Class: GMP::Z

Inherits:
Integer
  • Object
show all
Defined in:
ext/gmpz.c,
ext/gmp.c,
ext/gmpz.c,
ext/gmprandstate.c

Overview

GMP Multiple Precision Integer.

Instances of this class can store variables of the type ‘gmp_randstate_t`. This class also contains many methods that act as the functions for `gmp_randstate_t` variables, as well as a few methods that attempt to make this library more Ruby-ish.

The following list is just a simple checklist for me, really. A better reference should be found in the rdocs.

Ruby method    C Extension function     GMP function
new            r_gmprandstatesg_new     gmp_randinit_default
seed           r_gmprandstate_seed      gmp_randseed
\---           \------------------      gmp_randseed_ui
urandomb       r_gmprandstate_urandomb  mpz_urandomb

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(*args) ⇒ Object 



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# File 'ext/gmpz.c', line 689

VALUE r_gmpz_initialize(int argc, VALUE *argv, VALUE self)
{
  MP_INT *self_val;
  int base = 0;

  /* Set up the base if 2 arguments are passed */
  if (argc == 2) {                              /* only ok if String, Fixnum */
    if (STRING_P(argv[0])) {                   /* first arg must be a String */
      if (FIXNUM_P(argv[1])) {                /* second arg must be a Fixnum */
        base = FIX2INT(argv[1]);
        if ( base != 0 && ( base < 2 || base > 62) )
          rb_raise (rb_eRangeError, "base must be either 0 or between 2 and 62");
      } else {
        rb_raise (rb_eTypeError, "base must be a Fixnum between 2 and 62, not a %s.", rb_class2name (rb_class_of (argv[1])));
      }
    } else {
      rb_raise(
        rb_eTypeError,
        "GMP::Z.new() must be passed a String as the 1st argument (not a %s), if a base is passed as the 2nd argument.",
        rb_class2name (rb_class_of (argv[0]))
      );
    }
  }

  if (argc != 0) {
    mpz_get_struct (self,self_val);
    mpz_set_value (self_val, argv[0], base);
  }
  return Qnil;
}

Class Method Details

.2fac ⇒ Object

.abs ⇒ Object

call-seq:

a.abs

Returns the absolute value of a.

.add ⇒ Object

TODO:

Document this

call-seq:

GMP::Z.add(rop, op1, op2)

.addmul ⇒ Object

.cdiv_q_2exp ⇒ Object

.cdiv_r_2exp ⇒ Object

.com ⇒ Object

Returns the one’s complement of a.

.congruent?(c, d) ⇒ Boolean

Returns true if n is congruent to c modulo d. c and d can be an instance any of the following:

  • GMP::Z

  • Fixnum

  • Bignum

Returns:

  • (Boolean)

Since:

  • 0.6.19

.divexact ⇒ Object

Functional Mappings

.divisible?(b) ⇒ Boolean

Returns true if a is divisible by b. b can be an instance any of the following:

  • GMP::Z

  • Fixnum

  • Bignum

Returns:

  • (Boolean)

Since:

  • 0.5.23

.GMP::Z.double_fac(n) ⇒ Object .GMP::Z.send(: "2fac", n) ⇒ Object

Returns _n!!_, the double factorial of n.

Examples:

GMP::Z.double_fac(  0)  #=>    1
GMP::Z.double_fac(  1)  #=>    1
GMP::Z.double_fac(  2)  #=>    2
GMP::Z.double_fac(  3)  #=>    3
GMP::Z.double_fac(  4)  #=>    8
GMP::Z.double_fac(  5)  #=>   15
GMP::Z.double_fac(  6)  #=>   48
GMP::Z.double_fac(  7)  #=>  105
GMP::Z.double_fac(  8)  #=>  384
GMP::Z.double_fac(  9)  #=>  945
GMP::Z.double_fac( 10)  #=> 3840
GMP::Z.double_fac(100)  #=> 34243224702511976248246432895208185975118675053719198827915654463488000000000000

.GMP::Z.fac(n) ⇒ Object

Returns n!, the factorial of n.

Examples:

GMP::Z.fac(0)  #=>  1
GMP::Z.fac(1)  #=>  1
GMP::Z.fac(2)  #=>  2
GMP::Z.fac(3)  #=>  6
GMP::Z.fac(4)  #=> 24

.fdiv_q_2exp ⇒ Object

.fdiv_r_2exp ⇒ Object

.GMP::Z.fib(n) ⇒ Object

Returns _F [n]_, the nth Fibonacci number.

Examples:

GMP::Z.fib(1)  #=>  1
GMP::Z.fib(2)  #=>  1
GMP::Z.fib(3)  #=>  2
GMP::Z.fib(4)  #=>  3
GMP::Z.fib(5)  #=>  5
GMP::Z.fib(6)  #=>  8
GMP::Z.fib(7)  #=> 13

.GMP::Z.fib2(n) ⇒ Object

Returns [_F [n]_, _F [n-1]_], the nth and n-1th Fibonacci numbers.

Examples:

GMP::Z.fib2(1)  #=> [ 1, 0]
GMP::Z.fib2(2)  #=> [ 1, 1]
GMP::Z.fib2(3)  #=> [ 2, 1]
GMP::Z.fib2(4)  #=> [ 3, 2]
GMP::Z.fib2(5)  #=> [ 5, 3]
GMP::Z.fib2(6)  #=> [ 8, 5]
GMP::Z.fib2(7)  #=> [13, 8]

Since:

  • 0.6.41

.GMP::Z.import(str, order = -1) ⇒ Object

Return a GMP::Z from a String, ‘str`.

‘order` can be 1 for most significant word first or -1 for least significant first.

There is no sign taken from the data, the result will simply be a positive integer. An application can handle any sign itself, and apply it for instance with ‘GMP::Z#neg`.



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# File 'ext/gmpz.c', line 2926

VALUE r_gmpzsg_import(int argc, VALUE *argv, VALUE klass)
{
  MP_INT *res;
  VALUE string_val, order_val, res_val;
  char *string;
  int order, endian;
  size_t nails;
  (void)klass;

  endian = 0;
  nails = 0;
  order = 1;

  rb_scan_args (argc, argv, "11", &string_val, &order_val);

  if (NIL_P (order_val))
    order = -1;
  else if (! FIXNUM_P (order_val))
    typeerror_as (X, "order");
  else
    order = FIX2INT (order_val);

  mpz_make_struct(res_val, res);
  mpz_init(res);

  string = StringValuePtr (string_val);

  mpz_import (res, RSTRING_LEN(string_val), order, sizeof(char), endian, nails, string);
  return res_val;
}

.GMP::Z.inp_raw(a, stream) ⇒ Object

Input from IO object stream in the format written by ‘GMP::Z#out_raw`, and put the result in a. Return the number of bytes read, or if an error occurred, return 0.



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# File 'ext/gmpz.c', line 2889

VALUE r_gmpzsg_inp_raw(VALUE klass, VALUE a_val, VALUE stream_val)
{
  MP_INT *a;
  FILE *stream;
  (void)klass;

  if (! GMPZ_P(a_val))
    typeerror_as(Z, "a");

  if (TYPE (stream_val) != T_FILE)
    rb_raise (rb_eTypeError, "stream must be an IO.");

  mpz_get_struct(a_val, a);
  stream = rb_io_stdio_file (RFILE (stream_val)->fptr);
  return INT2FIX (mpz_inp_raw (a, stream));
}

.GMP::Z.jacobi(a, b) ⇒ Object

Calculate the Jacobi symbol _(a/b)_. This is defined only for b odd and positive.



