D. J. Bernstein
Fast arithmetic
Integer multiplication benchmarks

FreeLIP

FreeLIP was written by Arjen Lenstra and Paul Leyland; it is based on LIP, written by Arjen Lenstra. Sample code using FreeLIP: 
     #include "lip.h"
     main()
     {
       verylong a = 0;
       verylong b = 0;
       verylong c = 0;
       zread(&a);
       zread(&b);
       zmul(a,b,&c);
       zwriteln(c);
     }

Old timings of FreeLIP 1.1 with OPT=-O6 -fomit-frame-pointer on a Pentium II: 

      1:       8140        240        220        202        214        196 
      2:        196        196        196        198        196        196 
      4:        196        196        196        196        196        196 
      8:        196        196        196        196        196        196 
     16:        208        193        193        193        193        193 
     32:        410        360        345        296        296        296 
     64:        578        489        478        470        448        448 
    128:       1002        929        910        910        910        910 
    256:       2620       2572       2588       2572       2588       2572 
    512:      16481       8892       8939       8939       8939       8939 
   1024:      36609      30810      30547      30349      30324      30324 
   2048:     116149      96315      96111      96087      96087      96087 
   4096:     322305     298968     298725     298681     298682     298681 
   8192:     970417     922626     922291     922291     927174     922342 
  16384:    2917120    2852675    2833643    2832689    2827251    2832695 
  32768:    8733502    8568181    8585784    8568664    8567679    8576064 
  65536:   26150235   25894959   25907288   25900580   25893276   25909971 
 131072:   79471052   79055520   79031231   78984854   78981792   78974699 
 262144:  236560941  235560460  235528154  235563659  235532305  235539827 
 524288:  711056759  708804782  709176124  709322751  709544495  709431258 
1048576: 2164154529 2159665862 2159789556 2159629278 2159717352 2159852375