Integer Algorithm Performance

Table 1.43. Operator %

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	1.51155 (0.0481508s)	1.60666 (0.0825917s)	1.75956 (0.127209s)	1.87154 (0.171986s)	2.58143 (0.368469s)	1 (0.512768s)	1.42429 (1.03083s)	1 (1.96988s)
cpp_int(fixed)	1 (0.0318553s)	1.2913 (0.0663805s)	1.33672 (0.0966394s)	1.97924 (0.181883s)
gmp_int	1.4659 (0.0466966s)	1 (0.0514059s)	1 (0.0722958s)	1 (0.0918952s)	1 (0.142738s)	1 (0.24073s)	1.17701 (0.603534s)	1 (0.723753s)
tommath_int	27.46 (0.874748s)	20.1749 (1.03711s)	17.9774 (1.29969s)	19.0867 (1.75398s)	23.3789 (3.33706s)	26.6546 (6.41658s)	33.4553 (17.1548s)	70.788 (51.233s)

Table 1.44. Operator %(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	1 (0.00790481s)	1.45288 (0.0215141s)	2.71488 (0.065874s)	4.05695 (0.1044s)	6.59285 (0.288068s)	3.58045 (0.429244s)	6.18417 (0.851447s)	1 (1.57951s)
cpp_int(fixed)	2.18748 (0.0172916s)	1.67119 (0.0247468s)	2.83861 (0.0688759s)	4.3186 (0.111133s)
gmp_int	1.50165 (0.0118703s)	1 (0.0148079s)	1 (0.024264s)	1 (0.0257336s)	1 (0.0436939s)	1 (0.0571251s)	1 (0.119886s)	1 (0.137682s)
tommath_int	68.9623 (0.545134s)	54.52 (0.807325s)	38.3573 (0.930702s)	53.0833 (1.36603s)	59.6958 (2.60834s)	103.597 (5.91797s)	133.648 (16.0225s)	392.812 (54.083s)

Table 1.45. Operator &

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	2.82137 (0.0101034s)	3.08842 (0.0128886s)	3.46566 (0.018172s)	2.55025 (0.0204051s)	2.97241 (0.0461406s)	1 (0.0440714s)	1 (0.0811524s)	1 (0.146531s)
cpp_int(fixed)	1 (0.00358104s)	1.5374 (0.00641591s)	1.70378 (0.0089337s)	2.40825 (0.019269s)
gmp_int	1.10071 (0.00394167s)	1 (0.00417321s)	1 (0.00524347s)	1 (0.00800121s)	1 (0.015523s)	1.04806 (0.0384586s)	2.0133 (0.0887291s)	1.38531 (0.112421s)
tommath_int	2.18066 (0.00780901s)	2.22528 (0.00928657s)	2.15567 (0.0113032s)	3.05906 (0.0244762s)	2.34741 (0.0364387s)	1.50551 (0.0552444s)	2.29355 (0.10108s)	3.0313 (0.245997s)

Table 1.46. Operator &(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	3.24695 (0.0124861s)	1.81002 (0.0114113s)	2.11984 (0.0179186s)	2.56949 (0.0262296s)	3.62157 (0.063826s)	3.95427 (0.0593859s)	4.84754 (0.102968s)	1 (0.168385s)
cpp_int(fixed)	1 (0.0038455s)	1 (0.00630453s)	1 (0.00845281s)	2.20848 (0.0225444s)
gmp_int	3.87448 (0.0148993s)	1.50343 (0.00947844s)	1.59793 (0.013507s)	1 (0.0102081s)	1 (0.0176239s)	1 (0.0121449s)	1 (0.0150182s)	1 (0.0212413s)
tommath_int	25.1094 (0.0965583s)	15.7147 (0.0990734s)	9.65097 (0.0815778s)	8.5208 (0.0869813s)	5.74798 (0.101302s)	10.598 (0.128712s)	12.0534 (0.18102s)	13.0183 (0.276527s)

