1)
- c = X[1];
- else if (p == 2)
- c = X[1] + R * X[2];
- else if (p == 3)
- c = X[1] + R * (X[2] + R * X[3]);
- else if (p == 4)
- c = (X[1] + R * X[2]) + R * R * (X[3] + R * X[4]);
- }
- else
- {
- for (a = ONE, z[1] = X[1]; z[1] < TWO23;)
- {
- a *= TWO;
- z[1] *= TWO;
- }
-
- for (i = 2; i < 5; i++)
- {
- z[i] = X[i] * a;
- u = (z[i] + CUTTER) - CUTTER;
- if (u > z[i])
- u -= RADIX;
- z[i] -= u;
- z[i - 1] += u * RADIXI;
- }
-
- u = (z[3] + TWO71) - TWO71;
- if (u > z[3])
- u -= TWO19;
- v = z[3] - u;
-
- if (v == TWO18)
- {
- if (z[4] == ZERO)
- {
- for (i = 5; i <= p; i++)
- {
- if (X[i] == ZERO)
- continue;
- else
- {
- z[3] += ONE;
- break;
- }
- }
- }
- else
- z[3] += ONE;
- }
-
- c = (z[1] + R * (z[2] + R * z[3])) / a;
- }
-
- c *= X[0];
-
- for (i = 1; i < EX; i++)
- c *= RADIX;
- for (i = 1; i > EX; i--)
- c *= RADIXI;
-
- *y = c;
-#undef R
-}
-
-/* Convert a multiple precision number *X into a double precision
- number *Y, Denormal case (|x| < 2**(-1022))). */
-static void
-denorm (const mp_no *x, double *y, int p)
-{
- long i, k;
- long p2 = p;
- double c, u, z[5];
-
-#define R RADIXI
- if (EX < -44 || (EX == -44 && X[1] < TWO5))
- {
- *y = ZERO;
- return;
- }
-
- if (p2 == 1)
- {
- if (EX == -42)
- {
- z[1] = X[1] + TWO10;
- z[2] = ZERO;
- z[3] = ZERO;
- k = 3;
- }
- else if (EX == -43)
- {
- z[1] = TWO10;
- z[2] = X[1];
- z[3] = ZERO;
- k = 2;
- }
- else
- {
- z[1] = TWO10;
- z[2] = ZERO;
- z[3] = X[1];
- k = 1;
- }
- }
- else if (p2 == 2)
- {
- if (EX == -42)
- {
- z[1] = X[1] + TWO10;
- z[2] = X[2];
- z[3] = ZERO;
- k = 3;
- }
- else if (EX == -43)
- {
- z[1] = TWO10;
- z[2] = X[1];
- z[3] = X[2];
- k = 2;
- }
- else
- {
- z[1] = TWO10;
- z[2] = ZERO;
- z[3] = X[1];
- k = 1;
- }
- }
- else
- {
- if (EX == -42)
- {
- z[1] = X[1] + TWO10;
- z[2] = X[2];
- k = 3;
- }
- else if (EX == -43)
- {
- z[1] = TWO10;
- z[2] = X[1];
- k = 2;
- }
- else
- {
- z[1] = TWO10;
- z[2] = ZERO;
- k = 1;
- }
- z[3] = X[k];
- }
-
- u = (z[3] + TWO57) - TWO57;
- if (u > z[3])
- u -= TWO5;
-
- if (u == z[3])
- {
- for (i = k + 1; i <= p2; i++)
- {
- if (X[i] == ZERO)
- continue;
- else
- {
- z[3] += ONE;
- break;
- }
- }
- }
-
- c = X[0] * ((z[1] + R * (z[2] + R * z[3])) - TWO10);
-
- *y = c * TWOM1032;
-#undef R
-}
-
-/* Convert multiple precision number *X into double precision number *Y. The
- result is correctly rounded to the nearest/even. */
-void
-__mp_dbl (const mp_no *x, double *y, int p)
-{
- if (X[0] == ZERO)
- {
- *y = ZERO;
- return;
- }
-
- if (__glibc_likely (EX > -42 || (EX == -42 && X[1] >= TWO10)))
- norm (x, y, p);
- else
- denorm (x, y, p);
-}
-
-/* Get the multiple precision equivalent of X into *Y. If the precision is too
- small, the result is truncated. */
-void
-__dbl_mp (double x, mp_no *y, int p)
-{
- long i, n;
- long p2 = p;
- double u;
-
- /* Sign. */
- if (x == ZERO)
- {
- Y[0] = ZERO;
- return;
- }
- else if (x > ZERO)
- Y[0] = ONE;
- else
- {
- Y[0] = MONE;
- x = -x;
- }
-
- /* Exponent. */
- for (EY = ONE; x >= RADIX; EY += ONE)
- x *= RADIXI;
- for (; x < ONE; EY -= ONE)
- x *= RADIX;
-
- /* Digits. */
- n = MIN (p2, 4);
- for (i = 1; i <= n; i++)
- {
- u = (x + TWO52) - TWO52;
- if (u > x)
- u -= ONE;
- Y[i] = u;
- x -= u;
