This optimized Collatz Conjecture tester can test the provided numbers for how many iterations they need before they reach the number 1. The path is not printed, only statistics: the number of 3*n+1 ("mul3") and n/2 ("div2") operations, and total. As a progress indicator prints the current length of the number in bytes (every 25000 iterations).
If you're lucky to find a number that proves that Collatz Conjecture is false (or a bug in the program), then the program will hang in an infinite loop.
- Note: Doesn't work with negative numbers.
make all
default buildmake profile PROF_ARGS="--ones 1000000"
build with the profile-guided optimizations using GCC (add CLANG=1 when using Clang)
make checkfor a simple build check.- Compile-time option
NBITS, greatly affects performance, should be the number of bits in the machine register. The default is 64 for 64-bit machines (also needs the __int64 type supported by the compiler), otherwise 32.
collatz_test [--lut 1..26] [mode] {num|file}
--lut N builds a lookup table to speed up the process by a factor of N (default 20). LUT consumes 2^n * 3 * NBITS/8 bytes of memory. The LUT depth is also limited to 5 * NBITS/8.
- Doesn't affect performance in the latest version with dynamic expansion of LUT values.
--num read decimal number from command line (default)
--file load specified file as a little endian number
--ones test 2^n-1
$ ./collatz_test 989345275647
mul3 = 506, div2 = 842, total = 1348
$ ./collatz_test 0xffffffff
mul3 = 162, div2 = 289, total = 451
$ ./collatz_test --ones 1000000
lut: 0.016s
bytes: 198128
bytes: 145760
bytes: 94000
bytes: 41896
mul3 = 4805005, div2 = 8615753, total = 13420758
time: 1.155s
$ head -c100000 /dev/urandom > random.bin
$ ./collatz_test --file random.bin
lut: 0.016s
bytes: 47936
mul3 = 1923602, div2 = 3848837, total = 5772439
time: 0.213s