Comparison of multiple-precision floating-point software

Maple Mathematica Sage GMP MPF MPFR PARI NTL CLN
commercial commercial free (GPL) free (LGPL) free (LGPL) free (GPL) free (GPL) free (GPL)
12.00 6.0.1 4.5.2 5.0.1 3.0.0 2.4.2.alpha 5.5.2 1.3.1
interactive interactive interactive library library library library library

The following tables give the cpu time in milliseconds spent by several systems or libraries for different operations, at different precisions (in digits). Those timings were obtained on a 24-core Intel Xeon X7460 at 2.66GHz (sage.math.washington.edu) with 717GB of swap and 132GB of RAM under Linux 2.6.24-28-server. The version of GCC is 4.2.4 (Ubuntu 4.2.4-1ubuntu4).

GMP was configured with --disable-shared. MPFR was built with --with-gmp-build, and make tune. PARI was built with GMP support. NTL was built with native support. CLN has been built with GMP support.

An entry "na" means a function not available in the corresponding software tool. The boldface entries are the fastest in each row.

100 digits Maple Mathematica Sage MPF MPFR Pari NTL CLN
mult 0.0020 0.0006 0.00053 0.00011 0.00012 0.00013 0.000367 0.000174
div 0.0029 0.0017 0.00076 0.00031 0.00032 0.00034 0.00070 0.000486
sqrt 0.032 0.0018 0.00132 0.00055 0.00049 0.00050 0.00442 0.00068
exp 0.070 0.019 0.0103 na 0.0083 0.0112 0.069 0.0194
log 0.100 0.028 0.0173 na 0.0102 0.0120 0.386 0.0279
sin 0.131 0.017 0.0112 na 0.0070 0.0105 0.074 0.0250
cos 0.119 0.018 0.0078 na 0.0052 0.0091 0.082 0.0212
acos 0.450 0.053 0.058 na 0.044 0.028 na 0.032
atan 0.280 0.048 0.051 na 0.037 0.026 na 0.028
1000 digits Maple Mathematica Sage MPF MPFR Pari NTL CLN
mult 0.0200 0.007 0.0039 0.0036 0.0028 0.0035 0.0137 0.0036
div 0.0200 0.015 0.0071 0.0040 0.0058 0.0059 0.0201 0.0079
sqrt 0.160 0.011 0.0064 0.0049 0.0047 0.0047 0.187 0.0063
exp 0.90 0.63 0.208 na 0.182 0.364 5.96 0.330
log 0.300 0.67 0.195 na 0.161 0.204 48.1 0.400
sin 1.89 0.41 0.210 na 0.192 0.310 6.78 0.288
cos 1.91 0.40 0.190 na 0.181 0.298 6.98 0.269
acos 2.50 0.82 0.81 na 0.38 0.75 na 0.48
atan 2.10 0.80 0.70 na 0.36 0.74 na 0.45
10000 digits Maple Mathematica Sage MPF MPFR Pari NTL CLN
mult 0.80 0.28 0.11 0.107 0.095 0.109 0.508 0.107
div 0.80 0.56 0.28 0.198 0.261 0.264 1.662 0.454
sqrt 3.70 0.36 0.224 0.179 0.176 0.176 20.48 0.295
exp 50.0 17.6 9.6 na 9.1 12.5 1560 13.4
log 20.0 15.9 7.6 na 7.2 8.3 16080 16.7
sin 93.0 44.4 17.3 na 15.6 21.7 1650 17.8
cos 92.0 44.4 17.1 na 15.7 21.0 7710 16.7
acos 87.0 91.2 29.4 na 16.8 31.7 na 28.6
atan 82.0 87.2 26.4 na 15.3 30.2 na 27.0

The source file of these tests is available for Maple, Mathematica, Sage, MPF, MPFR, Pari, NTL, CLN.

Please acknowledge "National Science Foundation Grant No. DMS-0821725" in any published work that uses this computer.

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