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Demystify the magic number 134217729.0

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The number 134217729.0 gets used in various places in e_pow.c but
there is no explanation of what that number is.  Add that explanation.
This commit is contained in:
Siddhesh Poyarekar 2012-12-29 06:56:04 +05:30
parent c93c5dec54
commit 085ec079e3
4 changed files with 20 additions and 8 deletions
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10
ChangeLog
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@ -1,3 +1,13 @@
2012-12-29 Siddhesh Poyarekar <siddhesh@redhat.com>
* sysdeps/ieee754/dbl-64/branred.h: Include dla.h.
(split): Use macro CN instead of the bare value.
* sysdeps/ieee754/dbl-64/dla.h: Add comment to explain why CN
could be used.
* sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Use CN
instead of the bare value.
(power1): Likewise.
2012-12-28 Siddhesh Poyarekar <siddhesh@redhat.com>
* sysdeps/ieee754/dbl-64/mpatan.c (__mpatan): Remove

5
sysdeps/ieee754/dbl-64/branred.h
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@ -1,7 +1,7 @@
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
* Copyright (C) 2001-2012 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
@ -26,6 +26,7 @@
#ifndef BRANRED_H
#define BRANRED_H
#include <dla.h>
#ifdef BIG_ENDI
static const mynumber
@ -74,6 +75,6 @@ static const double toverp[75] = { /* 2/ PI base 24*/
12618859.0, 4703257.0, 12806093.0, 14477321.0, 2786137.0,
12875403.0, 9837734.0, 14528324.0, 13719321.0, 343717.0 };
static const double split = 134217729.0;
static const double split = CN; /* 2^27 + 1 */
#endif

5
sysdeps/ieee754/dbl-64/dla.h
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@ -1,7 +1,7 @@
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001, 2011 Free Software Foundation, Inc.
* Copyright (C) 2001-2012 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
@ -34,7 +34,8 @@
/* IEEE double. */
/***********************************************************************/
/* CN = 1+2**27 = '41a0000002000000' IEEE double format */
/* CN = 1+2**27 = '41a0000002000000' IEEE double format. Use it to split a
double for better accuracy. */
#define CN 134217729.0

8
sysdeps/ieee754/dbl-64/e_pow.c
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@ -95,10 +95,10 @@ __ieee754_pow(double x, double y) {
if (ABS (y) < 0x1p-64)
y = y < 0 ? -0x1p-64 : 0x1p-64;
z = log1(x,&aa,&error); /* x^y =e^(y log (X)) */
t = y*134217729.0;
t = y*CN;
y1 = t - (t-y);
y2 = y - y1;
t = z*134217729.0;
t = z*CN;
a1 = t - (t-z);
a2 = (z - a1)+aa;
a = y1*a1;
@ -182,10 +182,10 @@ SECTION
power1(double x, double y) {
double z,a,aa,error, t,a1,a2,y1,y2;
z = my_log2(x,&aa,&error);
t = y*134217729.0;
t = y*CN;
y1 = t - (t-y);
y2 = y - y1;
t = z*134217729.0;
t = z*CN;
a1 = t - (t-z);
a2 = z - a1;
a = y*z;