D. J. Bernstein
Fast arithmetic
Integer multiplication benchmarks

Piologie

Piologie was written by Sebasian Wedeniwski. Apparently Piologie has turned into a commercial product; the Piologie home page is now www.hipilib.de/piologie.htm. Sample code using Piologie:
     #include "natural.h"
     main()
     {
       Natural a;
       Natural b;
       Natural c;
       cin >> a;
       cin >> b;
       c = a * b;
       cout << c << "\n";
     }

Old timings of Piologie version 1.2.1 with gnu28 on a Pentium II:

      1:       3259        211        195        195        195        195 
      2:        195        195        212        195        195        195 
      4:        195        195        195        195        195        195 
      8:        195        195        195        195        195        195 
     16:        195        195        195        195        195        195 
     32:        207        191        208        191        191        191 
     64:       1019        251        219        219        233        219 
    128:       3292        707        668        605        605        605 
    256:      19315       2016       1943       1943       1943       1943 
    512:      10299       7517      13538       7460       7349       7351 
   1024:      21819      21080      20942      20850      20848      20833 
   2048:      74801      61769      61577      61535      61497      61487 
   4096:     184363     183370     183270     183229     183239     183223 
   8192:     574100     556556     556409     556377     561745     556457 
  16384:    1706530    1686702    1680814    1680399    1696757    1681091 
  32768:    5125561    5063941    5063827    5062925    5088401    5064519 
  65536:   15309097   15218517   15211688   15217003   15224084   15230181 
 131072:   45956221   45875696   45872172   46170082   46044884   45871802 
 262144:  188127221  187341410  186751698  188404101  191006430  196335726 
 524288:  401388177  408309790  398813394  405937758  408024530  409753518 
1048576:  853281037  849272306  837103138  849243102  853955790  861154162 
2097152: 1786958400 1786214606 1770347502 1776749654 1768287894 1772058398 
4194304: 3825998674 3797897334 3785570298 3745774750 3739175198 3729148150 
8388608: 7877856605 7873270370 7873672090 7879864630 7896917590 7880339746