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Demystify the magic number 134217729.0
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.
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ChangeLog
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ChangeLog
@ -1,3 +1,13 @@
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2012-12-29 Siddhesh Poyarekar <siddhesh@redhat.com>
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* sysdeps/ieee754/dbl-64/branred.h: Include dla.h.
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(split): Use macro CN instead of the bare value.
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* sysdeps/ieee754/dbl-64/dla.h: Add comment to explain why CN
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could be used.
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* sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Use CN
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instead of the bare value.
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(power1): Likewise.
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2012-12-28 Siddhesh Poyarekar <siddhesh@redhat.com>
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* sysdeps/ieee754/dbl-64/mpatan.c (__mpatan): Remove
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@ -1,7 +1,7 @@
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/*
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* IBM Accurate Mathematical Library
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* Written by International Business Machines Corp.
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* Copyright (C) 2001 Free Software Foundation, Inc.
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* Copyright (C) 2001-2012 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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@ -26,6 +26,7 @@
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#ifndef BRANRED_H
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#define BRANRED_H
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#include <dla.h>
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#ifdef BIG_ENDI
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static const mynumber
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@ -74,6 +75,6 @@ static const double toverp[75] = { /* 2/ PI base 24*/
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12618859.0, 4703257.0, 12806093.0, 14477321.0, 2786137.0,
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12875403.0, 9837734.0, 14528324.0, 13719321.0, 343717.0 };
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static const double split = 134217729.0;
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static const double split = CN; /* 2^27 + 1 */
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#endif
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@ -1,7 +1,7 @@
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/*
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* IBM Accurate Mathematical Library
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* Written by International Business Machines Corp.
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* Copyright (C) 2001, 2011 Free Software Foundation, Inc.
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* Copyright (C) 2001-2012 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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@ -34,7 +34,8 @@
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/* IEEE double. */
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/***********************************************************************/
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/* CN = 1+2**27 = '41a0000002000000' IEEE double format */
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/* CN = 1+2**27 = '41a0000002000000' IEEE double format. Use it to split a
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double for better accuracy. */
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#define CN 134217729.0
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@ -95,10 +95,10 @@ __ieee754_pow(double x, double y) {
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if (ABS (y) < 0x1p-64)
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y = y < 0 ? -0x1p-64 : 0x1p-64;
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z = log1(x,&aa,&error); /* x^y =e^(y log (X)) */
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t = y*134217729.0;
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t = y*CN;
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y1 = t - (t-y);
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y2 = y - y1;
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t = z*134217729.0;
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t = z*CN;
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a1 = t - (t-z);
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a2 = (z - a1)+aa;
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a = y1*a1;
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@ -182,10 +182,10 @@ SECTION
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power1(double x, double y) {
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double z,a,aa,error, t,a1,a2,y1,y2;
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z = my_log2(x,&aa,&error);
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t = y*134217729.0;
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t = y*CN;
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y1 = t - (t-y);
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y2 = y - y1;
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t = z*134217729.0;
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t = z*CN;
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a1 = t - (t-z);
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a2 = z - a1;
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a = y*z;
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