- x *= RADIX;
- }
- for (; i <= p2; i++)
- Y[i] = ZERO;
-}
-
-/* Add magnitudes of *X and *Y assuming that abs (*X) >= abs (*Y) > 0. The
- sign of the sum *Z is not changed. X and Y may overlap but not X and Z or
- Y and Z. No guard digit is used. The result equals the exact sum,
- truncated. */
-static void
-add_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- long i, j, k;
- long p2 = p;
-
- EZ = EX;
-
- i = p2;
- j = p2 + EY - EX;
- k = p2 + 1;
-
- if (j < 1)
- {
- __cpy (x, z, p);
- return;
- }
- else
- Z[k] = ZERO;
-
- for (; j > 0; i--, j--)
- {
- Z[k] += X[i] + Y[j];
- if (Z[k] >= RADIX)
- {
- Z[k] -= RADIX;
- Z[--k] = ONE;
- }
- else
- Z[--k] = ZERO;
- }
-
- for (; i > 0; i--)
- {
- Z[k] += X[i];
- if (Z[k] >= RADIX)
- {
- Z[k] -= RADIX;
- Z[--k] = ONE;
- }
- else
- Z[--k] = ZERO;
- }
-
- if (Z[1] == ZERO)
- {
- for (i = 1; i <= p2; i++)
- Z[i] = Z[i + 1];
- }
- else
- EZ += ONE;
-}
-
-/* Subtract the magnitudes of *X and *Y assuming that abs (*x) > abs (*y) > 0.
- The sign of the difference *Z is not changed. X and Y may overlap but not X
- and Z or Y and Z. One guard digit is used. The error is less than one
- ULP. */
-static void
-sub_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- long i, j, k;
- long p2 = p;
-
- EZ = EX;
-
- if (EX == EY)
- {
- i = j = k = p2;
- Z[k] = Z[k + 1] = ZERO;
- }
- else
- {
- j = EX - EY;
- if (j > p2)
- {
- __cpy (x, z, p);
- return;
- }
- else
- {
- i = p2;
- j = p2 + 1 - j;
- k = p2;
- if (Y[j] > ZERO)
- {
- Z[k + 1] = RADIX - Y[j--];
- Z[k] = MONE;
- }
- else
- {
- Z[k + 1] = ZERO;
- Z[k] = ZERO;
- j--;
- }
- }
- }
-
- for (; j > 0; i--, j--)
- {
- Z[k] += (X[i] - Y[j]);
- if (Z[k] < ZERO)
- {
- Z[k] += RADIX;
- Z[--k] = MONE;
- }
- else
- Z[--k] = ZERO;
- }
-
- for (; i > 0; i--)
- {
- Z[k] += X[i];
- if (Z[k] < ZERO)
- {
- Z[k] += RADIX;
- Z[--k] = MONE;
- }
- else
- Z[--k] = ZERO;
- }
-
- for (i = 1; Z[i] == ZERO; i++);
- EZ = EZ - i + 1;
- for (k = 1; i <= p2 + 1;)
- Z[k++] = Z[i++];
- for (; k <= p2;)
- Z[k++] = ZERO;
-}
-
-/* Add *X and *Y and store the result in *Z. X and Y may overlap, but not X
- and Z or Y and Z. One guard digit is used. The error is less than one
- ULP. */
-void
-__add (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- int n;
-
- if (X[0] == ZERO)
- {
- __cpy (y, z, p);
- return;
- }
- else if (Y[0] == ZERO)
- {
- __cpy (x, z, p);
- return;
- }
-
- if (X[0] == Y[0])
- {
- if (__acr (x, y, p) > 0)
- {
- add_magnitudes (x, y, z, p);
- Z[0] = X[0];
- }
- else
- {
- add_magnitudes (y, x, z, p);
- Z[0] = Y[0];
- }
- }
- else
- {
- if ((n = __acr (x, y, p)) == 1)
- {
- sub_magnitudes (x, y, z, p);
- Z[0] = X[0];
- }
- else if (n == -1)
- {
- sub_magnitudes (y, x, z, p);
- Z[0] = Y[0];
- }
- else
- Z[0] = ZERO;
- }
-}
-
-/* Subtract *Y from *X and return the result in *Z. X and Y may overlap but
- not X and Z or Y and Z. One guard digit is used. The error is less than
- one ULP. */
-void
-__sub (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- int n;
-
- if (X[0] == ZERO)
- {
- __cpy (y, z, p);
- Z[0] = -Z[0];
- return;
- }
- else if (Y[0] == ZERO)
- {
- __cpy (x, z, p);
- return;
- }
-
- if (X[0] != Y[0])
- {
- if (__acr (x, y, p) > 0)
- {
- add_magnitudes (x, y, z, p);
