Update.

2001-03-11  Ulrich Drepper  <drepper@redhat.com>

	Last-bit accurate math library implementation by IBM Haifa.
	Contributed by Abraham Ziv <ziv@il.ibm.com>, Moshe Olshansky
	<olshansk@il.ibm.com>, Ealan Henis <ealan@il.ibm.com>, and
	Anna Reitman <reitman@il.ibm.com>.
	* math/Makefile (dbl-only-routines): New variable.
	(libm-routines): Add $(dbl-only-routines).
	* sysdeps/ieee754/dbl-64/e_acos.c: Empty, definition is in e_asin.c.
	* sysdeps/ieee754/dbl-64/e_asin.c: Replaced with accurate asin
	implementation.
	* sysdeps/ieee754/dbl-64/e_atan2.c: Replaced with accurate atan2
	implementation.
	* sysdeps/ieee754/dbl-64/e_exp.c: Replaced with accurate exp
	implementation.
	* sysdeps/ieee754/dbl-64/e_lgamma_r.c: Don't use __kernel_sin and
	__kernel_cos.
	* sysdeps/ieee754/dbl-64/e_log.c: Replaced with accurate log
	implementation.
	* sysdeps/ieee754/dbl-64/e_remainder.c: Replaced with accurate
	remainder implementation.
	* sysdeps/ieee754/dbl-64/e_pow.c: Replaced with accurate pow
	implementation.
	* sysdeps/ieee754/dbl-64/e_sqrt.c: Replaced with accurate sqrt
	implementation.
	* sysdeps/ieee754/dbl-64/k_cos.c: Empty, definition is in s_sin.c.
	* sysdeps/ieee754/dbl-64/k_sin.c: Empty, definition is in s_sin.c.
	* sysdeps/ieee754/dbl-64/s_atan.c: Replaced with accurate atan
	implementation.
	* sysdeps/ieee754/dbl-64/s_cos.c: Empty, definition is in s_sin.c.
	* sysdeps/ieee754/dbl-64/s_sin.c: Replaced with accurate sin/cos
	implementation.
	* sysdeps/ieee754/dbl-64/s_sincos.c: Rewritten to not use __kernel_sin
	and __kernel_cos.
	* sysdeps/ieee754/dbl-64/s_tan.c: Replaced with accurate tan
	implementation.
	* sysdeps/ieee754/dbl-64/Dist: Add new non-code files.
	* sysdeps/ieee754/dbl-64/MathLib.h: New file.
	* sysdeps/ieee754/dbl-64/asincos.tbl: New file.
	* sysdeps/ieee754/dbl-64/atnat.h: New file.
	* sysdeps/ieee754/dbl-64/atnat2.h: New file.
	* sysdeps/ieee754/dbl-64/branred.c: New file.
	* sysdeps/ieee754/dbl-64/branred.h: New file.
	* sysdeps/ieee754/dbl-64/dla.h: New file.
	* sysdeps/ieee754/dbl-64/doasin.c: New file.
	* sysdeps/ieee754/dbl-64/doasin.h: New file.
	* sysdeps/ieee754/dbl-64/dosincos.c: New file.
	* sysdeps/ieee754/dbl-64/dosincos.h: New file.
	* sysdeps/ieee754/dbl-64/endian.h: New file.
	* sysdeps/ieee754/dbl-64/halfulp.c: New file.
	* sysdeps/ieee754/dbl-64/mpa.c: New file.
	* sysdeps/ieee754/dbl-64/mpa.h: New file.
	* sysdeps/ieee754/dbl-64/mpa2.h: New file.
	* sysdeps/ieee754/dbl-64/mpatan.c: New file.
	* sysdeps/ieee754/dbl-64/mpatan.h: New file.
	* sysdeps/ieee754/dbl-64/mpatan2.c: New file.
	* sysdeps/ieee754/dbl-64/mpexp.c: New file.
	* sysdeps/ieee754/dbl-64/mpexp.h: New file.
	* sysdeps/ieee754/dbl-64/mplog.c: New file.
	* sysdeps/ieee754/dbl-64/mplog.h: New file.
	* sysdeps/ieee754/dbl-64/mpsqrt.c: New file.
