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The FORM project for symbolic manipulation of very big expressions
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gcd_ crashes for zero $-variables #191

Closed tueda closed 7 years ago

tueda commented 7 years ago

gcd_ has a memory bug when the first argument is a zero $-variable.

#$a = 0;
#$b = 1;
#$c = gcd_($a,$b);  * must be 1
.end
FORM 4.1 (May 24 2017, v4.1-20131025-346-gcf71752) 64-bits  Run: Tue Jun  6 10:05:01 2017
    #$a = 0;
    #$b = 1;
*** glibc detected *** form: free(): invalid next size (fast): 0x0000000002518430 ***
======= Backtrace: =========
/lib64/libc.so.6[0x32e1275f3e]
/lib64/libc.so.6[0x32e1278dd0]
form[0x5406fd]
form[0x52c4cf]
form[0x447eb3]
form[0x51e275]
form[0x4032e8]
/lib64/libc.so.6(__libc_start_main+0xfd)[0x32e121ed1d]
form[0x403325]
======= Memory map: ========
00400000-0060f000 r-xp 00000000 fd:03 7088816                            /localstore/theorie/tueda/build/linuxbrew/Cellar/form/HEAD-cf71752/bin/form
0080f000-00810000 r--p 0020f000 fd:03 7088816                            /localstore/theorie/tueda/build/linuxbrew/Cellar/form/HEAD-cf71752/bin/form
00810000-00814000 rw-p 00210000 fd:03 7088816                            /localstore/theorie/tueda/build/linuxbrew/Cellar/form/HEAD-cf71752/bin/form
00814000-0086d000 rw-p 00000000 00:00 0
024ea000-02569000 rw-p 00000000 00:00 0                                  [heap]
32e0e00000-32e0e20000 r-xp 00000000 fd:00 651535                         /lib64/ld-2.12.so
32e101f000-32e1021000 r--p 0001f000 fd:00 651535                         /lib64/ld-2.12.so
32e1021000-32e1022000 rw-p 00021000 fd:00 651535                         /lib64/ld-2.12.so
32e1022000-32e1023000 rw-p 00000000 00:00 0
32e1200000-32e138a000 r-xp 00000000 fd:00 651536                         /lib64/libc-2.12.so
32e138a000-32e158a000 ---p 0018a000 fd:00 651536                         /lib64/libc-2.12.so
32e158a000-32e158e000 r--p 0018a000 fd:00 651536                         /lib64/libc-2.12.so
32e158e000-32e1590000 rw-p 0018e000 fd:00 651536                         /lib64/libc-2.12.so
32e1590000-32e1594000 rw-p 00000000 00:00 0
32e1600000-32e1683000 r-xp 00000000 fd:00 651538                         /lib64/libm-2.12.so
32e1683000-32e1882000 ---p 00083000 fd:00 651538                         /lib64/libm-2.12.so
32e1882000-32e1883000 r--p 00082000 fd:00 651538                         /lib64/libm-2.12.so
32e1883000-32e1884000 rw-p 00083000 fd:00 651538                         /lib64/libm-2.12.so
32e8600000-32e8656000 r-xp 00000000 fd:00 807941                         /usr/lib64/libgmp.so.3.5.0
32e8656000-32e8856000 ---p 00056000 fd:00 807941                         /usr/lib64/libgmp.so.3.5.0
32e8856000-32e885b000 rw-p 00056000 fd:00 807941                         /usr/lib64/libgmp.so.3.5.0
7ff3c8000000-7ff3c8021000 rw-p 00000000 00:00 0
7ff3c8021000-7ff3cc000000 ---p 00000000 00:00 0
7ff3cc9c8000-7ff3e54b5000 rw-p 00000000 00:00 0
7ff3e54b5000-7ff3e54c6000 r-xp 00000000 fd:03 17969798                   /localstore/theorie/tueda/build/linuxbrew/Cellar/gcc/5.3.0/lib/libgcc_s.so.1
7ff3e54c6000-7ff3e56c6000 ---p 00011000 fd:03 17969798                   /localstore/theorie/tueda/build/linuxbrew/Cellar/gcc/5.3.0/lib/libgcc_s.so.1
7ff3e56c6000-7ff3e56c7000 rw-p 00011000 fd:03 17969798                   /localstore/theorie/tueda/build/linuxbrew/Cellar/gcc/5.3.0/lib/libgcc_s.so.1
7ff3e56c7000-7ff3e56c8000 rw-p 00000000 00:00 0
7ff3e56c8000-7ff3e57f4000 r-xp 00000000 fd:03 17971137                   /localstore/theorie/tueda/build/linuxbrew/Cellar/gcc/5.3.0/lib/libstdc++.so.6.0.21
7ff3e57f4000-7ff3e59f4000 ---p 0012c000 fd:03 17971137                   /localstore/theorie/tueda/build/linuxbrew/Cellar/gcc/5.3.0/lib/libstdc++.so.6.0.21
7ff3e59f4000-7ff3e59fe000 r--p 0012c000 fd:03 17971137                   /localstore/theorie/tueda/build/linuxbrew/Cellar/gcc/5.3.0/lib/libstdc++.so.6.0.21
7ff3e59fe000-7ff3e5a02000 rw-p 00136000 fd:03 17971137                   /localstore/theorie/tueda/build/linuxbrew/Cellar/gcc/5.3.0/lib/libstdc++.so.6.0.21
7ff3e5a02000-7ff3e5a06000 rw-p 00000000 00:00 0
7ff3e5a26000-7ff3e5a38000 r-xp 00000000 fd:03 20726621                   /localstore/theorie/tueda/build/linuxbrew/Cellar/zlib/1.2.11/lib/libz.so.1.2.11
7ff3e5a38000-7ff3e5c37000 ---p 00012000 fd:03 20726621                   /localstore/theorie/tueda/build/linuxbrew/Cellar/zlib/1.2.11/lib/libz.so.1.2.11
7ff3e5c37000-7ff3e5c38000 rw-p 00011000 fd:03 20726621                   /localstore/theorie/tueda/build/linuxbrew/Cellar/zlib/1.2.11/lib/libz.so.1.2.11
7ff3e5c38000-7ff3e5c39000 rw-p 00000000 00:00 0
7ffd711fe000-7ffd71219000 rw-p 00000000 00:00 0                          [stack]
7ffd71349000-7ffd7134a000 r-xp 00000000 00:00 0                          [vdso]
ffffffffff600000-ffffffffff601000 r-xp 00000000 00:00 0                  [vsyscall]
Aborted (core dumped)