Table 1.47. Operator *

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	12.4201 (0.0145016s)	1.838 (0.0246772s)	2.10406 (0.0631704s)	2.22846 (0.224062s)	2.53789 (0.918685s)	1 (2.65154s)	1 (7.83314s)	1 (26.1836s)
cpp_int(fixed)	1 (0.00116759s)	1.76789 (0.0237359s)	1.58515 (0.047591s)	1.52628 (0.153461s)
gmp_int	4.80091 (0.00560549s)	1 (0.0134261s)	1 (0.0300231s)	1 (0.100546s)	1 (0.361988s)	1 (1.11701s)	2.08347 (5.52441s)	1.44767 (11.3398s)
tommath_int	16.9604 (0.0198027s)	2.43157 (0.0326465s)	2.82213 (0.0847288s)	1.67653 (0.168568s)	1.27293 (0.460786s)	1.41678 (1.58255s)	2.69181 (7.13744s)	3.30421 (25.8824s)

Table 1.48. Operator *(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	10.9781 (0.0072726s)	1.52901 (0.00991594s)	3.35266 (0.0194072s)	2.30215 (0.0214459s)	1.95214 (0.047049s)	1 (0.0576663s)	1 (0.0955853s)	1 (0.167493s)
cpp_int(fixed)	1 (0.000662467s)	1 (0.00648519s)	1.52643 (0.0088359s)	2.26708 (0.0211192s)
gmp_int	7.14641 (0.00473426s)	1.74133 (0.0112929s)	1 (0.00578859s)	1 (0.00931559s)	1 (0.0241013s)	1.12075 (0.0477494s)	1.96831 (0.113505s)	1.44107 (0.137745s)
tommath_int	156.154 (0.103447s)	14.5292 (0.0942242s)	16.82 (0.0973642s)	11.9029 (0.110883s)	5.61803 (0.135402s)	4.61241 (0.196512s)	5.30415 (0.30587s)	5.73424 (0.548109s)

Table 1.49. Operator *(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	8.98335 (0.00669928s)	1.79861 (0.00820918s)	1.86924 (0.0119122s)	1.71773 (0.0175683s)	2.57826 (0.0539343s)	1 (0.0432066s)	1 (0.0813634s)	1 (0.159452s)
cpp_int(fixed)	1 (0.000745744s)	1.07211 (0.00489332s)	1.19888 (0.00764018s)	1.53618 (0.0157115s)
gmp_int	4.97741 (0.00371188s)	1 (0.00456418s)	1 (0.00637276s)	1 (0.0102277s)	1 (0.0209189s)	1 (0.0321931s)	2.05197 (0.0886586s)	1.59261 (0.12958s)
tommath_int	143.938 (0.107341s)	24.0751 (0.109883s)	16.9325 (0.107907s)	11.5473 (0.118102s)	8.08283 (0.169084s)	6.84808 (0.220461s)	8.37134 (0.361697s)	8.20104 (0.667264s)

Table 1.50. Operator *=(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	15.7803 (0.0131299s)	1.67116 (0.00790233s)	1.66661 (0.0119079s)	1.51408 (0.0203561s)	1.23815 (0.0373067s)	1 (0.0424701s)	1 (0.0946934s)	1 (0.177219s)
cpp_int(fixed)	1 (0.000832044s)	1 (0.00472864s)	1 (0.00714494s)	1 (0.0134446s)
gmp_int	6.73473 (0.00560359s)	1.81651 (0.00858963s)	1.36813 (0.00977523s)	1.00404 (0.0134989s)	1 (0.0301309s)	1 (0.0457849s)	2.56449 (0.108914s)	2.20384 (0.208689s)
tommath_int	115.266 (0.0959064s)	24.7701 (0.117129s)	15.9941 (0.114277s)	11.3798 (0.152996s)	5.69861 (0.171704s)	5.47882 (0.250847s)	10.6875 (0.453899s)	7.29439 (0.690731s)

