gmp

GMP::Z.new()
GMP::Z.new(Fixnum)
GMP::Z.new(Bignum)
GMP::Z.new(GMP::Z)
GMP::Z.new(Float)
GMP::Z.new(GMP::F)
GMP::Z.new(String)
GMP::Q.new()
GMP::Q.new(Fixnum)
GMP::Q.new(GMP::Z)
GMP::Q.new(GMP::Q)
GMP::Q.new(String)
GMP::Q.new(any GMP::Z initializer)
GMP::Q.new(Fixnum, Fixnum)
GMP::Q.new(any GMP::Z initializer, any GMP::Z initializer)
GMP::F.new()
GMP::F.new(GMP::Z, precision=0, rounding_mode=default)
GMP::F.new(GMP::Q, precision=0, rounding_mode=default)
GMP::F.new(GMP::F, precision=0, rounding_mode=default)
GMP::F.new(String, precision=0)
GMP::F.new(String, precision=0, base=10)
GMP::F.new(String, precision=0, base=10, rounding_mode=default)
GMP::F.new(Fixnum, precision=0, rounding_mode=default)
GMP::F.new(Bignum, precision=0, rounding_mode=default)
GMP::F.new(Float,  precision=0, roundung_mode=default)
GMP::F.new_2exp(Fixnum, exp, precision=0, rounding_mode=default)
GMP::F.new_2exp(Bignum, exp, precision=0, rounding_mode=default)
GMP::F.new_2exp(GMP::Z, exp, precision=0, rounding_mode=default)
GMP::RandState.new(\[algorithm\] \[, algorithm_args\])

GMP.Z(args)
GMP.Q(args)
GMP.F(args)
GMP.RandState()

GMP::Z, GMP::Q and GMP::F
  +                        addition
  -                        substraction
  *                        multiplication
  /                        division
  to_s                     convert to string. For GMP::Z and GMP::F, this
                           method takes one optional argument, a base. The
                           base can be a Fixnum in the ranges \[2, 62\] or
                           \[-36, -2\] or a Symbol: one of :bin, :oct,
                           :dec, or :hex.
  inspect                  alias for #to_s
  -@                       negation
  neg!                     in-place negation
  abs                      absolute value
  abs!                     in-place absolute value
  coerce                   promotion of arguments
  ==                       equality test
  <=>, >=, >, <=, <        comparisons
class methods of GMP::Z
  fac(n)                   factorial of n
  2fac(n), double_fac(n)   double factorial of n
  mfac(n)                  m-multi-factorial of n
  primorial(n)             primorial of n
  fib(n)                   nth Fibonacci number
  fib2(n)                  nth and (n-1)th Fibonacci numbers
  pow(n,m)                 n to mth power
GMP::Z and GMP::Q
  swap                     efficiently swap contents of two objects, there
                           is no GMP::F.swap because various GMP::F objects
                           may have different precisions, which would make
                           them unswapable
GMP::Z
  to_i                     convert to Fixnum or Bignum
  add!                     in-place addition
  sub!                     in-place subtraction
  addmul!(b,c)             in-place += b*c
  submul!(b,c)             in-place -= b*c
  tdiv,fdiv,cdiv           truncate, floor and ceil division
  tmod,fmod,cmod           truncate, floor and ceil modulus
  >>                       shift right, floor
  divisible?(b)            true if divisible by b
  congruent?(c,d)          true if congruent to c modulus d
  **                       power
  powmod                   power modulo
  \[\],\[\]=                   testing and setting bits (as booleans)
  scan0,scan1              starting at bitnr (1st arg), scan for a 0 or 1
                           (respectively), then return the index of the
                           first instance.
  cmpabs                   comparison of absolute value
  com                      2's complement
  com!                     in-place 2's complement
  &,|,^                    logical operations: and, or, xor
  even?                    is even
  odd?                     is odd
  <<                       shift left
  tshr                     shift right, truncate
  lastbits_pos(n)          last n bits of object, modulo if negative
  lastbits_sgn(n)          last n bits of object, preserve sign
  power?                   is perfect power
  square?                  is perfect square
  sqrt                     square root
  sqrt!                    change the object into its square root
  sqrtrem                  square root, with remainder
  root(n)                  nth root
  rootrem(n)               nth root, with remainder
  probab_prime?            0 if composite, 1 if probably prime, 2 if
                           certainly prime
  nextprime                next *probable* prime
  nextprime!               change the object into its next *probable* prime
  gcd, gcdext, gcdext2     greatest common divisor
  lcm                      least common multiple
  invert(m)                invert mod m
  jacobi                   jacobi symbol
  legendre                 legendre symbol
  remove(n)                remove all occurences of factor n
  popcount                 the number of bits equal to 1
  hamdist                  the hamming distance between two integers
  out_raw                  output to IO object
  inp_raw                  input from IO object
  export                   export to a byte array (String)
  import                   import from a byte array (String)
  sizeinbase(b)            digits in base b
  size_in_bin              digits in binary
  size                     number of limbs
GMP::Q
  num                      numerator
  den                      denominator
  inv                      inversion
  inv!                     in-place inversion
  floor,ceil,trunc         nearest integer
class methods of GMP::F
  default_prec             get default precision
  default_prec=            set default precision
  fac(n)                   new GMP::F, equal to factorial of n
GMP::F
  prec                     get precision
  floor,ceil,trunc         nearest integer, GMP::F is returned, not GMP::Z
  floor!,ceil!,trunc!      in-place nearest integer
GMP::RandState
  seed(integer)            seed the generator with a Fixnum or GMP::Z
  urandomb(fixnum)         get uniformly distributed random number between 0
                           and 2^fixnum-1, inclusive
  urandomm(integer)        get uniformly distributed random number between 0
                           and integer-1, inclusive
GMP (timing functions for GMPbench (0.2))
  cputime                  milliseconds of cpu time since Ruby start
  time                     times the execution of a block

