Use GMP as default implementation of integers in Python3

[Torbjorn Granlund]

Victor Stinner <victor.stinner at haypocalc.com> writes:

  First, I have a questions about GMP: I'm unable to find the pow() function 
  with only mpz_t arguments. mpz_powm() only uses mpz_t variables but it 
  computes the modulo, not just base^exp. How can I compute base^exp with an 
  exponent bigger than a unsigned long? Eg. 2^(2^40) with a 32 bits CPU.
  
You cannot, since that wouldn't fit in the memory of your computer.

  I wrote a patch for the Python language to use the GMP library for the 
  integers. My patch works correctly but Python is a little bit slower (3% to 
  14%) because most of the time, integers are (very) small. I guess that the 
  most common range is [-2^32-1; 2^32-1]. Should I use a better memory 
  allocator? I also changed it to use Python memory managment. How can I speed 
  it Python+GMP?
  
  In Python2, an integer is 31 bits + sign and automatically switch to long 
  integer (unlimited) on overflow. In Python3, all integers are long integers.
  About the long integers:
   - base = 2^15 (32768)
   - multiply: grade school multiplicatin or Karatsuba (cutfoff = 70 digits,
     and 2x70 digits for square (a*a))
   - divide: no idea (see x_divrem())
  
  The base is very small but was choosed because it works on any platform or 
  CPU.
  
  Do you know other successful integration of GMP in languages?
  
I cannot answer, but perhaps somebody else on this list can be of more
help!

-- 
Torbjörn