Comparison of multiple-precision floating-point software

Sage	GMP MPF	MPFR	PARI	NTL	CLN	ARB	MPFI
free (GPL)	free (LGPL)	free (LGPL)	free (GPL)	free (GPL)	free (GPL)	free (GPL)	free (LGPL)
8.1	6.1.2	4.0.1	2.9.4	11.0.0	1.3.4	2.13.0	1.5.3
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 8-core AMD Ryzen 5 2400G at 1.5Ghz (gcc67.fsffrance.org) with 32GB of RAM under Debian GNU/Linux 9.4 (stretch). The version of GCC is 6.3.0 (Debian 6.3.0-18+deb9u1).

Sage 8.1 is using MPFR 3.1.5. GMP was configured with --disable-shared. MPFR was configured with --with-gmp-build and after make tune; ARB was configured with FLINT 2.5.2 and that version of MPFR. PARI was built with GMP support (we used the PARI library at C level, and not the interactive GP program). NTL was built with native support and GMP as primary long integer package. 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	Sage	MPF	MPFR	Pari	NTL	CLN	ARB	MPFI
mult	0.000351	0.000043	0.000046	0.000043	0.000097	0.000076	0.000066	0.000137
sqr	0.000320	0.000032	0.000033	0.000036	0.000092	0.000067	0.000058	0.000076
div	0.000390	0.000119	0.000120	0.000150	0.000213	0.000201	0.000134	0.000304
sqrt	0.000626	0.000172	0.000174	0.000191	0.000405	0.000262	0.000202	0.000379
exp	0.00423	na	0.00234	0.00440	0.0256	0.00845	0.000756	0.00495
log	0.00651	na	0.00433	0.00638	0.143	0.0111	0.000587	0.00996
sin	0.00401	na	0.00252	0.00388	0.0270	0.0104	0.000727	0.00833
cos	0.00324	na	0.00198	0.00347	0.0287	0.00910	0.000728	0.00694
acos	0.0234	na	0.0160	0.0114	na	0.0138	0.00153	0.0397
atan	0.0197	na	0.0136	0.0108	na	0.0123	0.000674	0.0330

1000 digits	Sage	MPF	MPFR	Pari	NTL	CLN	ARB	MPFI
mult	0.00302	0.00150	0.00117	0.00173	0.00155	0.00167	0.00119	0.00289
sqr	0.00154	0.00086	0.00068	0.00170	0.00100	0.00098	0.00073	0.00152
div	0.00360	0.00151	0.00203	0.00237	0.00263	0.00316	0.00149	0.00475
sqrt	0.00314	0.00125	0.00124	0.00172	0.00256	0.00216	0.00127	0.00288
exp	0.152	na	0.0695	0.147	0.875	0.146	0.0416	0.156
log	0.128	na	0.0537	0.0815	7.05	0.178	0.0434	0.123
sin	0.143	na	0.0650	0.127	0.952	0.139	0.0476	0.165
cos	0.136	na	0.0618	0.123	0.993	0.129	0.0476	0.159
acos	0.243	na	0.141	0.317	na	0.219	0.0569	0.329
atan	0.231	na	0.134	0.312	na	0.203	0.0482	0.318

10000 digits	Sage	MPF	MPFR	Pari	NTL	CLN	ARB	MPFI
mult	0.121	0.0450	0.0403	0.0443	0.0438	0.0447	0.0403	0.0937
sqr	0.0620	0.0327	0.0253	0.0331	0.0331	0.0333	0.0255	0.0531
div	0.197	0.0795	0.0802	0.102	0.103	0.204	0.0781	0.186
sqrt	0.170	0.0485	0.0484	0.0669	0.0829	0.122	0.0486	0.105
exp	8.60	na	3.60	4.84	136	6.05	2.24	7.98
log	8.29	na	2.35	3.20	1456	7.63	2.34	5.13
sin	19.0	na	6.19	8.99	149	7.72	2.56	14.1
cos	19.1	na	6.20	8.87	352	7.31	2.48	14.5
acos	15.4	na	6.35	13.5	na	12.4	3.85	14.0
atan	13.7	na	5.77	13.4	na	11.7	3.59	12.0

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

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