Add BigInt support to Lisp

[vinc]

• Add num-bigint crate
• Add Number enum for BigInt, i64, and f64
• Add overflow from i64 to BigInt
• Add example of pi computation

[vinc]

The code result in an allocation error:

> lisp
MOROS Lisp v0.4.0

> (+ 1 2 3)
Error: Could not allocate address 0xfffffffff8
DEBUG: panicked at 'explicit panic', src/sys/idt.rs:121:13

[vinc]

The next step after getting this to work will be to start with Number::Int by default and use Number::Float when the parser detect a dot in a number like 1.5 or when one of the argument of an operation is a Number::Float like (+ 1 2 3.5) resulting in 6.5.

Another step would be to use i64 for Number::Int and add Number::BigInt.

One issue will be to handle the overflowing conversion of a big integer into a float, resulting in Inf

[vinc]

Parsing a &str into a BigInt result in the following linker error:

  = note: rust-lld: error: undefined symbol: fmod
          >>> referenced by num_bigint.01a97d26-cgu.3
          >>>               num_bigint-e7ac2962d814313a.num_bigint.01a97d26-cgu.3.rcgu.o:(num_bigint::biguint::convert::from_radix_digits_be::h7271e1decf7a3dd9) in archive /home/v/src/vinc/moros/target/x86_64-moros/release/deps/libnum_bigint-e7ac2962d814313a.rlib

[vinc]

Some issues with leading and trailing zeros:

> 1234567890
1234567890

> 1234567890123456789
1234567890123456789

> 12345678901234567890
1234567890123456789

> 123456789012345678900
1234567890123456789

> 1234567890123456789000
1234567890123456789

> 12345678901234567890001
12345678901234567890001

> 0000000111111111111111111111111111111111111111111
0000000111111111111111111111111111111111111111111

[vinc]

> lisp /tmp/lisp/factorial.lsp 1000
40238726007709377354370243392300398571937486421071463254379991042993851239862902
05920442084869694048004799886101971960586316668729948085589013238296699445909974
24504087073759918823627727188732519779505950995276120874975462497043601418278094
64649629105639388743788648733711918104582578364784997701247663288983595573543251
31853239584630755574091142624174743493475534286465766116677973966688202912073791
43853719588249808126867838374559731746136085379534524221586593201928090878297308
43139284440328123155861103697680135730421616874760967587134831202547858932076716
91324484262361314125087802080002616831510273418279777047846358681701643650241536
91398281264810213092761244896359928705114964975419909342221566832572080821333186
11681155361583654698404670897560290095053761647584772842188967964624494516076535
34081989013854424879849599533191017233555566021394503997362807501378376153071277
61926849034352625200015888535147331611702103968175921510907788019393178114194545
25722386554146106289218796022383897147608850627686296714667469756291123408243920
81601537808898939645182632436716167621791689097799119037540312746222899880051954
44414282012187361745992642956581746628302955570299024324153181617210465832036786
90611726015878352075151628422554026517048330422614397428693306169089796848259012
54583271682264580665267699586526822728070757813918581788896522081643483448259932
66043367660176999612831860788386150279465955131156552036093988180612138558600301
43569452722420634463179746059468257310379008402443243846565724501440282188525247
09351906209290231364932734975655139587205596542287497740114133469627154228458623
77387538230483865688976461927383814900140767310446640259899490222221765904339901
88601856652648506179970235619389701786004081188972991831102117122984590164192106
88843871218556461249607987229085192968193723886426148396573822911231250241866493
53143970137428531926649875337218940694281434118520158014123344828015051399694290
15348307764456909907315243327828826986460278986432113908350621709500259738986355
42771967428222487575867657523442202075736305694988250879689281627538488633969099
59826280956121450994871701244516461260379029309120889086942028510640182154399457
15680594187274899809425474217358240106367740459574178516082923013535808184009699
63725242305608559037006242712434169090041536901059339838357779394109700277534720
00000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000

[vinc]

