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base/SOURCES/glibc-rh731833-libm-2.patch

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From 66bf22e129f0b8621903a8b0489b2684e70fad65 Mon Sep 17 00:00:00 2001
From: Siddhesh Poyarekar <siddhesh@redhat.com>
Date: Fri, 8 Mar 2013 11:38:41 +0530
Subject: [PATCH 17/42] Consolidate copies of mp code in powerpc
Retain a single copy of the mp code in power4 instead of the two
identical copies in powerpc32 and powerpc64.
(backported from commit 6d9145d817e570cd986bb088cf2af0bf51ac7dde)
---
sysdeps/powerpc/power4/fpu/Makefile | 5 +
sysdeps/powerpc/power4/fpu/mpa.c | 548 ++++++++++++++++++++++++++
sysdeps/powerpc/powerpc32/power4/Implies | 2 +
sysdeps/powerpc/powerpc32/power4/fpu/Makefile | 5 -
sysdeps/powerpc/powerpc32/power4/fpu/mpa.c | 548 --------------------------
sysdeps/powerpc/powerpc64/power4/Implies | 2 +
sysdeps/powerpc/powerpc64/power4/fpu/Makefile | 5 -
sysdeps/powerpc/powerpc64/power4/fpu/mpa.c | 548 --------------------------
9 files changed, 568 insertions(+), 1106 deletions(-)
create mode 100644 sysdeps/powerpc/power4/fpu/Makefile
create mode 100644 sysdeps/powerpc/power4/fpu/mpa.c
create mode 100644 sysdeps/powerpc/powerpc32/power4/Implies
delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/Makefile
delete mode 100644 sysdeps/powerpc/powerpc32/power4/fpu/mpa.c
create mode 100644 sysdeps/powerpc/powerpc64/power4/Implies
delete mode 100644 sysdeps/powerpc/powerpc64/power4/fpu/Makefile
delete mode 100644 sysdeps/powerpc/powerpc64/power4/fpu/mpa.c
diff --git glibc-2.17-c758a686/sysdeps/powerpc/power4/fpu/Makefile glibc-2.17-c758a686/sysdeps/powerpc/power4/fpu/Makefile
new file mode 100644
index 0000000..f487ed6
--- /dev/null
+++ glibc-2.17-c758a686/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 glibc-2.17-c758a686/sysdeps/powerpc/power4/fpu/mpa.c glibc-2.17-c758a686/sysdeps/powerpc/power4/fpu/mpa.c
new file mode 100644
index 0000000..d15680e
--- /dev/null
+++ glibc-2.17-c758a686/sysdeps/powerpc/power4/fpu/mpa.c
@@ -0,0 +1,548 @@
+
+/*
+ * IBM Accurate Mathematical Library
+ * written by International Business Machines Corp.
+ * Copyright (C) 2001, 2006 Free Software Foundation
+ *
+ * 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 */
+/* cr */
+/* cpy */
+/* cpymn */
+/* 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 "mpa2.h"
+#include <sys/param.h> /* For MIN() */
+/* mcr() compares the sizes of the mantissas of two multiple precision */
+/* numbers. Mantissas are compared regardless of the signs of the */
+/* numbers, even if x->d[0] or y->d[0] are zero. Exponents are also */
+/* disregarded. */
+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;
+}
+
+
+
+/* acr() compares 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;
+}
+
+
+/* cr90 compares the values of two multiple precision numbers */
+int __cr(const mp_no *x, const mp_no *y, int p) {
+ int i;
+
+ if (X[0] > Y[0]) i= 1;
+ else if (X[0] < Y[0]) i=-1;
+ else if (X[0] < ZERO ) i= __acr(y,x,p);
+ else i= __acr(x,y,p);
+
+ return i;
+}
+
+
+/* Copy a multiple precision number. Set *y=*x. x=y is permissible. */
+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];
+
+ return;
+}
+
+
+/* Copy a multiple precision number x of precision m into a */
+/* multiple precision number y of precision n. In case n>m, */
+/* the digits of y beyond the m'th are set to zero. In case */
+/* n<m, the digits of x beyond the n'th are ignored. */
+/* x=y is permissible. */
+
+void __cpymn(const mp_no *x, int m, mp_no *y, int n) {
+
+ long i,k;
+ long n2 = n;
+ long m2 = m;
+
+ EY = EX; k=MIN(m2,n2);
+ for (i=0; i <= k; i++) Y[i] = X[i];
+ for ( ; i <= n2; i++) Y[i] = ZERO;
+
+ return;
+}
+
+/* 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.d
+ long i;
+#if 0
+ int k;
+#endif
+ 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;
+ return;
+#undef R
+}
+
+/* Convert a multiple precision number *x into a double precision */
+/* number *y, denormalized 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];
+#if 0
+ double a,v;
+#endif
+
+#define R radixi.d
+ 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;
+ return;
+
+#undef R
+}
+
+/* Convert a multiple precision number *x into a double precision number *y. */
+/* The result is correctly rounded to the nearest/even. *x is left unchanged */
+
+void __mp_dbl(const mp_no *x, double *y, int p) {
+#if 0
+ int i,k;
