Incorrect results concerning "large" primes and Wilson's theorem
Andrea Franceschini
andrea.franceschini at gmail.com
Wed Aug 13 03:22:08 CDT 2008
Bug report for Octave 3.0.1 configured for i686-pc-linux-gnu
Description:
-----------
* While I wasn't able to check whether the factorial function
produced correct results for "large" numbers, I still found an
evidence of something wrong with very big integers.
Wilson's theorem I'm referring to is the one that states that
(let me rephrase it a bit) for p being a prime then
mod(factorial(p-1),p) = p-1.
What I found is that this stops working for me after p = 19.
Repeat-By:
---------
octave:1> mod(factorial(4), 5)
ans = 4
octave:2> mod(factorial(6), 7)
ans = 6
octave:3> mod(factorial(10), 11)
ans = 10
octave:4> mod(factorial(12), 13)
ans = 12
octave:5> mod(factorial(16), 17)
ans = 16
octave:6> mod(factorial(18), 19)
ans = 12
octave:7> mod(factorial(22), 23)
ans = 0
octave:8> mod(factorial(26), 27)
ans = 0
octave:9> version
ans = 3.0.1
Fix:
---
* I actually don't know where the problem lies, but assuming that the
functions are properly working, I think it may be in the library that
manages the big integers. Otherwise it is in the functions.
As a last resource, it may even be my machine.
Configuration (please do not edit this section):
-----------------------------------------------
uname output: Linux porto 2.6.25-gentoo-r6 #1 PREEMPT Wed Jul 30
14:42:58 CEST 2008 i686 Intel(R) Pentium(R) M processor 1.73GHz
GenuineIntel GNU/Linux
configure opts: '--prefix=/usr' '--host=i686-pc-linux-gnu'
'--mandir=/usr/share/man' '--infodir=/usr/share/info'
'--datadir=/usr/share' '--sysconfdir=/etc' '--localstatedir=/var/lib'
'--without-hdf5' '--without-curl' '--with-zlib' '--with-fftw'
'--enable-readline' '--localstatedir=/var/state/octave'
'--enable-rpath' '--with-blas=blas' '--with-lapack=lapack'
'--enable-static' '--enable-shared' '--enable-dl' '--without-umfpack'
'--without-colamd' '--without-ccolamd' '--without-cholmod'
'--without-cxsparse' '--build=i686-pc-linux-gnu'
'build_alias=i686-pc-linux-gnu' 'host_alias=i686-pc-linux-gnu'
'CFLAGS=-O2 -march=pentium-m -mtune=pentium-m -pipe
-fomit-frame-pointer' 'LDFLAGS=-Wl,-s' 'CXXFLAGS=-O2 -march=pentium-m
-mtune=pentium-m -pipe -fomit-frame-pointer'
Fortran compiler: i686-pc-linux-gnu-gfortran
FFLAGS: -O -mieee-fp
F2C: @F2C@
F2CFLAGS: @F2CFLAGS@
FLIBS: -L/usr/lib/gcc/i686-pc-linux-gnu/4.1.2
-L/usr/lib/gcc/i686-pc-linux-gnu/4.1.2/../../../../i686-pc-linux-gnu/lib
-L/usr/lib/gcc/i686-pc-linux-gnu/4.1.2/../../.. -lz -lgfortranbegin
-lgfortran -lm
CPPFLAGS:
INCFLAGS: -I. -I. -I./liboctave -I./src -I./libcruft/misc
C compiler: i686-pc-linux-gnu-gcc, version 4.1.2 (Gentoo 4.1.2 p1.1)
CFLAGS: -O2 -march=pentium-m -mtune=pentium-m -pipe
-fomit-frame-pointer
CPICFLAG: -fPIC
C++ compiler: i686-pc-linux-gnu-g++, version 4.1.2
CXXFLAGS: -O2 -march=pentium-m -mtune=pentium-m -pipe
-fomit-frame-pointer
CXXPICFLAG: -fPIC
LD_CXX: i686-pc-linux-gnu-g++
LDFLAGS: -Wl,-s
LIBFLAGS: -L.
RLD_FLAG: -Wl,-rpath -Wl,/usr/lib/octave-3.0.1
BLAS_LIBS: -llapack -lblas
FFTW_LIBS: -lfftw3
LIBS: -lreadline -lncurses -ldl -lz -lm
LEXLIB:
LIBGLOB:
SED: /bin/sed
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-DHAVE_TIMES=1 -DYYTEXT_POINTER=1 -DGNUPLOT_BINARY="gnuplot"
User-preferences (please do not edit this section):
--------------------------------------------------
EDITOR = /bin/nano
EXEC_PATH = /usr/libexec/octave/3.0.1/site/exec/i686-pc-linux-gnu:/usr/libexec/octave/api-v32/site/exec/i686-pc-linux-gnu:/usr/libexec/octave/site/exec/i686-pc-linux-gnu:/usr/libexec/octave/3.0.1/exec/i686-pc-linux-gnu:/usr/bin:/usr/local/bin:/usr/bin:/bin:/opt/bin:/usr/i686-pc-linux-gnu/gcc-bin/4.1.2:/usr/kde/3.5/bin:/usr/qt/3/bin:/opt/panda3d/bin:/home/morpheu5/src/android/tools:/opt/java/bin:/home/morpheu5/src/ns/ns-allinone-2.33/bin:/home/morpheu5/src/ns/ns-allinone-2.33/tcl8.4.18/unix:/home/morpheu5/src/ns/ns-allinone-2.33/tk8.4.18/unix:/home/morpheu5/src/ns/ns-allinone-2.33/tclcl
IMAGE_PATH = .:/usr/share/octave/3.0.1/imagelib
PAGER = /usr/bin/less
PS1 = \s:\#>
PS2 = >
PS4 = +
beep_on_error = 0
completion_append_char =
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gnuplot_binary = gnuplot
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