Table 1.51. Operator +

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	9.80738 (0.0086037s)	2.34204 (0.0160922s)	1.00627 (0.0131305s)	1.67865 (0.0163002s)	1.88916 (0.033949s)	1 (0.0412289s)	1 (0.083134s)	1 (0.190174s)
cpp_int(fixed)	1 (0.000877268s)	1 (0.00687102s)	1.82016 (0.0237507s)	1.90391 (0.0184876s)
gmp_int	5.87168 (0.00515104s)	1.45191 (0.00997612s)	1 (0.0130487s)	1 (0.00971031s)	1 (0.0179704s)	1 (0.0300729s)	1.96754 (0.0811195s)	1.62045 (0.134715s)
tommath_int	13.6707 (0.0119929s)	1.03266 (0.00709542s)	1.02249 (0.0133422s)	1.4749 (0.0143218s)	1.17551 (0.0211244s)	1.08462 (0.0326177s)	1.47125 (0.060658s)	2.75813 (0.229295s)

Table 1.52. Operator +(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	7.65014 (0.00534018s)	1.8992 (0.0063589s)	1.56778 (0.00666443s)	1.29719 (0.00836612s)	1.73231 (0.0204874s)	1 (0.0198385s)	1 (0.0338486s)	1 (0.0760202s)
cpp_int(fixed)	1 (0.000698051s)	1.72665 (0.00578118s)	1.57164 (0.00668085s)	1.90796 (0.0123052s)
gmp_int	4.97679 (0.00347405s)	1 (0.0033482s)	1 (0.00425087s)	1 (0.0064494s)	1 (0.0118266s)	1 (0.0195694s)	3.53343 (0.0700979s)	2.28146 (0.0772241s)
tommath_int	127.407 (0.0889366s)	24.8716 (0.0832749s)	20.4864 (0.0870848s)	12.5462 (0.0809152s)	7.07209 (0.083639s)	4.79434 (0.0938225s)	5.93694 (0.11778s)	5.20775 (0.176275s)

Table 1.53. Operator +(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	9.92952 (0.00893714s)	2.68575 (0.0136811s)	1.73024 (0.0102989s)	1.43961 (0.0115471s)	1.46556 (0.0237404s)	1 (0.0253811s)	1 (0.0350422s)	1 (0.0761856s)
cpp_int(fixed)	1 (0.000900057s)	1.27396 (0.00648945s)	1.38787 (0.008261s)	1.56798 (0.0125768s)
gmp_int	5.22669 (0.00470432s)	1 (0.00509394s)	1 (0.00595229s)	1 (0.00802101s)	1 (0.0161988s)	1 (0.0174726s)	1.83602 (0.0466003s)	1.90731 (0.0668364s)
tommath_int	100.859 (0.0907784s)	19.2654 (0.0981367s)	14.4537 (0.0860324s)	10.0594 (0.0806864s)	5.71755 (0.0926177s)	6.23483 (0.108939s)	4.63528 (0.117648s)	5.01743 (0.175822s)

Table 1.54. Operator +=(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	12.2366 (0.0106404s)	1.48157 (0.00996803s)	1.58862 (0.0108279s)	2.06658 (0.0131949s)	1.1631 (0.0186902s)	1 (0.0218483s)	1 (0.0394761s)	1 (0.0783171s)
cpp_int(fixed)	1 (0.000869555s)	1.34779 (0.00906799s)	1 (0.00681593s)	1 (0.00638493s)
gmp_int	11.3522 (0.00987134s)	1 (0.00672804s)	1.27495 (0.00868995s)	2.42237 (0.0154667s)	1 (0.0160693s)	1.09672 (0.0221405s)	2.61199 (0.0570676s)	2.13093 (0.0841208s)
tommath_int	88.4252 (0.0768906s)	14.139 (0.0951277s)	11.6282 (0.0792569s)	14.5551 (0.0929332s)	6.86867 (0.110375s)	5.67471 (0.11456s)	7.29502 (0.159384s)	5.733 (0.226317s)

