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big-integers.md

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Big Integers

Headers

  • Header Mode : include "APA/core.hpp"

  • Static Lib : include <APA/bint.hpp>


Namespace

  • apa::bint

Initializing from an integral type.

apa::bint num1 = 255;
apa::bint num2 = -128;
// base 10 equivalent = 255 and -128

Initializing from a base2 (binary) number represented by a string.

Binary formatter 0b

apa::bint num1 = "0b11001001110100111110100010101";
apa::bint num2 = "-0b11001001110100111110100010101";
// base 10 equivalent = 423263509 and -423263509

Initializing from a base8 (octal) number represented by a string.

Octal formatter 0o

apa::bint num1 = "0o122333444455555666666777777700000000";
apa::bint num2 = "-0o122333444455555666666777777700000000";
// base 10 equivalent
// num1 =  52245490915446306574707453853696
// num2 = -52245490915446306574707453853696

Initializing from a base10 (decimal) number represented by a string.

Decimal numbers don't need a formatter.

apa::bint num1 = "1192098127666217730001983712379812737234";
apa::bint num2 = "-1192098127666217730001983712379812737234";
// base10 equivalent
// num1 =  1192098127666217730001983712379812737234
// num2 = -1192098127666217730001983712379812737234

Initializing from a base16 (hex) number represented by a string.

Hex formatter 0x

apa::bint num1 = "0xdeed0feed0dead0beef0fac0bae";
apa::bint num2 = "-0xdeed0feed0dead0beef0fac0bae";
// base10 equivalent
// num1 =  282592308594525234095480996891566
// num2 = -282592308594525234095480996891566

Initializing with specific limb values.

apa::bint positive_num({ 0xfeed, 0xdead, 0xbeef },apa::POSITIVE);
apa::bint negative_num({ 0xfeed, 0xdead, 0xbeef },apa::NEGATIVE);

The values 0xfeed, 0xdead and 0xbeef values will be assigned to each limb of the bint instance.

Each element in the initializer list can only hold a max value of the base size (depending on the base size you choose during compilation).

  • Base 216 max value = 0xffff
  • Base 232 max value = 0xffffffff
  • Base 264 max value = 0xffffffffffffffff

Supported Operators of apa::bint.

Labels Operators
Negation -
Arithmetic +, -, *, /, %, +=, -=, *=, /=, %=
Increment ++ (Post-Fix and Pre-Fix)
Decrement -- (Post-Fix and Pre-Fix)
Relational <, >, ==, <=, >=, !=
Logical !, &&, ||
Bitwise Logical ~, &, ^, |=, &=, ^=
Bitwise Shifts (for size_t only) <<, >>, <<=, >>=
Standard I/O (std cin and cout) <<, >> (only accepts and output hex format)

bint methods.

  • .printHex() - prints the value of bint in hex format
  • .to_base10_string() - returns a string that represents the value of bint in base 10 (decimal)
  • .to_base16_string() - returns a string that represents the value of bint in base 16 (hex)
  • .capacity_size() - returns the total allocated number of limbs of a bint variable
  • .limb_size() - returns the number of limbs currently used by a bint variable
  • .byte_size() - returns the total number of bytes
  • .bit_size() - returns the total number of bits
  • .limb_view() - returns a const *limb_t pointer array
  • .byte_view() - returns a const *uint8_t pointer array
  • .detach() - returns a pointer that points to the limbs array of bint instance, while setting the limbs of the bint instance to NULL

Available using the header:

// for static library users only.
#include <APA/math.hpp>

If you are not using the static library and just compiling directly using the core header file: #include "APA/core.hpp", there is no need to include the math.hpp header.

apa namespace functions.

  • swap(bint& a, bint& b) - swap values of two bint class.
  • factorial(size_t n) - returns bint factorial
  • fibonacci(size_t nth) - returns bint Fibonacci
  • power(const bint& base, const bint& exponent) - returns bint power

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