- Z[0] = X[0];
- }
- else
- {
- add_magnitudes (y, x, z, p);
- Z[0] = -Y[0];
- }
- }
- else
- {
- if ((n = __acr (x, y, p)) == 1)
- {
- sub_magnitudes (x, y, z, p);
- Z[0] = X[0];
- }
- else if (n == -1)
- {
- sub_magnitudes (y, x, z, p);
- Z[0] = -Y[0];
- }
- else
- Z[0] = ZERO;
- }
-}
-
-/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X
- and Z or Y and Z. For P in [1, 2, 3], the exact result is truncated to P
- digits. In case P > 3 the error is bounded by 1.001 ULP. */
-void
-__mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- long i, i1, i2, j, k, k2;
- long p2 = p;
- double u, zk, zk2;
-
- /* Is z=0? */
- if (__glibc_unlikely (X[0] * Y[0] == ZERO))
- {
- Z[0] = ZERO;
- return;
- }
-
- /* Multiply, add and carry */
- k2 = (p2 < 3) ? p2 + p2 : p2 + 3;
- zk = Z[k2] = ZERO;
- for (k = k2; k > 1;)
- {
- if (k > p2)
- {
- i1 = k - p2;
- i2 = p2 + 1;
- }
- else
- {
- i1 = 1;
- i2 = k;
- }
-#if 1
- /* Rearrange this inner loop to allow the fmadd instructions to be
- independent and execute in parallel on processors that have
- dual symmetrical FP pipelines. */
- if (i1 < (i2 - 1))
- {
- /* Make sure we have at least 2 iterations. */
- if (((i2 - i1) & 1L) == 1L)
- {
- /* Handle the odd iterations case. */
- zk2 = x->d[i2 - 1] * y->d[i1];
- }
- else
- zk2 = 0.0;
- /* Do two multiply/adds per loop iteration, using independent
- accumulators; zk and zk2. */
- for (i = i1, j = i2 - 1; i < i2 - 1; i += 2, j -= 2)
- {
- zk += x->d[i] * y->d[j];
- zk2 += x->d[i + 1] * y->d[j - 1];
- }
- zk += zk2; /* Final sum. */
- }
- else
- {
- /* Special case when iterations is 1. */
- zk += x->d[i1] * y->d[i1];
- }
-#else
- /* The original code. */
- for (i = i1, j = i2 - 1; i < i2; i++, j--)
- zk += X[i] * Y[j];
-#endif
-
- u = (zk + CUTTER) - CUTTER;
- if (u > zk)
- u -= RADIX;
- Z[k] = zk - u;
- zk = u * RADIXI;
- --k;
- }
- Z[k] = zk;
-
- /* Is there a carry beyond the most significant digit? */
- if (Z[1] == ZERO)
- {
- for (i = 1; i <= p2; i++)
- Z[i] = Z[i + 1];
- EZ = EX + EY - 1;
- }
- else
- EZ = EX + EY;
-
- Z[0] = X[0] * Y[0];
-}
-
-/* Square *X and store result in *Y. X and Y may not overlap. For P in
- [1, 2, 3], the exact result is truncated to P digits. In case P > 3 the
- error is bounded by 1.001 ULP. This is a faster special case of
- multiplication. */
-void
-__sqr (const mp_no *x, mp_no *y, int p)
-{
- long i, j, k, ip;
- double u, yk;
-
- /* Is z=0? */
- if (__glibc_unlikely (X[0] == ZERO))
- {
- Y[0] = ZERO;
- return;
- }
-
- /* We need not iterate through all X's since it's pointless to
- multiply zeroes. */
- for (ip = p; ip > 0; ip--)
- if (X[ip] != ZERO)
- break;
-
- k = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
-
- while (k > 2 * ip + 1)
- Y[k--] = ZERO;
-
- yk = ZERO;
-
- while (k > p)
- {
- double yk2 = 0.0;
- long lim = k / 2;
-
- if (k % 2 == 0)
- {
- yk += X[lim] * X[lim];
- lim--;
- }
-
- /* In __mul, this loop (and the one within the next while loop) run
- between a range to calculate the mantissa as follows:
-
- Z[k] = X[k] * Y[n] + X[k+1] * Y[n-1] ... + X[n-1] * Y[k+1]
- + X[n] * Y[k]
-
- For X == Y, we can get away with summing halfway and doubling the
- result. For cases where the range size is even, the mid-point needs
