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	4.7	5.0.2	3.1.0	2.5.0	5.5.2	1.3.2
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. 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	0.00056	0.00011	0.00013	0.00012	0.000367	0.00018
sqr			0.00051	0.00009	0.00010	0.00011		0.00015
div	0.0029	0.0017	0.00078	0.00031	0.00031	0.00034	0.00070	0.00049
sqrt	0.032	0.0018	0.00114	0.00056	0.00049	0.00049	0.00442	0.00067
exp	0.070	0.019	0.0098	na	0.0073	0.0106	0.069	0.0197
log	0.100	0.028	0.0172	na	0.0108	0.0117	0.386	0.0278
sin	0.131	0.017	0.0107	na	0.0074	0.0095	0.074	0.0253
cos	0.119	0.018	0.0075	na	0.0054	0.0085	0.082	0.0212
acos	0.450	0.053	0.062	na	0.045	0.028	na	0.033
atan	0.280	0.048	0.053	na	0.039	0.026	na	0.028

1000 digits	Maple	Mathematica	Sage	MPF	MPFR	Pari	NTL	CLN
mult	0.0200	0.007	0.0040	0.0036	0.0030	0.0035	0.0137	0.0037
sqr			0.0029	0.0024	0.0018	0.0024		0.0026
div	0.0200	0.015	0.0070	0.0041	0.0048	0.0060	0.0201	0.0080
sqrt	0.160	0.011	0.0061	0.0050	0.0047	0.0047	0.187	0.0063
exp	0.90	0.63	0.196	na	0.183	0.364	5.96	0.332
log	0.300	0.67	0.192	na	0.162	0.203	48.1	0.400
sin	1.89	0.41	0.200	na	0.167	0.310	6.78	0.291
cos	1.91	0.40	0.187	na	0.157	0.300	6.98	0.266
acos	2.50	0.82	0.77	na	0.36	0.73	na	0.49
atan	2.10	0.80	0.69	na	0.34	0.72	na	0.45

10000 digits	Maple	Mathematica	Sage	MPF	MPFR	Pari	NTL	CLN
mult	0.80	0.28	0.113	0.107	0.095	0.108	0.508	0.106
sqr			0.086	0.076	0.064	0.076		0.076
div	0.80	0.56	0.267	0.198	0.183	0.264	1.662	0.503
sqrt	3.70	0.36	0.183	0.178	0.176	0.176	20.48	0.295
exp	50.0	17.6	9.5	na	8.7	12.6	1560	13.6
log	20.0	15.9	7.7	na	7.1	8.2	16080	16.7
sin	93.0	44.4	17.3	na	15.4	21.7	1650	17.6
cos	92.0	44.4	17.0	na	15.5	21.6	7710	16.5
acos	87.0	91.2	28.9	na	15.2	31.1	na	28.6
atan	82.0	87.2	26.5	na	13.9	31.0	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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