Valgrind output:

==30839== Memcheck, a memory error detector
==30839== Copyright (C) 2002-2015, and GNU GPL'd, by Julian Seward et al.
==30839== Using Valgrind-3.12.0 and LibVEX; rerun with -h for copyright info
==30839== Command: vorm 1
==30839==
FORM 4.1 (May 24 2017, v4.1-20131025-346-gcf71752) 64-bits  Run: Tue Jun  6 10:05:51 2017
    #$a = 0;
    #$b = 1;
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4BFADB: GCDterms (ratio.c:2063)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C0082: GCDterms (ratio.c:2066)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C009F: GCDterms (ratio.c:2225)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C00B8: GCDterms (ratio.c:2225)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4CA7C9: AccumGCD (reken.c:653)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C4FE1: UnPack (reken.c:104)
==30839==    by 0x4CA80D: AccumGCD (reken.c:655)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C4FF2: UnPack (reken.c:106)
==30839==    by 0x4CA80D: AccumGCD (reken.c:655)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C502E: UnPack (reken.c:114)
==30839==    by 0x4CA80D: AccumGCD (reken.c:655)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C79DA: GcdLong (reken.c:2275)
==30839==    by 0x4CA83D: AccumGCD (reken.c:657)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C79E4: GcdLong (reken.c:2276)
==30839==    by 0x4CA83D: AccumGCD (reken.c:657)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C7A01: GcdLong (reken.c:2283)
==30839==    by 0x4CA83D: AccumGCD (reken.c:657)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Use of uninitialised value of size 8
==30839==    at 0x4CA85C: AccumGCD (reken.c:659)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C79DA: GcdLong (reken.c:2275)
==30839==    by 0x4CA88D: AccumGCD (reken.c:660)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C79E4: GcdLong (reken.c:2276)
==30839==    by 0x4CA88D: AccumGCD (reken.c:660)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C7A01: GcdLong (reken.c:2283)
==30839==    by 0x4CA88D: AccumGCD (reken.c:660)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Use of uninitialised value of size 8
==30839==    at 0x4CA8B2: AccumGCD (reken.c:662)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Use of uninitialised value of size 8
==30839==    at 0x4C4FAB: Pack (reken.c:86)
==30839==    by 0x4CA8CF: AccumGCD (reken.c:663)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Use of uninitialised value of size 8
==30839==    at 0x4C4FAE: Pack (reken.c:86)
==30839==    by 0x4CA8CF: AccumGCD (reken.c:663)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Invalid write of size 4
==30839==    at 0x4C4FAE: Pack (reken.c:86)
==30839==    by 0x4CA8CF: AccumGCD (reken.c:663)
==30839==    by 0x4C00F6: GCDterms (ratio.c:2228)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==  Address 0x5708928 is 0 bytes after a block of size 72 alloc'd
==30839==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==30839==    by 0x4FE1DF: Malloc1 (tools.c:2236)
==30839==    by 0x42FDFC: DolToTerms (dollar.c:1539)
==30839==    by 0x4C10C2: GCDfunction (ratio.c:969)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Use of uninitialised value of size 8
==30839==    at 0x4C0148: GCDterms (ratio.c:2235)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Invalid write of size 4
==30839==    at 0x4C0148: GCDterms (ratio.c:2235)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==  Address 0x570892c is 4 bytes after a block of size 72 alloc'd
==30839==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==30839==    by 0x4FE1DF: Malloc1 (tools.c:2236)
==30839==    by 0x42FDFC: DolToTerms (dollar.c:1539)
==30839==    by 0x4C10C2: GCDfunction (ratio.c:969)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Invalid write of size 4
==30839==    at 0x4C015C: GCDterms (ratio.c:2236)
==30839==    by 0x4C1211: GCDfunction (ratio.c:1000)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==  Address 0x5708930 is 8 bytes after a block of size 72 alloc'd
==30839==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==30839==    by 0x4FE1DF: Malloc1 (tools.c:2236)
==30839==    by 0x42FDFC: DolToTerms (dollar.c:1539)
==30839==    by 0x4C10C2: GCDfunction (ratio.c:969)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C121E: GCDfunction (ratio.c:1001)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Invalid read of size 4