+ double a,c,u,v,z[5];
+#endif
+
+ if (X[0] == ZERO) {*y = ZERO; return; }
+
+ if (EX> -42) norm(x,y,p);
+ else if (EX==-42 && X[1]>=TWO10) norm(x,y,p);
+ else denorm(x,y,p);
+}
+
+
+/* dbl_mp() converts a double precision number x into a multiple precision */
+/* number *y. If the precision p is too small the result is truncated. x is */
+/* left unchanged. */
+
+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;
+ return;
+}
+
+
+/* add_magnitudes() adds the magnitudes of *x & *y assuming that */
+/* abs(*x) >= abs(*y) > 0. */
+/* The sign of the sum *z is undefined. x&y may overlap but not x&z or y&z. */
+/* No guard digit is used. The result equals the exact sum, truncated. */
+/* *x & *y are left unchanged. */
+
+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;
+}
+
+
+/* sub_magnitudes() subtracts the magnitudes of *x & *y assuming that */
+/* abs(*x) > abs(*y) > 0. */
+/* The sign of the difference *z is undefined. x&y may overlap but not x&z */
+/* or y&z. One guard digit is used. The error is less than one ulp. */
+/* *x & *y are left unchanged. */
+
+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;
+
+ return;
+}
+
+
+/* Add two multiple precision numbers. Set *z = *x + *y. x&y may overlap */
+/* but not x&z or y&z. One guard digit is used. The error is less than */
+/* one ulp. *x & *y are left unchanged. */
+
+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;
+ }
+ return;
+}
+
+
+/* Subtract two multiple precision numbers. *z is set to *x - *y. x&y may */
+/* overlap but not x&z or y&z. One guard digit is used. The error is */
+/* less than one ulp. *x & *y are left unchanged. */
+
+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;
+ }
+ return;
+}
+
+
+/* Multiply two multiple precision numbers. *z is set to *x * *y. x&y */
+/* may overlap but not x&z or y&z. In case p=1,2,3 the exact result is */
+/* truncated to p digits. In case p>3 the error is bounded by 1.001 ulp. */
+/* *x & *y are left unchanged. */
+
+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 (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
+ /* rearange this inner loop to allow the fmadd instructions to be
+ independent and execute in parallel on processors that have
+ dual symetrical 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 = zero.d;
+ /* 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 orginal 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];
+ return;
+}
+
+
+/* Invert a multiple precision number. Set *y = 1 / *x. */
+/* Relative error bound = 1.001*r**(1-p) for p=2, 1.063*r**(1-p) for p=3, */
+/* 2.001*r**(1-p) for p>3. */
+/* *x=0 is not permissible. *x is left unchanged. */
+
+void __inv(const mp_no *x, mp_no *y, int p) {
+ long i;
+#if 0
+ int l;
+#endif
+ 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};
+ const mp_no mptwo = {1,{1.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
+ 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
+ 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
+ 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
+
+ __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);
+ }
+ return;
+}
+
+
+/* Divide one multiple precision number by another.Set *z = *x / *y. *x & *y */
+/* are left unchanged. x&y may overlap but not x&z or y&z. */
+/* Relative error bound = 2.001*r**(1-p) for p=2, 2.063*r**(1-p) for p=3 */
+/* and 3.001*r**(1-p) for p>3. *y=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);}
+ return;
+}
diff --git glibc-2.17-c758a686/sysdeps/powerpc/powerpc32/power4/Implies glibc-2.17-c758a686/sysdeps/powerpc/powerpc32/power4/Implies
new file mode 100644
index 0000000..a372141
--- /dev/null
+++ glibc-2.17-c758a686/sysdeps/powerpc/powerpc32/power4/Implies
@@ -0,0 +1,2 @@
+powerpc/power4/fpu
+powerpc/power4
diff --git glibc-2.17-c758a686/sysdeps/powerpc/powerpc32/power4/fpu/Makefile glibc-2.17-c758a686/sysdeps/powerpc/powerpc32/power4/fpu/Makefile
deleted file mode 100644
index f487ed6..0000000
--- glibc-2.17-c758a686/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 glibc-2.17-c758a686/sysdeps/powerpc/powerpc32/power4/fpu/mpa.c glibc-2.17-c758a686/sysdeps/powerpc/powerpc32/power4/fpu/mpa.c
deleted file mode 100644
index d15680e..0000000
--- glibc-2.17-c758a686/sysdeps/powerpc/powerpc32/power4/fpu/mpa.c
+++ /dev/null
@@ -1,548 +0,0 @@
-
-/*
- * IBM Accurate Mathematical Library
- * written by International Business Machines Corp.