	* sysdeps/ieee754/dbl-64/mpsqrt.h: New file.
	* sysdeps/ieee754/dbl-64/mptan.c: New file.
	* sysdeps/ieee754/dbl-64/mydefs.h: New file.
	* sysdeps/ieee754/dbl-64/powtwo.tbl: New file.
	* sysdeps/ieee754/dbl-64/root.tbl: New file.
	* sysdeps/ieee754/dbl-64/sincos.tbl: New file.
	* sysdeps/ieee754/dbl-64/sincos32.c: New file.
	* sysdeps/ieee754/dbl-64/sincos32.h: New file.
	* sysdeps/ieee754/dbl-64/slowexp.c: New file.
	* sysdeps/ieee754/dbl-64/slowpow.c: New file.
	* sysdeps/ieee754/dbl-64/uasncs.h: New file.
	* sysdeps/ieee754/dbl-64/uatan.tbl: New file.
	* sysdeps/ieee754/dbl-64/uexp.h: New file.
	* sysdeps/ieee754/dbl-64/uexp.tbl: New file.
	* sysdeps/ieee754/dbl-64/ulog.h: New file.
	* sysdeps/ieee754/dbl-64/ulog.tbl: New file.
	* sysdeps/ieee754/dbl-64/upow.h: New file.
	* sysdeps/ieee754/dbl-64/upow.tbl: New file.
	* sysdeps/ieee754/dbl-64/urem.h: New file.
	* sysdeps/ieee754/dbl-64/uroot.h: New file.
	* sysdeps/ieee754/dbl-64/usncs.h: New file.
	* sysdeps/ieee754/dbl-64/utan.h: New file.
	* sysdeps/ieee754/dbl-64/utan.tbl: New file.
	* sysdeps/i386/fpu/branred.c: New file.
	* sysdeps/i386/fpu/doasin.c: New file.
	* sysdeps/i386/fpu/dosincos.c: New file.
	* sysdeps/i386/fpu/halfulp.c: New file.
	* sysdeps/i386/fpu/mpa.c: New file.
	* sysdeps/i386/fpu/mpatan.c: New file.
	* sysdeps/i386/fpu/mpatan2.c: New file.
	* sysdeps/i386/fpu/mpexp.c: New file.
	* sysdeps/i386/fpu/mplog.c: New file.
	* sysdeps/i386/fpu/mpsqrt.c: New file.
	* sysdeps/i386/fpu/mptan.c: New file.
	* sysdeps/i386/fpu/sincos32.c: New file.
	* sysdeps/i386/fpu/slowexp.c: New file.
	* sysdeps/i386/fpu/slowpow.c: New file.
	* sysdeps/ia64/fpu/branred.c: New file.
	* sysdeps/ia64/fpu/doasin.c: New file.
	* sysdeps/ia64/fpu/dosincos.c: New file.
	* sysdeps/ia64/fpu/halfulp.c: New file.
	* sysdeps/ia64/fpu/mpa.c: New file.
	* sysdeps/ia64/fpu/mpatan.c: New file.
	* sysdeps/ia64/fpu/mpatan2.c: New file.
	* sysdeps/ia64/fpu/mpexp.c: New file.
	* sysdeps/ia64/fpu/mplog.c: New file.
	* sysdeps/ia64/fpu/mpsqrt.c: New file.
	* sysdeps/ia64/fpu/mptan.c: New file.
	* sysdeps/ia64/fpu/sincos32.c: New file.
	* sysdeps/ia64/fpu/slowexp.c: New file.
	* sysdeps/ia64/fpu/slowpow.c: New file.
	* sysdeps/m68k/fpu/branred.c: New file.
	* sysdeps/m68k/fpu/doasin.c: New file.
	* sysdeps/m68k/fpu/dosincos.c: New file.
	* sysdeps/m68k/fpu/halfulp.c: New file.
	* sysdeps/m68k/fpu/mpa.c: New file.
	* sysdeps/m68k/fpu/mpatan.c: New file.
	* sysdeps/m68k/fpu/mpatan2.c: New file.
	* sysdeps/m68k/fpu/mpexp.c: New file.
	* sysdeps/m68k/fpu/mplog.c: New file.