==30839==    at 0x4C1228: GCDfunction (ratio.c:1001)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==  Address 0x5708928 is 0 bytes after a block of size 72 alloc'd
==30839==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==30839==    by 0x4FE1DF: Malloc1 (tools.c:2236)
==30839==    by 0x42FDFC: DolToTerms (dollar.c:1539)
==30839==    by 0x4C10C2: GCDfunction (ratio.c:969)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Invalid read of size 4
==30839==    at 0x4C1230: GCDfunction (ratio.c:1001)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==  Address 0x570892c is 4 bytes after a block of size 72 alloc'd
==30839==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==30839==    by 0x4FE1DF: Malloc1 (tools.c:2236)
==30839==    by 0x42FDFC: DolToTerms (dollar.c:1539)
==30839==    by 0x4C10C2: GCDfunction (ratio.c:969)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Use of uninitialised value of size 8
==30839==    at 0x4C1260: GCDfunction (ratio.c:1007)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Invalid read of size 4
==30839==    at 0x4C1260: GCDfunction (ratio.c:1007)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==  Address 0x570892c is 4 bytes after a block of size 72 alloc'd
==30839==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==30839==    by 0x4FE1DF: Malloc1 (tools.c:2236)
==30839==    by 0x42FDFC: DolToTerms (dollar.c:1539)
==30839==    by 0x4C10C2: GCDfunction (ratio.c:969)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Use of uninitialised value of size 8
==30839==    at 0x4C1274: GCDfunction (ratio.c:1008)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Invalid read of size 4
==30839==    at 0x4C1274: GCDfunction (ratio.c:1008)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==  Address 0x570892c is 4 bytes after a block of size 72 alloc'd
==30839==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==30839==    by 0x4FE1DF: Malloc1 (tools.c:2236)
==30839==    by 0x42FDFC: DolToTerms (dollar.c:1539)
==30839==    by 0x4C10C2: GCDfunction (ratio.c:969)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Conditional jump or move depends on uninitialised value(s)
==30839==    at 0x4C12B8: GCDfunction (ratio.c:1010)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Use of uninitialised value of size 8
==30839==    at 0x4C9827: MulRat (reken.c:382)
==30839==    by 0x4C131F: GCDfunction (ratio.c:1015)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Use of uninitialised value of size 8
==30839==    at 0x4C982E: MulRat (reken.c:382)
==30839==    by 0x4C131F: GCDfunction (ratio.c:1015)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
==30839== Invalid read of size 4
==30839==    at 0x4C982E: MulRat (reken.c:382)
==30839==    by 0x4C131F: GCDfunction (ratio.c:1015)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==  Address 0x5708928 is 0 bytes after a block of size 72 alloc'd
==30839==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==30839==    by 0x4FE1DF: Malloc1 (tools.c:2236)
==30839==    by 0x42FDFC: DolToTerms (dollar.c:1539)
==30839==    by 0x4C10C2: GCDfunction (ratio.c:969)
==30839==    by 0x4B7455: Generator (proces.c:3686)
==30839==    by 0x42E4CE: CatchDollar (dollar.c:112)
==30839==    by 0x4AF440: PreProcessor (pre.c:1050)
==30839==    by 0x4E770F: main (startup.c:1605)
==30839==
    #$c = gcd_($a,$b);  * must be 1
    .end
  0.08 sec out of 0.08 sec
==30839==
==30839== HEAP SUMMARY:
==30839==     in use at exit: 391,558,976 bytes in 132 blocks
==30839==   total heap usage: 545 allocs, 413 frees, 414,465,023 bytes allocated
==30839==
==30839== LEAK SUMMARY:
==30839==    definitely lost: 0 bytes in 0 blocks
==30839==    indirectly lost: 0 bytes in 0 blocks
==30839==      possibly lost: 0 bytes in 0 blocks
==30839==    still reachable: 391,558,976 bytes in 132 blocks
==30839==         suppressed: 0 bytes in 0 blocks
==30839== Rerun with --leak-check=full to see details of leaked memory
==30839==
==30839== For counts of detected and suppressed errors, rerun with: -v
==30839== Use --track-origins=yes to see where uninitialised values come from
==30839== ERROR SUMMARY: 33 errors from 33 contexts (suppressed: 4 from 4)
spj101 commented 7 years ago

gcd_ also crashes occasionally on mac os x (though not on my linux machine) when a zero expression is in the first argument. Input:

#-
off statistics;
L p1 = 0;
L p2 = 1;
#do i = 1,100000
*L gcd = gcd_(p2,p1); * Works
L gcd = gcd_(p1,p2);  * Fails
.sort
#enddo
.end

Output of form (on mac):

FORM 4.1 (Jun  6 2017, v4.1-20131025-347-g76561be) 64-bits  Run: Wed Jun  7 00:07:13 2017
    #-
Program terminating at bug.frm Line 7 -->
  0.00 sec out of 0.00 sec

Output of tform (on mac):

TFORM 4.1 (Jun  6 2017, v4.1-20131025-347-g76561be) 64-bits 0 workers  Run: Wed Jun  7 00:14:06 2017
    #-
Term too complex during normalization
Called from GCDfunction
Program terminating in thread 0 at bug.frm Line 7 -->
tform(4759,0x7fff774eb000) malloc: *** error for object 0x7fe370d00250: pointer being freed was not allocated
*** set a breakpoint in malloc_error_break to debug
Abort trap: 6
spj101 commented 7 years ago

I think gcd_ also gives wrong results when called with a zero. Input:

#-
off statistics;
S x;
L p1 = 0;
L p2 = x+x^2;
L gcd = gcd_(p2,p1);
print;
.end

Output:

TFORM 4.1 (Jun  6 2017, v4.1-20131025-347-g76561be) 64-bits 0 workers  Run: Wed Jun  7 00:17:22 2017
    #-

   p1 = 0;

   p2 =
      x + x^2;

   gcd =
      1;

Should we not expect gcd = x+x^2?

If the polynomial has only 1 term the result seems fine. Input:

#-
off statistics;
S x;
L p1 = 0;
L p2 = x^2;
L gcd = gcd_(p2,p1);
print;
.end

Output:

FORM 4.1 (Jun  6 2017, v4.1-20131025-347-g76561be) 64-bits  Run: Wed Jun  7 00:19:24 2017
    #-

   p1 = 0;

   p2 =
      x^2;

   gcd =
      x^2;
tueda commented 7 years ago

gcd_ also crashes occasionally on mac os x (though not on my linux machine) when a zero expression is in the first argument.

I think gcd_ also gives wrong results when called with a zero.

Actually Valgrind tells us something goes wrong at ratio.c:2063 in these cases, too:

FORM 4.1 (Jun  6 2017, v4.1-20131025-347-g76561be) 64-bits  Run: Wed Jun  7 00:49:52 2017
    L p1 = 0;
    L p2 = 1;
    L gcd = gcd_(p1,p2);
    .end

Time =       0.06 sec    Generated terms =          0
              p1         Terms in output =          0
                         Bytes used      =          4

Time =       0.08 sec    Generated terms =          1
              p2         Terms in output =          1
                         Bytes used      =         20
==23356== Invalid read of size 4
==23356==    at 0x4BFDDD: GCDterms (ratio.c:2063)
==23356==    by 0x4C1518: GCDfunction (ratio.c:1000)
==23356==    by 0x4B7725: Generator (proces.c:3688)
==23356==    by 0x4B7C7A: Generator (proces.c:3886)
==23356==    by 0x4B93FA: Processor (proces.c:404)
==23356==    by 0x437480: DoExecute (execute.c:812)
==23356==    by 0x44D8FE: ExecModule (module.c:274)
==23356==    by 0x4AF44B: PreProcessor (pre.c:962)
==23356==    by 0x4E7A30: main (startup.c:1605)
==23356==  Address 0x570977c is 4 bytes before a block of size 96 alloc'd
==23356==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==23356==    by 0x4FE510: Malloc1 (tools.c:2236)
==23356==    by 0x4E230B: EndSort (sort.c:741)
==23356==    by 0x4BFD85: CreateExpression (ratio.c:2037)
==23356==    by 0x4C141C: GCDfunction (ratio.c:977)
==23356==    by 0x4B7725: Generator (proces.c:3688)
==23356==    by 0x4B7C7A: Generator (proces.c:3886)
==23356==    by 0x4B93FA: Processor (proces.c:404)
==23356==    by 0x437480: DoExecute (execute.c:812)
==23356==    by 0x44D8FE: ExecModule (module.c:274)
==23356==    by 0x4AF44B: PreProcessor (pre.c:962)
==23356==    by 0x4E7A30: main (startup.c:1605)
==23356==
==23356== Invalid read of size 4
==23356==    at 0x4C0392: GCDterms (ratio.c:2224)
==23356==    by 0x4C1518: GCDfunction (ratio.c:1000)
==23356==    by 0x4B7725: Generator (proces.c:3688)
==23356==    by 0x4B7C7A: Generator (proces.c:3886)
==23356==    by 0x4B93FA: Processor (proces.c:404)
==23356==    by 0x437480: DoExecute (execute.c:812)
==23356==    by 0x44D8FE: ExecModule (module.c:274)
==23356==    by 0x4AF44B: PreProcessor (pre.c:962)
==23356==    by 0x4E7A30: main (startup.c:1605)
==23356==  Address 0x570977c is 4 bytes before a block of size 96 alloc'd
==23356==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==23356==    by 0x4FE510: Malloc1 (tools.c:2236)
==23356==    by 0x4E230B: EndSort (sort.c:741)
==23356==    by 0x4BFD85: CreateExpression (ratio.c:2037)
==23356==    by 0x4C141C: GCDfunction (ratio.c:977)
==23356==    by 0x4B7725: Generator (proces.c:3688)
==23356==    by 0x4B7C7A: Generator (proces.c:3886)
==23356==    by 0x4B93FA: Processor (proces.c:404)
==23356==    by 0x437480: DoExecute (execute.c:812)
==23356==    by 0x44D8FE: ExecModule (module.c:274)
==23356==    by 0x4AF44B: PreProcessor (pre.c:962)
==23356==    by 0x4E7A30: main (startup.c:1605)
==23356==