- * Copyright (C) 2001, 2006 Free Software Foundation
- *
- * 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 */
-/* cr */
-/* cpy */
-/* cpymn */
-/* 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 "mpa2.h"
-#include <sys/param.h> /* For MIN() */
-/* mcr() compares the sizes of the mantissas of two multiple precision */
-/* numbers. Mantissas are compared regardless of the signs of the */
-/* numbers, even if x->d[0] or y->d[0] are zero. Exponents are also */
-/* disregarded. */
-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;
-}
-
-
-
-/* acr() compares 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;
-}
-
-
-/* cr90 compares the values of two multiple precision numbers */
-int __cr(const mp_no *x, const mp_no *y, int p) {
- int i;
-
- if (X[0] > Y[0]) i= 1;
- else if (X[0] < Y[0]) i=-1;
- else if (X[0] < ZERO ) i= __acr(y,x,p);
- else i= __acr(x,y,p);
-
- return i;
-}
-
-
-/* Copy a multiple precision number. Set *y=*x. x=y is permissible. */
-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];
-
- return;
-}
-
-
-/* Copy a multiple precision number x of precision m into a */
-/* multiple precision number y of precision n. In case n>m, */
-/* the digits of y beyond the m'th are set to zero. In case */
-/* n<m, the digits of x beyond the n'th are ignored. */
-/* x=y is permissible. */
-
-void __cpymn(const mp_no *x, int m, mp_no *y, int n) {
-
- long i,k;
- long n2 = n;
- long m2 = m;
-
- EY = EX; k=MIN(m2,n2);
- for (i=0; i <= k; i++) Y[i] = X[i];
- for ( ; i <= n2; i++) Y[i] = ZERO;
-
- return;
-}
-
-/* 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.d
- long i;
-#if 0
- int k;
-#endif
- 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;
- return;
-#undef R
-}
-
-/* Convert a multiple precision number *x into a double precision */
-/* number *y, denormalized 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];
-#if 0
- double a,v;
-#endif
-
-#define R radixi.d
- 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;
- return;
-
-#undef R
-}
-
-/* Convert a multiple precision number *x into a double precision number *y. */
-/* The result is correctly rounded to the nearest/even. *x is left unchanged */
-
-void __mp_dbl(const mp_no *x, double *y, int p) {
-#if 0
- int i,k;
- double a,c,u,v,z[5];
-#endif
-
- if (X[0] == ZERO) {*y = ZERO; return; }
-
- if (EX> -42) norm(x,y,p);
- else if (EX==-42 && X[1]>=TWO10) norm(x,y,p);
- else denorm(x,y,p);
-}
-
-
-/* dbl_mp() converts a double precision number x into a multiple precision */
-/* number *y. If the precision p is too small the result is truncated. x is */
-/* left unchanged. */
-
-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;
- return;
-}
-
-
-/* add_magnitudes() adds the magnitudes of *x & *y assuming that */
-/* abs(*x) >= abs(*y) > 0. */
-/* The sign of the sum *z is undefined. x&y may overlap but not x&z or y&z. */
-/* No guard digit is used. The result equals the exact sum, truncated. */
-/* *x & *y are left unchanged. */
-
-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;
-}
-
-
-/* sub_magnitudes() subtracts the magnitudes of *x & *y assuming that */
-/* abs(*x) > abs(*y) > 0. */
-/* The sign of the difference *z is undefined. x&y may overlap but not x&z */
-/* or y&z. One guard digit is used. The error is less than one ulp. */
-/* *x & *y are left unchanged. */
-
