pub fn numberOfDigitsLeftShift(self: *Self, shift: usize) usize {
const ShiftCutoff = struct {
delta: u8,
cutoff: []const u8,
};
// Leading digits of 1/2^i = 5^i.
//
// ```
// import math
//
// bits = 128
// for i in range(bits):
// log2 = math.log(2)/math.log(10)
// print(f'.{{ .delta = {int(log2*i+1)}, .cutoff = "{5**i}" }}, // {2**i}')
// ```
const pow2_to_pow5_table = [_]ShiftCutoff{
.{ .delta = 0, .cutoff = "" },
.{ .delta = 1, .cutoff = "5" }, // 2
.{ .delta = 1, .cutoff = "25" }, // 4
.{ .delta = 1, .cutoff = "125" }, // 8
.{ .delta = 2, .cutoff = "625" }, // 16
.{ .delta = 2, .cutoff = "3125" }, // 32
.{ .delta = 2, .cutoff = "15625" }, // 64
.{ .delta = 3, .cutoff = "78125" }, // 128
.{ .delta = 3, .cutoff = "390625" }, // 256
.{ .delta = 3, .cutoff = "1953125" }, // 512
.{ .delta = 4, .cutoff = "9765625" }, // 1024
.{ .delta = 4, .cutoff = "48828125" }, // 2048
.{ .delta = 4, .cutoff = "244140625" }, // 4096
.{ .delta = 4, .cutoff = "1220703125" }, // 8192
.{ .delta = 5, .cutoff = "6103515625" }, // 16384
.{ .delta = 5, .cutoff = "30517578125" }, // 32768
.{ .delta = 5, .cutoff = "152587890625" }, // 65536
.{ .delta = 6, .cutoff = "762939453125" }, // 131072
.{ .delta = 6, .cutoff = "3814697265625" }, // 262144
.{ .delta = 6, .cutoff = "19073486328125" }, // 524288
.{ .delta = 7, .cutoff = "95367431640625" }, // 1048576
.{ .delta = 7, .cutoff = "476837158203125" }, // 2097152
.{ .delta = 7, .cutoff = "2384185791015625" }, // 4194304
.{ .delta = 7, .cutoff = "11920928955078125" }, // 8388608
.{ .delta = 8, .cutoff = "59604644775390625" }, // 16777216
.{ .delta = 8, .cutoff = "298023223876953125" }, // 33554432
.{ .delta = 8, .cutoff = "1490116119384765625" }, // 67108864
.{ .delta = 9, .cutoff = "7450580596923828125" }, // 134217728
.{ .delta = 9, .cutoff = "37252902984619140625" }, // 268435456
.{ .delta = 9, .cutoff = "186264514923095703125" }, // 536870912
.{ .delta = 10, .cutoff = "931322574615478515625" }, // 1073741824
.{ .delta = 10, .cutoff = "4656612873077392578125" }, // 2147483648
.{ .delta = 10, .cutoff = "23283064365386962890625" }, // 4294967296
.{ .delta = 10, .cutoff = "116415321826934814453125" }, // 8589934592
.{ .delta = 11, .cutoff = "582076609134674072265625" }, // 17179869184
.{ .delta = 11, .cutoff = "2910383045673370361328125" }, // 34359738368
.{ .delta = 11, .cutoff = "14551915228366851806640625" }, // 68719476736
.{ .delta = 12, .cutoff = "72759576141834259033203125" }, // 137438953472
.{ .delta = 12, .cutoff = "363797880709171295166015625" }, // 274877906944
.{ .delta = 12, .cutoff = "1818989403545856475830078125" }, // 549755813888
.{ .delta = 13, .cutoff = "9094947017729282379150390625" }, // 1099511627776
.{ .delta = 13, .cutoff = "45474735088646411895751953125" }, // 2199023255552
.{ .delta = 13, .cutoff = "227373675443232059478759765625" }, // 4398046511104
.{ .delta = 13, .cutoff = "1136868377216160297393798828125" }, // 8796093022208
.{ .delta = 14, .cutoff = "5684341886080801486968994140625" }, // 17592186044416
.{ .delta = 14, .cutoff = "28421709430404007434844970703125" }, // 35184372088832
.{ .delta = 14, .cutoff = "142108547152020037174224853515625" }, // 70368744177664
.{ .delta = 15, .cutoff = "710542735760100185871124267578125" }, // 140737488355328
.{ .delta = 15, .cutoff = "3552713678800500929355621337890625" }, // 281474976710656
.{ .delta = 15, .cutoff = "17763568394002504646778106689453125" }, // 562949953421312