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# File 'ext/gmpz.c', line 2141

VALUE r_gmpzsg_jacobi(VALUE klass, VALUE a, VALUE b)
{
  MP_INT *a_val = NULL, *b_val = NULL;
  int res_val;
  int free_a_val = 0;
  int free_b_val = 0;
  (void)klass;

  if (GMPZ_P(a)) {
    mpz_get_struct(a, a_val);
  } else if (FIXNUM_P(a)) {
    mpz_temp_alloc(a_val);
    mpz_init_set_ui(a_val, FIX2NUM(a));
    free_a_val = 1;
  } else if (BIGNUM_P(a)) {
    mpz_temp_from_bignum(a_val, a);
    free_a_val = 1;
  } else {
    typeerror_as(ZXB, "a");
  }

  if (GMPZ_P(b)) {
    mpz_get_struct(b, b_val);
    if (mpz_sgn(b_val) != 1)
      rb_raise(rb_eRangeError, "Cannot take Jacobi symbol (a/b) where b is non-positive.");
    if (mpz_even_p(b_val))
      rb_raise(rb_eRangeError, "Cannot take Jacobi symbol (a/b) where b is even.");
  } else if (FIXNUM_P(b)) {
    if (FIX2NUM(b) <= 0)
      rb_raise(rb_eRangeError, "Cannot take Jacobi symbol (a/b) where b is non-positive.");
    if (FIX2NUM(b) % 2 == 0)
      rb_raise(rb_eRangeError, "Cannot take Jacobi symbol (a/b) where b is even.");
    mpz_temp_alloc(b_val);
    mpz_init_set_ui(b_val, FIX2NUM(b));
    free_b_val = 1;
  } else if (BIGNUM_P(b)) {
    mpz_temp_from_bignum(b_val, b);
    if (mpz_sgn(b_val) != 1) {
      mpz_temp_free(b_val);
      rb_raise(rb_eRangeError, "Cannot take Jacobi symbol (a/b) where b is non-positive.");
    }
    if (mpz_even_p(b_val)) {
      mpz_temp_free(b_val);
      rb_raise(rb_eRangeError, "Cannot take Jacobi symbol (a/b) where b is even.");
    }
    free_b_val = 1;
  } else {
    typeerror_as(ZXB, "b");
  }

  res_val = mpz_jacobi(a_val, b_val);
  if (free_a_val) { mpz_temp_free(a_val); }
  if (free_b_val) { mpz_temp_free(b_val); }
  return INT2FIX(res_val);
}

.lcm(b) ⇒ Object

Returns the least common multiple of a and b. The result is always positive even if one or both of a or b are negative.

Since:

  • 0.2.11

.lucnum ⇒ Object

.GMP::Z.mfac(n, m) ⇒ Object

Returns _n!^(m)_, the m-multi-factorial of n.

Examples:

GMP::Z.mfac(0,   3)  #=>    1
GMP::Z.mfac(1,   3)  #=>    1
GMP::Z.mfac(2,   3)  #=>    2
GMP::Z.mfac(3,   3)  #=>    3
GMP::Z.mfac(4,   3)  #=>    4
GMP::Z.mfac(5,   3)  #=>   10
GMP::Z.mfac(6,   3)  #=>   18
GMP::Z.mfac(7,   3)  #=>   28
GMP::Z.mfac(8,   3)  #=>   80
GMP::Z.mfac(9,   3)  #=>  162
GMP::Z.mfac(10,  3)  #=>  280
GMP::Z.mfac(11,  3)  #=>  880
GMP::Z.mfac(12,  3)  #=> 1944

.mul ⇒ Object

.mul_2exp ⇒ Object

.neg ⇒ Object .- ⇒ Object

Returns -a.

.GMP::Z.new(value = 0) ⇒ Object

Creates a new GMP::Z integer, with ‘value` as its value, converting where necessary. `value` must be an instance of one of the following classes:

  • GMP::Z

  • Fixnum

  • String

  • Bignum

Examples:

GMP::Z.new(5)         #=> 5
GMP::Z.new(2**32)     #=> 4_294_967_296
GMP::Z.new(2**101)    #=> 2_535_301_200_456_458_802_993_406_410_752
GMP::Z.new("20")      #=> 20
GMP::Z.new("0x20")    #=> 32
GMP::Z.new("020")     #=> 16
GMP::Z.new("0b101")   #=> 5
GMP::Z.new("20", 16)  #=> 32
GMP::Z.new("1Z", 36)  #=> 71

.nextprime ⇒ Object .next_prime ⇒ Object

Returns the next prime greater than n.

This function uses a probabilistic algorithm to identify primes. For practical purposes it’s adequate, the chance of a composite passing will be extremely small.

.GMP::Z.pow(a, b) ⇒ Object

Returns a raised to b. The case 0^0 yields 1.

.GMP::Z.primorial(n) ⇒ Object

Returns the primorial of n.

Examples:

GMP::Z.primorial(0)  #=>   1
GMP::Z.primorial(1)  #=>   1
GMP::Z.primorial(2)  #=>   2
GMP::Z.primorial(3)  #=>   6
GMP::Z.primorial(4)  #=>   6
GMP::Z.primorial(5)  #=>  30
GMP::Z.primorial(6)  #=>  30
GMP::Z.primorial(7)  #=> 210

.sqrt ⇒ Object

Returns the truncated integer part of the square root of a.

.sub ⇒ Object

.submul ⇒ Object

.tdiv_q_2exp ⇒ Object

.tdiv_r_2exp ⇒ Object

Instance Method Details

#%(b) ⇒ Object

Returns a mod b. b can be an instance any of the following:

  • GMP::Z

  • Fixnum

  • Bignum

Since:

  • 0.2.10

#&(b) ⇒ Object

Returns a bitwise-and b. b must be an instance of one of the following:

  • GMP::Z

  • Fixnum

  • Bignum

#*(b) ⇒ Object

Multiplies a with b. a must be an instance of one of

  • GMP::Z

  • Fixnum

  • GMP::Q

  • GMP::F

  • Bignum



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# File 'ext/gmpz.c', line 1109

VALUE r_gmpz_mul(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val, *res_val;
  VALUE res = 0;

  mpz_get_struct (self, self_val);

  if (GMPZ_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_get_struct (arg,arg_val);
    mpz_mul (res_val, self_val, arg_val);
  } else if (FIXNUM_P (arg)) {
    mpz_make_struct_init (res, res_val);
    if (FIX2NUM (arg) >= 0)
      mpz_mul_ui (res_val, self_val, FIX2NUM (arg));
    else
      mpz_mul_si (res_val, self_val, FIX2NUM (arg));
  } else if (GMPQ_P (arg)) {
    return r_gmpq_mul (arg, self);
  } else if (GMPF_P (arg)) {
#ifndef MPFR
    return r_gmpf_mul (arg, self);
#else
    return rb_funcall (arg, rb_intern ("*"), 1, self);
#endif
  } else if (BIGNUM_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_set_bignum (res_val, arg);
    mpz_mul (res_val, res_val, self_val);
  } else {
    typeerror (ZQFXB);
  }
  return res;
}

#**(b) ⇒ Object

Returns a raised to b. The case 0^0 yields 1.