Time =       0.09 sec    Generated terms =          1
             gcd         Terms in output =          1
                         Bytes used      =         20
FORM 4.1 (Jun  6 2017, v4.1-20131025-347-g76561be) 64-bits  Run: Wed Jun  7 00:51:07 2017
    S x;
    L p1 = 0;
    L p2 = x+x^2;
    L gcd = gcd_(p2,p1);
    .end

Time =       0.06 sec    Generated terms =          0
              p1         Terms in output =          0
                         Bytes used      =          4

Time =       0.08 sec    Generated terms =          2
              p2         Terms in output =          2
                         Bytes used      =         60
==23416== Invalid read of size 4
==23416==    at 0x4BFDDD: GCDterms (ratio.c:2063)
==23416==    by 0x4C1518: GCDfunction (ratio.c:1000)
==23416==    by 0x4B7725: Generator (proces.c:3688)
==23416==    by 0x4B7C7A: Generator (proces.c:3886)
==23416==    by 0x4B93FA: Processor (proces.c:404)
==23416==    by 0x437480: DoExecute (execute.c:812)
==23416==    by 0x44D8FE: ExecModule (module.c:274)
==23416==    by 0x4AF44B: PreProcessor (pre.c:962)
==23416==    by 0x4E7A30: main (startup.c:1605)
==23416==  Address 0x1c9a566c is 4 bytes before a block of size 96 alloc'd
==23416==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==23416==    by 0x4FE510: Malloc1 (tools.c:2236)
==23416==    by 0x4E230B: EndSort (sort.c:741)
==23416==    by 0x4BFD85: CreateExpression (ratio.c:2037)
==23416==    by 0x4C141C: GCDfunction (ratio.c:977)
==23416==    by 0x4B7725: Generator (proces.c:3688)
==23416==    by 0x4B7C7A: Generator (proces.c:3886)
==23416==    by 0x4B93FA: Processor (proces.c:404)
==23416==    by 0x437480: DoExecute (execute.c:812)
==23416==    by 0x44D8FE: ExecModule (module.c:274)
==23416==    by 0x4AF44B: PreProcessor (pre.c:962)
==23416==    by 0x4E7A30: main (startup.c:1605)
==23416==
==23416== Invalid read of size 4
==23416==    at 0x4C0392: GCDterms (ratio.c:2224)
==23416==    by 0x4C1518: GCDfunction (ratio.c:1000)
==23416==    by 0x4B7725: Generator (proces.c:3688)
==23416==    by 0x4B7C7A: Generator (proces.c:3886)
==23416==    by 0x4B93FA: Processor (proces.c:404)
==23416==    by 0x437480: DoExecute (execute.c:812)
==23416==    by 0x44D8FE: ExecModule (module.c:274)
==23416==    by 0x4AF44B: PreProcessor (pre.c:962)
==23416==    by 0x4E7A30: main (startup.c:1605)
==23416==  Address 0x1c9a566c is 4 bytes before a block of size 96 alloc'd
==23416==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==23416==    by 0x4FE510: Malloc1 (tools.c:2236)
==23416==    by 0x4E230B: EndSort (sort.c:741)
==23416==    by 0x4BFD85: CreateExpression (ratio.c:2037)
==23416==    by 0x4C141C: GCDfunction (ratio.c:977)
==23416==    by 0x4B7725: Generator (proces.c:3688)
==23416==    by 0x4B7C7A: Generator (proces.c:3886)
==23416==    by 0x4B93FA: Processor (proces.c:404)
==23416==    by 0x437480: DoExecute (execute.c:812)
==23416==    by 0x44D8FE: ExecModule (module.c:274)
==23416==    by 0x4AF44B: PreProcessor (pre.c:962)
==23416==    by 0x4E7A30: main (startup.c:1605)
==23416==

Time =       0.10 sec    Generated terms =          1
             gcd         Terms in output =          1
                         Bytes used      =         20
vermaseren commented 7 years ago

OK, it is clear that the case that one of those arguments (or both) is zero is not intercepted. I guess there should be a runtime error, rather than a crash (or no crash but a nonsense answer). The gcd of 0 and any other number makes no sense. I will put some if statements in the code.

