Rational Type Performance

Note that these tests are carefully designed to test performance of the underlying algorithms and not memory allocation or variable copying. As usual, performance results should be taken with a healthy dose of scepticism, and real-world performance may vary widely depending upon the specifics of the program. In each table relative times are given first, with the best performer given a score of 1. Total actual times are given in brackets, measured in seconds for 500000 operations.

Table 1.62. Operator +

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	5.89417 (18.4116s)	6.87256 (47.4698s)	6.65008 (107.715s)	6.53801 (256.244s)
mpq_rational	1 (3.1237s)	1 (6.90715s)	1 (16.1975s)	1 (39.1929s)

Table 1.63. Operator +(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	3.62367 (2.46488s)	4.18291 (2.94603s)	4.726 (3.74866s)	6.1388 (5.56817s)
mpq_rational	1 (0.680215s)	1 (0.704303s)	1 (0.7932s)	1 (0.907046s)

Table 1.64. Operator +(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1.1527 (2.6378s)	1.31751 (3.09863s)	1.58996 (4.00714s)	2.15642 (5.75702s)
mpq_rational	1 (2.28837s)	1 (2.35189s)	1 (2.52028s)	1 (2.66971s)

Table 1.65. Operator +=(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1.18436 (2.7059s)	1.32279 (3.11099s)	1.61398 (4.05389s)	2.20048 (5.84623s)
mpq_rational	1 (2.2847s)	1 (2.35183s)	1 (2.51174s)	1 (2.6568s)

Table 1.66. Operator -

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	5.81893 (18.3457s)	6.82209 (47.1928s)	6.64143 (107.498s)	6.51362 (255.137s)
mpq_rational	1 (3.15277s)	1 (6.91765s)	1 (16.1859s)	1 (39.1698s)

Table 1.67. Operator -(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	3.72441 (2.48756s)	4.27663 (2.98713s)	4.62109 (3.72114s)	6.17605 (5.56503s)
mpq_rational	1 (0.667908s)	1 (0.698479s)	1 (0.805252s)	1 (0.901066s)

Table 1.68. Operator -(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1.15627 (2.63239s)	1.32096 (3.12092s)	1.61044 (4.00106s)	2.19378 (5.7644s)
mpq_rational	1 (2.27663s)	1 (2.36262s)	1 (2.48445s)	1 (2.62761s)

Table 1.69. Operator -=(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1.1984 (2.73444s)	1.34141 (3.15698s)	1.64159 (4.06997s)	2.23017 (5.88108s)
mpq_rational	1 (2.28174s)	1 (2.35348s)	1 (2.47929s)	1 (2.63706s)

Table 1.70. Operator *

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	5.4306 (32.5882s)	6.91805 (89.9436s)	6.94556 (207.307s)	6.88704 (492.151s)
mpq_rational	1 (6.00084s)	1 (13.0013s)	1 (29.8475s)	1 (71.4604s)

Table 1.71. Operator *(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	2.12892 (2.51376s)	2.47245 (3.07841s)	2.86832 (3.93619s)	3.94086 (6.02565s)
mpq_rational	1 (1.18077s)	1 (1.24508s)	1 (1.3723s)	1 (1.52902s)

Table 1.72. Operator *(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1.32254 (5.43565s)	1.56078 (6.73163s)	1.97701 (9.32522s)	2.85404 (15.1573s)
mpq_rational	1 (4.11002s)	1 (4.313s)	1 (4.71682s)	1 (5.31082s)

Table 1.73. Operator *=(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	6.29806 (58.1188s)	6.30556 (59.5076s)	6.3385 (62.1007s)	6.55345 (67.6905s)
mpq_rational	1 (9.22804s)	1 (9.43733s)	1 (9.79739s)	1 (10.329s)

Table 1.74. Operator /

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	4.4269 (66.8031s)	6.40103 (173.527s)	6.32347 (348.193s)	6.61148 (824.063s)
mpq_rational	1 (15.0903s)	1 (27.1093s)	1 (55.0637s)	1 (124.641s)

Table 1.75. Operator /(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1.78772 (2.50984s)	2.10623 (3.10606s)	2.46986 (3.99358s)	3.37428 (5.96678s)
mpq_rational	1 (1.40393s)	1 (1.4747s)	1 (1.61693s)	1 (1.76831s)

Table 1.76. Operator /(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1.29695 (5.45454s)	1.55248 (6.85353s)	1.93237 (9.28765s)	2.75211 (14.8541s)
mpq_rational	1 (4.20568s)	1 (4.41458s)	1 (4.80635s)	1 (5.39734s)

Table 1.77. Operator /=(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	6.19401 (58.4278s)	6.20135 (59.643s)	6.21327 (62.0338s)	6.40576 (67.6778s)
mpq_rational	1 (9.43295s)	1 (9.61774s)	1 (9.98407s)	1 (10.5652s)

Table 1.78. Operator construct

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1 (0.00978288s)	1 (0.0100574s)	1 (0.0101393s)	1 (0.0101847s)
mpq_rational	39.1516 (0.383015s)	38.3523 (0.385725s)	37.5812 (0.381048s)	37.6007 (0.382953s)

Table 1.79. Operator construct(unsigned)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1 (0.0548151s)	1 (0.0557542s)	1 (0.055825s)	1 (0.0552808s)
mpq_rational	7.21073 (0.395257s)	7.1016 (0.395944s)	7.02046 (0.391917s)	7.16881 (0.396297s)

Table 1.80. Operator construct(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1 (0.0605156s)	1 (0.0616657s)	1 (0.0592056s)	1 (0.0603081s)
mpq_rational	35.1604 (2.12775s)	34.7575 (2.14335s)	35.7232 (2.11502s)	35.0437 (2.11342s)

Table 1.81. Operator str

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	5.48898 (0.0208949s)	8.49668 (0.0546688s)	10.107 (0.121897s)	10.5339 (0.310584s)
mpq_rational	1 (0.0038067s)	1 (0.00643413s)	1 (0.0120606s)	1 (0.0294843s)

Test code was compiled with Microsoft Visual Studio 2010 with all optimisations turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. The tests were run on 32-bit Windows Vista machine.