#+(b) ⇒ Object

Adds a to b. b must be an instance of one of:

  • GMP::Z

  • Fixnum

  • GMP::Q

  • GMP::F

  • Bignum



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# File 'ext/gmpz.c', line 931

VALUE r_gmpz_add(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val, *res_val;
  VALUE res = 0;

  mpz_get_struct(self,self_val);

  if (GMPZ_P(arg)) {
    mpz_get_struct(arg,arg_val);
    mpz_make_struct_init(res, res_val);
    mpz_add(res_val, self_val, arg_val);
  } else if (FIXNUM_P(arg)) {
    mpz_make_struct_init(res, res_val);
    if (FIX2NUM(arg) > 0)
      mpz_add_ui(res_val, self_val, FIX2NUM(arg));
    else
      mpz_sub_ui(res_val, self_val, -FIX2NUM(arg));
  } else if (GMPQ_P(arg)) {
    return r_gmpq_add(arg, self);
  } else if (GMPF_P(arg)) {
#ifndef MPFR
    return r_gmpf_add(arg, self);
#else
    return rb_funcall(arg, rb_intern("+"), 1, self);
#endif
  } else if (BIGNUM_P(arg)) {
    mpz_make_struct_init(res, res_val);
    mpz_init(res_val);
    mpz_set_bignum(res_val, arg);
    mpz_add(res_val, res_val, self_val);
  } else {
    typeerror(ZQFXB);
  }
  return res;
}

#-(b) ⇒ Object

Subtracts b from a. b must be an instance of one of:

  • GMP::Z

  • Fixnum

  • GMP::Q

  • GMP::F

  • Bignum



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# File 'ext/gmpz.c', line 1017

VALUE r_gmpz_sub(VALUE self, VALUE arg)
{
  MP_RAT *res_val_q, *arg_val_q;
  MP_INT *self_val, *arg_val, *res_val;
  MP_FLOAT *arg_val_f, *res_val_f;
  unsigned long prec;
  VALUE res = 0;

  mpz_get_struct(self,self_val);

  if (GMPZ_P(arg)) {
    mpz_make_struct_init(res, res_val);
    mpz_get_struct(arg,arg_val);
    mpz_sub (res_val, self_val, arg_val);
  } else if (FIXNUM_P(arg)) {
    mpz_make_struct_init(res, res_val);
    if (FIX2NUM(arg) > 0)
      mpz_sub_ui (res_val, self_val, FIX2NUM(arg));
    else
      mpz_add_ui (res_val, self_val, -FIX2NUM(arg));
  } else if (GMPQ_P(arg)) {
    mpq_make_struct_init(res, res_val_q);
    mpq_get_struct(arg,arg_val_q);
    mpz_set (mpq_denref(res_val_q), mpq_denref(arg_val_q));
    mpz_mul (mpq_numref(res_val_q), mpq_denref(arg_val_q), self_val);
    mpz_sub (mpq_numref(res_val_q), mpq_numref(res_val_q), mpq_numref(arg_val_q));
  } else if (GMPF_P(arg)) {
    mpf_get_struct_prec (arg, arg_val_f, prec);
    mpf_make_struct_init(res, res_val_f, prec);
    mpf_set_z (res_val_f, self_val);
    mpf_sub (res_val_f, res_val_f, arg_val_f);
  } else if (BIGNUM_P(arg)) {
    mpz_make_struct_init(res, res_val);
    mpz_set_bignum (res_val, arg);
    mpz_sub (res_val, self_val, res_val);
  } else {
    typeerror (ZQFXB);
  }
  return res;
}

#-@ ⇒ Object

#/(b) ⇒ Object

Divides a by b. Combines the different GMP division functions to provide what one is hopefully looking for. The result will either be an instance of GMP::Q or GMP::F, depending on b. b must be an instance of one of the following:

  • GMP::Z

  • Fixnum

  • GMP::Q

  • GMP::F

  • Bignum

If b is a GMP::Z, Fixnum, GMP::Q, or Bignum, then no division is actually performed. Instead, we simply construct a new GMP::Q number, using a and b as the numerator and denominator (not exactly true for the GMP::Q case).

If b is a GMP::F, then the result is calculated via ‘mpf_div`.

#<(b) ⇒ Object

Returns whether a is strictly less than b.

#<<(n) ⇒ Object

Returns a times 2 raised to n. This operation can also be defined as a left shift by n bits.

#<=(b) ⇒ Object

Returns whether a is less than or equal to b.

#<=>(b) ⇒ Object

Returns negative if a is less than b.

Returns 0 if a is equal to b.

Returns positive if a is greater than b.



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# File 'ext/gmpz.c', line 2482

VALUE r_gmpz_cmp(VALUE self, VALUE arg)
{
  MP_INT *self_val;
  int res;
  mpz_get_struct(self,self_val);
  res = mpz_cmp_value(self_val, arg);
  if (res > 0)
    return INT2FIX(1);
  else if (res == 0)
    return INT2FIX(0);
  else
    return INT2FIX(-1);
}

#==(b) ⇒ Object

Returns true if a is equal to b, and false otherwise.

#>(b) ⇒ Object

Returns whether a is strictly greater than b.

#>=(b) ⇒ Object

Returns whether a is greater than or equal to b.

#>> ⇒ Object

unsorted

#[](index) ⇒ Object

Gets the bit at index, returned as either true or false.



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# File 'ext/gmpz.c', line 2834

VALUE r_gmpz_getbit(VALUE self, VALUE bitnr)
{
  MP_INT *self_val;
  unsigned long bitnr_val = 0;

  mpz_get_struct (self, self_val);
  if (FIXNUM_P (bitnr)) {
    bitnr_val = FIX2NUM (bitnr);
  } else {
    typeerror_as (X, "index");
  }
  return mpz_tstbit (self_val, bitnr_val) ? Qtrue : Qfalse;
}

#[]=(index) ⇒ Object

Sets the bit at index to x.



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# File 'ext/gmpz.c', line 2803

VALUE r_gmpz_setbit(VALUE self, VALUE bitnr, VALUE set_to)
{
  MP_INT *self_val;
  unsigned long bitnr_val = 0;

  mpz_get_struct (self, self_val);

  if (FIXNUM_P (bitnr)) {
    if (FIX2NUM (bitnr) < 0) {
      rb_raise (rb_eRangeError, "index must be nonnegative");
    }
    bitnr_val = FIX2NUM (bitnr);
  } else {
    typeerror_as (X, "index");
  }

  if (RTEST (set_to)) {
    mpz_setbit (self_val, bitnr_val);
  } else {
    mpz_clrbit (self_val, bitnr_val);
  }
  return Qnil;
}

#^(b) ⇒ Object

Returns a bitwise exclusive-or b. b must be an instance of one of the following:

  • GMP::Z

  • Fixnum

  • Bignum

#abs ⇒ Object

call-seq:

a.abs

Returns the absolute value of a.

#abs! ⇒ Object

Sets a to its absolute value.