- to be added separately (above). */
- for (i = k - p, j = p; i <= lim; i++, j--)
- yk2 += X[i] * X[j];
-
- yk += 2.0 * yk2;
-
- u = (yk + CUTTER) - CUTTER;
- if (u > yk)
- u -= RADIX;
- Y[k--] = yk - u;
- yk = u * RADIXI;
- }
-
- while (k > 1)
- {
- double yk2 = 0.0;
- long lim = k / 2;
-
- if (k % 2 == 0)
- {
- yk += X[lim] * X[lim];
- lim--;
- }
-
- /* Likewise for this loop. */
- for (i = 1, j = k - 1; i <= lim; i++, j--)
- yk2 += X[i] * X[j];
-
- yk += 2.0 * yk2;
-
- u = (yk + CUTTER) - CUTTER;
- if (u > yk)
- u -= RADIX;
- Y[k--] = yk - u;
- yk = u * RADIXI;
- }
- Y[k] = yk;
-
- /* Squares are always positive. */
- Y[0] = 1.0;
-
- EY = 2 * EX;
- /* Is there a carry beyond the most significant digit? */
- if (__glibc_unlikely (Y[1] == ZERO))
- {
- for (i = 1; i <= p; i++)
- Y[i] = Y[i + 1];
- EY--;
- }
-}
-
-/* Invert *X and store in *Y. Relative error bound:
- - For P = 2: 1.001 * R ^ (1 - P)
- - For P = 3: 1.063 * R ^ (1 - P)
- - For P > 3: 2.001 * R ^ (1 - P)
-
- *X = 0 is not permissible. */
-static void
-__inv (const mp_no *x, mp_no *y, int p)
-{
- long i;
- double t;
- mp_no z, w;
- static const int np1[] =
- { 0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3,
- 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
- };
-
- __cpy (x, &z, p);
- z.e = 0;
- __mp_dbl (&z, &t, p);
- t = ONE / t;
- __dbl_mp (t, y, p);
- EY -= EX;
-
- for (i = 0; i < np1[p]; i++)
- {
- __cpy (y, &w, p);
- __mul (x, &w, y, p);
- __sub (&mptwo, y, &z, p);
- __mul (&w, &z, y, p);
- }
-}
-
-/* Divide *X by *Y and store result in *Z. X and Y may overlap but not X and Z
- or Y and Z. Relative error bound:
- - For P = 2: 2.001 * R ^ (1 - P)
- - For P = 3: 2.063 * R ^ (1 - P)
- - For P > 3: 3.001 * R ^ (1 - P)
-
- *X = 0 is not permissible. */
-void
-__dvd (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- mp_no w;
-
- if (X[0] == ZERO)
- Z[0] = ZERO;
- else
- {
- __inv (y, &w, p);
- __mul (x, &w, z, p);
- }
-}
diff --git a/sysdeps/powerpc/powerpc64/power4/Implies b/sysdeps/powerpc/powerpc64/power4/Implies
new file mode 100644
index 0000000..a372141
--- /dev/null
+++ b/sysdeps/powerpc/powerpc64/power4/Implies
@@ -0,0 +1,2 @@
+powerpc/power4/fpu
+powerpc/power4
diff --git a/sysdeps/powerpc/powerpc64/power4/fpu/Makefile b/sysdeps/powerpc/powerpc64/power4/fpu/Makefile
deleted file mode 100644
index f8bb3ef..0000000
--- a/sysdeps/powerpc/powerpc64/power4/fpu/Makefile
+++ /dev/null
@@ -1,5 +0,0 @@
-# Makefile fragment for POWER4/5/5+ platforms with FPU.
-
-ifeq ($(subdir),math)
-CFLAGS-mpa.c += --param max-unroll-times=4 -funroll-loops -fpeel-loops
-endif
diff --git a/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c b/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c
deleted file mode 100644
index f30d2cb..0000000
--- a/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c
+++ /dev/null
@@ -1,829 +0,0 @@
-
-/*
- * IBM Accurate Mathematical Library
- * written by International Business Machines Corp.
- * Copyright (C) 2001-2013 Free Software Foundation, Inc.
- *
- * This program 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.
- *
- * This program 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 this program; if not, see <http://www.gnu.org/licenses/>.