.{ .delta = 16, .cutoff = "88817841970012523233890533447265625" }, // 1125899906842624
.{ .delta = 16, .cutoff = "444089209850062616169452667236328125" }, // 2251799813685248
.{ .delta = 16, .cutoff = "2220446049250313080847263336181640625" }, // 4503599627370496
.{ .delta = 16, .cutoff = "11102230246251565404236316680908203125" }, // 9007199254740992
.{ .delta = 17, .cutoff = "55511151231257827021181583404541015625" }, // 18014398509481984
.{ .delta = 17, .cutoff = "277555756156289135105907917022705078125" }, // 36028797018963968
.{ .delta = 17, .cutoff = "1387778780781445675529539585113525390625" }, // 72057594037927936
.{ .delta = 18, .cutoff = "6938893903907228377647697925567626953125" }, // 144115188075855872
.{ .delta = 18, .cutoff = "34694469519536141888238489627838134765625" }, // 288230376151711744
.{ .delta = 18, .cutoff = "173472347597680709441192448139190673828125" }, // 576460752303423488
.{ .delta = 19, .cutoff = "867361737988403547205962240695953369140625" }, // 1152921504606846976
.{ .delta = 19, .cutoff = "4336808689942017736029811203479766845703125" }, // 2305843009213693952
.{ .delta = 19, .cutoff = "21684043449710088680149056017398834228515625" }, // 4611686018427387904
.{ .delta = 19, .cutoff = "108420217248550443400745280086994171142578125" }, // 9223372036854775808
.{ .delta = 20, .cutoff = "542101086242752217003726400434970855712890625" }, // 18446744073709551616
.{ .delta = 20, .cutoff = "2710505431213761085018632002174854278564453125" }, // 36893488147419103232
.{ .delta = 20, .cutoff = "13552527156068805425093160010874271392822265625" }, // 73786976294838206464
.{ .delta = 21, .cutoff = "67762635780344027125465800054371356964111328125" }, // 147573952589676412928
.{ .delta = 21, .cutoff = "338813178901720135627329000271856784820556640625" }, // 295147905179352825856
.{ .delta = 21, .cutoff = "1694065894508600678136645001359283924102783203125" }, // 590295810358705651712
.{ .delta = 22, .cutoff = "8470329472543003390683225006796419620513916015625" }, // 1180591620717411303424
.{ .delta = 22, .cutoff = "42351647362715016953416125033982098102569580078125" }, // 2361183241434822606848
.{ .delta = 22, .cutoff = "211758236813575084767080625169910490512847900390625" }, // 4722366482869645213696
.{ .delta = 22, .cutoff = "1058791184067875423835403125849552452564239501953125" }, // 9444732965739290427392
.{ .delta = 23, .cutoff = "5293955920339377119177015629247762262821197509765625" }, // 18889465931478580854784
.{ .delta = 23, .cutoff = "26469779601696885595885078146238811314105987548828125" }, // 37778931862957161709568
.{ .delta = 23, .cutoff = "132348898008484427979425390731194056570529937744140625" }, // 75557863725914323419136
.{ .delta = 24, .cutoff = "661744490042422139897126953655970282852649688720703125" }, // 151115727451828646838272
.{ .delta = 24, .cutoff = "3308722450212110699485634768279851414263248443603515625" }, // 302231454903657293676544
.{ .delta = 24, .cutoff = "16543612251060553497428173841399257071316242218017578125" }, // 604462909807314587353088
.{ .delta = 25, .cutoff = "82718061255302767487140869206996285356581211090087890625" }, // 1208925819614629174706176
.{ .delta = 25, .cutoff = "413590306276513837435704346034981426782906055450439453125" }, // 2417851639229258349412352
.{ .delta = 25, .cutoff = "2067951531382569187178521730174907133914530277252197265625" }, // 4835703278458516698824704
.{ .delta = 25, .cutoff = "10339757656912845935892608650874535669572651386260986328125" }, // 9671406556917033397649408
.{ .delta = 26, .cutoff = "51698788284564229679463043254372678347863256931304931640625" }, // 19342813113834066795298816
.{ .delta = 26, .cutoff = "258493941422821148397315216271863391739316284656524658203125" }, // 38685626227668133590597632
.{ .delta = 26, .cutoff = "1292469707114105741986576081359316958696581423282623291015625" }, // 77371252455336267181195264
.{ .delta = 27, .cutoff = "6462348535570528709932880406796584793482907116413116455078125" }, // 154742504910672534362390528
.{ .delta = 27, .cutoff = "32311742677852643549664402033982923967414535582065582275390625" }, // 309485009821345068724781056
.{ .delta = 27, .cutoff = "161558713389263217748322010169914619837072677910327911376953125" }, // 618970019642690137449562112
.{ .delta = 28, .cutoff = "807793566946316088741610050849573099185363389551639556884765625" }, // 1237940039285380274899124224
.{ .delta = 28, .cutoff = "4038967834731580443708050254247865495926816947758197784423828125" }, // 2475880078570760549798248448
.{ .delta = 28, .cutoff = "20194839173657902218540251271239327479634084738790988922119140625" }, // 4951760157141521099596496896
.{ .delta = 28, .cutoff = "100974195868289511092701256356196637398170423693954944610595703125" }, // 9903520314283042199192993792
.{ .delta = 29, .cutoff = "504870979341447555463506281780983186990852118469774723052978515625" }, // 19807040628566084398385987584
.{ .delta = 29, .cutoff = "2524354896707237777317531408904915934954260592348873615264892578125" }, // 39614081257132168796771975168
.{ .delta = 29, .cutoff = "12621774483536188886587657044524579674771302961744368076324462890625" }, // 79228162514264337593543950336
.{ .delta = 30, .cutoff = "63108872417680944432938285222622898373856514808721840381622314453125" }, // 158456325028528675187087900672
.{ .delta = 30, .cutoff = "315544362088404722164691426113114491869282574043609201908111572265625" }, // 316912650057057350374175801344
.{ .delta = 30, .cutoff = "1577721810442023610823457130565572459346412870218046009540557861328125" }, // 633825300114114700748351602688
.{ .delta = 31, .cutoff = "7888609052210118054117285652827862296732064351090230047702789306640625" }, // 1267650600228229401496703205376
.{ .delta = 31, .cutoff = "39443045261050590270586428264139311483660321755451150238513946533203125" }, // 2535301200456458802993406410752
.{ .delta = 31, .cutoff = "197215226305252951352932141320696557418301608777255751192569732666015625" }, // 5070602400912917605986812821504
.{ .delta = 32, .cutoff = "986076131526264756764660706603482787091508043886278755962848663330078125" }, // 10141204801825835211973625643008
.{ .delta = 32, .cutoff = "4930380657631323783823303533017413935457540219431393779814243316650390625" }, // 20282409603651670423947251286016
.{ .delta = 32, .cutoff = "24651903288156618919116517665087069677287701097156968899071216583251953125" }, // 40564819207303340847894502572032
.{ .delta = 32, .cutoff = "123259516440783094595582588325435348386438505485784844495356082916259765625" }, // 81129638414606681695789005144064
.{ .delta = 33, .cutoff = "616297582203915472977912941627176741932192527428924222476780414581298828125" }, // 162259276829213363391578010288128
.{ .delta = 33, .cutoff = "3081487911019577364889564708135883709660962637144621112383902072906494140625" }, // 324518553658426726783156020576256