-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;
-
- return;
-}
-
-
-/* Add two multiple precision numbers. Set *z = *x + *y. x&y may overlap */
-/* but not x&z or y&z. One guard digit is used. The error is less than */
-/* one ulp. *x & *y are left unchanged. */
-
-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;
- }
- return;
-}
-
-
-/* Subtract two multiple precision numbers. *z is set to *x - *y. x&y may */
-/* overlap but not x&z or y&z. One guard digit is used. The error is */
-/* less than one ulp. *x & *y are left unchanged. */
-
-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;
- }
- return;
-}
-
-
-/* Multiply two multiple precision numbers. *z is set to *x * *y. x&y */
-/* may overlap but not x&z or y&z. In case p=1,2,3 the exact result is */
-/* truncated to p digits. In case p>3 the error is bounded by 1.001 ulp. */
-/* *x & *y are left unchanged. */
-
-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 (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
- /* rearange this inner loop to allow the fmadd instructions to be
- independent and execute in parallel on processors that have
- dual symetrical 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 = zero.d;
- /* 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 orginal 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];
- return;
-}
-
-
-/* Invert a multiple precision number. Set *y = 1 / *x. */
-/* Relative error bound = 1.001*r**(1-p) for p=2, 1.063*r**(1-p) for p=3, */
-/* 2.001*r**(1-p) for p>3. */
-/* *x=0 is not permissible. *x is left unchanged. */
-
-void __inv(const mp_no *x, mp_no *y, int p) {
- long i;
-#if 0
- int l;
-#endif
- 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};
- const mp_no mptwo = {1,{1.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
- 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
- 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
- 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
-
- __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);
- }
- return;
-}
-
-
-/* Divide one multiple precision number by another.Set *z = *x / *y. *x & *y */
-/* are left unchanged. x&y may overlap but not x&z or y&z. */
-/* Relative error bound = 2.001*r**(1-p) for p=2, 2.063*r**(1-p) for p=3 */
-/* and 3.001*r**(1-p) for p>3. *y=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);}
- return;
-}
diff --git glibc-2.17-c758a686/sysdeps/powerpc/powerpc64/power4/Implies glibc-2.17-c758a686/sysdeps/powerpc/powerpc64/power4/Implies
new file mode 100644
index 0000000..a372141
--- /dev/null
+++ glibc-2.17-c758a686/sysdeps/powerpc/powerpc64/power4/Implies
@@ -0,0 +1,2 @@
+powerpc/power4/fpu
+powerpc/power4
diff --git glibc-2.17-c758a686/sysdeps/powerpc/powerpc64/power4/fpu/Makefile glibc-2.17-c758a686/sysdeps/powerpc/powerpc64/power4/fpu/Makefile
deleted file mode 100644
index f8bb3ef..0000000
--- glibc-2.17-c758a686/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 glibc-2.17-c758a686/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c glibc-2.17-c758a686/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c
deleted file mode 100644
index d15680e..0000000
--- glibc-2.17-c758a686/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c
+++ /dev/null
@@ -1,548 +0,0 @@
-
-/*
- * IBM Accurate Mathematical Library
- * written by International Business Machines Corp.