- */
-/************************************************************************/
-/* MODULE_NAME: mpa.c */
-/* */
-/* FUNCTIONS: */
-/* mcr */
-/* acr */
-/* cpy */
-/* norm */
-/* denorm */
-/* mp_dbl */
-/* dbl_mp */
-/* add_magnitudes */
-/* sub_magnitudes */
-/* add */
-/* sub */
-/* mul */
-/* inv */
-/* dvd */
-/* */
-/* Arithmetic functions for multiple precision numbers. */
-/* Relative errors are bounded */
-/************************************************************************/
-
-
-#include "endian.h"
-#include "mpa.h"
-#include <sys/param.h>
-
-const mp_no mpone = {1, {1.0, 1.0}};
-const mp_no mptwo = {1, {1.0, 2.0}};
-
-/* Compare mantissa of two multiple precision numbers regardless of the sign
- and exponent of the numbers. */
-static int
-mcr (const mp_no *x, const mp_no *y, int p)
-{
- long i;
- long p2 = p;
- for (i = 1; i <= p2; i++)
- {
- if (X[i] == Y[i])
- continue;
- else if (X[i] > Y[i])
- return 1;
- else
- return -1;
- }
- return 0;
-}
-
-/* Compare the absolute values of two multiple precision numbers. */
-int
-__acr (const mp_no *x, const mp_no *y, int p)
-{
- long i;
-
- if (X[0] == ZERO)
- {
- if (Y[0] == ZERO)
- i = 0;
- else
- i = -1;
- }
- else if (Y[0] == ZERO)
- i = 1;
- else
- {
- if (EX > EY)
- i = 1;
- else if (EX < EY)
- i = -1;
- else
- i = mcr (x, y, p);
- }
-
- return i;
-}
-
-/* Copy multiple precision number X into Y. They could be the same
- number. */
-void
-__cpy (const mp_no *x, mp_no *y, int p)
-{
- long i;
-
- EY = EX;
- for (i = 0; i <= p; i++)
- Y[i] = X[i];
-}
-
-/* Convert a multiple precision number *X into a double precision
- number *Y, normalized case (|x| >= 2**(-1022))). */
-static void
-norm (const mp_no *x, double *y, int p)
-{
-#define R RADIXI
- long i;
- double a, c, u, v, z[5];
- if (p < 5)
- {
- if (p == 1)
- c = X[1];
- else if (p == 2)
- c = X[1] + R * X[2];
- else if (p == 3)
- c = X[1] + R * (X[2] + R * X[3]);
- else if (p == 4)
- c = (X[1] + R * X[2]) + R * R * (X[3] + R * X[4]);
- }
- else
- {
- for (a = ONE, z[1] = X[1]; z[1] < TWO23;)
- {
- a *= TWO;
- z[1] *= TWO;
- }
-
- for (i = 2; i < 5; i++)
- {
- z[i] = X[i] * a;
- u = (z[i] + CUTTER) - CUTTER;
- if (u > z[i])
- u -= RADIX;
- z[i] -= u;
- z[i - 1] += u * RADIXI;
- }
-
- u = (z[3] + TWO71) - TWO71;
- if (u > z[3])
- u -= TWO19;
- v = z[3] - u;
-
- if (v == TWO18)
- {
- if (z[4] == ZERO)
- {
- for (i = 5; i <= p; i++)
- {
- if (X[i] == ZERO)
- continue;
- else
- {
- z[3] += ONE;
- break;
- }
- }
- }
- else
- z[3] += ONE;
- }
-
- c = (z[1] + R * (z[2] + R * z[3])) / a;
- }
-
- c *= X[0];
-
- for (i = 1; i < EX; i++)
- c *= RADIX;
- for (i = 1; i > EX; i--)
- c *= RADIXI;
-
- *y = c;
-#undef R
-}
-
-/* Convert a multiple precision number *X into a double precision
- number *Y, Denormal case (|x| < 2**(-1022))). */
-static void
-denorm (const mp_no *x, double *y, int p)
-{
- long i, k;
- long p2 = p;
- double c, u, z[5];
-
-#define R RADIXI
- if (EX < -44 || (EX == -44 && X[1] < TWO5))
- {
- *y = ZERO;
- return;
- }
-