Table 1.55. Operator -

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	4.45457 (0.00859678s)	1.28478 (0.013219s)	1.27873 (0.0117779s)	1.43649 (0.0151597s)	2.82516 (0.0507822s)	1 (0.0463464s)	1 (0.0813138s)	1 (0.191562s)
cpp_int(fixed)	1 (0.00192988s)	1 (0.010289s)	1 (0.00921062s)	1.5372 (0.0162226s)
gmp_int	3.4436 (0.00664573s)	1.25045 (0.0128659s)	1.10953 (0.0102195s)	1 (0.0105533s)	1 (0.017975s)	1 (0.0321962s)	2.54862 (0.11812s)	1.83623 (0.14931s)
tommath_int	9.3224 (0.0179911s)	1.08796 (0.011194s)	1.93265 (0.017801s)	1.82306 (0.0192393s)	1.55663 (0.0279804s)	1.6544 (0.0532653s)	1.90928 (0.0884881s)	4.41259 (0.358805s)

Table 1.56. Operator -(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	3.07164 (0.00347144s)	1.38957 (0.00531251s)	1.29053 (0.00548206s)	1.35239 (0.00759591s)	1.50007 (0.0176467s)	1 (0.0209158s)	1 (0.0402632s)	1 (0.0674681s)
cpp_int(fixed)	1 (0.00113016s)	1.26281 (0.00482789s)	1.25074 (0.00531307s)	3.3923 (0.0190533s)
gmp_int	3.22069 (0.00363988s)	1 (0.00382312s)	1 (0.00424793s)	1 (0.00561665s)	1 (0.0117639s)	1 (0.0225873s)	2.75829 (0.0576919s)	2.03214 (0.0818204s)
tommath_int	81.1433 (0.0917047s)	21.4543 (0.0820224s)	19.3098 (0.0820267s)	16.2994 (0.0915478s)	7.23608 (0.0851246s)	4.48441 (0.101291s)	5.51882 (0.115431s)	4.44737 (0.179066s)

Table 1.57. Operator -(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	7.02787 (0.00807189s)	1.85949 (0.00922027s)	1.40179 (0.00830959s)	1.22546 (0.00988039s)	1.27526 (0.0235442s)	1 (0.0242017s)	1 (0.0317445s)	1 (0.0783054s)
cpp_int(fixed)	1 (0.00114855s)	1.03947 (0.00515424s)	1.22566 (0.00726552s)	1.56568 (0.0126235s)
gmp_int	7.54669 (0.00866778s)	1 (0.0049585s)	1 (0.00592785s)	1 (0.00806262s)	1 (0.0184622s)	1 (0.0220616s)	1.79985 (0.0435595s)	2.08427 (0.0661641s)
tommath_int	72.1332 (0.0828488s)	18.985 (0.0941371s)	13.9301 (0.0825755s)	9.93889 (0.0801335s)	5.42256 (0.100113s)	4.58437 (0.101139s)	4.91664 (0.118991s)	5.5407 (0.175887s)

Table 1.58. Operator -=(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	10.8565 (0.0103583s)	2.00541 (0.0102937s)	1.73348 (0.0103591s)	2.53718 (0.0189898s)	1.21308 (0.0265754s)	1 (0.0249248s)	1 (0.0377524s)	1 (0.070851s)
cpp_int(fixed)	1 (0.000954108s)	1 (0.00513296s)	1 (0.00597589s)	1 (0.00748462s)
gmp_int	6.6602 (0.00635455s)	1.61345 (0.00828179s)	1.41745 (0.00847054s)	1.41728 (0.0106078s)	1 (0.0219074s)	1 (0.0250737s)	2.12439 (0.05295s)	2.51074 (0.0947863s)
tommath_int	88.858 (0.0847801s)	18.6448 (0.0957029s)	13.7283 (0.0820388s)	13.4423 (0.100611s)	4.83335 (0.105886s)	4.6829 (0.117418s)	7.59449 (0.189292s)	5.86189 (0.2213s)