#add!(_b_) ⇒ Object

Adds a to b in-place, setting a to the sum. b must be an instance of one of:

  • GMP::Z

  • Fixnum

  • GMP::Q

  • GMP::F

  • Bignum



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# File 'ext/gmpz.c', line 980

VALUE r_gmpz_add_self(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val;

  mpz_get_struct(self,self_val);

  if (GMPZ_P(arg)) {
    mpz_get_struct(arg,arg_val);
    mpz_add(self_val, self_val, arg_val);
  } else if (FIXNUM_P(arg)) {
    if (FIX2NUM(arg) > 0)
      mpz_add_ui(self_val, self_val, FIX2NUM(arg));
    else
      mpz_sub_ui(self_val, self_val, -FIX2NUM(arg));
  } else if (BIGNUM_P(arg)) {
    mpz_temp_from_bignum(arg_val, arg);
    mpz_add(self_val, self_val, arg_val);
    mpz_temp_free(arg_val);
  } else {
    typeerror(ZXB);
  }
  return Qnil;
}

#addmul!(b, c) ⇒ Object

Sets a to a plus b times c. b and c must each be an instance of one of

  • GMP::Z

  • Fixnum

  • Bignum

Since:

  • 0.4.19



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# File 'ext/gmpz.c', line 1158

static VALUE r_gmpz_addmul_self(VALUE self, VALUE b, VALUE c)
{
  MP_INT *self_val, *b_val, *c_val;
  int free_b_val = 0;

  if (GMPZ_P (b)) {
    mpz_get_struct (b, b_val);
  } else if (FIXNUM_P (b)) {
    mpz_temp_alloc (b_val);
    mpz_init_set_si (b_val, FIX2NUM (b));
    free_b_val = 1;
  } else if (BIGNUM_P (b)) {
    mpz_temp_from_bignum (b_val, b);
    free_b_val = 1;
  } else {
    typeerror_as (ZXB, "addend");
  }
  mpz_get_struct (self, self_val);

  if (GMPZ_P (c)) {
    mpz_get_struct (c, c_val);
    mpz_addmul (self_val, b_val, c_val);
  } else if (FIXNUM_P (c) && FIX2NUM (c) >= 0) {
    mpz_addmul_ui (self_val, b_val, FIX2NUM (c));
  } else if (FIXNUM_P (c) || BIGNUM_P (c)) {
    mpz_temp_from_bignum (c_val, c);
    mpz_addmul (self_val, b_val, c_val);
    mpz_temp_free (c_val);
  } else {
    if (free_b_val)
      mpz_temp_free (b_val);
    typeerror_as (ZXB, "multiplicand");
  }
  if (free_b_val)
    mpz_temp_free (b_val);
  return self;
}

#cdiv(d) ⇒ Object

Divide n by d, forming a quotient q. cdiv rounds q up towards _+infinity_. The c stands for “ceil”.

q will satisfy _n=q*d+r_.

This function calculates only the quotient.

#cmod(d) ⇒ Object

Divides n by d, forming a remainder r. r will have the opposite sign of d. The c stands for “ceil”.

r will satisfy _n=q*d+r_, and r will satisfy _0 <= abs(r ) < abs(d)_.

This function calculates only the remainder.

#cmpabs(b) ⇒ Object

Returns negative if _abs(a)_ is less than _abs(b)_.

Returns 0 if _abs(a)_ is equal to _abs(b)_.

Returns positive if _abs(a)_ is greater than _abs(b)_.

#coerce(arg) ⇒ Object 



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# File 'ext/gmp.c', line 23

static VALUE r_gmpz_coerce(VALUE self, VALUE arg)
{
  return rb_assoc_new(r_gmpzsg_new(1, &arg, cGMP_Z), self);
}

#com ⇒ Object

Returns the one’s complement of a.

#com! ⇒ Object

Sets a to its one’s complement.

#congruent?(c, d) ⇒ Boolean

Returns true if n is congruent to c modulo d. c and d can be an instance any of the following:

  • GMP::Z

  • Fixnum

  • Bignum

Returns:

  • (Boolean)

Since:

  • 0.6.19



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# File 'ext/gmpz.c', line 1575

static VALUE r_gmpz_congruent(VALUE self_val, VALUE c_val, VALUE d_val)
{
  MP_INT *self, *c = NULL, *d = NULL;
  int res, free_c, free_d;
  mpz_get_struct (self_val, self);
  free_c = free_d = 0;

  if (FIXNUM_P (c_val) && FIX2NUM (c_val) > 0 &&
      FIXNUM_P (d_val) && FIX2NUM (d_val) > 0) {
    res = mpz_congruent_ui_p (self, FIX2NUM (c_val), FIX2NUM (d_val));
  } else {
    if (FIXNUM_P (c_val)) {
      mpz_make_struct_init (c_val, c);
      mpz_init_set_si (c, FIX2NUM (c_val));
    } else if (BIGNUM_P (c_val)) {
      mpz_temp_from_bignum (c, c_val);
      free_c = 1;
    } else if (GMPZ_P (c_val)) {
      mpz_get_struct (c_val, c);
    } else {
      typeerror_as (ZXB, "c");
    }

    if (FIXNUM_P (d_val)) {
      mpz_make_struct_init (d_val, d);
      mpz_init_set_si (d, FIX2NUM (d_val));
    } else if (BIGNUM_P (d_val)) {
      mpz_temp_from_bignum (d, d_val);
      free_d = 1;
    } else if (GMPZ_P (d_val)) {
      mpz_get_struct (d_val, d);
    } else {
      if (free_c) { mpz_temp_free (c); }
      typeerror_as (ZXB, "d");
    }

    res = mpz_congruent_p (self, c, d);
    if (free_c) { mpz_temp_free (c); }
    if (free_d) { mpz_temp_free (d); }
  }
  return (res != 0) ? Qtrue : Qfalse;
}

#divisible?(b) ⇒ Boolean

Returns true if a is divisible by b. b can be an instance any of the following:

  • GMP::Z

  • Fixnum

  • Bignum

Returns:

  • (Boolean)

Since:

  • 0.5.23



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# File 'ext/gmpz.c', line 1531

static VALUE r_gmpz_divisible(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val;
  int res = 0;
  mpz_get_struct (self, self_val);

  if (FIXNUM_P (arg) && FIX2NUM (arg) > 0) {
    mpz_temp_alloc (arg_val);
    mpz_init_set_ui (arg_val, FIX2NUM (arg));
    res = mpz_divisible_ui_p (self_val, FIX2NUM (arg));
    mpz_temp_free (arg_val);
  } else if (TYPE (arg) == T_FIXNUM) {
    mpz_temp_alloc (arg_val);
    mpz_make_struct_init (arg, arg_val);
    mpz_init_set_si (arg_val, FIX2NUM (arg));
    res = mpz_divisible_p (self_val, arg_val);
    mpz_temp_free (arg_val);
  } else if (BIGNUM_P (arg)) {
    mpz_temp_from_bignum (arg_val, arg);
    res = mpz_divisible_p (self_val, arg_val);
    mpz_temp_free (arg_val);
  } else if (GMPZ_P (arg)) {
    mpz_get_struct (arg, arg_val);
    res = mpz_divisible_p (self_val, arg_val);
  } else {
    typeerror_as (ZXB, "argument");
  }
  return (res != 0) ? Qtrue : Qfalse;
}

#eql?(b) ⇒ Boolean

Returns true if a is equal to b. a and b must then be equal in cardinality, and both be instances of GMP::Z. Otherwise, returns false. ‘a.eql?(b)` if and only if `b.class == GMP::Z`, and `a.hash == b.hash`.