- if (p2 == 1)
- {
- if (EX == -42)
- {
- z[1] = X[1] + TWO10;
- z[2] = ZERO;
- z[3] = ZERO;
- k = 3;
- }
- else if (EX == -43)
- {
- z[1] = TWO10;
- z[2] = X[1];
- z[3] = ZERO;
- k = 2;
- }
- else
- {
- z[1] = TWO10;
- z[2] = ZERO;
- z[3] = X[1];
- k = 1;
- }
- }
- else if (p2 == 2)
- {
- if (EX == -42)
- {
- z[1] = X[1] + TWO10;
- z[2] = X[2];
- z[3] = ZERO;
- k = 3;
- }
- else if (EX == -43)
- {
- z[1] = TWO10;
- z[2] = X[1];
- z[3] = X[2];
- k = 2;
- }
- else
- {
- z[1] = TWO10;
- z[2] = ZERO;
- z[3] = X[1];
- k = 1;
- }
- }
- else
- {
- if (EX == -42)
- {
- z[1] = X[1] + TWO10;
- z[2] = X[2];
- k = 3;
- }
- else if (EX == -43)
- {
- z[1] = TWO10;
- z[2] = X[1];
- k = 2;
- }
- else
- {
- z[1] = TWO10;
- z[2] = ZERO;
- k = 1;
- }
- z[3] = X[k];
- }
-
- u = (z[3] + TWO57) - TWO57;
- if (u > z[3])
- u -= TWO5;
-
- if (u == z[3])
- {
- for (i = k + 1; i <= p2; i++)
- {
- if (X[i] == ZERO)
- continue;
- else
- {
- z[3] += ONE;
- break;
- }
- }
- }
-
- c = X[0] * ((z[1] + R * (z[2] + R * z[3])) - TWO10);
-
- *y = c * TWOM1032;
-#undef R
-}
-
-/* Convert multiple precision number *X into double precision number *Y. The
- result is correctly rounded to the nearest/even. */
-void
-__mp_dbl (const mp_no *x, double *y, int p)
-{
- if (X[0] == ZERO)
- {
- *y = ZERO;
- return;
- }
-
- if (__glibc_likely (EX > -42 || (EX == -42 && X[1] >= TWO10)))
- norm (x, y, p);
- else
- denorm (x, y, p);
-}
-
-/* Get the multiple precision equivalent of X into *Y. If the precision is too
- small, the result is truncated. */
-void
-__dbl_mp (double x, mp_no *y, int p)
-{
- long i, n;
- long p2 = p;
- double u;
-
- /* Sign. */
- if (x == ZERO)
- {
- Y[0] = ZERO;
- return;
- }
- else if (x > ZERO)
- Y[0] = ONE;
- else
- {
- Y[0] = MONE;
- x = -x;
- }
-
- /* Exponent. */
- for (EY = ONE; x >= RADIX; EY += ONE)
- x *= RADIXI;
- for (; x < ONE; EY -= ONE)
- x *= RADIX;
-
- /* Digits. */
- n = MIN (p2, 4);
- for (i = 1; i <= n; i++)
- {
- u = (x + TWO52) - TWO52;
- if (u > x)
- u -= ONE;
- Y[i] = u;
- x -= u;
- x *= RADIX;
- }
- for (; i <= p2; i++)
- Y[i] = ZERO;
-}
-
-/* Add magnitudes of *X and *Y assuming that abs (*X) >= abs (*Y) > 0. The
- sign of the sum *Z is not changed. X and Y may overlap but not X and Z or
- Y and Z. No guard digit is used. The result equals the exact sum,
- truncated. */
-static void
-add_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- long i, j, k;
- long p2 = p;
-
- EZ = EX;
-
- i = p2;
- j = p2 + EY - EX;
- k = p2 + 1;
-
- if (j < 1)
- {
- __cpy (x, z, p);
- return;
- }
- else
- Z[k] = ZERO;
-
- for (; j > 0; i--, j--)
- {
- Z[k] += X[i] + Y[j];
- if (Z[k] >= RADIX)
- {
- Z[k] -= RADIX;
- Z[--k] = ONE;
- }
- else
- Z[--k] = ZERO;
- }
-
- for (; i > 0; i--)
- {
- Z[k] += X[i];
- if (Z[k] >= RADIX)
- {
- Z[k] -= RADIX;
- Z[--k] = ONE;
- }
- else
- Z[--k] = ZERO;
- }
-
- if (Z[1] == ZERO)
- {
- for (i = 1; i <= p2; i++)
- Z[i] = Z[i + 1];
- }
- else
- EZ += ONE;
-}
-
-/* Subtract the magnitudes of *X and *Y assuming that abs (*x) > abs (*y) > 0.
