Some tweaks to _num.scm - Gambit-list

18 Mai 2006


      Marc:
Here's a _num.scm with some small tweaks to the fft multiplication  
code.  Memory allocation is cut by roughly 40% when squaring large  
integers; memory allocation is also cut when the length of one  
integer is > 2^M bits, but the some of the lengths of the two  
integers is <= 2^{2M} bits.  And I've defined a new macro for the  
constant inexact-pi/4 to remove a small dependence on the accuracy of  
the atan routine on fft multiplication.  (It still depends on the  
accuracy of sin and cos in the interval [0,pi/4), which, on all  
modern systems, is excellent.)
So, we have
Old:
...
(time (* 0 (* (expt 3 1000000) (expt 3 100001))))
(time (* 0 (* (expt 3 1000000) (expt 3 100001))))
     427 ms real time
     424 ms cpu time (340 user, 84 system)
     22 collections accounting for 45 ms real time (14 user, 30 system)
     43347960 bytes allocated
     no minor faults
     no major faults
New:
...
(time (* 0 (* (expt 3 1000000) (expt 3 100001))))
(time (* 0 (* (expt 3 1000000) (expt 3 100001))))
     422 ms real time
     388 ms cpu time (334 user, 54 system)
     24 collections accounting for 38 ms real time (23 user, 16 system)
     38710968 bytes allocated
     no minor faults
     no major faults
0
Old:
...
(time (* 0 (expt 3 1000000)))
(time (* 0 (expt 3 1000000)))
     200 ms real time
     194 ms cpu time (162 user, 32 system)
     13 collections accounting for 17 ms real time (9 user, 8 system)
     17846920 bytes allocated
     no minor faults
     no major faults
0
New:
...
(time (* 0 (expt 3 1000000)))
(time (* 0 (expt 3 1000000)))
     172 ms real time
     167 ms cpu time (150 user, 17 system)
     10 collections accounting for 12 ms real time (9 user, 3 system)
     13683504 bytes allocated
     no minor faults
     no major faults
0
Brad