Returns:

  • (Boolean)

Since:

  • 0.4.7



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# File 'ext/gmpz.c', line 2606

VALUE r_gmpz_eql(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val;
  mpz_get_struct(self,self_val);
  
  if (GMPZ_P(arg)) {
    mpz_get_struct(arg, arg_val);
    return (mpz_cmp (self_val, arg_val) == 0) ? Qtrue : Qfalse;
  }
  else {
    return Qfalse;
  }
}

#even? ⇒ Boolean

Determines whether a is even. Returns true or false.

Returns:

  • (Boolean)

#export(order = -1) ⇒ Object

Return a String with word data from a.

‘order` can be 1 for most significant word first or -1 for least significant first.

If ‘a` is non-zero then the most significant word produced will be non-zero. `GMP::Z(0).export` returns `“”`.

The sign of a is ignored, just the absolute value is exported. An application can use ‘GMP::Z#sgn` to get the sign and handle it as desired.



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# File 'ext/gmpz.c', line 2973

VALUE r_gmpz_export(int argc, VALUE *argv, VALUE self_val)
{
  MP_INT *self;
  VALUE order_val, res;
  int order, endian;
  size_t countp, nails;
  char *string;

  endian = 0;
  nails = 0;
  order = 1;
  mpz_get_struct(self_val, self);

  rb_scan_args (argc, argv, "01", &order_val);

  if (NIL_P (order_val))
    order = -1;
  else if (! FIXNUM_P (order_val))
    typeerror_as (X, "order");
  else
    order = FIX2INT (order_val);

  string = mpz_export (NULL, &countp, order, sizeof(char), endian, nails, self);
  res = rb_str_new (string, countp);
  free (string);

  return res;
}

#fdiv(d) ⇒ Object

Divide n by d, forming a quotient q. fdiv rounds q down towards -infinity. The f stands for “floor”.

q will satisfy _n=q*d+r_.

This function calculates only the quotient.

#fmod(d) ⇒ Object

Divides n by d, forming a remainder r. r will have the same sign as d. The f stands for “floor”.

r will satisfy _n=q*d+r_, and r will satisfy _0 <= abs(r ) < abs(d)_.

This function calculates only the remainder.

The remainder can be negative, so the return value is the absolute value of the remainder.

#gcd(b) ⇒ Object

Returns the greatest common divisor of a and b. The result is always positive even if one or both of a or b are negative.

Since:

  • 0.2.11

#gcdext(b) ⇒ Object

Returns the greatest common divisor of a and b, in addition to s and t, the coefficients satisfying _a*s + b*t = g_. g is always positive, even if one or both of a and b are negative. s and t are chosen such that _abs(s) <= abs(b)_ and _abs(t) <= abs(a)_.

Since:

  • 0.5.23



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# File 'ext/gmpz.c', line 1953

VALUE r_gmpz_gcdext(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val, *res_val, *s_val, *t_val;
  VALUE res = 0, s = 0, t = 0, ary;
  int free_arg_val = 0;

  mpz_get_struct (self,self_val);

  if (GMPZ_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_make_struct_init (s, s_val);
    mpz_make_struct_init (t, t_val);
    mpz_get_struct (arg, arg_val);
    mpz_gcdext (res_val, s_val, t_val, self_val, arg_val);
  } else if (FIXNUM_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_make_struct_init (s, s_val);
    mpz_make_struct_init (t, t_val);
    mpz_temp_alloc (arg_val);
    mpz_init_set_ui (arg_val, FIX2NUM (arg));
    free_arg_val = 1;
    mpz_gcdext (res_val, s_val, t_val, self_val, arg_val);
  } else if (BIGNUM_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_make_struct_init (s, s_val);
    mpz_make_struct_init (t, t_val);
    mpz_set_bignum (res_val, arg);
    mpz_gcdext (res_val, s_val, t_val, res_val, self_val);
  } else {
    typeerror (ZXB);
  }

  if (free_arg_val)
    mpz_temp_free (arg_val);

  ary = rb_ary_new3 (3, res, s, t);
  return ary;
}

#gcdext2(b) ⇒ Object

Returns the greatest common divisor of a and b, in addition to s, the coefficient satisfying _a*s + b*t = g_. g is always positive, even if one or both of a and b are negative. s and t are chosen such that _abs(s) <= abs(b)_ and _abs(t) <= abs(a)_.

Since:

  • 0.5.x



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# File 'ext/gmpz.c', line 2004

VALUE r_gmpz_gcdext2(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val, *res_val, *s_val;
  VALUE res = 0, s = 0, ary;
  int free_arg_val = 0;

  mpz_get_struct (self,self_val);

  if (GMPZ_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_make_struct_init (s, s_val);
    mpz_get_struct (arg, arg_val);
    mpz_gcdext (res_val, s_val, NULL, self_val, arg_val);
  } else if (FIXNUM_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_make_struct_init (s, s_val);
    mpz_temp_alloc (arg_val);
    mpz_init_set_ui (arg_val, FIX2NUM(arg));
    free_arg_val = 1;
    mpz_gcdext (res_val, s_val, NULL, self_val, arg_val);
  } else if (BIGNUM_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_make_struct_init (s, s_val);
    mpz_set_bignum (res_val, arg);
    mpz_gcdext (res_val, s_val, NULL, res_val, self_val);
  } else {
    typeerror (ZXB);
  }

  if (free_arg_val)
    mpz_temp_free (arg_val);

  ary = rb_ary_new3 (2, res, s);
  return ary;
}

#hamdist(b) ⇒ Object

If a and b are both >= 0 or both < 0, calculate the hamming distance between a and b. If one operand is >= 0 and the other is less than 0, then return “infinity” (the largest possible ‘mp_bitcnt_t`).



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# File 'ext/gmpz.c', line 2726

VALUE r_gmpz_hamdist(VALUE self_val, VALUE b_val)
{
  MP_INT *self, *b;
  mpz_get_struct (self_val, self);
  mpz_get_struct (   b_val,    b);
  if (! GMPZ_P (b_val)) {
    typeerror_as (Z, "b");
  }

  return INT2FIX (mpz_hamdist(self, b));
}

#hash ⇒ Object

Returns the computed hash value of a. This method first converts a into a String (base 10), then calls String#hash on the result, returning the hash value. ‘a.eql?(b)` if and only if `b.class == GMP::Z`, and `a.hash == b.hash`.

Since:

  • 0.4.7



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# File 'ext/gmpz.c', line 2632

VALUE r_gmpz_hash(VALUE self)
{
  ID to_s_sym = rb_intern("to_s");
  ID hash_sym = rb_intern("hash");
  return rb_funcall(rb_funcall(self, to_s_sym, 0), hash_sym, 0);
}

#initialize_copy(orig_val) ⇒ Object 



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# File 'ext/gmpz.c', line 720

static VALUE r_gmpz_initialize_copy(VALUE copy_val, VALUE orig_val) {
  MP_INT *orig, *copy;

  if (copy_val == orig_val) return copy_val;

  if (TYPE(orig_val) != T_DATA) {
    rb_raise(rb_eTypeError, "wrong argument type");
  }

  mpz_get_struct (orig_val, orig);
  mpz_get_struct (copy_val, copy);
  mpz_set (copy, orig);

  return copy_val;
}

#invert(b) ⇒ Object

Returns the inverse of a modulo b. If the inverse exists, the return value is non-zero and the result will be non-negative and less than b. If an inverse doesn’t exist, the result is undefined.