	* sysdeps/m68k/fpu/mpsqrt.c: New file.
	* sysdeps/m68k/fpu/mptan.c: New file.
	* sysdeps/m68k/fpu/sincos32.c: New file.
	* sysdeps/m68k/fpu/slowexp.c: New file.
	* sysdeps/m68k/fpu/slowpow.c: New file.

	* iconvdata/gconv-modules: Add a number of alias, mostly for IBM
	codepages.

1 files changed, 339 insertions, 0 deletions

diff --git a/sysdeps/ieee754/dbl-64/sincos32.c b/sysdeps/ieee754/dbl-64/sincos32.c
new file mode 100644
index 0000000000..41fe2f281a
--- /dev/null
+++ b/sysdeps/ieee754/dbl-64/sincos32.c
@@ -0,0 +1,339 @@
+
+/*
+ * IBM Accurate Mathematical Library
+ * Copyright (c) International Business Machines Corp., 2001
+ *
+ * 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 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 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, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  
+ */
+/****************************************************************/
+/*  MODULE_NAME: sincos32.c                                     */
+/*                                                              */
+/*  FUNCTIONS: ss32                                             */
+/*             cc32                                             */
+/*             c32                                              */
+/*             sin32                                            */
+/*             cos32                                            */
+/*             mpsin                                            */
+/*             mpcos                                            */
+/*             mpranred                                         */
+/*             mpsin1                                           */
+/*             mpcos1                                           */
+/*                                                              */
+/* FILES NEEDED: endian.h mpa.h sincos32.h                      */
+/*               mpa.c                                          */
+/*                                                              */
+/* Multi Precision sin() and cos() function with p=32  for sin()*/
+/* cos() arcsin() and arccos() routines                         */
+/* In addition mpranred() routine  performs range  reduction of */
+/* a double number x into multi precision number   y,           */
+/* such that y=x-n*pi/2, abs(y)<pi/4,  n=0,+-1,+-2,....         */
+/****************************************************************/
+#include "endian.h"
+#include "mpa.h"
+#include "sincos32.h"
+
+/****************************************************************/
+/* Compute Multi-Precision sin() function for given p.  Receive */
+/* Multi  Precision number x and result stored at y             */
+/****************************************************************/
+void ss32(mp_no *x, mp_no *y, int p) {
+  int i;
+  double a,b;
+  static const mp_no mpone = {1,1.0,1.0};
+  mp_no mpt1,mpt2,x2,gor,sum ,mpk={1,1.0};
+  for (i=1;i<=p;i++) mpk.d[i]=0;
+
+  mul(x,x,&x2,p);
+  cpy(&oofac27,&gor,p);
+  cpy(&gor,&sum,p);
+  for (a=27.0;a>1.0;a-=2.0) {
+    mpk.d[1]=a*(a-1.0);
+    mul(&gor,&mpk,&mpt1,p);
+    cpy(&mpt1,&gor,p);
+    mul(&x2,&sum,&mpt1,p);
+    sub(&gor,&mpt1,&sum,p);
+  }
+  mul(x,&sum,y,p);
+}
+
+/**********************************************************************/
+/* Compute Multi-Precision cos() function for given p. Receive Multi  */
+/* Precision number x and result stored at y                          */
+/**********************************************************************/
+void cc32(mp_no *x, mp_no *y, int p) {
+  int i;
+  double a,b;
+  static const mp_no mpone = {1,1.0,1.0};
