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bignum.c
golf_prelude.rb
integer.rb
numeric.c
rational.c

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Class/Module Index

Integer

Holds Integer values. You cannot add a singleton method to an Integer object, any attempt to do so will raise a TypeError.

Constants

GMP_VERSION: The version of loaded GMP.

Public Class Methods

sqrt(n) → integer click to toggle source

Returns the integer square root of the non-negative integer n, i.e. the largest non-negative integer less than or equal to the square root of n.

Integer.sqrt(0)        #=> 0
Integer.sqrt(1)        #=> 1
Integer.sqrt(24)       #=> 4
Integer.sqrt(25)       #=> 5
Integer.sqrt(10**400)  #=> 10**200

Equivalent to Math.sqrt(n).floor, except that the result of the latter code may differ from the true value due to the limited precision of floating point arithmetic.

Integer.sqrt(10**46)     #=> 100000000000000000000000
Math.sqrt(10**46).floor  #=>  99999999999999991611392 (!)

If n is not an Integer, it is converted to an Integer first. If n is negative, a Math::DomainError is raised.

 
               static VALUE
rb_int_s_isqrt(VALUE self, VALUE num)
{
    unsigned long n, sq;
    num = rb_to_int(num);
    if (FIXNUM_P(num)) {
        if (FIXNUM_NEGATIVE_P(num)) {
            domain_error("isqrt");
        }
        n = FIX2ULONG(num);
        sq = rb_ulong_isqrt(n);
        return LONG2FIX(sq);
    }
    else {
        size_t biglen;
        if (RBIGNUM_NEGATIVE_P(num)) {
            domain_error("isqrt");
        }
        biglen = BIGNUM_LEN(num);
        if (biglen == 0) return INT2FIX(0);
#if SIZEOF_BDIGIT <= SIZEOF_LONG
        /* short-circuit */
        if (biglen == 1) {
            n = BIGNUM_DIGITS(num)[0];
            sq = rb_ulong_isqrt(n);
            return ULONG2NUM(sq);
        }
#endif
        return rb_big_isqrt(num);
    }
}

Public Instance Methods

int % other → real click to toggle source

Returns int modulo other.

See Numeric#divmod for more information.

 
               VALUE
rb_int_modulo(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_mod(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_modulo(x, y);
    }
    return num_modulo(x, y);
}

int & other_int → integer click to toggle source

Bitwise AND.

 
               VALUE
rb_int_and(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_and(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_and(x, y);
    }
    return Qnil;
}

int * numeric → numeric_result click to toggle source

Performs multiplication: the class of the resulting object depends on the class of numeric.

 
               VALUE
rb_int_mul(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_mul(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_mul(x, y);
    }
    return rb_num_coerce_bin(x, y, '*');
}

int ** numeric → numeric_result click to toggle source

Raises int to the power of numeric, which may be negative or fractional. The result may be an Integer, a Float, a Rational, or a complex number.

2 ** 3        #=> 8
2 ** -1       #=> (1/2)
2 ** 0.5      #=> 1.4142135623730951
(-1) ** 0.5   #=> (0.0+1.0i)

123456789 ** 2     #=> 15241578750190521
123456789 ** 1.2   #=> 5126464716.0993185
123456789 ** -2    #=> (1/15241578750190521)

 
               VALUE
rb_int_pow(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_pow(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_pow(x, y);
    }
    return Qnil;
}

int + numeric → numeric_result click to toggle source

Performs addition: the class of the resulting object depends on the class of numeric.

 
               VALUE
rb_int_plus(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_plus(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_plus(x, y);
    }
    return rb_num_coerce_bin(x, y, '+');
}

int - numeric → numeric_result click to toggle source

Performs subtraction: the class of the resulting object depends on the class of numeric.

 
               VALUE
rb_int_minus(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_minus(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_minus(x, y);
    }
    return rb_num_coerce_bin(x, y, '-');
}

-int → integer click to toggle source

Returns int, negated.

 
               # File integer.rb, line 6
def -@
  Primitive.attr! 'inline'
  Primitive.cexpr! 'rb_int_uminus(self)'
end

int / numeric → numeric_result click to toggle source

Performs division: the class of the resulting object depends on the class of numeric.

 
               VALUE
rb_int_div(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_div(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_div(x, y);
    }
    return Qnil;
}

int < real → true or false click to toggle source

Returns true if the value of int is less than that of real.

 
               static VALUE
int_lt(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_lt(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_lt(x, y);
    }
    return Qnil;
}

int << count → integer click to toggle source

Returns int shifted left count positions, or right if count is negative.

 
               VALUE
rb_int_lshift(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return rb_fix_lshift(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_lshift(x, y);
    }
    return Qnil;
}

int <= real → true or false click to toggle source

Returns true if the value of int is less than or equal to that of real.

 
               static VALUE
int_le(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_le(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_le(x, y);
    }
    return Qnil;
}

int <=> numeric → -1, 0, +1, or nil click to toggle source

Comparison---Returns -1, 0, or +1 depending on whether int is less than, equal to, or greater than numeric.

This is the basis for the tests in the Comparable module.

nil is returned if the two values are incomparable.

 
               VALUE
rb_int_cmp(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_cmp(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_cmp(x, y);
    }
    else {
        rb_raise(rb_eNotImpError, "need to define `<=>' in %s", rb_obj_classname(x));
    }
}

int == other → true or false click to toggle source

Returns true if int equals other numerically. Contrast this with Numeric#eql?, which requires other to be an Integer.

1 == 2     #=> false
1 == 1.0   #=> true

 
               VALUE
rb_int_equal(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_equal(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_eq(x, y);
    }
    return Qnil;
}

int == other → true or false click to toggle source

Returns true if int equals other numerically. Contrast this with Numeric#eql?, which requires other to be an Integer.

1 == 2     #=> false
1 == 1.0   #=> true

 
               VALUE
rb_int_equal(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_equal(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_eq(x, y);
    }
    return Qnil;
}

int > real → true or false click to toggle source

Returns true if the value of int is greater than that of real.

 
               VALUE
rb_int_gt(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_gt(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_gt(x, y);
    }
    return Qnil;
}

int >= real → true or false click to toggle source

Returns true if the value of int is greater than or equal to that of real.

 
               VALUE
rb_int_ge(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_ge(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_ge(x, y);
    }
    return Qnil;
}

int >> count → integer click to toggle source

Returns int shifted right count positions, or left if count is negative.

 
               static VALUE
rb_int_rshift(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return rb_fix_rshift(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_rshift(x, y);
    }
    return Qnil;
}

int[n] → 0, 1 click to toggle source

int[n, m] → num

int[range] → num

Bit Reference---Returns the nth bit in the binary representation of int, where int[0] is the least significant bit.

a = 0b11001100101010
30.downto(0) {|n| print a[n] }
#=> 0000000000000000011001100101010

a = 9**15
50.downto(0) {|n| print a[n] }
#=> 000101110110100000111000011110010100111100010111001

In principle, n[i] is equivalent to (n >> i) & 1. Thus, any negative index always returns zero:

p 255[-1] #=> 0

Range operations n[i, len] and n[i..j] are naturally extended.

n[i, len] equals to (n >> i) & ((1 << len) - 1).
n[i..j] equals to (n >> i) & ((1 << (j - i + 1)) - 1).
n[i...j] equals to (n >> i) & ((1 << (j - i)) - 1).
n[i..] equals to (n >> i).
n[..j] is zero if n & ((1 << (j + 1)) - 1) is zero. Otherwise, raises an ArgumentError.
n[...j] is zero if n & ((1 << j) - 1) is zero. Otherwise, raises an ArgumentError.

Note that range operation may exhaust memory. For example, -1[0, 1000000000000] will raise NoMemoryError.

 
               static VALUE
int_aref(int const argc, VALUE * const argv, VALUE const num)
{
    rb_check_arity(argc, 1, 2);
    if (argc == 2) {
        return int_aref2(num, argv[0], argv[1]);
    }
    return int_aref1(num, argv[0]);

    return Qnil;
}

int ^ other_int → integer click to toggle source

Bitwise EXCLUSIVE OR.

 
               static VALUE
int_xor(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_xor(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_xor(x, y);
    }
    return Qnil;
}

abs() click to toggle source

 
               # File integer.rb, line 27
def abs
  Primitive.attr! 'inline'
  Primitive.cexpr! 'rb_int_abs(self)'
end

allbits?(mask) → true or false click to toggle source

Returns true if all bits of int & mask are 1.

 
               static VALUE
int_allbits_p(VALUE num, VALUE mask)
{
    mask = rb_to_int(mask);
    return rb_int_equal(rb_int_and(num, mask), mask);
}

anybits?(mask) → true or false click to toggle source

Returns true if any bits of int & mask are 1.

 
               static VALUE
int_anybits_p(VALUE num, VALUE mask)
{
    mask = rb_to_int(mask);
    return int_zero_p(rb_int_and(num, mask)) ? Qfalse : Qtrue;
}

bit_length → integer click to toggle source

Returns the number of bits of the value of int.

“Number of bits” means the bit position of the highest bit which is different from the sign bit (where the least significant bit has bit position 1). If there is no such bit (zero or minus one), zero is returned.

I.e. this method returns ceil(log2(int < 0 ? -int : int+1)).

(-2**1000-1).bit_length   #=> 1001
(-2**1000).bit_length     #=> 1000
(-2**1000+1).bit_length   #=> 1000
(-2**12-1).bit_length     #=> 13
(-2**12).bit_length       #=> 12
(-2**12+1).bit_length     #=> 12
-0x101.bit_length         #=> 9
-0x100.bit_length         #=> 8
-0xff.bit_length          #=> 8
-2.bit_length             #=> 1
-1.bit_length             #=> 0
0.bit_length              #=> 0
1.bit_length              #=> 1
0xff.bit_length           #=> 8
0x100.bit_length          #=> 9
(2**12-1).bit_length      #=> 12
(2**12).bit_length        #=> 13
(2**12+1).bit_length      #=> 13
(2**1000-1).bit_length    #=> 1000
(2**1000).bit_length      #=> 1001
(2**1000+1).bit_length    #=> 1001

This method can be used to detect overflow in Array#pack as follows:

if n.bit_length < 32
  [n].pack("l") # no overflow
else
  raise "overflow"
end

 
               # File integer.rb, line 73
def bit_length
  Primitive.attr! 'inline'
  Primitive.cexpr! 'rb_int_bit_length(self)'
end

ceil([ndigits]) → integer or float click to toggle source

Returns the smallest number greater than or equal to int with a precision of ndigits decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least ndigits.abs trailing zeros.

Returns self when ndigits is zero or positive.

1.ceil           #=> 1
1.ceil(2)        #=> 1
18.ceil(-1)      #=> 20
(-18).ceil(-1)   #=> -10

 
               static VALUE
int_ceil(int argc, VALUE* argv, VALUE num)
{
    int ndigits;

    if (!rb_check_arity(argc, 0, 1)) return num;
    ndigits = NUM2INT(argv[0]);
    if (ndigits >= 0) {
        return num;
    }
    return rb_int_ceil(num, ndigits);
}

chr([encoding]) → string click to toggle source

Returns a string containing the character represented by the int's value according to encoding.

65.chr    #=> "A"
230.chr   #=> "\xE6"
255.chr(Encoding::UTF_8)   #=> "\u00FF"

 
               static VALUE
int_chr(int argc, VALUE *argv, VALUE num)
{
    char c;
    unsigned int i;
    rb_encoding *enc;

    if (rb_num_to_uint(num, &i) == 0) {
    }
    else if (FIXNUM_P(num)) {
        rb_raise(rb_eRangeError, "%ld out of char range", FIX2LONG(num));
    }
    else {
        rb_raise(rb_eRangeError, "bignum out of char range");
    }

    switch (argc) {
      case 0:
        if (0xff < i) {
            enc = rb_default_internal_encoding();
            if (!enc) {
                rb_raise(rb_eRangeError, "%u out of char range", i);
            }
            goto decode;
        }
        c = (char)i;
        if (i < 0x80) {
            return rb_usascii_str_new(&c, 1);
        }
        else {
            return rb_str_new(&c, 1);
        }
      case 1:
        break;
      default:
        rb_error_arity(argc, 0, 1);
    }
    enc = rb_to_encoding(argv[0]);
    if (!enc) enc = rb_ascii8bit_encoding();
  decode:
    return rb_enc_uint_chr(i, enc);
}

coerce(numeric) → array click to toggle source

Returns an array with both a numeric and a big represented as Bignum objects.

This is achieved by converting numeric to a Bignum.

A TypeError is raised if the numeric is not a Fixnum or Bignum type.

(0x3FFFFFFFFFFFFFFF+1).coerce(42)   #=> [42, 4611686018427387904]

 
               static VALUE
rb_int_coerce(VALUE x, VALUE y)
{
    if (RB_INTEGER_TYPE_P(y)) {
        return rb_assoc_new(y, x);
    }
    else {
        x = rb_Float(x);
        y = rb_Float(y);
        return rb_assoc_new(y, x);
    }
}

denominator → 1 click to toggle source

Returns 1.

 
               static VALUE
integer_denominator(VALUE self)
{
    return INT2FIX(1);
}

digits → array click to toggle source

digits(base) → array

Returns the digits of int's place-value representation with radix base (default: 10). The digits are returned as an array with the least significant digit as the first array element.

base must be greater than or equal to 2.

12345.digits      #=> [5, 4, 3, 2, 1]
12345.digits(7)   #=> [4, 6, 6, 0, 5]
12345.digits(100) #=> [45, 23, 1]

-12345.digits(7)  #=> Math::DomainError

 
               static VALUE
rb_int_digits(int argc, VALUE *argv, VALUE num)
{
    VALUE base_value;
    long base;

    if (rb_num_negative_p(num))
        rb_raise(rb_eMathDomainError, "out of domain");

    if (rb_check_arity(argc, 0, 1)) {
        base_value = rb_to_int(argv[0]);
        if (!RB_INTEGER_TYPE_P(base_value))
            rb_raise(rb_eTypeError, "wrong argument type %s (expected Integer)",
                     rb_obj_classname(argv[0]));
        if (RB_TYPE_P(base_value, T_BIGNUM))
            return rb_int_digits_bigbase(num, base_value);

        base = FIX2LONG(base_value);
        if (base < 0)
            rb_raise(rb_eArgError, "negative radix");
        else if (base < 2)
            rb_raise(rb_eArgError, "invalid radix %ld", base);
    }
    else
        base = 10;

    if (FIXNUM_P(num))
        return rb_fix_digits(num, base);
    else if (RB_TYPE_P(num, T_BIGNUM))
        return rb_int_digits_bigbase(num, LONG2FIX(base));

    return Qnil;
}

div(numeric) → integer click to toggle source

Performs integer division: returns the integer result of dividing int by numeric.

 
               VALUE
rb_int_idiv(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_idiv(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_idiv(x, y);
    }
    return num_div(x, y);
}

divmod(numeric) → array click to toggle source

See Numeric#divmod.

 
               VALUE
rb_int_divmod(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_divmod(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_divmod(x, y);
    }
    return Qnil;
}

downto(limit) {|i| block } → self click to toggle source

downto(limit) → an_enumerator

Iterates the given block, passing in decreasing values from int down to and including limit.

If no block is given, an Enumerator is returned instead.

5.downto(1) { |n| print n, ".. " }
puts "Liftoff!"
#=> "5.. 4.. 3.. 2.. 1.. Liftoff!"

 
               static VALUE
int_downto(VALUE from, VALUE to)
{
    RETURN_SIZED_ENUMERATOR(from, 1, &to, int_downto_size);
    if (FIXNUM_P(from) && FIXNUM_P(to)) {
        long i, end;

        end = FIX2LONG(to);
        for (i=FIX2LONG(from); i >= end; i--) {
            rb_yield(LONG2FIX(i));
        }
    }
    else {
        VALUE i = from, c;

        while (!(c = rb_funcall(i, '<', 1, to))) {
            rb_yield(i);
            i = rb_funcall(i, '-', 1, INT2FIX(1));
        }
        if (NIL_P(c)) rb_cmperr(i, to);
    }
    return from;
}

each() click to toggle source

Alias for: times

even? → true or false click to toggle source

Returns true if int is an even number.

 
               # File integer.rb, line 82
def even?
  Primitive.attr! 'inline'
  Primitive.cexpr! 'rb_int_even_p(self)'
end

fdiv(numeric) → float click to toggle source

Returns the floating point result of dividing int by numeric.

654321.fdiv(13731)      #=> 47.652829364212366
654321.fdiv(13731.24)   #=> 47.65199646936475
-654321.fdiv(13731)     #=> -47.652829364212366

 
               VALUE
rb_int_fdiv(VALUE x, VALUE y)
{
    if (RB_INTEGER_TYPE_P(x)) {
        return DBL2NUM(rb_int_fdiv_double(x, y));
    }
    return Qnil;
}

floor([ndigits]) → integer or float click to toggle source

Returns the largest number less than or equal to int with a precision of ndigits decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least ndigits.abs trailing zeros.

Returns self when ndigits is zero or positive.

1.floor           #=> 1
1.floor(2)        #=> 1
18.floor(-1)      #=> 10
(-18).floor(-1)   #=> -20

 
               static VALUE
int_floor(int argc, VALUE* argv, VALUE num)
{
    int ndigits;

    if (!rb_check_arity(argc, 0, 1)) return num;
    ndigits = NUM2INT(argv[0]);
    if (ndigits >= 0) {
        return num;
    }
    return rb_int_floor(num, ndigits);
}

gcd(other_int) → integer click to toggle source

Returns the greatest common divisor of the two integers. The result is always positive. 0.gcd(x) and x.gcd(0) return x.abs.

36.gcd(60)                  #=> 12
2.gcd(2)                    #=> 2
3.gcd(-7)                   #=> 1
((1<<31)-1).gcd((1<<61)-1)  #=> 1

 
               VALUE
rb_gcd(VALUE self, VALUE other)
{
    other = nurat_int_value(other);
    return f_gcd(self, other);
}

gcdlcm(other_int) → array click to toggle source

Returns an array with the greatest common divisor and the least common multiple of the two integers, [gcd, lcm].

36.gcdlcm(60)                  #=> [12, 180]
2.gcdlcm(2)                    #=> [2, 2]
3.gcdlcm(-7)                   #=> [1, 21]
((1<<31)-1).gcdlcm((1<<61)-1)  #=> [1, 4951760154835678088235319297]

 
               VALUE
rb_gcdlcm(VALUE self, VALUE other)
{
    other = nurat_int_value(other);
    return rb_assoc_new(f_gcd(self, other), f_lcm(self, other));
}

inspect(*args) click to toggle source

Alias for: to_s

integer? → true click to toggle source

Since int is already an Integer, this always returns true.

 
               # File integer.rb, line 91
def integer?
  return true
end

lcm(other_int) → integer click to toggle source

Returns the least common multiple of the two integers. The result is always positive. 0.lcm(x) and x.lcm(0) return zero.

36.lcm(60)                  #=> 180
2.lcm(2)                    #=> 2
3.lcm(-7)                   #=> 21
((1<<31)-1).lcm((1<<61)-1)  #=> 4951760154835678088235319297

 
               VALUE
rb_lcm(VALUE self, VALUE other)
{
    other = nurat_int_value(other);
    return f_lcm(self, other);
}

magnitude() click to toggle source

 
               # File integer.rb, line 95
def magnitude
  Primitive.attr! 'inline'
  Primitive.cexpr! 'rb_int_abs(self)'
end

modulo(other) → real click to toggle source

Returns int modulo other.

See Numeric#divmod for more information.

 
               VALUE
rb_int_modulo(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_mod(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_modulo(x, y);
    }
    return num_modulo(x, y);
}

next → integer click to toggle source

Returns the successor of int, i.e. the Integer equal to int+1.

1.next      #=> 2
(-1).next   #=> 0
1.succ      #=> 2
(-1).succ   #=> 0

 
               VALUE
rb_int_succ(VALUE num)
{
    if (FIXNUM_P(num)) {
        long i = FIX2LONG(num) + 1;
        return LONG2NUM(i);
    }
    if (RB_TYPE_P(num, T_BIGNUM)) {
        return rb_big_plus(num, INT2FIX(1));
    }
    return num_funcall1(num, '+', INT2FIX(1));
}

nobits?(mask) → true or false click to toggle source

Returns true if no bits of int & mask are 1.

 
               static VALUE
int_nobits_p(VALUE num, VALUE mask)
{
    mask = rb_to_int(mask);
    return int_zero_p(rb_int_and(num, mask));
}

numerator → self click to toggle source

Returns self.

 
               static VALUE
integer_numerator(VALUE self)
{
    return self;
}

odd? → true or false click to toggle source

Returns true if int is an odd number.

 
               # File integer.rb, line 104
def odd?
  Primitive.attr! 'inline'
  Primitive.cexpr! 'rb_int_odd_p(self)'
end

ord → self click to toggle source

Returns the int itself.

97.ord   #=> 97

This method is intended for compatibility to character literals in Ruby 1.9.

For example, ?a.ord returns 97 both in 1.8 and 1.9.