Since:

  • 0.2.11



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# File 'ext/gmpz.c', line 2085

VALUE r_gmpz_invert(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val, *res_val;
  VALUE res = 0;

  mpz_get_struct (self,self_val);

  if (GMPZ_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_get_struct (arg, arg_val);
    mpz_invert (res_val, self_val, arg_val);
  } else if (FIXNUM_P (arg)) {
    mpz_temp_alloc(arg_val);
    mpz_init_set_ui(arg_val, FIX2NUM(arg));
    mpz_make_struct_init (res, res_val);
    mpz_invert (res_val, self_val, arg_val);
  } else if (BIGNUM_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_set_bignum (res_val, arg);
    mpz_invert (res_val, res_val, self_val);
  } else {
    typeerror (ZXB);
  }
  return res;
}

#jacobi(b) ⇒ Object

Calculate the Jacobi symbol _(a/b)_. This is defined only for b odd and positive.



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# File 'ext/gmpz.c', line 2119

VALUE r_gmpz_jacobi(VALUE self, VALUE b)
{
  MP_INT *self_val, *b_val;
  int res_val;
  mpz_get_struct(self, self_val);
  mpz_get_struct(   b,    b_val);
  if (mpz_sgn(b_val) != 1)
    rb_raise(rb_eRangeError, "Cannot take Jacobi symbol (a/b) where b is non-positive.");
  if (mpz_even_p(b_val))
    rb_raise(rb_eRangeError, "Cannot take Jacobi symbol (a/b) where b is even.");
  res_val = mpz_jacobi(self_val, b_val);
  return INT2FIX(res_val);
}

#lastbits_pos ⇒ Object

#lastbits_sgn ⇒ Object

#lcm(b) ⇒ Object

Returns the least common multiple of a and b. The result is always positive even if one or both of a or b are negative.

Since:

  • 0.2.11



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# File 'ext/gmpz.c', line 2050

VALUE r_gmpz_lcm(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val, *res_val;
  VALUE res = 0;

  mpz_get_struct (self,self_val);

  if (GMPZ_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_get_struct (arg, arg_val);
    mpz_lcm (res_val, self_val, arg_val);
  } else if (FIXNUM_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_lcm_ui (res_val, self_val, FIX2NUM(arg));
  } else if (BIGNUM_P (arg)) {
    mpz_make_struct_init (res, res_val);
    mpz_set_bignum (res_val, arg);
    mpz_lcm (res_val, res_val, self_val);
  } else {
    typeerror (ZXB);
  }
  return res;
}

#legendre(p) ⇒ Object

Calculate the Legendre symbol _(a/p)_. This is defined only for p an odd positive prime, and for such p it’s identical to the Jacobi symbol.



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# File 'ext/gmpz.c', line 2205

VALUE r_gmpz_legendre(VALUE self, VALUE p)
{
  MP_INT *self_val, *p_val;
  int res_val;
  mpz_get_struct(self, self_val);
  mpz_get_struct(   p,    p_val);
  if (mpz_sgn(p_val) != 1)
    rb_raise(rb_eRangeError, "Cannot take Legendre symbol (a/p) where p is non-positive.");
  if (mpz_even_p(p_val))
    rb_raise(rb_eRangeError, "Cannot take Legendre symbol (a/p) where p is even.");
  if (mpz_probab_prime_p(p_val, 5) == 0)
    rb_raise(rb_eRangeError, "Cannot take Legendre symbol (a/p) where p is composite.");
  res_val = mpz_legendre(self_val, p_val);
  return INT2FIX(res_val);
}

#neg ⇒ Object #- ⇒ Object

Returns -a.

#neg! ⇒ Object

Sets a to -a.

#nextprime ⇒ Object #next_prime ⇒ Object Also known as: next_prime

Returns the next prime greater than n.

This function uses a probabilistic algorithm to identify primes. For practical purposes it’s adequate, the chance of a composite passing will be extremely small.

#nextprime! ⇒ Object #next_prime! ⇒ Object Also known as: next_prime!

Sets n to the next prime greater than n.

This function uses a probabilistic algorithm to identify primes. For practical purposes it’s adequate, the chance of a composite passing will be extremely small.

#odd? ⇒ Boolean

Determines whether a is odd. Returns true or false.

Returns:

  • (Boolean)

#out_raw(stream) ⇒ Object

Output a on IO object stream, in raw binary format. The integer is written in a portable format, with 4 bytes of size information, and that many bytes of limbs. Both the size and the limbs are written in decreasing significance order (i.e., in big-endian).

The output can be read with ‘GMP::Z.inp_raw`.

Return the number of bytes written, or if an error occurred, return 0.



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# File 'ext/gmpz.c', line 2868

VALUE r_gmpz_out_raw(VALUE self, VALUE stream)
{
  MP_INT *self_val;
  FILE *fd;
  mpz_get_struct(self, self_val);
  if (TYPE (stream) != T_FILE) {
    rb_raise (rb_eTypeError, "stream must be an IO.");
  }
  fd = rb_io_stdio_file (RFILE (stream)->fptr);
  return INT2FIX (mpz_out_raw (fd, self_val));
}

#popcount ⇒ Object

If a >= 0, return the population count of a, which is the number of 1 bits in the binary representation. If a < 0, the number of 1s is infinite, and the return value is ‘INT2FIX(ULONG_MAX)`, the largest possible unsigned long.

#power? ⇒ Boolean

Returns true if p is a perfect power, i.e., if there exist integers a and b, with _b > 1_, such that p equals a raised to the power b.

Under this definition both 0 and 1 are considered to be perfect powers. Negative values of integers are accepted, but of course can only be odd perfect powers.

Returns:

  • (Boolean)

#powmod(b, c) ⇒ Object

Returns a raised to b modulo c.

Negative b is supported if an inverse _a^-1_ mod c exists. If an inverse doesn’t exist then a divide by zero is raised.



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# File 'ext/gmpz.c', line 1667

VALUE r_gmpz_powm(VALUE self, VALUE exp, VALUE mod)
{
  MP_INT *self_val, *res_val, *mod_val, *exp_val;
  VALUE res;
  int free_mod_val = 0;

  if (GMPZ_P(mod)) {
    mpz_get_struct(mod, mod_val);
    if (mpz_sgn(mod_val) <= 0) {
      rb_raise(rb_eRangeError, "modulus must be positive");
    }
  } else if (FIXNUM_P(mod)) {
    if (FIX2NUM(mod) <= 0) {
      rb_raise(rb_eRangeError, "modulus must be positive");
    }
    mpz_temp_alloc(mod_val);
    mpz_init_set_ui(mod_val, FIX2NUM(mod));
    free_mod_val = 1;
  } else if (BIGNUM_P(mod)) {
    mpz_temp_from_bignum(mod_val, mod);
    if (mpz_sgn(mod_val) <= 0) {
      mpz_temp_free(mod_val);
      rb_raise(rb_eRangeError, "modulus must be positive");
    }
    free_mod_val = 1;
  } else {
    typeerror_as(ZXB, "modulus");
  }
  mpz_make_struct_init(res, res_val);
  mpz_get_struct(self, self_val);

