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 



608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
 
# File 'ext/gmpz.c', line 608

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

.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.

.congruent? ⇒ Boolean

Returns:

  • (Boolean)

.divexact ⇒ Object

Functional Mappings

.divisible? ⇒ Boolean

Returns:

  • (Boolean)

.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.



1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
 
# File 'ext/gmpz.c', line 1864

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



1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
 
# File 'ext/gmpz.c', line 1016

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



846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
 
# File 'ext/gmpz.c', line 846

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



928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
 
# File 'ext/gmpz.c', line 928

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.



2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
 
# File 'ext/gmpz.c', line 2108

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.



2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
 
# File 'ext/gmpz.c', line 2426

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.



2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
 
# File 'ext/gmpz.c', line 2397

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



893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
 
# File 'ext/gmpz.c', line 893

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



1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
 
# File 'ext/gmpz.c', line 1059

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 



23
24
25
26
 
# 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

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



1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
 
# File 'ext/gmpz.c', line 1435

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 b.class == GMP::Z, and a.hash == b.hash.

Returns:

  • (Boolean)

Since:

  • 0.4.7



2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
 
# File 'ext/gmpz.c', line 2228

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



1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
 
# File 'ext/gmpz.c', line 1761

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 b.class == GMP::Z, and a.hash == b.hash.

Since:

  • 0.4.7



2252
2253
2254
2255
2256
2257
 
# File 'ext/gmpz.c', line 2252

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



1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
 
# File 'ext/gmpz.c', line 1810

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.



1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
 
# File 'ext/gmpz.c', line 1843

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.



1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
 
# File 'ext/gmpz.c', line 1927

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.



1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
 
# File 'ext/gmpz.c', line 1515

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.



1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
 
# File 'ext/gmpz.c', line 1950

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.



2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
 
# File 'ext/gmpz.c', line 2349

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.



2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
 
# File 'ext/gmpz.c', line 2375

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.



2211
2212
2213
2214
2215
2216
 
# File 'ext/gmpz.c', line 2211

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



2514
2515
2516
2517
2518
2519
 
# File 'ext/gmpz.c', line 2514

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



2493
2494
2495
2496
2497
2498
 
# File 'ext/gmpz.c', line 2493

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



981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
 
# File 'ext/gmpz.c', line 981

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



1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
 
# File 'ext/gmpz.c', line 1113

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



689
690
691
692
693
694
695
696
697
698
699
 
# File 'ext/gmpz.c', line 689

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).



749
750
751
752
753
754
755
 
# File 'ext/gmpz.c', line 749

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).



720
721
722
723
724
725
726
727
728
729
730
731
732
733
 
# File 'ext/gmpz.c', line 720

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.



779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
 
# File 'ext/gmpz.c', line 779

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