Table 1.59. Operator /

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	3.20876 (0.0878919s)	3.17469 (0.181536s)	3.14517 (0.250544s)	4.14655 (0.365546s)	4.70812 (0.702366s)	2.28619 (1.18106s)	3.54663 (2.26453s)	1 (4.52755s)
cpp_int(fixed)	1 (0.0273912s)	1.72404 (0.098585s)	2.12584 (0.169344s)	3.71442 (0.327451s)
gmp_int	1.70383 (0.04667s)	1 (0.0571824s)	1 (0.0796599s)	1 (0.0881567s)	1 (0.149182s)	1 (0.208719s)	1 (0.516606s)	1 (0.638503s)
tommath_int	40.8044 (1.11768s)	17.2975 (0.989116s)	17.4097 (1.38686s)	20.9668 (1.84837s)	20.6415 (3.07934s)	31.5839 (6.59216s)	33.0087 (17.0525s)	81.0894 (51.7759s)

Table 1.60. Operator /(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	4.50037 (0.0520677s)	6.30243 (0.108097s)	8.34437 (0.193637s)	7.02879 (0.296939s)	6.47793 (0.630264s)	2.64044 (1.08346s)	3.92627 (2.33772s)	1 (4.22641s)
cpp_int(fixed)	1.27227 (0.0147198s)	4.34067 (0.0744498s)	6.08699 (0.141253s)	6.56549 (0.277366s)
gmp_int	1 (0.0115696s)	1 (0.0171517s)	1 (0.0232057s)	1 (0.0422461s)	1 (0.0972941s)	1 (0.156597s)	1 (0.410334s)	1 (0.595404s)
tommath_int	60.4712 (0.69963s)	44.8464 (0.769191s)	40.4334 (0.938285s)	35.0752 (1.48179s)	26.8178 (2.60921s)	37.2616 (5.83504s)	37.7146 (15.4756s)	84.1326 (50.0929s)

Table 1.61. Operator /(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	6.09203 (0.0582351s)	6.42997 (0.0982056s)	6.2137 (0.151642s)	6.62408 (0.281298s)	9.30105 (0.706562s)	3.66307 (1.0584s)	4.10257 (2.14867s)	1 (4.2547s)
cpp_int(fixed)	1.76794 (0.0169001s)	3.59379 (0.0548884s)	5.55499 (0.135566s)	6.36274 (0.2702s)
gmp_int	1 (0.00955921s)	1 (0.0152731s)	1 (0.0244044s)	1 (0.042466s)	1 (0.0759658s)	1 (0.125208s)	1 (0.288938s)	1 (0.523737s)
tommath_int	63.2738 (0.604848s)	57.3767 (0.876321s)	43.9301 (1.07209s)	40.0122 (1.69916s)	41.1147 (3.12331s)	57.9739 (7.25882s)	68.6676 (19.8407s)	109.312 (57.2509s)

Table 1.62. Operator /=(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	5.21402 (0.0701172s)	4.76442 (0.105309s)	5.1245 (0.171387s)	7.39587 (0.299993s)	6.88568 (0.632889s)	3.2993 (1.05399s)	3.52936 (2.14442s)	1 (4.37618s)
cpp_int(fixed)	1.68246 (0.0226255s)	3.12633 (0.0691018s)	3.98733 (0.133354s)	6.62903 (0.268888s)
gmp_int	1 (0.0134478s)	1 (0.0221032s)	1 (0.0334445s)	1 (0.0405622s)	1 (0.0919138s)	1 (0.14699s)	1 (0.319457s)	1 (0.607595s)
tommath_int	46.0731 (0.619583s)	43.6571 (0.964961s)	30.1861 (1.00956s)	41.4936 (1.68307s)	32.6785 (3.0036s)	48.2935 (7.09868s)	64.9093 (20.7357s)	111.801 (67.9296s)