  if (GMPZ_P(exp)) {
    mpz_get_struct(exp, exp_val);
    if (mpz_sgn(mod_val) < 0) {
      rb_raise(rb_eRangeError, "exponent must be nonnegative");
    }
    mpz_powm(res_val, self_val, exp_val, mod_val);
  } else if (FIXNUM_P(exp)) {
    if (FIX2NUM(exp) < 0)
    {
      if (free_mod_val)
        mpz_temp_free(mod_val);
      rb_raise(rb_eRangeError, "exponent must be nonnegative");
    }
    mpz_powm_ui(res_val, self_val, FIX2NUM(exp), mod_val);
  } else if (BIGNUM_P(exp)) {
    mpz_temp_from_bignum(exp_val, exp);
    mpz_powm(res_val, self_val, exp_val, mod_val);
    mpz_temp_free(exp_val);
  } else {
    if (free_mod_val)
      mpz_temp_free(mod_val);
    typeerror_as(ZXB, "exponent");
  }
  if (free_mod_val)
    mpz_temp_free(mod_val);
  return res;
}

#probab_prime?(reps = 5) ⇒ Boolean

Determine whether n is prime. Returns 2 if n is definitely prime, returns 1 if n is probably prime (without being certain), or returns 0 if n is definitely composite.

This function does some trial divisions, then some Miller-Rabin probabilistic primality tests. ‘reps` controls how many such tests are done, 5 to 10 is a reasonable number, more will reduce the chances of a composite being returned as “probably prime”.

Miller-Rabin and similar tests can be more properly called compositeness tests. Numbers which fail are known to be composite but those which pass might be prime or might be composite. Only a few composites pass, hence those which pass are considered probably prime.

Returns:

  • (Boolean)

#remove(f) ⇒ Object

Remove all occurrences of the factor f from n, returning the result as r. t, the number of occurrences that were removed, is also returned.



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# File 'ext/gmpz.c', line 2229

VALUE r_gmpz_remove(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val, *res_val;
  VALUE res;
#if __GNU_MP_VERSION>2
  unsigned long removed_val;
#else
  int removed_val;
#endif
  int free_arg_val = 0;
  arg_val = NULL;

  mpz_get_struct (self, self_val);

  if (GMPZ_P (arg)) {
    mpz_get_struct (arg,arg_val);
    if (mpz_sgn (arg_val) != 1)
      rb_raise (rb_eRangeError, "argument must be positive");
  } else if (FIXNUM_P (arg)) {
    if (FIX2NUM (arg) <= 0)
      rb_raise (rb_eRangeError, "argument must be positive");
    mpz_temp_alloc (arg_val);
    mpz_init_set_ui (arg_val, FIX2NUM (arg));
  } else if (BIGNUM_P (arg)) {
    mpz_temp_from_bignum (arg_val, arg);
    if (mpz_sgn (arg_val) != 1) {
      mpz_temp_free (arg_val);
      rb_raise (rb_eRangeError, "argument must be positive");
    }
  } else {
    typeerror (ZXB);
  }

  mpz_make_struct_init (res, res_val);
  removed_val = mpz_remove (res_val, self_val, arg_val);

  if (free_arg_val)
    mpz_temp_free (arg_val);

  return rb_assoc_new (res, INT2FIX (removed_val));
}

#root(b) ⇒ Object

Returns the truncated integer part of the _b_th root of a.

#rootrem(b) ⇒ Object

Returns the truncated integer part of the _b_th root of a, and the remainder, _a - root**b_.

#scan0(starting_bit) ⇒ Object

Scan a, starting from bit starting_bit, towards more significant bits, until the first 0 bit is found. Return the index of the found bit.

If the bit at starting_bit is already what’s sought, then starting_bit is returned.

If there’s no bit found, then ‘INT2FIX(ULONG_MAX)` is returned. This will happen in #scan0 past the end of a negative number.



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# File 'ext/gmpz.c', line 2752

VALUE r_gmpz_scan0(VALUE self, VALUE bitnr)
{
  MP_INT *self_val;
  int bitnr_val = 0;

  mpz_get_struct (self, self_val);
  if (FIXNUM_P (bitnr)) {
    bitnr_val = FIX2INT (bitnr);
  } else {
    typeerror_as (X, "index");
  }
  return INT2FIX (mpz_scan0 (self_val, bitnr_val));
}

#scan1(starting_bit) ⇒ Object

Scan a, starting from bit starting_bit, towards more significant bits, until the first 1 bit is found. Return the index of the found bit.

If the bit at starting_bit is already what’s sought, then starting_bit is returned.

If there’s no bit found, then ‘INT2FIX(ULONG_MAX)` is returned. This will happen in scan1 past the end of a nonnegative number.



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# File 'ext/gmpz.c', line 2780

VALUE r_gmpz_scan1(VALUE self, VALUE bitnr)
{
  MP_INT *self_val;
  int bitnr_val = 0;

  mpz_get_struct (self, self_val);

  if (FIXNUM_P (bitnr)) {
    bitnr_val = FIX2INT (bitnr);
  } else {
    typeerror_as (X, "index");
  }

  return INT2FIX (mpz_scan1 (self_val, bitnr_val));
}

#sgn ⇒ Object

Returns +1 if a > 0, 0 if a == 0, and -1 if a < 0.



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# File 'ext/gmpz.c', line 2588

VALUE r_gmpz_sgn(VALUE self)
{
  MP_INT *self_val;
  mpz_get_struct(self, self_val);
  return INT2FIX(mpz_sgn(self_val));
}

#size ⇒ Object

Return the size of a measured in number of limbs. If a is zero, the returned value will be zero.

Since:

  • 0.4.19



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# File 'ext/gmpz.c', line 3079

VALUE r_gmpz_size(VALUE self)
{
  MP_INT *self_val;
  mpz_get_struct(self, self_val);
  return INT2FIX(mpz_size(self_val));
}

#size_in_bin ⇒ Object

Return the size of a measured in number of digits in binary. The sign of a is ignored, just the absolute value is used. If a is zero the return value is 1.

Since:

  • 0.2.11



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# File 'ext/gmpz.c', line 3057

VALUE r_gmpz_size_in_bin(VALUE self)
{
  MP_INT *self_val;
  mpz_get_struct (self, self_val);
  return INT2FIX (mpz_sizeinbase (self_val, 2));
}

#sizeinbase(base) ⇒ Object #size_in_base(base) ⇒ Object Also known as: size_in_base

Return the size of a measured in number of digits in ‘base`. `base` can vary from 2 to 62. The sign of a is ignored, just the absolute value is used. The result will be either exact or 1 too big. If `base` is a power of 2, the result is always exact. If a is zero the return value is always 1.

Since:

  • 0.2.11

#sqrt ⇒ Object

Returns the truncated integer part of the square root of a.

#sqrt! ⇒ Object

Sets a to the truncated integer part of its square root.

#sqrtrem ⇒ Object

Returns the truncated integer part of the square root of a as s and the remainder _a - s * s_ as r, which will be zero if a is a perfect square.

