https://gcc.gnu.org/bugzilla/show_bug.cgi?id=81630
Bug ID: 81630
Summary: powl returns values with insufficient accuracy
Product: gcc
Version: 8.0
Status: UNCONFIRMED
Severity: normal
Priority: P3
Component: c
Assignee: unassigned at gcc dot gnu.org
Reporter: kakehi at waseda dot jp
Target Milestone: ---
Created attachment 41870
--> https://gcc.gnu.org/bugzilla/attachment.cgi?id=41870&action=edit
compare powl(t,N) with exp2l(N*log2l(t))
I calculated powl(t,N) where t= (N+1)/N, N: an integer value 2^n (n: positive
integer) to get an approximation to Napier's constant.
Here is some results:
n powl(t, N) exp2l(N*log2l(t))
25: 2.7182817879534639155837683e+00 2.7182817879534906457209692e+00
26: 2.7182818082062409458920377e+00 2.7182818082062676638861742e+00
27: 2.7182818183325918449770586e+00 2.7182818183326563803766523e+00
28: 2.7182818233957862993910304e+00 2.7182818233958507905551755e+00
29: 2.7182818259273639105617903e+00 2.7182818259274480086548631e+00
30: 2.7182818271931621957604452e+00 2.7182818271932466208488932e+00
31: 2.7182818278260525070993969e+00 2.7182818278261459278132700e+00
32: 2.7182818278260525070993969e+00 2.7182818281425955814038786e+00
33: 2.7182818278260525070993969e+00 2.7182818283008204083076031e+00
34: 2.7182818278260525070993969e+00 2.7182818283799328217594654e+00
35: 2.7182818278260525070993969e+00 2.7182818284194890285938168e+00
As you see, powl(t,N) values have saturated when n>30, where exp2l(N*log2l(t)),
which is a formula mathematically equivalent to powl(t,N), produces increasing
values in converging to Napier's constant.
The values are obtained by the program "comparePow.c":
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
/* checking the powl function.
*/
int main(int argc, char *argv[]){
if( argc==1 ){ printf("usage: $ comparePOW n [m]"); exit(-1);}
int n= atoi(argv[1]), m;
if( argc==2 ) m= n; else m= atoi(argv[2]);
for(int i= n; i<=m; i++){
long double N=powl(2.0, (long double)i);
if( N==N+1 ){ printf("too large N\n"); exit(-1); }
long double t= (N+1)/N;
long double powlx= powl(t,N);
long double powly= exp2l(N*log2l(t));
printf("%3d: %.25Le %.25Le\n", i, powlx, powly);
}
return 0;
}
by running it with the command "./a.out 25 35".
The command "gcc -v" produces:
Configured with: --prefix=/Applications/Xcode.app/Contents/Developer/usr
--with-gxx-include-dir=/Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.12.sdk/usr/include/c++/4.2.1
Apple LLVM version 8.1.0 (clang-802.0.42)
Target: x86_64-apple-darwin16.7.0
Thread model: posix
InstalledDir:
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin
