lambdaway :: bigint

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_h1 bigint | [[curzon_numbers]]

_p [[BigInt|https://developer.mozilla.org/fr/docs/Web/JavaScript/Reference/Global_Objects/BigInt]] est un objet natif qui permet de représenter des nombres entiers supérieurs à 2^53 (la plus grande valeur entière qui puisse être représentée par le type primitif Number). BigInt peut être utilisé afin de représenter de grands entiers de n'importe quelle taille.

{prewrap
'{pow 2 128}
-> {pow 2 128}
'{BigInt {pow 2 128}}
-> {BigInt {pow 2 128}}
'{BI.** 2 128}
-> {BI.** 2 128}

'{BI.+ {BigInt 340282366920938463463374607431768211456} {BigInt 2}}
->            {BI.+ {BigInt 340282366920938463463374607431768211456} {BigInt 2}}
'{BI.- {BigInt 340282366920938463463374607431768211456} {BigInt 2}}
->            {BI.- {BigInt 340282366920938463463374607431768211456} {BigInt 2}}
'{BI.* {BigInt 340282366920938463463374607431768211456} {BigInt 2}}
->            {BI.* {BigInt 340282366920938463463374607431768211456} {BigInt 2}}
'{BI./ {BigInt 340282366920938463463374607431768211456} {BigInt 2}}
->            {BI./ {BigInt 340282366920938463463374607431768211456} {BigInt 2}}
'{BI.** {BigInt 340282366920938463463374607431768211456} {BigInt 2}}
-> {BI.** {BigInt 340282366920938463463374607431768211456} {BigInt 2}}

'{floor {/ 123456789 2}} -> {floor {/ 123456789 2}}
'{% 123456789 2}         -> {% 123456789 2}

'{BI./ {BigInt 123456789} {BigInt 2}} -> {BI./ {BigInt 123456789} {BigInt 2}}
'{BI.% {BigInt 123456789} {BigInt 2}} -> {BI.% {BigInt 123456789} {BigInt 2}}

'{* {pow 2 64} {pow 2 64}} 
-> {* {pow 2 64} {pow 2 64}}
'{long_mult {long_mult {pow 2 32} {pow 2 32}}
           {long_mult {pow 2 32} {pow 2 32}}} 
-> {long_mult {long_mult {pow 2 32} {pow 2 32}} {long_mult {pow 2 32} {pow 2 32}}}
'{BI.* {pow 2 64} {pow 2 64}} 
-> {BI.* {pow 2 64} {pow 2 64}}

'{def fac
 {lambda {:a :b}
  {if {< :b 1}
   then :a
   else {fac {BI.* :a :b} {- :b 1}}}}}
-> {def fac
 {lambda {:a :b}
  {if {< :b 1}
   then :a
   else {fac {BI.* :a :b} {- :b 1}}}}}

'{fac 1 100}
-> {fac 1 100}

'{bigfac 100} 
-> {bigfac 100}

'{nthPrime 1000} -> {nthPrime 1000}  
}

_h2 computing N = {sup 5 {sup 4 {sup 3 {sup 2}}}}

{pre
'{def N {BI.** 5 {BI.** 4 {BI.** 3 2}}}} -> {def N {BI.** 5 {BI.** 4 {BI.** 3 2}}}}
length: '{def L {W.length {N}}} -> {def L {W.length {N}}} = {L}
20 first digits: '{W.slice 0 20 {N}} -> {W.slice 0 20 {N}}
20 last digits:  '{W.slice -20 {L} {N}} -> {W.slice -20 {L} {N}}

}

_p {i alain marty 2022/03/28}

{script 
LAMBDATALK.DICT['BigInt'] = function() {
  var args = arguments[0].trim();
  return BigInt( Number(args) )
};

LAMBDATALK.DICT['BI.+'] = function() {
  var args = arguments[0].trim().split(' ');
  return BigInt( args[0] ) + BigInt( args[1] )
};
LAMBDATALK.DICT['BI.-'] = function() {
  var args = arguments[0].trim().split(' ');
  return BigInt( args[0] ) - BigInt( args[1] )
};
LAMBDATALK.DICT['BI.*'] = function() {
  var args = arguments[0].trim().split(' ');
  return BigInt( args[0] ) * BigInt( args[1] )
};
LAMBDATALK.DICT['BI./'] = function() {
  var args = arguments[0].trim().split(' ');
  return BigInt( args[0] ) / BigInt( args[1] )
};
LAMBDATALK.DICT['BI.%'] = function() {
  var args = arguments[0].trim().split(' ');
  return BigInt( args[0] ) % BigInt( args[1] )
};
LAMBDATALK.DICT['BI.**'] = function() {
  var args = arguments[0].trim().split(' ');
  return BigInt( args[0] ) ** BigInt( args[1] )
};

// more

LAMBDATALK.DICT['bigfac'] = function() {
  var args = arguments[0].trim();
  var fac = function(n) {
    return (n===0n)? 1n : n*fac(n-1n)
  };
  return fac( BigInt( args ) )
};

LAMBDATALK.DICT['nthPrime'] = function() {
  var isPrime = function(p) {
    for (let i = 2n; i * i <= p; i++) {
      if (p % i === 0n) return false;
    }
    return true;
  };

// Takes a BigInt as an argument and returns a BigInt
  var nthPrime = function(nth) { 
    let maybePrime = 2n;
    let prime = 0n;
    while (nth >= 0n) {
      if (isPrime(maybePrime)) {
        nth -= 1n;
        prime = maybePrime;
      }
      maybePrime += 1n;
    }
    return prime;
  };

//nthPrime(20n)  // ↪ 73n
 
  var args = arguments[0].trim();
  return nthPrime( BigInt( args ) )
};
}