*only if MPFR is available*
class methods of GMP::F
  nan                      returns NaN
  inf(sign = 1)            returns Inf or -Inf
  zero(sign = 1)           returns zero or -zero
  const_log2               returns the natural log of 2
  const_pi                 returns pi
  const_euler              returns euler
  const_catalan            returns catalan
  emin                     returns the smallest allowed exponent
  emax                     returns the largest allowed exponent
  emin=(exp)               sets the smallest allowed exponent
  emax=(exp)               sets the largest allowed exponent
  emin_min                 returns the smallest exponent allowed for GMP::F.emin=
  emin_max                 returns the largest exponent allowed for GMP::F.emin=
  emax_min                 returns the smallest exponent allowed for GMP::F.emax=
  emax_max                 returns the largest exponent allowed for GMP::F.emax=
  mpfr_buildopt_tls_p      returns whether MPFR was built as thread safe
  mpfr_buildopt_decimal_p  returns whether MPFR was compiled with decimal
                           float support
GMP::F
  frexp                    frexp
  lessgreater?(y)          x < y or y < x?
  unordered?(y)            either x or y is NaN?
  sqrt                     square root of the object
  rec_sqrt                 square root of the recprical of the object
  cbrt                     cube root of the object
  **                       power
  log                      natural logarithm of object
  log2                     binary logarithm of object
  log10                    decimal logarithm of object
  exp                      e^object
  exp2                     2^object
  exp10                    10^object
  log1p                    the same as (object + 1).log, with better
                           precision
  expm1                    the same as (object.exp) - 1, with better
                           precision
  eint                     exponential integral of object
  li2                      real part of the dilogarithm of object
  gamma                    Gamma fucntion of object
  lngamma                  logarithm of the Gamma function of object
  digamma                  Digamma function of object (MPFR_VERSION >= "3.0.0")
  zeta                     Reimann Zeta function of object
  erf                      error function of object
  erfc                     complementary error function of object
  j0                       first kind Bessel function of order 0 of object
  j1                       first kind Bessel function of order 1 of object
  jn                       first kind Bessel function of order n of object
  y0                       second kind Bessel function of order 0 of object
  y1                       second kind Bessel function of order 1 of object
  yn                       second kind Bessel function of order n of object
  agm                      arithmetic-geometric mean
  hypot
  cos                      \
  sin                      |
  tan                      |
  sin_cos                  |
  sec                      |
  csc                      |
  cot                      |
  acos                     |
  asin                     |
  atan                     | trigonometric functions
  atan2                    |
  cosh                     | of the object
  sinh                     |
  tanh                     |
  sinh_cosh                |
  sec                      |
  csc                      |
  cot                      |
  acosh                    |
  asinh                    |
  atanh                    /
  nan?                     \
  infinite?                | type of floating point number
  finite?                  |
  number?                  |
  regular?                 / (MPFR_VERSION >= "3.0.0")
GMP::RandState
  mpfr_urandomb(prec = default)   get uniformly distributed random floating-point
                                  number within 0 <= rop < 1
  mpfr_urandom(prec = default)    get uniformly distributed random floating-point
                                  number (MPFR_VERSION >= "3.0.0")

a = GMP::Z(0)
b = GMP::Z(13)
c = GMP::Z(17)
GMP::Z.add(a, b, c)
a  #=> 30

GMP::Z
  .abs          .add          .addmul       .cdiv_q_2exp  .cdiv_r_2exp  .com
  .congruent?   .divexact     .divisible?   .fdiv_q_2exp  .fdiv_r_2exp  .lcm
  .mul          .mul_2exp
  .neg          .nextprime    .sqrt         .sub          .submul       .tdiv_q_2exp
  .tdiv_r_2exp

cd test
ruby some_test_file.rb

new_obj = GMP::F.new(old_obj, 0)