Jos

On 7 jun. 2017, at 01:01, Takahiro Ueda notifications@github.com wrote:

gcd_ also crashes occasionally on mac os x (though not on my linux machine) when a zero expression is in the first argument.

I think gcd_ also gives wrong results when called with a zero.

Actually Valgrind tells us something goes wrong at ratio.c:2063 https://github.com/vermaseren/form/blob/76561be553a6215cf4ef70c6d1a5b848bda7e12d/sources/ratio.c#L2063 in these cases, too:

FORM 4.1 (Jun 6 2017, v4.1-20131025-347-g76561be) 64-bits Run: Wed Jun 7 00:49:52 2017 L p1 = 0; L p2 = 1; L gcd = gcd_(p1,p2); .end

Time = 0.06 sec Generated terms = 0 p1 Terms in output = 0 Bytes used = 4

Time = 0.08 sec Generated terms = 1 p2 Terms in output = 1 Bytes used = 20 ==23356== Invalid read of size 4 ==23356== at 0x4BFDDD: GCDterms (ratio.c:2063) ==23356== by 0x4C1518: GCDfunction (ratio.c:1000) ==23356== by 0x4B7725: Generator (proces.c:3688) ==23356== by 0x4B7C7A: Generator (proces.c:3886) ==23356== by 0x4B93FA: Processor (proces.c:404) ==23356== by 0x437480: DoExecute (execute.c:812) ==23356== by 0x44D8FE: ExecModule (module.c:274) ==23356== by 0x4AF44B: PreProcessor (pre.c:962) ==23356== by 0x4E7A30: main (startup.c:1605) ==23356== Address 0x570977c is 4 bytes before a block of size 96 alloc'd ==23356== at 0x4A05A57: malloc (vg_replace_malloc.c:299) ==23356== by 0x4FE510: Malloc1 (tools.c:2236) ==23356== by 0x4E230B: EndSort (sort.c:741) ==23356== by 0x4BFD85: CreateExpression (ratio.c:2037) ==23356== by 0x4C141C: GCDfunction (ratio.c:977) ==23356== by 0x4B7725: Generator (proces.c:3688) ==23356== by 0x4B7C7A: Generator (proces.c:3886) ==23356== by 0x4B93FA: Processor (proces.c:404) ==23356== by 0x437480: DoExecute (execute.c:812) ==23356== by 0x44D8FE: ExecModule (module.c:274) ==23356== by 0x4AF44B: PreProcessor (pre.c:962) ==23356== by 0x4E7A30: main (startup.c:1605) ==23356== ==23356== Invalid read of size 4 ==23356== at 0x4C0392: GCDterms (ratio.c:2224) ==23356== by 0x4C1518: GCDfunction (ratio.c:1000) ==23356== by 0x4B7725: Generator (proces.c:3688) ==23356== by 0x4B7C7A: Generator (proces.c:3886) ==23356== by 0x4B93FA: Processor (proces.c:404) ==23356== by 0x437480: DoExecute (execute.c:812) ==23356== by 0x44D8FE: ExecModule (module.c:274) ==23356== by 0x4AF44B: PreProcessor (pre.c:962) ==23356== by 0x4E7A30: main (startup.c:1605) ==23356== Address 0x570977c is 4 bytes before a block of size 96 alloc'd ==23356== at 0x4A05A57: malloc (vg_replace_malloc.c:299) ==23356== by 0x4FE510: Malloc1 (tools.c:2236) ==23356== by 0x4E230B: EndSort (sort.c:741) ==23356== by 0x4BFD85: CreateExpression (ratio.c:2037) ==23356== by 0x4C141C: GCDfunction (ratio.c:977) ==23356== by 0x4B7725: Generator (proces.c:3688) ==23356== by 0x4B7C7A: Generator (proces.c:3886) ==23356== by 0x4B93FA: Processor (proces.c:404) ==23356== by 0x437480: DoExecute (execute.c:812) ==23356== by 0x44D8FE: ExecModule (module.c:274) ==23356== by 0x4AF44B: PreProcessor (pre.c:962) ==23356== by 0x4E7A30: main (startup.c:1605) ==23356==

Time = 0.09 sec Generated terms = 1 gcd Terms in output = 1 Bytes used = 20 FORM 4.1 (Jun 6 2017, v4.1-20131025-347-g76561be) 64-bits Run: Wed Jun 7 00:51:07 2017 S x; L p1 = 0; L p2 = x+x^2; L gcd = gcd_(p2,p1); .end

