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.

3 files changed, 10 insertions, 8 deletions

diff --git a/sysdeps/ieee754/dbl-64/branred.h b/sysdeps/ieee754/dbl-64/branred.h
index c1e7354..c0a6e78 100644
--- a/sysdeps/ieee754/dbl-64/branred.h
+++ b/sysdeps/ieee754/dbl-64/branred.h
@@ -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
diff --git a/sysdeps/ieee754/dbl-64/dla.h b/sysdeps/ieee754/dbl-64/dla.h
index c92fcfe..3feb3d4 100644
--- a/sysdeps/ieee754/dbl-64/dla.h
+++ b/sysdeps/ieee754/dbl-64/dla.h
@@ -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
 
 
diff --git a/sysdeps/ieee754/dbl-64/e_pow.c b/sysdeps/ieee754/dbl-64/e_pow.c
index 5131718..1d535cb 100644
--- a/sysdeps/ieee754/dbl-64/e_pow.c
+++ b/sysdeps/ieee754/dbl-64/e_pow.c
@@ -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;