Arithmetic without limitations?

[Paul Zimmermann]

as promised, here are more experiments, still with GMP 5.0.1. I added a swap
file of 16GB to the computer I use (with 16GB of RAM and initially 4GB of swap)
thus I have now 16GB of RAM and 20GB of swap.

With GMP 5.0.1 I tried to multiply two numbers of 10G decimal digits, i.e.,
519051266 limbs. Each number occupies about 4GB.

After more than 6 hours of elapsed time, the computation is still running,
and top says (no other job is running on this machine):

Mem:  16475444k total, 16394992k used,    80452k free,      424k buffers
Swap: 20688996k total, 20688924k used,       72k free,      432k cached
  PID USER      PR  NI  VIRT  RES  SHR S %CPU %MEM    TIME+  COMMAND           
 3392 pzimmerm  20   0 38.7g  15g  128 D    9 96.2 101:19.42 a.out          

In comparison, Bellard's "mptest" program multiplied two integers of 10G
decimal digits with only 4GB of swap and less than one hour of wall clock time:

griffon-92:~/tpi-0.9> time ./mptest.new -u -m 16G -p /tmp mul -n ntt_crt 10000M
Multiplication: limbs=519051266 size=3960.05 MB na/nb=1.000
Random a
  time=2.952 s speed=1341.40 MB/s
Checksum a
  time=7.368 s speed=537.43 MB/s
Random b
Checksum b
Multiplication
  time=1430.053 s
tag                cur   local max  global max (unit=4152.41 MB)
mpx               0.00        0.00        0.00 (0.00 MB)
mpt               0.00        0.00        0.00 (0.00 MB)
fft               0.00        0.00        0.00 (0.00 MB)
fftstate          0.00        0.00        0.00 (0.00 MB)
fac               0.00        0.00        0.00 (0.00 MB)
sieve             0.00        0.00        0.00 (0.00 MB)
ntt               0.00        0.00        0.00 (2.10 MB)
nttdisk           0.00        3.27        3.27 (13589.56 MB)
nttstate          0.00        0.00        0.00 (5.44 MB)
io_buf            0.00        0.06        0.06 (268.44 MB)
total             0.00        3.27        3.27 (13596.03 MB)
disk              2.00        6.37        6.37 (26447.76 MB)
disk I/O: read=23.10 write=21.11
FFT mul count=0, lost limbs=0.0%, init_count=0, remaining init=0.0%
NTT mul count=2, lost limbs=0.6%, max lost=6.089 MB
Checksum c
Cheksum OK [0x756d9cd71c874bb0]
1465.411u 574.399s 1:06:48.78 50.8%     0+0k 131423472+171221488io 44763pf+0w

Paul