+  mp_no mpt1,mpt2,x2,gor,sum ,mpk={1,1.0};
+  for (i=1;i<=p;i++) mpk.d[i]=0;
+
+  mul(x,x,&x2,p);
+  mpk.d[1]=27.0;
+  mul(&oofac27,&mpk,&gor,p);
+  cpy(&gor,&sum,p);
+  for (a=26.0;a>2.0;a-=2.0) {
+    mpk.d[1]=a*(a-1.0);
+    mul(&gor,&mpk,&mpt1,p);
+    cpy(&mpt1,&gor,p);
+    mul(&x2,&sum,&mpt1,p);
+    sub(&gor,&mpt1,&sum,p);
+  }
+  mul(&x2,&sum,y,p);
+}
+
+/***************************************************************************/
+/* c32()   computes both sin(x), cos(x) as Multi precision numbers         */
+/***************************************************************************/
+void c32(mp_no *x, mp_no *y, mp_no *z, int p) {
+  static const mp_no mpt={1,1.0,2.0}, one={1,1.0,1.0};
+  mp_no u,t,t1,t2,c,s;
+  int i;
+  cpy(x,&u,p);
+  u.e=u.e-1;
+  cc32(&u,&c,p);
+  ss32(&u,&s,p);
+  for (i=0;i<24;i++) {
+    mul(&c,&s,&t,p);
+    sub(&s,&t,&t1,p);
+    add(&t1,&t1,&s,p);
+    sub(&mpt,&c,&t1,p);
+    mul(&t1,&c,&t2,p);
+    add(&t2,&t2,&c,p);
+  }
+  sub(&one,&c,y,p);
+  cpy(&s,z,p);
+}
+
+/************************************************************************/
+/*Routine receive double x and two double results of sin(x) and return  */
+/*result which is more accurate                                         */
+/*Computing sin(x) with multi precision routine c32                     */
+/************************************************************************/
+double sin32(double x, double res, double res1) {
+  int p;
+  mp_no a,b,c;
+  p=32;
+  dbl_mp(res,&a,p);
+  dbl_mp(0.5*(res1-res),&b,p);
+  add(&a,&b,&c,p);
+  if (x>0.8)
+  { sub(&hp,&c,&a,p);
+    c32(&a,&b,&c,p);
+  }
+  else c32(&c,&a,&b,p);     /* b=sin(0.5*(res+res1))  */
+  dbl_mp(x,&c,p);           /* c = x                  */
+  sub(&b,&c,&a,p);    
+  /* if a>0 return min(res,res1), otherwise return max(res,res1) */
+  if (a.d[0]>0)  return (res<res1)?res:res1;
+  else  return (res>res1)?res:res1;
+}
+
+/************************************************************************/
+/*Routine receive double x and two double results of cos(x) and return  */
+/*result which is more accurate                                         */
+/*Computing cos(x) with multi precision routine c32                     */
+/************************************************************************/
+double cos32(double x, double res, double res1) {
+  int p;
+  mp_no a,b,c;
+  p=32;
+  dbl_mp(res,&a,p);
+  dbl_mp(0.5*(res1-res),&b,p);
+  add(&a,&b,&c,p);
+  if (x>2.4)
+  { sub(&pi,&c,&a,p);
+    c32(&a,&b,&c,p);
+    b.d[0]=-b.d[0];
+  }
+  else if (x>0.8) 
+       { sub(&hp,&c,&a,p);
+         c32(&a,&c,&b,p); 
+       }
+  else c32(&c,&b,&a,p);     /* b=cos(0.5*(res+res1))  */
+  dbl_mp(x,&c,p);    /* c = x                  */
+  sub(&b,&c,&a,p);
+             /* if a>0 return max(res,res1), otherwise return min(res,res1) */
+  if (a.d[0]>0)  return (res>res1)?res:res1;
+  else  return (res<res1)?res:res1;
+}
+
+/*******************************************************************/
+/*Compute sin(x+dx) as Multi Precision number and return result as */
+/* double                                                          */
+/*******************************************************************/
+double mpsin(double x, double dx) {
+  int p;
+  double y;
+  mp_no a,b,c;
+  p=32;
+  dbl_mp(x,&a,p);
+  dbl_mp(dx,&b,p);
+  add(&a,&b,&c,p);
+  if (x>0.8) { sub(&hp,&c,&a,p); c32(&a,&b,&c,p); }
+  else c32(&c,&a,&b,p);     /* b = sin(x+dx)     */
+  mp_dbl(&b,&y,p);
+  return y;
+}
+
+/*******************************************************************/
+/* Compute cos()of double-length number (x+dx) as Multi Precision  */
