Class: GMP::Z

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

Overview

GMP Multiple Precision Integer.

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

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(*args) ⇒ Object 



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# File 'ext/gmpz.c', line 498

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

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

Class Method Details

.abs ⇒ Object

call-seq:

a.abs

Returns the absolute value of a.

.add ⇒ Object

call-seq:

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

…

.addmul ⇒ Object

.cdiv_q_2exp ⇒ Object

.cdiv_r_2exp ⇒ Object

.com ⇒ Object

call-seq:

a.com

Returns the one’s complement of a.

.divexact ⇒ Object

Functional Mappings

.fac ⇒ Object

call-seq:

GMP::Z.fac(n)

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

.fib ⇒ Object

call-seq:

GMP::Z.fib(n)

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.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 1734

VALUE r_gmpzsg_jacobi(VALUE klass, VALUE a, VALUE b)
{
  MP_INT *a_val, *b_val;
  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 ⇒ Object

Functional Mappings

.mul ⇒ Object

.mul_2exp ⇒ Object

.neg ⇒ Object

call-seq:

a.neg
-a

Returns -a.

.new ⇒ Object

Initializing, Assigning Integers

.nextprime ⇒ Object

call-seq:

n.nextprime
n.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.

.pow ⇒ Object

call-seq:

GMP::Z.pow(a, b)

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

.sqrt ⇒ Object

call-seq:

a.sqrt

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

#% ⇒ Object

#& ⇒ Object

call-seq:

a & b

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 886

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

  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);
    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;
}

#** ⇒ Object

call-seq:

a ** b

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 716

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

  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 798

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;
  VALUE res;
  unsigned long prec;

  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

#/ ⇒ Object

Integer Division

#< ⇒ Object

call-seq:

a < b

Returns whether a is strictly less than b.

#<< ⇒ Object

call-seq:

a << n

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

#<= ⇒ Object

call-seq:

a <= b

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 1978

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);
}

#== ⇒ Object

#> ⇒ Object

call-seq:

a > b

Returns whether a is strictly greater than b.

#>= ⇒ Object

call-seq:

a >= b

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 2296

VALUE r_gmpz_getbit(VALUE self, VALUE bitnr)
{
  MP_INT *self_val;
  unsigned long bitnr_val;
  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 2267

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

  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;
}

#^ ⇒ Object

call-seq:

a ^ b

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

call-seq:

a.abs!

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 763

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 929

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)) {
    if (FIX2NUM(c) < 0)
    {
      if (free_b_val) { mpz_temp_free(b_val); }
      rb_raise(rb_eRangeError, "multiplicand (Fixnum) must be nonnegative");
    }
    mpz_addmul_ui(self_val, b_val, FIX2NUM(c));
  } else if (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 ⇒ Object

call-seq:

n.cdiv(d)

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 ⇒ Object

call-seq:

n.cmod(d)

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 ⇒ Object

#coerce(arg) ⇒ Object 



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# File 'ext/gmp.c', line 65

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

#com ⇒ Object

call-seq:

a.com

Returns the one’s complement of a.

#com! ⇒ Object

call-seq:

a.com!

Sets a to its one’s complement.

#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 1305

static VALUE r_gmpz_divisible(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val;
  int res;
  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 (FIXNUM_P (arg)) {
    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 a.hash == b.hash.

Returns:

  • (Boolean)

Since:

  • 0.4.7



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# File 'ext/gmpz.c', line 2098

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

call-seq:

a.even?

Determines whether a is even. Returns true or false.

Returns:

  • (Boolean)

#fdiv ⇒ Object

call-seq:

n.fdiv(d)

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 ⇒ Object

call-seq:

n.fmod(d)

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 ⇒ Object

#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 1631

VALUE r_gmpz_gcdext(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val, *res_val, *s_val, *t_val;
  VALUE res, s, t, 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;
}

#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 a.hash == b.hash.

Since:

  • 0.4.7



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# File 'ext/gmpz.c', line 2122

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);
}

#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 1680

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

  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 1713

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

#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 1797

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

call-seq:

a.neg
-a

Returns -a.

#neg! ⇒ Object

call-seq:

a.neg!

Sets a to -a.

