BigInteger

Usage

use BigInteger;

or

import BigInteger;

The bigint record supports arithmetic operations on arbitrary precision integers in a manner that is broadly consistent with the conventional operations on primitive fixed length integers.

The current implementation is based on the low-level types and functions defined in the GMP module i.e. it is implemented using the GNU Multiple Precision Integer Arithmetic library (GMP). More specifically the record bigint wraps the GMP type mpz_t.

The primary benefits of bigint over mpz_t are

  1. support for multi-locale programs

  2. the convenience of arithmetic operator overloads

  3. automatic memory management of GMP data structures

In addition to the expected set of operations, this record provides a number of methods that wrap GMP functions in a natural way:

use BigInteger;

var   a = new bigint(234958444);
const b = new bigint("4847382292989382987395534934347");
var   c = new bigint();

writeln(a * b);

c.fac(100);
writeln(c);

Casting and declarations can be used to create bigint records as well:

use BigInteger;

var   a = 234958444: bigint;
const b = "4847382292989382987395534934347": bigint;
var   c: bigint;

Warning

Creating a bigint from an integer literal that is larger than max(uint(64)) would cause integer overflow before the bigint is created, and so results in a compile-time error. Strings should be used instead of integer literals for cases like this:

// These would result in integer overflow and cause compile-time errors
var bad1 = 4847382292989382987395534934347: bigint;
var bad2 = new bigint(4847382292989382987395534934347);

// These give the desired result
var good1 = "4847382292989382987395534934347": bigint;
var good2 = new bigint("4847382292989382987395534934347");

Wrapping an mpz_t in a bigint record may introduce a measurable overhead in some cases.

The GMP library defines a low-level API that is based on side-effecting compound operations. The documentation recommends that one prefer to reuse a small number of existing mpz_t structures rather than using many values of short duration.

Matching this style using bigint records and the compound assignment operators is likely to provide comparable performance to an implementation based on mpz_t. So, for example:

x  = b
x *= c;
x += a;

is likely to achieve better performance than:

x = a + b * c;

In the fall of 2016 the Chapel compiler introduces two short lived temporaries for the intermediate results of the binary operators.

If peak performance is required, perhaps in a critical loop, then it is always possible to invoke the GMP functions directly. For example one might express:

a = a + b * c;

as:

mpz_addmul(a.mpz, b.mpz, c.mpz);

As usual the details are application specific and it is best to measure when peak performance is required.

The operators on bigint include variations that accept Chapel integers e.g.:

var a = new bigint("9738639463465935");
var b = 9395739153 * a;

The Chapel int(64) literal is converted to an underlying, platform-specific C integer, to invoke the underlying GMP primitive function. This example is likely to work well on popular 64-bit platforms but to fail on common 32-bit platforms. Runtime checks are used to ensure the Chapel types can safely be cast to the platform-specific types. Ths program will halt if the Chapel value cannot be represented using the GMP scalar type.

The checks are controlled by the compiler options --[no-]cast-checks, --fast, etc.

Casting from bigint to integral and real types is also supported. Values that are too large for the resultant type are truncated. GMP primitives are used to first cast to platform-specific C types, which are then cast to Chapel types. As a result, casting to 64-bit types on 32-bit platforms may result in additional truncation. Additionally, casting a negative bigint to a uint will result in the absolute value truncated to fit within the type.:

var a = new bigint(-1);
writeln(a:uint);        // prints "1"

See GMP for more information on how to use GMP with Chapel.

enum Round { DOWN = -1, ZERO = 0, UP = 1 }

Warning

The enum Round is deprecated, please use the enum round instead

enum round { down = -1, zero = 0, up = 1 }

An enumeration of the different rounding strategies, for use with e.g. divQ to determine how to round the quotient when performing the computation.

  • round.down indicates that the quotient should be rounded down towards -infinity and any remainder should have the same sign as the denominator.

  • round.zero indicates that the quotient should be rounded towards zero and any remainder should have the same sign as the numerator.

  • round.up indicates that the quotient should be rounded up towards +infinity and any remainder should have the opposite sign as the denominator.

record bigint
var mpz: mpz_t

The underlying GMP C structure

proc init()
proc init(const ref num: bigint)
proc init=(const ref num: bigint)
proc init(num: int)
proc init(num: uint)
proc init=(num: integral)
proc init(str: string, base: int = 0)
proc init(str: string, base: int = 0, out error: syserr)
proc size(): size_t

Warning

bigint.size() is deprecated

proc sizeinbase(base: int): uint

Warning

bigint.sizeinbase() is deprecated, use bigint.sizeInBase() instead

proc sizeInBase(base: int): int

Determine the size of this measured in number of digits in the given base. The sign of this is ignored, only the absolute value is used.

Arguments

base : int – The base in which to compute the number of digits used to represent this. Can be between 2 and 62.

Returns

The size of this measured in number of digits in the given base. Will either be exact or 1 too big. If base is a power of 2, will always be exact. If this is 0, will always return 1.

Return type

int

proc numLimbs: uint

Warning

This method is deprecated, please use GMP.chpl_gmp_mpz_nlimbs on the mpz field instead

proc get_limbn(n: integral): uint

Warning

This method is deprecated, please use GMP.chpl_gmp_mpz_getlimbn on the mpz field instead

proc mpzStruct(): __mpz_struct
proc get_d_2exp(): (uint(32), real)
proc get_str(base: int = 10): string
proc writeThis(writer) throws
proc type bigint.=(ref lhs: bigint, const ref rhs: bigint)
proc type bigint.=(ref lhs: bigint, rhs: int)
proc type bigint.=(ref lhs: bigint, rhs: uint)
proc type bigint.+(const ref a: bigint)
proc type bigint.-(const ref a: bigint)
proc type bigint.~(const ref a: bigint)
proc type bigint.+(const ref a: bigint, const ref b: bigint)
proc type bigint.+(const ref a: bigint, b: int)
proc type bigint.+(a: int, const ref b: bigint)
proc type bigint.+(const ref a: bigint, b: uint)
proc type bigint.+(a: uint, const ref b: bigint)
proc type bigint.-(const ref a: bigint, const ref b: bigint)
proc type bigint.-(const ref a: bigint, b: int)
proc type bigint.-(a: int, const ref b: bigint)
proc type bigint.-(const ref a: bigint, b: uint)
proc type bigint.-(a: uint, const ref b: bigint)
proc type bigint.*(const ref a: bigint, const ref b: bigint)
proc type bigint.*(const ref a: bigint, b: int)
proc type bigint.*(a: int, const ref b: bigint)
proc type bigint.*(const ref a: bigint, b: uint)
proc type bigint.*(a: uint, const ref b: bigint)
proc type bigint./(const ref a: bigint, const ref b: bigint)
proc type bigint./(const ref a: bigint, b: integral)
proc type bigint.**(const ref base: bigint, const ref exp: bigint)
proc type bigint.**(const ref base: bigint, exp: int)
proc type bigint.**(const ref base: bigint, exp: uint)
proc type bigint.%(const ref a: bigint, const ref b: bigint)
proc type bigint.%(const ref a: bigint, b: int)
proc type bigint.%(const ref a: bigint, b: uint)
proc type bigint.<<(const ref a: bigint, b: int)
proc type bigint.<<(const ref a: bigint, b: uint)
proc type bigint.>>(const ref a: bigint, b: int)
proc type bigint.>>(const ref a: bigint, b: uint)
proc type bigint.&(const ref a: bigint, const ref b: bigint)
proc type bigint.|(const ref a: bigint, const ref b: bigint)
proc type bigint.^(const ref a: bigint, const ref b: bigint)
proc type bigint.==(const ref a: bigint, const ref b: bigint)
proc type bigint.==(const ref a: bigint, b: int)
proc type bigint.==(a: int, const ref b: bigint)
proc type bigint.==(const ref a: bigint, b: uint)
proc type bigint.==(a: uint, const ref b: bigint)
proc type bigint.!=(const ref a: bigint, const ref b: bigint)
proc type bigint.!=(const ref a: bigint, b: int)
proc type bigint.!=(a: int, const ref b: bigint)
proc type bigint.!=(const ref a: bigint, b: uint)
proc type bigint.!=(a: uint, const ref b: bigint)
proc type bigint.>(const ref a: bigint, const ref b: bigint)
proc type bigint.>(const ref a: bigint, b: int)
proc type bigint.>(a: int, const ref b: bigint)
proc type bigint.>(const ref a: bigint, b: uint)
proc type bigint.>(a: uint, const ref b: bigint)
proc type bigint.<(const ref a: bigint, const ref b: bigint)
proc type bigint.<(const ref a: bigint, b: int)
proc type bigint.<(a: int, const ref b: bigint)
proc type bigint.<(const ref a: bigint, b: uint)
proc type bigint.<(a: uint, const ref b: bigint)
proc type bigint.>=(const ref a: bigint, const ref b: bigint)
proc type bigint.>=(const ref a: bigint, b: int)
proc type bigint.>=(a: int, const ref b: bigint)
proc type bigint.>=(const ref a: bigint, b: uint)
proc type bigint.>=(a: uint, const ref b: bigint)
proc type bigint.<=(const ref a: bigint, const ref b: bigint)
proc type bigint.<=(const ref a: bigint, b: int)
proc type bigint.<=(a: int, const ref b: bigint)
proc type bigint.<=(const ref a: bigint, b: uint)
proc type bigint.<=(a: uint, const ref b: bigint)
proc type bigint.+=(ref a: bigint, const ref b: bigint)
proc type bigint.+=(ref a: bigint, b: int)
proc type bigint.+=(ref a: bigint, b: uint)
proc type bigint.-=(ref a: bigint, const ref b: bigint)
proc type bigint.-=(ref a: bigint, b: int)
proc type bigint.-=(ref a: bigint, b: uint)
proc type bigint.*=(ref a: bigint, const ref b: bigint)
proc type bigint.*=(ref a: bigint, b: int)
proc type bigint.*=(ref a: bigint, b: uint)
proc type bigint./=(ref a: bigint, const ref b: bigint)
proc type bigint./=(ref a: bigint, b: integral)
proc type bigint.**=(ref base: bigint, const ref exp: bigint)
proc type bigint.**=(ref base: bigint, exp: int)
proc type bigint.**=(ref base: bigint, exp: uint)
proc type bigint.%=(ref a: bigint, const ref b: bigint)
proc type bigint.%=(ref a: bigint, b: int)
proc type bigint.%=(ref a: bigint, b: uint)
proc type bigint.&=(ref a: bigint, const ref b: bigint)
proc type bigint.|=(ref a: bigint, const ref b: bigint)
proc type bigint.^=(ref a: bigint, const ref b: bigint)
proc type bigint.<<=(ref a: bigint, b: int)
proc type bigint.<<=(ref a: bigint, b: uint)
proc type bigint.>>=(ref a: bigint, b: int)
proc type bigint.>>=(ref a: bigint, b: uint)
proc type bigint.<=>(ref a: bigint, ref b: bigint)
proc jacobi(const ref a: bigint, const ref b: bigint): int
proc legendre(const ref a: bigint, const ref p: bigint): int
proc kronecker(const ref a: bigint, const ref b: bigint): int
proc kronecker(const ref a: bigint, b: int): int
proc kronecker(a: int, const ref b: bigint): int
proc kronecker(const ref a: bigint, b: uint): int
proc kronecker(a: uint, const ref b: bigint): int
proc bigint.divexact(const ref n: bigint, const ref d: bigint)

Warning

n and d are deprecated - please use numer and denom respectively

proc bigint.divexact(const ref n: bigint, d: integral)

Warning

n and d are deprecated - please use numer and denom respectively

proc bigint.divexact(const ref numer: bigint, const ref denom: bigint)
proc bigint.divexact(const ref numer: bigint, denom: integral)

Computes numer/denom and stores the result in this, which is a bigint instance.

Warning

divexact is optimized to handle cases where numer/denom results in an integer. When numer/denom does not produce an integer, this method may produce incorrect results.

Arguments
  • numer : bigint – numerator

  • denom : bigint or integral – denominator

proc bigint.divisible_p(const ref d: bigint): int

Warning

bigint.divisible_p is deprecated, use bigint.isDivisible instead

proc bigint.divisible_p(d: int): int

Warning

bigint.divisible_p is deprecated, use bigint.isDivisible instead

proc bigint.divisible_p(d: uint): int

Warning

bigint.divisible_p is deprecated, use bigint.isDivisible instead

proc bigint.isDivisible(const ref div: bigint): bool
proc bigint.isDivisible(div: int): bool
proc bigint.isDivisible(div: uint): bool

Return true if this is exactly divisible by div. this is divisible by div if there exists an integer q satisfying this = q*div. Unlike the other division functions, 0 is an acceptable value for div and only 0 is considered divisible by 0.

Arguments

div : bigint, int or uint – number to check if this is divisible by

Returns

true if this is exactly divisible by div, false otherwise

Return type

bool

proc bigint.divisible_2exp_p(b: integral): int

Warning

bigint.divisible_2exp_p is deprecated, use bigint.isDivisibleBy2Pow instead

proc bigint.isDivisibleBy2Pow(exp: integral): bool

Return true if this is exactly divisible by 2^exp. this is divisible by 2^exp if there exists an integer q satisfying this = q*2^exp.

Arguments

exp : integral – power of 2 to check if this is divisible by

Returns

true if this is exactly divisible by 2^exp, false otherwise

Return type

bool

proc bigint.congruent_p(const ref c: bigint, const ref d: bigint): int

Warning

bigint.congruent_p is deprecated, use bigint.isCongruent instead

proc bigint.congruent_p(c: integral, d: integral): int

Warning

bigint.congruent_p is deprecated, use bigint.isCongruent instead

proc bigint.isCongruent(const ref con: bigint, const ref mod: bigint): bool
proc bigint.isCongruent(con: integral, mod: integral): bool

Return true if this is congruent to con % mod. this is congruent to con % mod if there exists an integer q satisfying this = con + q*mod. Unlike the other division functions, 0 is an acceptable value for mod. As a result this and con are considered congruent modulo 0 only when exactly equal.

Arguments
  • con : bigint or integral – number to determine if this is congruent to, modulo mod

  • mod : bigint or integral – divisor of con when determining if con is congruent to this

Returns

true if this is congruent to con modulo mod, false otherwise

Return type

bool

proc bigint.congruent_2exp_p(const ref c: bigint, b: integral): int

Warning

bigint.congruent_2exp_p is deprecated, use bigint.isCongruentBy2Pow instead

proc bigint.isCongruentBy2Pow(const ref con: bigint, modExp: integral): bool

Return true if this is congruent to con % 2^modExp. this is congruent to con % 2^modExp if there exists an integer q satisfying this = con + q*2^modExp.

Arguments
  • con : bigint or integral – number to determine if this is congruent to, modulo 2^modExp.

  • modExp : integral – power of 2 to use as the divisor of con when determining if con is congruent to this.

Returns

true if this is congruent to con modulo 2^modExp, false otherwise.

Return type

bool

proc bigint.powm(const ref base: bigint, const ref exp: bigint, const ref mod: bigint)

Warning

bigint.powm is deprecated, use bigint.powMod instead

proc bigint.powm(const ref base: bigint, exp: int, const ref mod: bigint)

Warning

bigint.powm is deprecated, use bigint.powMod instead

proc bigint.powm(const ref base: bigint, exp: uint, const ref mod: bigint)

Warning

bigint.powm is deprecated, use bigint.powMod instead

proc bigint.powMod(const ref base: bigint, const ref exp: bigint, const ref mod: bigint)
proc bigint.powMod(const ref base: bigint, exp: int, const ref mod: bigint)
proc bigint.powMod(const ref base: bigint, exp: uint, const ref mod: bigint)

Set this to the result of (base raised to exp) modulo mod.

Arguments
  • base : bigint – The value to be raised to the power of exp before performing a modulo operation on.

  • exp : bigint, int, or uint – The exponent to raise base to the power of prior to the modulo operation. Can be negative if the inverse (1/base) modulo mod exists.

  • mod : bigint – The divisor for the modulo operation.

Warning

The program behavior is undefined if exp is negative and the inverse (1/base) modulo mod does not exist.

proc bigint.pow(const ref base: bigint, exp: int)
proc bigint.pow(const ref base: bigint, exp: uint)
proc bigint.pow(base: int, exp: int)
proc bigint.pow(base: uint, exp: uint)

Set this to the result of base raised to exp.

Arguments
  • base : bigint, int or uint – The value to be raised to the power of exp.

  • exp : int or uint – The exponent to raise base to the power of.

proc bigint.root(const ref a: bigint, n: uint): int
proc bigint.rootrem(ref rem: bigint, const ref u: bigint, n: uint)
proc bigint.sqrt(const ref a: bigint)
proc bigint.sqrtrem(ref rem: bigint, const ref a: bigint)
proc bigint.perfect_power_p(): int

Warning

bigint.perfect_power_p is deprecated, use bigint.isPerfectPower instead

proc bigint.isPerfectPower(): bool

Return true if this is a perfect power, i.e., if there exist integers a and b with b > 1, such that this = a^b.

Under this definition both 0 and 1 are considered to be perfect powers. Negative values can only be odd perfect powers.

Returns

true if this is a perfect power, false otherwise.

proc bigint.perfect_square_p(): int

Warning

bigint.perfect_square_p is deprecated, use bigint.isPerfectSquare instead

proc bigint.isPerfectSquare(): bool

Return true if this is a perfect square, i.e., if the square root of this is an integer. Under this definition both 0 and 1 are considered to be perfect squares.

Returns

true if this is a perfect square, false otherwise.

Return type

bool

proc bigint.probab_prime_p(reps: int): int

Warning

bigint.probab_prime_p is deprecated, use bigint.probablyPrime instead

enum primality { notPrime = 0, maybePrime, isPrime }

An enumeration of the different possibilitites of a number being prime, for use with e.g. probablyPrime to determine if a number is prime or not.

  • primality.notPrime indicates that the number is not a prime.

  • primality.maybePrime indicates that the number may or may not be a prime.

  • primality.isPrime indicates that the number is a prime.

proc bigint.probablyPrime(reps: int): primality

Determine whether this is prime. Returns one of the primality constants - primality.isPrime, primality.maybePrime, or primality.notPrime.

Performs some trial divisions, a Baillie-PSW probable prime test, and reps-24 Miller-Rabin probabilistic primality tests. A higher reps value will reduce the chances of a non-prime being identified as “probably prime”. A composite number will be identified as a prime with an asymptotic probability of less than 4^(-reps). Reasonable values of reps are between 15 and 50.

Arguments

reps : int – number of attempts before returning primality.maybePrime if a definitive answer can’t be found before then.

Returns

primality.isPrime, primality.maybePrime or primality.notPrime.

Return type

primality

proc bigint.nextprime(const ref a: bigint)
proc bigint.gcd(const ref a: bigint, const ref b: bigint)
proc bigint.gcd(const ref a: bigint, b: int)
proc bigint.gcd(const ref a: bigint, b: uint)
proc bigint.gcdext(ref s: bigint, ref t: bigint, const ref a: bigint, const ref b: bigint)
proc bigint.lcm(const ref a: bigint, const ref b: bigint)
proc bigint.lcm(const ref a: bigint, b: int)
proc bigint.lcm(const ref a: bigint, b: uint)
proc bigint.invert(const ref a: bigint, const ref b: bigint): int
proc bigint.remove(const ref a: bigint, const ref f: bigint): uint

Warning

bigint.remove is deprecated, use bigint.removeFactor instead

proc bigint.removeFactor(const ref x: bigint, const ref fac: bigint): uint

Remove all occurrences of the factor fac from x and store the result in this. Return the number of occurrences removed.

Arguments
  • x : bigint – The value to remove all occurrences of fac from

  • fac : bigint – The factor to remove from x.

Returns

The number of occurrences of fac found in x.

Return type

uint

proc bigint.fac(a: integral)
proc bigint.bin(const ref n: bigint, k: integral)
proc bigint.bin(n: uint, k: integral)
proc bigint.fib(n: integral)
proc bigint.fib2(ref fnsub1: bigint, n: integral)
proc bigint.lucnum(n: integral)
proc bigint.lucnum2(ref fnsub1: bigint, n: integral)
proc bigint.popcount(): uint
proc bigint.hamdist(const ref b: bigint): uint
proc bigint.scan0(starting_bit: integral): uint
proc bigint.scan1(starting_bit: integral): uint
proc bigint.setbit(bit_index: integral)
proc bigint.clrbit(bit_index: integral)
proc bigint.combit(bit_index: integral)
proc bigint.tstbit(bit_index: integral): int
proc bigint.fits_ulong_p(): int
proc bigint.fits_slong_p(): int
proc bigint.fits_uint_p(): int
proc bigint.fits_sint_p(): int
proc bigint.fits_ushort_p(): int
proc bigint.fits_sshort_p(): int
proc bigint.even_p(): int

Warning

bigint.even_p is deprecated, use bigint.isEven instead

proc bigint.isEven(): bool

Returns true if this is an even number, false otherwise.

proc bigint.odd_p(): int

Warning

bigint.odd_p is deprecated, use bigint.isOdd instead

proc bigint.isOdd(): bool

Returns true if this is an odd number, false otherwise.

proc bigint.add(const ref a: bigint, const ref b: bigint)
proc bigint.add(const ref a: bigint, b: int)
proc bigint.add(const ref a: bigint, b: uint)
proc bigint.sub(const ref a: bigint, const ref b: bigint)
proc bigint.sub(const ref a: bigint, b: int)
proc bigint.sub(const ref a: bigint, b: uint)
proc bigint.sub(a: int, const ref b: bigint)
proc bigint.sub(a: uint, const ref b: bigint)
proc bigint.mul(const ref a: bigint, const ref b: bigint)
proc bigint.mul(const ref a: bigint, b: int)
proc bigint.mul(const ref a: bigint, b: uint)
proc bigint.addmul(const ref a: bigint, const ref b: bigint)
proc bigint.addmul(const ref a: bigint, b: int)
proc bigint.addmul(const ref a: bigint, b: uint)
proc bigint.submul(const ref a: bigint, const ref b: bigint)
proc bigint.submul(const ref a: bigint, b: int)
proc bigint.submul(const ref a: bigint, b: uint)
proc bigint.mul_2exp(const ref a: bigint, b: integral)
proc bigint.neg(const ref a: bigint)
proc bigint.abs(const ref a: bigint)
proc bigint.div_q(const ref n: bigint, const ref d: bigint, param rounding = Round.ZERO)

Warning

bigint.div_q using Round is deprecated, use bigint.divQ with round instead

proc bigint.div_q(const ref n: bigint, d: integral, param rounding = Round.ZERO)

Warning

bigint.div_q using Round is deprecated, use bigint.divQ with round instead

proc bigint.divQ(const ref numer: bigint, const ref denom: bigint, param rounding = round.zero)
proc bigint.divQ(const ref numer: bigint, denom: integral, param rounding = round.zero)

Divide numer by denom, forming a quotient and storing it in this.

Arguments
  • numer : bigint – The numerator of the division operation to be performed

  • denom : bigint, integral – The denominator of the division operation to be performed

  • rounding : round – The rounding style to use, see round for a description of what the rounding styles entail. Defaults to zero if unspecified

Warning

If the denominator is zero, the program behavior is undefined.

proc bigint.div_r(const ref n: bigint, const ref d: bigint, param rounding = Round.ZERO)

Warning

bigint.div_r using Round is deprecated, use bigint.divR with round instead

proc bigint.div_r(const ref n: bigint, d: integral, param rounding = Round.ZERO)

Warning

bigint.div_r using Round is deprecated, use bigint.divR with round instead

proc bigint.divR(const ref numer: bigint, const ref denom: bigint, param rounding = round.zero)
proc bigint.divR(const ref numer: bigint, denom: integral, param rounding = round.zero)

Divide numer by denom, forming a remainder and storing it in this. The absolute value of the remainder will always be less than the absolute value of the denominator (i.e. abs(this) < abs(denom)).

Arguments
  • numer : bigint – The numerator of the division operation to be performed

  • denom : bigint, integral – The denominator of the division operation to be performed

  • rounding : round – The rounding style to use, see round for a description of what the rounding styles entail. Defaults to zero if unspecified

Warning

If the denominator is zero, the program behavior is undefined.

proc bigint.div_qr(ref r: bigint, const ref n: bigint, const ref d: bigint, param rounding = Round.ZERO)

Warning

bigint.div_qr using Round is deprecated, use bigint.divQR with round instead

proc bigint.div_qr(ref r: bigint, const ref n: bigint, d: integral, param rounding = Round.ZERO)

Warning

bigint.div_qr using Round is deprecated, use bigint.divQR with round instead

proc bigint.divQR(ref remain: bigint, const ref numer: bigint, const ref denom: bigint, param rounding = round.zero)
proc bigint.divQR(ref remain: bigint, const ref numer: bigint, denom: integral, param rounding = round.zero)

Divide numer by denom, forming a quotient and storing it in this, and a remainder and storing it in remain. The quotient and remainder will always satisfy numer = this*denom + remain after the operation has finished. The absolute value of the remainder will always be less than the absolute value of the denominator (i.e. abs(this) < abs(denom)).

Warning

If this is also passed as the remain argument, the program behavior is undefined.

Arguments
  • remain : bigint – Stores the remainder of the division

  • numer : bigint – The numerator of the division operation to be performed

  • denom : bigint, integral – The denominator of the division operation to be performed

  • rounding : round – The rounding style to use, see round for a description of what the rounding styles entail. Defaults to zero if unspecified

Warning

If the denominator is zero, the program behavior is undefined.

proc bigint.div_q_2exp(const ref n: bigint, b: integral, param rounding = Round.ZERO)

Warning

bigint.div_q_2exp using Round is deprecated, use bigint.divQ2Exp with round instead

proc bigint.divQ2Exp(const ref numer: bigint, exp: integral, param rounding = round.zero)

Divide numer by 2^exp, forming a quotient and storing it in this.

Arguments
  • numer : bigint – The numerator of the division operation to be performed

  • exp : integral – The exponent that 2 should be raised to before being used as the denominator of the division operation to be performed

  • rounding : round – The rounding style to use, see round for a description of what the rounding styles entail. Defaults to zero if unspecified

proc bigint.div_r_2exp(const ref n: bigint, b: integral, param rounding = Round.ZERO)

Warning

bigint.div_r_2exp using Round is deprecated, use bigint.divR2Exp with round instead

proc bigint.divR2Exp(const ref numer: bigint, exp: integral, param rounding = round.zero)

Divide numer by 2^exp, forming a remainder and storing it in this.

Arguments
  • numer : bigint – The numerator of the division operation to be performed

  • exp : integral – The exponent that 2 should be raised to before being used as the denominator of the division operation to be performed

  • rounding : round – The rounding style to use, see round for a description of what the rounding styles entail. Defaults to zero if unspecified

proc bigint.mod(const ref a: bigint, const ref b: bigint)
proc bigint.mod(const ref a: bigint, b: integral): uint
proc bigint.cmp(const ref b: bigint): int
proc bigint.cmp(b: int): int
proc bigint.cmp(b: uint): int
proc bigint.cmp(b: real): int
proc bigint.cmpabs(const ref b: bigint): int
proc bigint.cmpabs(b: uint): int
proc bigint.cmpabs(b: real): int
proc bigint.sgn(): int
proc bigint.and(const ref a: bigint, const ref b: bigint)
proc bigint.ior(const ref a: bigint, const ref b: bigint)
proc bigint.xor(const ref a: bigint, const ref b: bigint)
proc bigint.com(const ref a: bigint)
proc bigint.set(const ref a: bigint)
proc bigint.set(num: int)
proc bigint.set(num: uint)
proc bigint.set(num: real)
proc bigint.set(str: string, base: int = 0)
proc bigint.swap(ref a: bigint)