- The sign of the difference *Z is not changed. X and Y may overlap but not X
- and Z or Y and Z. One guard digit is used. The error is less than one
- ULP. */
-static void
-sub_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- long i, j, k;
- long p2 = p;
-
- EZ = EX;
-
- if (EX == EY)
- {
- i = j = k = p2;
- Z[k] = Z[k + 1] = ZERO;
- }
- else
- {
- j = EX - EY;
- if (j > p2)
- {
- __cpy (x, z, p);
- return;
- }
- else
- {
- i = p2;
- j = p2 + 1 - j;
- k = p2;
- if (Y[j] > ZERO)
- {
- Z[k + 1] = RADIX - Y[j--];
- Z[k] = MONE;
- }
- else
- {
- Z[k + 1] = ZERO;
- Z[k] = ZERO;
- j--;
- }
- }
- }
-
- for (; j > 0; i--, j--)
- {
- Z[k] += (X[i] - Y[j]);
- if (Z[k] < ZERO)
- {
- Z[k] += RADIX;
- Z[--k] = MONE;
- }
- else
- Z[--k] = ZERO;
- }
-
- for (; i > 0; i--)
- {
- Z[k] += X[i];
- if (Z[k] < ZERO)
- {
- Z[k] += RADIX;
- Z[--k] = MONE;
- }
- else
- Z[--k] = ZERO;
- }
-
- for (i = 1; Z[i] == ZERO; i++);
- EZ = EZ - i + 1;
- for (k = 1; i <= p2 + 1;)
- Z[k++] = Z[i++];
- for (; k <= p2;)
- Z[k++] = ZERO;
-}
-
-/* Add *X and *Y and store the result in *Z. X and Y may overlap, but not X
- and Z or Y and Z. One guard digit is used. The error is less than one
- ULP. */
-void
-__add (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- int n;
-
- if (X[0] == ZERO)
- {
- __cpy (y, z, p);
- return;
- }
- else if (Y[0] == ZERO)
- {
- __cpy (x, z, p);
- return;
- }
-
- if (X[0] == Y[0])
- {
- if (__acr (x, y, p) > 0)
- {
- add_magnitudes (x, y, z, p);
- Z[0] = X[0];
- }
- else
- {
- add_magnitudes (y, x, z, p);
- Z[0] = Y[0];
- }
- }
- else
- {
- if ((n = __acr (x, y, p)) == 1)
- {
- sub_magnitudes (x, y, z, p);
- Z[0] = X[0];
- }
- else if (n == -1)
- {
- sub_magnitudes (y, x, z, p);
- Z[0] = Y[0];
- }
- else
- Z[0] = ZERO;
- }
-}
-
-/* Subtract *Y from *X and return the result in *Z. X and Y may overlap but
- not X and Z or Y and Z. One guard digit is used. The error is less than
- one ULP. */
-void
-__sub (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- int n;
-
- if (X[0] == ZERO)
- {
- __cpy (y, z, p);
- Z[0] = -Z[0];
- return;
- }
- else if (Y[0] == ZERO)
- {
- __cpy (x, z, p);
- return;
- }
-
- if (X[0] != Y[0])
- {
- if (__acr (x, y, p) > 0)
- {
- add_magnitudes (x, y, z, p);
- Z[0] = X[0];
- }
- else
- {
- add_magnitudes (y, x, z, p);
- Z[0] = -Y[0];
- }
- }
- else
- {
- if ((n = __acr (x, y, p)) == 1)
- {
- sub_magnitudes (x, y, z, p);
- Z[0] = X[0];
- }
- else if (n == -1)
- {
- sub_magnitudes (y, x, z, p);
- Z[0] = -Y[0];
- }
- else
- Z[0] = ZERO;
- }
-}
-
-/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X
- and Z or Y and Z. For P in [1, 2, 3], the exact result is truncated to P
- digits. In case P > 3 the error is bounded by 1.001 ULP. */
-void
-__mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- long i, i1, i2, j, k, k2;
- long p2 = p;
- double u, zk, zk2;
-
- /* Is z=0? */
- if (__glibc_unlikely (X[0] * Y[0] == ZERO))
- {
- Z[0] = ZERO;
- return;
- }
-
- /* Multiply, add and carry */
- k2 = (p2 < 3) ? p2 + p2 : p2 + 3;
- zk = Z[k2] = ZERO;
- for (k = k2; k > 1;)
- {
- if (k > p2)
- {
- i1 = k - p2;
- i2 = p2 + 1;
- }
- else
- {
- i1 = 1;
- i2 = k;
- }
-#if 1
- /* Rearrange this inner loop to allow the fmadd instructions to be
- independent and execute in parallel on processors that have
- dual symmetrical FP pipelines. */
- if (i1 < (i2 - 1))
- {
- /* Make sure we have at least 2 iterations. */
- if (((i2 - i1) & 1L) == 1L)
- {
- /* Handle the odd iterations case. */
- zk2 = x->d[i2 - 1] * y->d[i1];
- }
- else
- zk2 = 0.0;
- /* Do two multiply/adds per loop iteration, using independent
- accumulators; zk and zk2. */
- for (i = i1, j = i2 - 1; i < i2 - 1; i += 2, j -= 2)
- {
- zk += x->d[i] * y->d[j];