Table 1.63. Operator <<

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	9.93178 (0.0116142s)	1.74005 (0.0147029s)	2.68859 (0.0238748s)	2.04419 (0.0394659s)	2.15112 (0.0859331s)	1 (0.0889652s)	1 (0.190562s)	1 (0.32803s)
cpp_int(fixed)	1 (0.00116939s)	1 (0.00844969s)	1.94851 (0.0173029s)	1.55242 (0.0299716s)
gmp_int	4.60815 (0.00538874s)	1.02939 (0.00869801s)	1 (0.00888006s)	1 (0.0193064s)	1 (0.039948s)	1 (0.0597248s)	1.65224 (0.146992s)	1.08567 (0.206887s)
tommath_int	10.7935 (0.0126218s)	2.38166 (0.0201243s)	2.42444 (0.0215291s)	1.87488 (0.0361972s)	1.73489 (0.0693055s)	1.93177 (0.115375s)	2.49667 (0.222116s)	2.82346 (0.538044s)

Table 1.64. Operator >>

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	12.5304 (0.011709s)	6.85524 (0.0153366s)	8.77866 (0.0209131s)	3.21549 (0.0146098s)	4.04361 (0.0183489s)	3.04276 (0.0219967s)	8.19636 (0.0537598s)	1 (0.0745484s)
cpp_int(fixed)	1 (0.000934446s)	6.55349 (0.0146615s)	6.51353 (0.0155169s)	4.90631 (0.0222922s)
gmp_int	2.59712 (0.00242687s)	1 (0.0022372s)	1 (0.00238226s)	1 (0.00454358s)	1 (0.00453774s)	1 (0.00313265s)	1 (0.00722919s)	1 (0.00655899s)
tommath_int	102.662 (0.0959319s)	42.5337 (0.0951565s)	39.1437 (0.0932504s)	21.0397 (0.0955953s)	29.6104 (0.134364s)	62.7092 (0.196446s)	49.6167 (0.358689s)	137.105 (0.899272s)

Table 1.65. Operator ^

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	2.8103 (0.0101384s)	4.11932 (0.0282768s)	2.25923 (0.0139063s)	1.94172 (0.0187085s)	1.66067 (0.0405646s)	1 (0.0369865s)	1 (0.0918676s)	1 (0.150955s)
cpp_int(fixed)	1 (0.00360758s)	1 (0.00686442s)	1.50683 (0.00927498s)	1.79076 (0.0172541s)
gmp_int	1.35398 (0.0048846s)	1.00969 (0.00693092s)	1 (0.00615531s)	1 (0.00963503s)	1 (0.0244266s)	1 (0.0429561s)	2.17737 (0.0805332s)	1.3521 (0.124214s)
tommath_int	2.28701 (0.00825059s)	1.65996 (0.0113947s)	2.06089 (0.0126854s)	2.03244 (0.0195826s)	1.4173 (0.0346198s)	1.32237 (0.0568037s)	2.69468 (0.0996668s)	2.55626 (0.234837s)

Table 1.66. Operator ^(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	2.67312 (0.00991885s)	1.57246 (0.0115174s)	2.50193 (0.0198209s)	1 (0.0153479s)	1 (0.0264078s)	1 (0.0235546s)	1 (0.0392727s)	1 (0.0657809s)
cpp_int(fixed)	1 (0.00371059s)	1 (0.0073244s)	1 (0.00792226s)	1.04763 (0.0160789s)
gmp_int	2.86377 (0.0106263s)	2.18619 (0.0160125s)	2.18777 (0.0173321s)	1.01844 (0.0156309s)	1.13176 (0.0298873s)	1.9665 (0.0406408s)	3.34613 (0.0788165s)	3.54952 (0.139399s)
tommath_int	26.101 (0.0968501s)	14.6444 (0.107261s)	10.0538 (0.079649s)	5.64392 (0.0866224s)	3.8806 (0.102478s)	6.36386 (0.131519s)	8.07216 (0.190136s)	8.01428 (0.314742s)