- * Copyright (C) 2001, 2006 Free Software Foundation
- *
- * 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 */
-/* cr */
-/* cpy */
-/* cpymn */
-/* 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 "mpa2.h"
-#include <sys/param.h> /* For MIN() */
-/* mcr() compares the sizes of the mantissas of two multiple precision */
-/* numbers. Mantissas are compared regardless of the signs of the */
-/* numbers, even if x->d[0] or y->d[0] are zero. Exponents are also */
-/* disregarded. */
-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;
-}
-
-
-
-/* acr() compares 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;
-}
-
-
-/* cr90 compares the values of two multiple precision numbers */
-int __cr(const mp_no *x, const mp_no *y, int p) {
- int i;
-
- if (X[0] > Y[0]) i= 1;
- else if (X[0] < Y[0]) i=-1;
- else if (X[0] < ZERO ) i= __acr(y,x,p);
- else i= __acr(x,y,p);
-
- return i;
-}
-
-
-/* Copy a multiple precision number. Set *y=*x. x=y is permissible. */
-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];
-
- return;
-}
-
-
-/* Copy a multiple precision number x of precision m into a */
-/* multiple precision number y of precision n. In case n>m, */
-/* the digits of y beyond the m'th are set to zero. In case */
-/* n<m, the digits of x beyond the n'th are ignored. */
-/* x=y is permissible. */
-
-void __cpymn(const mp_no *x, int m, mp_no *y, int n) {
-
- long i,k;
- long n2 = n;
- long m2 = m;
-
- EY = EX; k=MIN(m2,n2);
- for (i=0; i <= k; i++) Y[i] = X[i];
- for ( ; i <= n2; i++) Y[i] = ZERO;
-
- return;
-}
-
-/* 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.d
- long i;
-#if 0
- int k;
-#endif
- 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;
- return;
-#undef R
-}
-
-/* Convert a multiple precision number *x into a double precision */
-/* number *y, denormalized 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];
-#if 0
- double a,v;
-#endif
-
-#define R radixi.d
- 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;
- return;
-
-#undef R
-}
-
-/* Convert a multiple precision number *x into a double precision number *y. */
-/* The result is correctly rounded to the nearest/even. *x is left unchanged */
-
-void __mp_dbl(const mp_no *x, double *y, int p) {
-#if 0
- int i,k;
- double a,c,u,v,z[5];
-#endif
-
- if (X[0] == ZERO) {*y = ZERO; return; }
-
- if (EX> -42) norm(x,y,p);
- else if (EX==-42 && X[1]>=TWO10) norm(x,y,p);
- else denorm(x,y,p);
-}
-
-
-/* dbl_mp() converts a double precision number x into a multiple precision */
-/* number *y. If the precision p is too small the result is truncated. x is */
-/* left unchanged. */
-
-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;
- return;
-}
-
-
-/* add_magnitudes() adds the magnitudes of *x & *y assuming that */
-/* abs(*x) >= abs(*y) > 0. */
-/* The sign of the sum *z is undefined. x&y may overlap but not x&z or y&z. */
-/* No guard digit is used. The result equals the exact sum, truncated. */
-/* *x & *y are left unchanged. */
-
-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;
-}
-
-
-/* sub_magnitudes() subtracts the magnitudes of *x & *y assuming that */
-/* abs(*x) > abs(*y) > 0. */
-/* The sign of the difference *z is undefined. x&y may overlap but not x&z */
-/* or y&z. One guard digit is used. The error is less than one ulp. */
-/* *x & *y are left unchanged. */
-
-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;
-
- return;
-}
-
-
-/* Add two multiple precision numbers. Set *z = *x + *y. x&y may overlap */
-/* but not x&z or y&z. One guard digit is used. The error is less than */
-/* one ulp. *x & *y are left unchanged. */
-
-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;
- }
- return;
-}
-
-
-/* Subtract two multiple precision numbers. *z is set to *x - *y. x&y may */
-/* overlap but not x&z or y&z. One guard digit is used. The error is */
-/* less than one ulp. *x & *y are left unchanged. */
-
-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;
- }
- return;
-}
-
-
-/* Multiply two multiple precision numbers. *z is set to *x * *y. x&y */
-/* may overlap but not x&z or y&z. In case p=1,2,3 the exact result is */
-/* truncated to p digits. In case p>3 the error is bounded by 1.001 ulp. */
-/* *x & *y are left unchanged. */
-
-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 (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
- /* rearange this inner loop to allow the fmadd instructions to be
- independent and execute in parallel on processors that have
- dual symetrical 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 = zero.d;
- /* 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 orginal 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];
- return;
-}
-
-
-/* Invert a multiple precision number. Set *y = 1 / *x. */
-/* Relative error bound = 1.001*r**(1-p) for p=2, 1.063*r**(1-p) for p=3, */
-/* 2.001*r**(1-p) for p>3. */
-/* *x=0 is not permissible. *x is left unchanged. */
-
-void __inv(const mp_no *x, mp_no *y, int p) {
- long i;
-#if 0
- int l;
-#endif
- 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};
- const mp_no mptwo = {1,{1.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
- 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
- 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
- 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
-
- __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);
- }
- return;
-}
-
-
-/* Divide one multiple precision number by another.Set *z = *x / *y. *x & *y */
-/* are left unchanged. x&y may overlap but not x&z or y&z. */
-/* Relative error bound = 2.001*r**(1-p) for p=2, 2.063*r**(1-p) for p=3 */
-/* and 3.001*r**(1-p) for p>3. *y=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);}
- return;
-}
--
1.7.11.7