+/* number and return result as double                              */
+/*******************************************************************/
+double mpcos(double x, double dx) {
+  int p;
+  double y;
+  mp_no a,b,c;
+  p=32;
+  dbl_mp(x,&a,p);
+  dbl_mp(dx,&b,p);
+  add(&a,&b,&c,p);
+  if (x>0.8) 
+  { sub(&hp,&c,&b,p);
+    c32(&b,&a,&c,p);
+  }
+  else c32(&c,&a,&b,p);     /* a = cos(x+dx)     */
+  mp_dbl(&a,&y,p);
+  return y;
+}
+
+/******************************************************************/
+/* mpranred() performs range reduction of a double number x into  */
+/* multi precision number y, such that y=x-n*pi/2, abs(y)<pi/4,   */
+/* n=0,+-1,+-2,....                                               */
+/* Return int which indicates in which quarter of circle x is     */
+/******************************************************************/
+int mpranred(double x, mp_no *y, int p)
+{
+  number v;
+  double t,xn;
+  int i,k,n;
+  static const mp_no one = {1,1.0,1.0};
+  mp_no a,b,c;
+  
+  if (ABS(x) < 2.8e14) {
+    t = (x*hpinv.d + toint.d);
+    xn = t - toint.d;
+    v.d = t;
+    n =v.i[LOW_HALF]&3;
+    dbl_mp(xn,&a,p);
+    mul(&a,&hp,&b,p);
+    dbl_mp(x,&c,p);
+    sub(&c,&b,y,p);
+    return n;
+  }
+  else {                      /* if x is very big more precision required */
+    dbl_mp(x,&a,p);
+    a.d[0]=1.0;
+    k = a.e-5;
+    if (k < 0) k=0;
+    b.e = -k;
+    b.d[0] = 1.0;
+    for (i=0;i<p;i++) b.d[i+1] = toverp[i+k];
+    mul(&a,&b,&c,p);
+    t = c.d[c.e];
+    for (i=1;i<=p-c.e;i++) c.d[i]=c.d[i+c.e];
+    for (i=p+1-c.e;i<=p;i++) c.d[i]=0;
+    c.e=0;
+    if (c.d[1] >=  8388608.0)  
+    { t +=1.0;
+      sub(&c,&one,&b,p);
+      mul(&b,&hp,y,p);
+    }
+    else mul(&c,&hp,y,p);
+    n = (int) t;
+    if (x < 0) { y->d[0] = - y->d[0]; n = -n; }
+    return (n&3);
+  }
+}
+
+/*******************************************************************/
+/* Multi-Precision sin() function subroutine, for p=32.  It is     */
+/* based on the routines mpranred() and c32().                     */
+/*******************************************************************/
+double mpsin1(double x)
+{
+  int p;
+  int n;
+  mp_no u,s,c;
+  double y;
+  p=32;
+  n=mpranred(x,&u,p);               /* n is 0, 1, 2 or 3 */
+  c32(&u,&c,&s,p);
+  switch (n) {                      /* in which quarter of unit circle y is*/
+  case 0:
+    mp_dbl(&s,&y,p);
+    return y;
+    break;
+
+  case 2:
+    mp_dbl(&s,&y,p);
+    return -y;
+    break;
+
+  case 1:
+    mp_dbl(&c,&y,p);
+    return y;
+    break;
+    
+  case 3:
+    mp_dbl(&c,&y,p);
+    return -y;
+    break;
+    
+  }
+  return 0;                     /* unreachable, to make the compiler happy */
+}
+
+/*****************************************************************/
+/* Multi-Precision cos() function subroutine, for p=32.  It is   */
+/* based  on the routines mpranred() and c32().                  */
+/*****************************************************************/
+
+double mpcos1(double x)
+{
+  int p;
+  int n;
+  mp_no u,s,c;
+  double y;
+  
+  p=32;
+  n=mpranred(x,&u,p);              /* n is 0, 1, 2 or 3 */
+  c32(&u,&c,&s,p);
+  switch (n) {                     /* in what quarter of unit circle y is*/
+    
+  case 0:
+    mp_dbl(&c,&y,p);
+    return y;
+    break;
+    
+  case 2:
+    mp_dbl(&c,&y,p);
+    return -y;
+    break;
+    
+  case 1:
+    mp_dbl(&s,&y,p);
+    return -y;
+    break;
+    
+  case 3:
+    mp_dbl(&s,&y,p);
+    return y;
+    break;
+    
+  }
+  return 0;                     /* unreachable, to make the compiler happy */
+}
+/******************************************************************/