Table 1.67. Operator construct

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	3.24638 (0.00190752s)	1.06172 (0.00258002s)	1 (0.00248269s)	1 (0.00191598s)	1 (0.00273948s)	1 (0.0017072s)	1 (0.00191549s)	1 (0.0016635s)
cpp_int(fixed)	1 (0.000587582s)	1 (0.00243004s)	1.51116 (0.00375174s)	4.66482 (0.00893771s)
gmp_int	5.61558 (0.00329962s)	1.52898 (0.0037155s)	2.51713 (0.00624925s)	1.755 (0.00336255s)	1.40183 (0.00384029s)	1.60131 (0.00385483s)	4.7818 (0.0081635s)	2.07779 (0.00397999s)
tommath_int	251.1 (0.147542s)	63.6186 (0.154596s)	54.6947 (0.13579s)	66.8839 (0.128148s)	47.8098 (0.130974s)	54.8252 (0.13198s)	74.1436 (0.126578s)	83.945 (0.160796s)

Table 1.68. Operator construct(unsigned long long)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	2.12644 (0.00192028s)	1 (0.00200418s)	1 (0.00223886s)	1 (0.00189442s)	1 (0.00190833s)	1 (0.00199036s)	1 (0.00200998s)	1 (0.00168004s)
cpp_int(fixed)	1 (0.000903049s)	1.26395 (0.00253319s)	1.78621 (0.00399907s)	5.10701 (0.0096748s)
gmp_int	27.1389 (0.0245077s)	10.3593 (0.020762s)	9.02272 (0.0202006s)	9.96334 (0.0188747s)	15.2262 (0.0290565s)	8.50239 (0.0244927s)	35.6564 (0.0709692s)	10.9129 (0.0219346s)
tommath_int	183.484 (0.165695s)	83.0709 (0.166489s)	69.5984 (0.155821s)	75.8903 (0.143768s)	85.5979 (0.163349s)	50.8174 (0.146389s)	70.0602 (0.139445s)	95.4952 (0.191943s)

Table 1.69. Operator construct(unsigned)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	2.00349 (0.00174712s)	1 (0.00225895s)	1 (0.00241092s)	1 (0.00177047s)	1 (0.00304865s)	1 (0.0018378s)	1 (0.0017583s)	1 (0.00197229s)
cpp_int(fixed)	1 (0.000872038s)	1.1805 (0.0026667s)	1.66167 (0.00400614s)	5.54475 (0.00981681s)
gmp_int	27.6419 (0.0241048s)	10.0723 (0.0227529s)	7.60577 (0.0183369s)	10.2725 (0.0181871s)	9.38419 (0.0286091s)	9.10394 (0.0220052s)	34.6032 (0.0635939s)	15.7134 (0.0276289s)
tommath_int	207.462 (0.180915s)	84.5379 (0.190967s)	65.2109 (0.157218s)	84.8572 (0.150237s)	47.0682 (0.143494s)	59.4466 (0.143689s)	78.5549 (0.144368s)	103.519 (0.182018s)

Table 1.70. Operator gcd

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	2.10743 (0.358587s)	1.8778 (1.42989s)	2.03859 (3.30534s)	2.01435 (7.01715s)	2.16957 (17.7583s)	1 (32.2572s)	1 (76.6459s)	1 (201.791s)
cpp_int(fixed)	3.65486 (0.621889s)	1.78424 (1.35865s)	2.02664 (3.28597s)	1.95328 (6.8044s)
gmp_int	1 (0.170154s)	1 (0.761472s)	1 (1.62139s)	1 (3.48358s)	1 (8.18516s)	1 (18.7879s)	1.82325 (58.8129s)	1.59356 (122.14s)
tommath_int	8.01966 (1.36458s)	4.44226 (3.38266s)	4.55056 (7.37824s)	4.42983 (15.4317s)	5.23788 (42.8729s)	7.25799 (136.362s)	14.6265 (471.81s)	23.1025 (1770.72s)

