Congratulation to the speedup. May I ask what function M is in O(M(n))? Jens Torbjorn Granlund <tg@swox.com> wrote:<blockquote class="replbq" style="border-left: 2px solid rgb(16, 16, 255); margin-left: 5px; padding-left: 5px;"> I only now regenerated the "Computing billions of pi digits using GMP" page for GMP 4.2, see http://swox.com/gmp/pi-with-gmp.html. The speedups I got for 4.1.4 => 4.2 was surprising. Computing 1e9 digits used to take 34300 seconds, now it takes just 8859 seconds on an Opteron. The main sources of speedup should be the x86_64 assembly and Paul Zimmermann's 2003 FFT improvements. But still a speedup of almost 4x is much, much more than I had expected. The numbers still suffers from that division in GMP is O(M(n)log(n)) instead of just O(M(n)). The divisions in Chudnovsky's algorithm are exact, and since we plan O(M(n)) exact division for a future GMP version, things will improve further in the future. -- Torbjörn _______________________________________________ gmp-discuss mailing list gmp-discuss@swox.com https://gmplib.org/mailman/listinfo/gmp-discuss </blockquote> <hr size=1>Yahoo! Messenger with Voice. <a href="http://us.rd.yahoo.com/mail_us/taglines/postman1/*http://us.rd.yahoo.com/evt=39663/*http://voice.yahoo.com">Make PC-to-Phone Calls</a> to the US (and 30+ countries) for 2¢/min or less.