.{ .delta = 33, .cutoff = "15407439555097886824447823540679418548304813185723105561919510364532470703125" }, // 649037107316853453566312041152512
.{ .delta = 34, .cutoff = "77037197775489434122239117703397092741524065928615527809597551822662353515625" }, // 1298074214633706907132624082305024
.{ .delta = 34, .cutoff = "385185988877447170611195588516985463707620329643077639047987759113311767578125" }, // 2596148429267413814265248164610048
.{ .delta = 34, .cutoff = "1925929944387235853055977942584927318538101648215388195239938795566558837890625" }, // 5192296858534827628530496329220096
.{ .delta = 35, .cutoff = "9629649721936179265279889712924636592690508241076940976199693977832794189453125" }, // 10384593717069655257060992658440192
.{ .delta = 35, .cutoff = "48148248609680896326399448564623182963452541205384704880998469889163970947265625" }, // 20769187434139310514121985316880384
.{ .delta = 35, .cutoff = "240741243048404481631997242823115914817262706026923524404992349445819854736328125" }, // 41538374868278621028243970633760768
.{ .delta = 35, .cutoff = "1203706215242022408159986214115579574086313530134617622024961747229099273681640625" }, // 83076749736557242056487941267521536
.{ .delta = 36, .cutoff = "6018531076210112040799931070577897870431567650673088110124808736145496368408203125" }, // 166153499473114484112975882535043072
.{ .delta = 36, .cutoff = "30092655381050560203999655352889489352157838253365440550624043680727481842041015625" }, // 332306998946228968225951765070086144
.{ .delta = 36, .cutoff = "150463276905252801019998276764447446760789191266827202753120218403637409210205078125" }, // 664613997892457936451903530140172288
.{ .delta = 37, .cutoff = "752316384526264005099991383822237233803945956334136013765601092018187046051025390625" }, // 1329227995784915872903807060280344576
.{ .delta = 37, .cutoff = "3761581922631320025499956919111186169019729781670680068828005460090935230255126953125" }, // 2658455991569831745807614120560689152
.{ .delta = 37, .cutoff = "18807909613156600127499784595555930845098648908353400344140027300454676151275634765625" }, // 5316911983139663491615228241121378304
.{ .delta = 38, .cutoff = "94039548065783000637498922977779654225493244541767001720700136502273380756378173828125" }, // 10633823966279326983230456482242756608
.{ .delta = 38, .cutoff = "470197740328915003187494614888898271127466222708835008603500682511366903781890869140625" }, // 21267647932558653966460912964485513216
.{ .delta = 38, .cutoff = "2350988701644575015937473074444491355637331113544175043017503412556834518909454345703125" }, // 42535295865117307932921825928971026432
.{ .delta = 38, .cutoff = "11754943508222875079687365372222456778186655567720875215087517062784172594547271728515625" }, // 85070591730234615865843651857942052864
.{ .delta = 39, .cutoff = "58774717541114375398436826861112283890933277838604376075437585313920862972736358642578125" }, // 170141183460469231731687303715884105728
};
std.debug.assert(shift < pow2_to_pow5_table.len);
const x = pow2_to_pow5_table[shift];
// Compare leading digits of current to check if lexicographically less than cutoff.
for (x.cutoff, 0..) |p5, i| {
if (i >= self.num_digits) {
return x.delta - 1;
} else if (self.digits[i] == p5 - '0') { // digits are stored as integers
continue;
} else if (self.digits[i] < p5 - '0') {
return x.delta - 1;
} else {
return x.delta;
}
return x.delta;
}
return x.delta;
}