Table 1.71. Operator powm

Backend	128 Bits	256 Bits	512 Bits	1024 Bits
cpp_int	14.8198 (0.565871s)	13.2096 (2.0199s)	11.8233 (9.06469s)	9.12533 (46.9932s)
cpp_int(fixed)	9.40069 (0.35895s)	10.0395 (1.53516s)	10.5353 (8.07714s)	8.49678 (43.7564s)
gmp_int	1 (0.0381833s)	1 (0.152912s)	1 (0.766677s)	1 (5.14976s)
tommath_int	11.0485 (0.421869s)	8.44037 (1.29063s)	4.18756 (3.21051s)	2.45216 (12.628s)

Table 1.72. Operator str

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	1.47697 (0.000264092s)	2.87174 (0.000644609s)	2.28911 (0.00141073s)	4.92453 (0.00383604s)	5.61647 (0.0137593s)	1.87264 (0.0491109s)	4.29909 (0.171316s)	1 (0.595522s)
cpp_int(fixed)	4.73326 (0.00084634s)	1.78742 (0.000401216s)	1.68455 (0.00103815s)	4.30889 (0.00335647s)
gmp_int	1 (0.000178807s)	1 (0.000224466s)	1 (0.00061628s)	1 (0.000778966s)	1 (0.00244981s)	1 (0.00486654s)	1 (0.0262254s)	1 (0.0398493s)
tommath_int	16.7304 (0.00299152s)	26.6015 (0.00597113s)	30.9815 (0.0190933s)	74.7467 (0.0582251s)	82.4773 (0.202054s)	154.996 (0.754295s)	107.534 (2.82013s)	279.178 (11.1251s)

Table 1.73. Operator |

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	2.26845 (0.00991773s)	1.955 (0.00939722s)	2.01122 (0.012635s)	1.76421 (0.0152013s)	1.92162 (0.0293243s)	1 (0.0377549s)	1 (0.0916779s)	1 (0.152323s)
cpp_int(fixed)	1.00452 (0.0043918s)	1.37689 (0.00661838s)	1.3138 (0.00825362s)	1.71906 (0.0148123s)
gmp_int	1 (0.00437203s)	1 (0.00480677s)	1 (0.00628228s)	1 (0.00861647s)	1 (0.0152602s)	1.09283 (0.0365187s)	2.43832 (0.0920584s)	1.21204 (0.111118s)
tommath_int	1.69103 (0.00739324s)	1.85402 (0.00891185s)	1.78526 (0.0112155s)	1.86487 (0.0160686s)	1.75184 (0.0267336s)	1.44011 (0.0481236s)	2.33195 (0.0880424s)	2.33204 (0.213797s)

Table 1.74. Operator |(int)

Backend	128 Bits	256 Bits	512 Bits	1024 Bits	2048 Bits	4096 Bits	8192 Bits	16384 Bits
cpp_int	2.11741 (0.00805945s)	2.16753 (0.0119795s)	1.5717 (0.012189s)	1.10016 (0.0134288s)	1.11289 (0.0309032s)	1 (0.0232284s)	1 (0.042441s)	1 (0.0711061s)
cpp_int(fixed)	1 (0.00380628s)	1 (0.00552682s)	1 (0.00775532s)	1 (0.0122062s)
gmp_int	2.62934 (0.010008s)	1.86878 (0.0103284s)	3.19589 (0.0247852s)	1.1073 (0.0135159s)	1 (0.0277685s)	1.67609 (0.0360071s)	3.76493 (0.0874534s)	2.72382 (0.115602s)
tommath_int	22.0502 (0.0839291s)	18.6272 (0.102949s)	9.99323 (0.0775007s)	6.28905 (0.0767652s)	3.28821 (0.0913086s)	5.0968 (0.109494s)	6.47865 (0.150489s)	4.8474 (0.205729s)

Table 1.75. Platform Details

	Version
Compiler	GNU C++ version 10.3.0
GMP	6.2.0
MPFR	262146
Boost	107800
Run date	Sep 30 2021