Time = 0.06 sec Generated terms = 0 p1 Terms in output = 0 Bytes used = 4

Time = 0.08 sec Generated terms = 2 p2 Terms in output = 2 Bytes used = 60 ==23416== Invalid read of size 4 ==23416== at 0x4BFDDD: GCDterms (ratio.c:2063) ==23416== by 0x4C1518: GCDfunction (ratio.c:1000) ==23416== by 0x4B7725: Generator (proces.c:3688) ==23416== by 0x4B7C7A: Generator (proces.c:3886) ==23416== by 0x4B93FA: Processor (proces.c:404) ==23416== by 0x437480: DoExecute (execute.c:812) ==23416== by 0x44D8FE: ExecModule (module.c:274) ==23416== by 0x4AF44B: PreProcessor (pre.c:962) ==23416== by 0x4E7A30: main (startup.c:1605) ==23416== Address 0x1c9a566c is 4 bytes before a block of size 96 alloc'd ==23416== at 0x4A05A57: malloc (vg_replace_malloc.c:299) ==23416== by 0x4FE510: Malloc1 (tools.c:2236) ==23416== by 0x4E230B: EndSort (sort.c:741) ==23416== by 0x4BFD85: CreateExpression (ratio.c:2037) ==23416== by 0x4C141C: GCDfunction (ratio.c:977) ==23416== by 0x4B7725: Generator (proces.c:3688) ==23416== by 0x4B7C7A: Generator (proces.c:3886) ==23416== by 0x4B93FA: Processor (proces.c:404) ==23416== by 0x437480: DoExecute (execute.c:812) ==23416== by 0x44D8FE: ExecModule (module.c:274) ==23416== by 0x4AF44B: PreProcessor (pre.c:962) ==23416== by 0x4E7A30: main (startup.c:1605) ==23416== ==23416== Invalid read of size 4 ==23416== at 0x4C0392: GCDterms (ratio.c:2224) ==23416== by 0x4C1518: GCDfunction (ratio.c:1000) ==23416== by 0x4B7725: Generator (proces.c:3688) ==23416== by 0x4B7C7A: Generator (proces.c:3886) ==23416== by 0x4B93FA: Processor (proces.c:404) ==23416== by 0x437480: DoExecute (execute.c:812) ==23416== by 0x44D8FE: ExecModule (module.c:274) ==23416== by 0x4AF44B: PreProcessor (pre.c:962) ==23416== by 0x4E7A30: main (startup.c:1605) ==23416== Address 0x1c9a566c is 4 bytes before a block of size 96 alloc'd ==23416== at 0x4A05A57: malloc (vg_replace_malloc.c:299) ==23416== by 0x4FE510: Malloc1 (tools.c:2236) ==23416== by 0x4E230B: EndSort (sort.c:741) ==23416== by 0x4BFD85: CreateExpression (ratio.c:2037) ==23416== by 0x4C141C: GCDfunction (ratio.c:977) ==23416== by 0x4B7725: Generator (proces.c:3688) ==23416== by 0x4B7C7A: Generator (proces.c:3886) ==23416== by 0x4B93FA: Processor (proces.c:404) ==23416== by 0x437480: DoExecute (execute.c:812) ==23416== by 0x44D8FE: ExecModule (module.c:274) ==23416== by 0x4AF44B: PreProcessor (pre.c:962) ==23416== by 0x4E7A30: main (startup.c:1605) ==23416==

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crmafra commented 7 years ago

On Wed, 7 Jun 2017 at 8:11:12 -0700, Jos Vermaseren wrote:

The gcd of 0 and any other number makes no sense.

Unless I am misunderstanding I believe the proper definitions are

gcd(0,a) = a gcd(0,0) = 0

See page 3 of the book http://williamstein.org/books/ent/ent.pdf

tueda commented 7 years ago

The gcd of 0 and any other number makes no sense.

It seems that mathematically it makes sense or at least there is some convention.

Mathematica 11.0.1

In[1]:= PolynomialGCD[0, 1+x]

Out[1] = 1 + x

In[2]:= PolynomialGCD[0, 0]

Out[2] = 0

Python 3.6.1

In [1]: import math

In [2]: math.gcd(0, 12)
Out[2]: 12

In [3]: math.gcd(0, 0)
Out[2]: 0

ginsh 1.7.2

> gcd(0, 1+x);
1+x
> gcd(0, 0);
0

gp/pari 2.9.2

? gcd(0, 1+x)
%1 = x + 1
? gcd(0, 0)
%2 = 0

GCD(0,0) = 0 would be true in mathematics, e.g., https://math.stackexchange.com/questions/495119/what-is-gcd0-0, but in practice I'm happy with the fact that FORM gives a wrong answer for gcd_(0,0) -> 1 because usually what we want to do after taking a GCD is dividing by the GCD:

$gcd = gcd_($a,$b);
$a = div_($a,$gcd);
$b = div_($b,$gcd);

If gcd_(0,0) gives 0, I need to put more code to check if the GCD is 0 before the divisions.

vermaseren commented 7 years ago

If I look in the book, it is more like a definition or convention. Specially when both are 0. If you have gcd(0,x) can you say that x divides zero? At the least that is very shady. I can make it like the ‘convention’ of course. It is not very elegant in my eyes, but if it is what people want…..