#square? ⇒ Boolean

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

Returns:

  • (Boolean)

#sub!(b) ⇒ Object

Subtracts b from a in-place, setting a to the difference. b must be an instance of one of:

  • GMP::Z

  • Fixnum

  • GMP::Q

  • GMP::F

  • Bignum



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# File 'ext/gmpz.c', line 1072

VALUE r_gmpz_sub_self(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val;

  mpz_get_struct(self,self_val);

  if (GMPZ_P(arg)) {
    mpz_get_struct(arg, arg_val);
    mpz_sub (self_val, self_val, arg_val);
  } else if (FIXNUM_P(arg)) {
    if (FIX2NUM(arg) > 0)
      mpz_sub_ui (self_val, self_val, FIX2NUM(arg));
    else
      mpz_add_ui (self_val, self_val, -FIX2NUM(arg));
  } else if (BIGNUM_P(arg)) {
    mpz_temp_from_bignum(arg_val, arg);
    mpz_sub (self_val, self_val, arg_val);
    mpz_temp_free (arg_val);
  } else {
    typeerror (ZXB);
  }
  return Qnil;
}

#submul!(b, c) ⇒ Object

Sets a to a minus b times c. b and c must each be an instance of one of

  • GMP::Z

  • Fixnum

  • Bignum

Since:

  • 0.5.23



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# File 'ext/gmpz.c', line 1208

static VALUE r_gmpz_submul_self(VALUE self, VALUE b, VALUE c)
{
  MP_INT *self_val, *b_val, *c_val;
  int free_b_val = 0;

  if (GMPZ_P (b)) {
    mpz_get_struct (b, b_val);
  } else if (FIXNUM_P (b)) {
    mpz_temp_alloc (b_val);
    mpz_init_set_si (b_val, FIX2NUM (b));
    free_b_val = 1;
  } else if (BIGNUM_P (b)) {
    mpz_temp_from_bignum (b_val, b);
    free_b_val = 1;
  } else {
    typeerror_as (ZXB, "addend");
  }
  mpz_get_struct (self, self_val);

  if (GMPZ_P (c)) {
    mpz_get_struct (c, c_val);
    mpz_submul (self_val, b_val, c_val);
  } else if (FIXNUM_P (c) && FIX2NUM (c) >= 0) {
    mpz_submul_ui (self_val, b_val, FIX2NUM (c));
  } else if (FIXNUM_P (c) || BIGNUM_P (c)) {
    mpz_temp_from_bignum (c_val, c);
    mpz_submul (self_val, b_val, c_val);
    mpz_temp_free (c_val);
  } else {
    if (free_b_val)
      mpz_temp_free (b_val);
  /* TODO?: rb_raise (rb_eTypeError, "base must be a Fixnum between 2 and 62, not a %s.", rb_class2name (rb_class_of (c)));*/
    typeerror_as (ZXB, "multiplicand");
  }
  if (free_b_val)
    mpz_temp_free (b_val);
  return self;
}

#swap(b) ⇒ Object

Efficiently swaps the contents of a with b. b must be an instance of GMP::Z.

Returns:

  • nil



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# File 'ext/gmpz.c', line 793

VALUE r_gmpz_swap(VALUE self_val, VALUE arg_val)
{
  MP_INT *self, *arg;

  if (!GMPZ_P(arg_val))
    rb_raise(rb_eTypeError, "Can't swap GMP::Z with object of other class");

  mpz_get_struct(self_val, self);
  mpz_get_struct(arg_val, arg);
  mpz_swap(self, arg);
  return Qnil;
}

#tdiv(d) ⇒ Object

Divides n by d, forming a quotient q. tdiv rounds q towards zero. The t stands for “truncate”.

q will satisfy _n=q*d+r_, and r will satisfy _0 <= abs(r ) < abs(d)_.

This function calculates only the quotient.

#tmod(d) ⇒ Object

Divides n by d, forming a remainder r. r will have the same sign as n. The t stands for “truncate”.

r will satisfy _n=q*d+r_, and r will satisfy _0 <= abs(r ) < abs(d)_.

This function calculates only the remainder.

The remainder can be negative, so the return value is the absolute value of the remainder.

#to_d ⇒ Object

TODO:

Implement mpz_fits_slong_p

Returns a as a Float if a fits in a Float.

Otherwise returns the least significant part of a, with the same sign as a.

If a is too big to fit in a Float, the returned result is probably not very useful. To find out if the value will fit, use the function ‘mpz_fits_slong_p` (Unimplemented).



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# File 'ext/gmpz.c', line 863

VALUE r_gmpz_to_d(VALUE self)
{
  MP_INT *self_val;
  mpz_get_struct(self, self_val);

  return rb_float_new(mpz_get_d(self_val));
}

#to_i ⇒ Object

TODO:

Implement mpz_fits_slong_p

Returns a as an Fixnum if a fits into a Fixnum.

Otherwise returns the least significant part of a, with the same sign as a.

If a is too big to fit in a Fixnum, the returned result is probably not very useful. To find out if the value will fit, use the function ‘mpz_fits_slong_p` (Unimplemented).



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# File 'ext/gmpz.c', line 826

VALUE r_gmpz_to_i(VALUE self)
{
  MP_INT *self_val;
  char *str;
  VALUE res;

  mpz_get_struct (self, self_val);
  if (mpz_fits_slong_p (self_val)) {
#ifdef RUBY_ENGINE_JRUBY
    /* JRuby has this as INT2FIX which is no good. Patch. */
    return FIXABLE (mpz_get_si (self_val)) ? LONG2FIX (mpz_get_si (self_val)) : rb_ll2inum (mpz_get_si (self_val));
#else
    return rb_int2inum (mpz_get_si (self_val));
#endif
  }

  str = mpz_get_str (NULL, 0, self_val);
  res = rb_cstr2inum (str, 10);
  free (str);
  return res;
}

#to_s(base = 10) ⇒ Object #to_s(: bin) ⇒ Object #to_s(: oct) ⇒ Object #to_s(: dec) ⇒ Object #to_s(: hex) ⇒ Object Also known as: inspect

Returns a, as a String. If ‘base` is not provided, then the decimal representation will be returned.

From the GMP Manual:

Convert a to a string of digits in base ‘base`. The `base` argument may vary from 2 to 62 or from -2 to -36.

For ‘base` in the range 2..36, digits and lower-case letters are used; for -2..-36, digits and upper-case letters are used; for 37..62, digits, upper-case letters, and lower-case letters (in that significance order) are used.



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# File 'ext/gmpz.c', line 893

VALUE r_gmpz_to_s(int argc, VALUE *argv, VALUE self_val)
{
  MP_INT *self;
  char *str;
  VALUE res;
  VALUE base_val;
  unsigned int base;

  rb_scan_args(argc, argv, "01", &base_val);
  if (NIL_P(base_val)) { base = 10; }                /* default value */
  else { base = get_base(base_val); }

  Data_Get_Struct(self_val, MP_INT, self);
  str = mpz_get_str(NULL, base, self);
  res = rb_str_new2(str);
  free (str);

  return res;
}

#tshr(d) ⇒ Object

Divides n by _2^d_, forming a quotient q. tshr rounds q towards zero. The t stands for “truncate”.

q will satisfy _n=q*d+r_, and r will satisfy _0 <= abs(r ) < abs(d)_.

This function calculates only the quotient.

#|(b) ⇒ Object

Returns a bitwise inclusive-or b. b must be an instance of one of the following:

  • GMP::Z

  • Fixnum

  • Bignum