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 1.72. Operator *

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	2.59318 (1.11835s)	3.74332 (6.61855s)	4.71871 (18.5981s)	5.48511 (47.0022s)
mpq_rational	1 (0.431264s)	1 (1.7681s)	1 (3.94136s)	1 (8.56905s)

Table 1.73. Operator *(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	5.63431 (0.612884s)	25.5205 (2.83784s)	64.6798 (7.61151s)	135.335 (19.4821s)
mpq_rational	1 (0.108777s)	1 (0.111198s)	1 (0.11768s)	1 (0.143955s)

Table 1.74. Operator *(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	4.44786 (0.691659s)	18.4155 (2.97414s)	44.4009 (7.64879s)	98.4603 (19.5719s)
mpq_rational	1 (0.155504s)	1 (0.161502s)	1 (0.172267s)	1 (0.19878s)

Table 1.75. Operator *=(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	4.12301 (0.690473s)	20.2597 (3.35519s)	42.8043 (7.47312s)	94.2742 (19.3092s)
mpq_rational	1 (0.167468s)	1 (0.165609s)	1 (0.174588s)	1 (0.20482s)

Table 1.76. Operator +

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	8.51825 (1.97719s)	7.8609 (7.34254s)	9.73008 (21.2507s)	11.1497 (49.7843s)
mpq_rational	1 (0.232113s)	1 (0.93406s)	1 (2.18402s)	1 (4.46507s)

Table 1.77. Operator +(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	7.17647 (0.669913s)	29.8489 (2.91217s)	75.7668 (7.40631s)	254.371 (29.7057s)
mpq_rational	1 (0.0933486s)	1 (0.0975637s)	1 (0.0977514s)	1 (0.116781s)

Table 1.78. Operator +(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	12.4996 (1.16835s)	33.6691 (3.37438s)	82.0167 (8.08959s)	171.692 (19.9733s)
mpq_rational	1 (0.0934708s)	1 (0.100222s)	1 (0.0986335s)	1 (0.116332s)

Table 1.79. Operator +=(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	11.7663 (1.14891s)	34.4202 (3.45541s)	78.1856 (8.17612s)	161.351 (20.0733s)
mpq_rational	1 (0.0976436s)	1 (0.100389s)	1 (0.104573s)	1 (0.124408s)

Table 1.80. Operator -

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	8.56942 (2.0234s)	7.88071 (7.38282s)	9.54207 (19.913s)	11.4343 (50.8786s)
mpq_rational	1 (0.236118s)	1 (0.936822s)	1 (2.08686s)	1 (4.44964s)

Table 1.81. Operator -(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	6.62286 (0.62794s)	30.6629 (2.96506s)	75.926 (7.56072s)	199.475 (23.42s)
mpq_rational	1 (0.094814s)	1 (0.0966986s)	1 (0.0995801s)	1 (0.117408s)

Table 1.82. Operator -(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	12.3835 (1.16081s)	36.0761 (3.40187s)	83.3673 (8.26011s)	169.239 (20.5682s)
mpq_rational	1 (0.0937381s)	1 (0.094297s)	1 (0.099081s)	1 (0.121534s)

Table 1.83. Operator -=(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	11.6833 (1.16049s)	36.6427 (3.64132s)	77.0952 (8.10257s)	160.444 (20.0829s)
mpq_rational	1 (0.0993285s)	1 (0.0993737s)	1 (0.105098s)	1 (0.12517s)

Table 1.84. Operator /

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	5.67626 (6.66075s)	5.99288 (21.0634s)	8.08809 (55.0195s)	10.5818 (149.774s)
mpq_rational	1 (1.17344s)	1 (3.51474s)	1 (6.80254s)	1 (14.1539s)

Table 1.85. Operator /(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	5.9046 (0.64166s)	25.5252 (2.84312s)	65.4027 (7.74325s)	134.42 (19.5619s)
mpq_rational	1 (0.108671s)	1 (0.111385s)	1 (0.118393s)	1 (0.145528s)

Table 1.86. Operator /(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	4.35172 (0.691696s)	18.2795 (2.94678s)	44.2487 (7.48547s)	99.1392 (19.5526s)
mpq_rational	1 (0.158948s)	1 (0.161207s)	1 (0.169168s)	1 (0.197224s)

Table 1.87. Operator /=(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	4.14511 (0.685733s)	18.3237 (3.08065s)	43.3784 (7.43555s)	94.2547 (19.2754s)
mpq_rational	1 (0.165432s)	1 (0.168124s)	1 (0.171411s)	1 (0.204503s)

Table 1.88. Operator construct

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1 (0.00323537s)	1 (0.00328614s)	1 (0.0032946s)	1 (0.00333283s)
mpq_rational	28.9199 (0.0935664s)	28.1463 (0.0924926s)	28.2564 (0.0930936s)	27.5848 (0.0919355s)

Table 1.89. Operator construct(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1 (0.00333944s)	1 (0.00335336s)	1 (0.00348777s)	1 (0.00345967s)
mpq_rational	29.1785 (0.09744s)	29.1475 (0.097742s)	27.4732 (0.0958203s)	28.6655 (0.099173s)

Table 1.90. Operator construct(unsigned)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	1 (0.00321917s)	1 (0.00319471s)	1 (0.00327131s)	1 (0.00366486s)
mpq_rational	30.8553 (0.0993283s)	30.5973 (0.0977495s)	29.5866 (0.0967869s)	28.3432 (0.103874s)

Table 1.91. Operator str

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_rational	5.80834 (0.00206821s)	11.5273 (0.00645497s)	18.1686 (0.0156602s)	38.1095 (0.0705044s)
mpq_rational	1 (0.000356077s)	1 (0.000559971s)	1 (0.000861937s)	1 (0.00185005s)

Table 1.92. Platform Details

Platform	Linux 5.3.0-24-generic, version #26-Ubuntu SMP Thu Nov 14 01:33:18 UTC 2019, x86_64
Compiler	GNU C++ version 9.2.1 20191008
GMP	6.1.2
MPFR	262146
Boost	107200
Run date	Dec 13 2019