Jos

On 7 jun. 2017, at 17:28, Takahiro Ueda notifications@github.com wrote:

The gcd of 0 and any other number makes no sense.

It seems that mathematically it makes sense or at least there is some convention.

Mathematica 11.0.1

In[1]:= PolynomialGCD[0, 1+x]

Out[1] = 1 + x

In[2]:= PolynomialGCD[0, 0]

Out[2] = 0 Python 3.6.1

In [1]: import math

In [2]: math.gcd(0, 12) Out[2]: 12

In [3]: math.gcd(0, 0) Out[2]: 0 ginsh 1.7.2

gcd(0, 1+x); 1+x gcd(0, 0); 0 gp/pari 2.9.2

? gcd(0, 1+x) %1 = x + 1 ? gcd(0, 0) %2 = 0 GCD(0,0) = 0 would be true in mathematics, e.g., https://math.stackexchange.com/questions/495119/what-is-gcd0-0 https://math.stackexchange.com/questions/495119/what-is-gcd0-0, but in practice I'm happy with the fact that FORM gives the "wrong" answer for gcd_(0,0) -> 1 because usually what we want to do after taking a GCD is divisions by the GCD:

$gcd = gcd($a,$b); $a = div($a,$gcd); $b = div($b,$gcd); If gcd(0,0) gives 0, I need to put more code to check if the GCD is 0 before the divisions.

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crmafra commented 7 years ago

On Wed, 7 Jun 2017 at 9:21:38 -0700, Jos Vermaseren wrote:

If you have gcd(0,x) can you say that x divides zero?

Yes, for 0/x = 0 is well defined.

At the least that is very shady. I can make it like the ‘convention’ of course. It is not very elegant in my eyes, but if it is what people want…..

I don't think one can "define" gcd(0,x) any differently than 'x' because one of the properties of the gcd() would be violated otherwise, namely

gcd(a,b) = gcd(a,b-a).

The above lemma would be inconsistent with gcd(a,a) = a unless gcd(a,0) = a.

spj101 commented 7 years ago

I believe @tueda and @crmafra are correct that gcd(0,a)=a when a !=0. This follows from 0/a=0 (i.e... a is a divisor of 0) this is not a convention.

That gcd(0,0)=0 is a (popular) convention. Perhaps this is convenient for polynomial gcd since we can compute gcd(0,a)=a with general a then set a=0 consistently.

tueda commented 7 years ago

After applying the patch 615cbcd52634, still broken...

FORM 4.1 (Jun  8 2017, v4.1-20131025-348-g615cbcd) 64-bits  Run: Thu Jun  8 14:59:51 2017
    S x;
    #$a = 0;
    #$b = 1+x;
    #$c = gcd_($a,$b);
==28608== Invalid read of size 4
==28608==    at 0x4BFDDD: GCDterms (ratio.c:2073)
==28608==    by 0x4C0519: GCDfunction3 (ratio.c:1146)
==28608==    by 0x4C1850: GCDfunction (ratio.c:1051)
==28608==    by 0x4B7725: Generator (proces.c:3688)
==28608==    by 0x42E4CE: CatchDollar (dollar.c:112)
==28608==    by 0x4AF710: PreProcessor (pre.c:1050)
==28608==    by 0x4E7B4B: main (startup.c:1605)
==28608==  Address 0x57094cc is 4 bytes before a block of size 8 alloc'd
==28608==    at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==28608==    by 0x4FE62B: Malloc1 (tools.c:2236)
==28608==    by 0x4C04E6: GCDfunction3 (ratio.c:1142)
==28608==    by 0x4C1850: GCDfunction (ratio.c:1051)
==28608==    by 0x4B7725: Generator (proces.c:3688)
==28608==    by 0x42E4CE: CatchDollar (dollar.c:112)
==28608==    by 0x4AF710: PreProcessor (pre.c:1050)
==28608==    by 0x4E7B4B: main (startup.c:1605)

... (many errors) ...

Full Log...

tueda commented 7 years ago

I found cases that are still broken...

FORM 4.1 (Jun  8 2017, v4.1-20131025-351-g31c5798) 64-bits  Run: Thu Jun  8 22:13:09 2017
    S x;
    L F1 = gcd_(100000000000000000000,0);
    L F2 = gcd_(-x,0);
    P;
    .end

Time =       0.00 sec    Generated terms =          0
              F1         Terms in output =          0
                         Bytes used      =          4

Time =       0.00 sec    Generated terms =          0
              F2         Terms in output =          0
                         Bytes used      =          4

   F1 = 0;

   F2 = 0;
tueda commented 7 years ago

It seems that 7cf7c42df5b6fb97 finally fixes bugs for gcd_(0,0), gcd_(a,0) and gcd_(0,a). I close this issue. (But still we have #196.)

spj101 commented 7 years ago

Thanks a lot for quickly fixing this. With 541f847 on Mac everything runs as expected.