- zk2 += x->d[i + 1] * y->d[j - 1];
- }
- zk += zk2; /* Final sum. */
- }
- else
- {
- /* Special case when iterations is 1. */
- zk += x->d[i1] * y->d[i1];
- }
-#else
- /* The original code. */
- for (i = i1, j = i2 - 1; i < i2; i++, j--)
- zk += X[i] * Y[j];
-#endif
-
- u = (zk + CUTTER) - CUTTER;
- if (u > zk)
- u -= RADIX;
- Z[k] = zk - u;
- zk = u * RADIXI;
- --k;
- }
- Z[k] = zk;
-
- /* Is there a carry beyond the most significant digit? */
- if (Z[1] == ZERO)
- {
- for (i = 1; i <= p2; i++)
- Z[i] = Z[i + 1];
- EZ = EX + EY - 1;
- }
- else
- EZ = EX + EY;
-
- Z[0] = X[0] * Y[0];
-}
-
-/* Square *X and store result in *Y. X and Y may not overlap. For P in
- [1, 2, 3], the exact result is truncated to P digits. In case P > 3 the
- error is bounded by 1.001 ULP. This is a faster special case of
- multiplication. */
-void
-__sqr (const mp_no *x, mp_no *y, int p)
-{
- long i, j, k, ip;
- double u, yk;
-
- /* Is z=0? */
- if (__glibc_unlikely (X[0] == ZERO))
- {
- Y[0] = ZERO;
- return;
- }
-
- /* We need not iterate through all X's since it's pointless to
- multiply zeroes. */
- for (ip = p; ip > 0; ip--)
- if (X[ip] != ZERO)
- break;
-
- k = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
-
- while (k > 2 * ip + 1)
- Y[k--] = ZERO;
-
- yk = ZERO;
-
- while (k > p)
- {
- double yk2 = 0.0;
- long lim = k / 2;
-
- if (k % 2 == 0)
- {
- yk += X[lim] * X[lim];
- lim--;
- }
-
- /* In __mul, this loop (and the one within the next while loop) run
- between a range to calculate the mantissa as follows:
-
- Z[k] = X[k] * Y[n] + X[k+1] * Y[n-1] ... + X[n-1] * Y[k+1]
- + X[n] * Y[k]
-
- For X == Y, we can get away with summing halfway and doubling the
- result. For cases where the range size is even, the mid-point needs
- to be added separately (above). */
- for (i = k - p, j = p; i <= lim; i++, j--)
- yk2 += X[i] * X[j];
-
- yk += 2.0 * yk2;
-
- u = (yk + CUTTER) - CUTTER;
- if (u > yk)
- u -= RADIX;
- Y[k--] = yk - u;
- yk = u * RADIXI;
- }
-
- while (k > 1)
- {
- double yk2 = 0.0;
- long lim = k / 2;
-
- if (k % 2 == 0)
- {
- yk += X[lim] * X[lim];
- lim--;
- }
-
- /* Likewise for this loop. */
- for (i = 1, j = k - 1; i <= lim; i++, j--)
- yk2 += X[i] * X[j];
-
- yk += 2.0 * yk2;
-
- u = (yk + CUTTER) - CUTTER;
- if (u > yk)
- u -= RADIX;
- Y[k--] = yk - u;
- yk = u * RADIXI;
- }
- Y[k] = yk;
-
- /* Squares are always positive. */
- Y[0] = 1.0;
-
- EY = 2 * EX;
- /* Is there a carry beyond the most significant digit? */
- if (__glibc_unlikely (Y[1] == ZERO))
- {
- for (i = 1; i <= p; i++)
- Y[i] = Y[i + 1];
- EY--;
- }
-}
-
-/* Invert *X and store in *Y. Relative error bound:
- - For P = 2: 1.001 * R ^ (1 - P)
- - For P = 3: 1.063 * R ^ (1 - P)
- - For P > 3: 2.001 * R ^ (1 - P)
-
- *X = 0 is not permissible. */
-static void
-__inv (const mp_no *x, mp_no *y, int p)
-{
- long i;
- double t;
- mp_no z, w;
- static const int np1[] =
- { 0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3,
- 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
- };
-
- __cpy (x, &z, p);
- z.e = 0;
- __mp_dbl (&z, &t, p);
- t = ONE / t;
- __dbl_mp (t, y, p);
- EY -= EX;
-
- for (i = 0; i < np1[p]; i++)
- {
- __cpy (y, &w, p);
- __mul (x, &w, y, p);
- __sub (&mptwo, y, &z, p);
- __mul (&w, &z, y, p);
- }
-}
-
-/* Divide *X by *Y and store result in *Z. X and Y may overlap but not X and Z
- or Y and Z. Relative error bound:
- - For P = 2: 2.001 * R ^ (1 - P)
- - For P = 3: 2.063 * R ^ (1 - P)
- - For P > 3: 3.001 * R ^ (1 - P)
-
- *X = 0 is not permissible. */
-void
-__dvd (const mp_no *x, const mp_no *y, mp_no *z, int p)
-{
- mp_no w;
-
- if (X[0] == ZERO)
- Z[0] = ZERO;
- else
- {
- __inv (y, &w, p);
- __mul (x, &w, z, p);
- }
-}