> (map (fn (x) (println (string "2 ^ " x " = " (^ 2 x)))) (range 0 129))
2 ^ 128 = 340282366920938463463374607431768211456
2 ^ 127 = 170141183460469231731687303715884105728
2 ^ 126 = 85070591730234615865843651857942052864
2 ^ 125 = 42535295865117307932921825928971026432
2 ^ 124 = 21267647932558653966460912964485513216
2 ^ 123 = 10633823966279326983230456482242756608
2 ^ 122 = 5316911983139663491615228241121378304
2 ^ 121 = 2658455991569831745807614120560689152
2 ^ 120 = 1329227995784915872903807060280344576
2 ^ 119 = 664613997892457936451903530140172288
2 ^ 118 = 332306998946228968225951765070086144
2 ^ 117 = 166153499473114484112975882535043072
2 ^ 116 = 83076749736557242056487941267521536
2 ^ 115 = 41538374868278621028243970633760768
2 ^ 114 = 20769187434139310514121985316880384
2 ^ 113 = 10384593717069655257060992658440192
2 ^ 112 = 5192296858534827628530496329220096
2 ^ 111 = 2596148429267413814265248164610048
2 ^ 110 = 1298074214633706907132624082305024
2 ^ 109 = 649037107316853453566312041152512
2 ^ 108 = 324518553658426726783156020576256
2 ^ 107 = 162259276829213363391578010288128
2 ^ 106 = 81129638414606681695789005144064
2 ^ 105 = 40564819207303340847894502572032
2 ^ 104 = 20282409603651670423947251286016
2 ^ 103 = 10141204801825835211973625643008
2 ^ 102 = 5070602400912917605986812821504
2 ^ 101 = 2535301200456458802993406410752
2 ^ 100 = 1267650600228229401496703205376
2 ^ 99 = 633825300114114700748351602688
2 ^ 98 = 316912650057057350374175801344
2 ^ 97 = 158456325028528675187087900672
2 ^ 96 = 79228162514264337593543950336
2 ^ 95 = 39614081257132168796771975168
2 ^ 94 = 19807040628566084398385987584
2 ^ 93 = 9903520314283042199192993792
2 ^ 92 = 4951760157141521099596496896
2 ^ 91 = 2475880078570760549798248448
2 ^ 90 = 1237940039285380274899124224
2 ^ 89 = 618970019642690137449562112
2 ^ 88 = 309485009821345068724781056
2 ^ 87 = 154742504910672534362390528
2 ^ 86 = 77371252455336267181195264
2 ^ 85 = 38685626227668133590597632
2 ^ 84 = 19342813113834066795298816
2 ^ 83 = 9671406556917033397649408
2 ^ 82 = 4835703278458516698824704
2 ^ 81 = 2417851639229258349412352
2 ^ 80 = 1208925819614629174706176
2 ^ 79 = 604462909807314587353088
2 ^ 78 = 302231454903657293676544
2 ^ 77 = 151115727451828646838272
2 ^ 76 = 75557863725914323419136
2 ^ 75 = 37778931862957161709568
2 ^ 74 = 18889465931478580854784
2 ^ 73 = 9444732965739290427392
2 ^ 72 = 4722366482869645213696
2 ^ 71 = 2361183241434822606848
2 ^ 70 = 1180591620717411303424
2 ^ 69 = 590295810358705651712
2 ^ 68 = 295147905179352825856
2 ^ 67 = 147573952589676412928
2 ^ 66 = 73786976294838206464
2 ^ 65 = 36893488147419103232
2 ^ 64 = 18446744073709551616
2 ^ 63 = 9223372036854775808
2 ^ 62 = 4611686018427387904
2 ^ 61 = 2305843009213693952
2 ^ 60 = 1152921504606846976
2 ^ 59 = 576460752303423488
2 ^ 58 = 288230376151711744
2 ^ 57 = 144115188075855872
2 ^ 56 = 72057594037927936
2 ^ 55 = 36028797018963968
2 ^ 54 = 18014398509481984
2 ^ 53 = 9007199254740992
2 ^ 52 = 4503599627370496
2 ^ 51 = 2251799813685248
2 ^ 50 = 1125899906842624
2 ^ 49 = 562949953421312
2 ^ 48 = 281474976710656
2 ^ 47 = 140737488355328
2 ^ 46 = 70368744177664
2 ^ 45 = 35184372088832
2 ^ 44 = 17592186044416
2 ^ 43 = 8796093022208
2 ^ 42 = 4398046511104
2 ^ 41 = 2199023255552
2 ^ 40 = 1099511627776
2 ^ 39 = 549755813888
2 ^ 38 = 274877906944
2 ^ 37 = 137438953472
2 ^ 36 = 68719476736
2 ^ 35 = 34359738368
2 ^ 34 = 17179869184
2 ^ 33 = 8589934592
2 ^ 32 = 4294967296
2 ^ 31 = 2147483648
2 ^ 30 = 1073741824
2 ^ 29 = 536870912
2 ^ 28 = 268435456
2 ^ 27 = 134217728
2 ^ 26 = 67108864
2 ^ 25 = 33554432
2 ^ 24 = 16777216
2 ^ 23 = 8388608
2 ^ 22 = 4194304
2 ^ 21 = 2097152
2 ^ 20 = 1048576
2 ^ 19 = 524288
2 ^ 18 = 262144
2 ^ 17 = 131072
2 ^ 16 = 65536
2 ^ 15 = 32768
2 ^ 14 = 16384
2 ^ 13 = 8192
2 ^ 12 = 4096
2 ^ 11 = 2048
2 ^ 10 = 1024
2 ^ 9 = 512
2 ^ 8 = 256
2 ^ 7 = 128
2 ^ 6 = 64
2 ^ 5 = 32
2 ^ 4 = 16
2 ^ 3 = 8
2 ^ 2 = 4
2 ^ 1 = 2
2 ^ 0 = 1

[vinc]

> (/ 1 0)
Error: Division by zero

> (/ 1 0.0)
Error: Division by zero

> (/ 1111111111111111111111111111111111111111 0)
Error: Division by zero

[vinc]

The shell builtin pi command can display any number of digits without issues:

> pi 500
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912

But the lisp version can't run much more than 500 iterations of the algorithm (not digits) without running into memory issues with 32MB:

> lisp /tmp/lisp/pi.lsp 500
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282303

> lisp /tmp/lisp/pi.lsp 600
DEBUG: panicked at 'allocation error: Layout { size: 10080, align: 8 (1 << 3) }', src/lib.rs:46:5

It's a little bit better when we increase the memory but we then run into other issues like slice index larger than 2^64