#nextprime ⇒ Object Also known as: next_prime

call-seq:

n.nextprime
n.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 Also known as: next_prime!

call-seq:

n.nextprime!
n.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

call-seq:

a.odd?

Determines whether a is odd. Returns true or false.

Returns:

  • (Boolean)

#popcount ⇒ Object

call-seq:

a.popcount

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

call-seq:

p.power?

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 1385

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? ⇒ Boolean

Number Theoretic Functions

Returns:

  • (Boolean)

#remove(f) ⇒ Object

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



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# File 'ext/gmpz.c', line 1820

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;

  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 ⇒ Object

call-seq:

a.root(b)

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

#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 2219

VALUE r_gmpz_scan0(VALUE self, VALUE bitnr)
{
  MP_INT *self_val;
  int bitnr_val;
  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 2245

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

  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 2081

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 2384

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 2363

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 ⇒ Object Also known as: size_in_base

#sqrt ⇒ Object

call-seq:

a.sqrt

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

#sqrt! ⇒ Object

call-seq:

a.sqrt!

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

#sqrtrem ⇒ Object

#square? ⇒ Boolean

call-seq:

p.square?

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 851

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 983

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)) {
    if (FIX2NUM(c) < 0)
    {
      if (free_b_val) { mpz_temp_free(b_val); }
      rb_raise(rb_eRangeError, "multiplicand (Fixnum) must be nonnegative");
    }
    mpz_submul_ui(self_val, b_val, FIX2NUM(c));
  } else if (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);
    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 559

VALUE r_gmpz_swap(VALUE self, VALUE arg)
{
  MP_INT *self_val, *arg_val;
  if (!GMPZ_P(arg)) {
    rb_raise(rb_eTypeError, "Can't swap GMP::Z with object of other class");
  }
  mpz_get_struct(self, self_val);
  mpz_get_struct(arg, arg_val);
  mpz_swap(self_val,arg_val);
  return Qnil;
}

#tdiv ⇒ Object

call-seq:

n.tdiv(d)

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 ⇒ Object

call-seq:

n.tmod(d)

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 619

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 590

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))
    return rb_int2inum(mpz_get_si(self_val));
  str = mpz_get_str(NULL, 0, self_val);
  res = rb_cstr2inum(str, 10);
  free(str);
  return res;
}

#to_s(*args) ⇒ Object

call-seq:

a.to_s(base = 10)
a.to_s(:bin)
a.to_s(:oct)
a.to_s(:dec)
a.to_s(:hex)

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 649

VALUE r_gmpz_to_s(int argc, VALUE *argv, VALUE self)
{
  MP_INT *self_val;
  char *str;
  VALUE res;
  VALUE base;
  int base_val = 10;
  ID base_id;
  const char * bin_base = "bin";                            /* binary */
  const char * oct_base = "oct";                             /* octal */
  const char * dec_base = "dec";                           /* decimal */
  const char * hex_base = "hex";                       /* hexadecimal */
  ID bin_base_id = rb_intern(bin_base);
  ID oct_base_id = rb_intern(oct_base);
  ID dec_base_id = rb_intern(dec_base);
  ID hex_base_id = rb_intern(hex_base);  
  
  rb_scan_args(argc, argv, "01", &base);
  if (NIL_P(base)) { base = INT2FIX(10); }           /* default value */
  if (FIXNUM_P(base)) {
    base_val = FIX2INT(base);
    if ((base_val >=   2 && base_val <= 62) ||
        (base_val >= -36 && base_val <= -2)) {
      /* good base */
    } else {
      base_val = 10;
      rb_raise(rb_eRangeError, "base must be within [2, 62] or [-36, -2].");
    }
  } else if (SYMBOL_P(base)) {
    base_id = rb_to_id(base);
    if (base_id == bin_base_id) {
      base_val =  2;
    } else if (base_id == oct_base_id) {
      base_val =  8;
    } else if (base_id == dec_base_id) {
      base_val = 10;
    } else if (base_id == hex_base_id) {
      base_val = 16;
    } else {
      base_val = 10;  /* should raise an exception here. */
    }
  }

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

  return res;
}

#tshr ⇒ Object

call-seq:

n.tshr(d)

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.

#| ⇒ Object

call-seq:

a | b

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

  • GMP::Z

  • Fixnum

  • Bignum