Comparison of multiple-precision floating-point software

Maple	Mathematica	Sage	GMP MPF	MPFR	PARI	NTL	CLN	ARB	MPFI
commercial	commercial	free (GPL)	free (LGPL)	free (LGPL)	free (GPL)	free (GPL)	free (GPL)	free (GPL)	free (LGPL)
12.00	6.0.1	5.9	5.0.2	3.1.2	2.5.0	5.5.2	1.3.2	2.7.0	1.5.1
interactive	interactive	interactive	library	library	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. The timings of MPFR and ARB were obtained with GMP 5.1.2, configured with --with-gmp-build and after make tune (ARB was configured with FLINT 2.4.1, and its timings were obtained on boxen.math.washington.edu, a machine with the same hardware, idem for MPFI). 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	ARB	MPFI
mult	0.0020	0.0006	0.00047	0.00011	0.00014	0.00012	0.000367	0.00018	0.00014	0.000265
sqr			0.00045	0.00009	0.00011	0.00011		0.00015	0.00012	0.000210
div	0.0029	0.0017	0.00067	0.00031	0.00030	0.00034	0.00070	0.00049	0.00037	0.00068
sqrt	0.032	0.0018	0.00106	0.00056	0.00050	0.00049	0.00442	0.00067	0.00061	0.00098
exp	0.070	0.019	0.0101	na	0.0084	0.0106	0.069	0.0197	0.0020	0.0143
log	0.100	0.028	0.0171	na	0.0121	0.0117	0.386	0.0278	0.0020	0.0208
sin	0.131	0.017	0.0098	na	0.0083	0.0095	0.074	0.0253	0.0025	0.0177
cos	0.119	0.018	0.0068	na	0.0059	0.0085	0.082	0.0212	0.0025	0.0139
acos	0.450	0.053	0.052	na	0.049	0.028	na	0.033	0.0067	0.088
atan	0.280	0.048	0.046	na	0.043	0.026	na	0.028	0.0024	0.075

1000 digits	Maple	Mathematica	Sage	MPF	MPFR	Pari	NTL	CLN	ARB	MPFI
mult	0.0200	0.007	0.0034	0.0036	0.0028	0.0035	0.0137	0.0037	0.0030	0.0059
sqr			0.0023	0.0024	0.0017	0.0024		0.0026	0.0019	0.0035
div	0.0200	0.015	0.0052	0.0041	0.0042	0.0060	0.0201	0.0080	0.0040	0.0096
sqrt	0.160	0.011	0.0058	0.0050	0.0047	0.0047	0.187	0.0063	0.0049	0.0091
exp	0.90	0.63	0.185	na	0.181	0.364	5.96	0.332	0.105	0.359
log	0.300	0.67	0.174	na	0.160	0.203	48.1	0.400	0.108	0.322
sin	1.89	0.41	0.168	na	0.165	0.310	6.78	0.291	0.120	0.364
cos	1.91	0.40	0.156	na	0.155	0.300	6.98	0.266	0.119	0.347
acos	2.50	0.82	0.37	na	0.35	0.73	na	0.49	0.15	0.71
atan	2.10	0.80	0.36	na	0.33	0.72	na	0.45	0.12	0.68

10000 digits	Maple	Mathematica	Sage	MPF	MPFR	Pari	NTL	CLN	ARB	MPFI
mult	0.80	0.28	0.092	0.107	0.091	0.108	0.508	0.106	0.095	0.188
sqr			0.063	0.076	0.060	0.076		0.076	0.063	0.123
div	0.80	0.56	0.196	0.198	0.181	0.264	1.662	0.503	0.194	0.364
sqrt	3.70	0.36	0.193	0.178	0.175	0.176	20.48	0.295	0.176	0.347
exp	50.0	17.6	8.2	na	8.5	12.6	1560	13.6	5.5	17.3
log	20.0	15.9	7.3	na	6.9	8.2	16080	16.7	7.0	13.9
sin	93.0	44.4	15.3	na	15.4	21.7	1650	17.6	15.3	31.7
cos	92.0	44.4	15.3	na	15.4	21.6	7710	16.5	15.4	31.9
acos	87.0	91.2	15.1	na	15.0	31.1	na	28.6	9.8	30.0
atan	82.0	87.2	13.7	na	13.7	31.0	na	27.0	9.1	27.3

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

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

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