 
               # File integer.rb, line 120
def ord
  return self
end

pow(numeric) → numeric click to toggle source

pow(integer, integer) → integer

Returns (modular) exponentiation as:

a.pow(b)     #=> same as a**b
a.pow(b, m)  #=> same as (a**b) % m, but avoids huge temporary values

 
               VALUE
rb_int_powm(int const argc, VALUE * const argv, VALUE const num)
{
    rb_check_arity(argc, 1, 2);

    if (argc == 1) {
        return rb_int_pow(num, argv[0]);
    }
    else {
        VALUE const a = num;
        VALUE const b = argv[0];
        VALUE m = argv[1];
        int nega_flg = 0;
        if ( ! RB_INTEGER_TYPE_P(b)) {
            rb_raise(rb_eTypeError, "Integer#pow() 2nd argument not allowed unless a 1st argument is integer");
        }
        if (rb_int_negative_p(b)) {
            rb_raise(rb_eRangeError, "Integer#pow() 1st argument cannot be negative when 2nd argument specified");
        }
        if (!RB_INTEGER_TYPE_P(m)) {
            rb_raise(rb_eTypeError, "Integer#pow() 2nd argument not allowed unless all arguments are integers");
        }

        if (rb_int_negative_p(m)) {
            m = rb_int_uminus(m);
            nega_flg = 1;
        }

        if (FIXNUM_P(m)) {
            long const half_val = (long)HALF_LONG_MSB;
            long const mm = FIX2LONG(m);
            if (!mm) rb_num_zerodiv();
            if (mm == 1) return INT2FIX(0);
            if (mm <= half_val) {
                return int_pow_tmp1(rb_int_modulo(a, m), b, mm, nega_flg);
            }
            else {
                return int_pow_tmp2(rb_int_modulo(a, m), b, mm, nega_flg);
            }
        }
        else {
            if (rb_bigzero_p(m)) rb_num_zerodiv();
	    if (bignorm(m) == INT2FIX(1)) return INT2FIX(0);
            return int_pow_tmp3(rb_int_modulo(a, m), b, m, nega_flg);
        }
    }
    UNREACHABLE_RETURN(Qnil);
}

pred → integer click to toggle source

Returns the predecessor of int, i.e. the Integer equal to int-1.

1.pred      #=> 0
(-1).pred   #=> -2

 
               static VALUE
rb_int_pred(VALUE num)
{
    if (FIXNUM_P(num)) {
        long i = FIX2LONG(num) - 1;
        return LONG2NUM(i);
    }
    if (RB_TYPE_P(num, T_BIGNUM)) {
        return rb_big_minus(num, INT2FIX(1));
    }
    return num_funcall1(num, '-', INT2FIX(1));
}

rationalize([eps]) → rational click to toggle source

Returns the value as a rational. The optional argument eps is always ignored.

 
               static VALUE
integer_rationalize(int argc, VALUE *argv, VALUE self)
{
    rb_check_arity(argc, 0, 1);
    return integer_to_r(self);
}

remainder(numeric) → real click to toggle source

Returns the remainder after dividing int by numeric.

x.remainder(y) means x-y*(x/y).truncate.

5.remainder(3)     #=> 2
-5.remainder(3)    #=> -2
5.remainder(-3)    #=> 2
-5.remainder(-3)   #=> -2
5.remainder(1.5)   #=> 0.5

See Numeric#divmod.

 
               static VALUE
int_remainder(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return num_remainder(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_remainder(x, y);
    }
    return Qnil;
}

round([ndigits] [, half: mode]) → integer or float click to toggle source

Returns int rounded to the nearest value with a precision of ndigits decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least ndigits.abs trailing zeros.

Returns self when ndigits is zero or positive.

1.round           #=> 1
1.round(2)        #=> 1
15.round(-1)      #=> 20
(-15).round(-1)   #=> -20

The optional half keyword argument is available similar to Float#round.

25.round(-1, half: :up)      #=> 30
25.round(-1, half: :down)    #=> 20
25.round(-1, half: :even)    #=> 20
35.round(-1, half: :up)      #=> 40
35.round(-1, half: :down)    #=> 30
35.round(-1, half: :even)    #=> 40
(-25).round(-1, half: :up)   #=> -30
(-25).round(-1, half: :down) #=> -20
(-25).round(-1, half: :even) #=> -20

 
               static VALUE
int_round(int argc, VALUE* argv, VALUE num)
{
    int ndigits;
    int mode;
    VALUE nd, opt;

    if (!rb_scan_args(argc, argv, "01:", &nd, &opt)) return num;
    ndigits = NUM2INT(nd);
    mode = rb_num_get_rounding_option(opt);
    if (ndigits >= 0) {
        return num;
    }
    return rb_int_round(num, ndigits, mode);
}

size → int click to toggle source

Returns the number of bytes in the machine representation of int (machine dependent).

1.size               #=> 8
-1.size              #=> 8
2147483647.size      #=> 8
(256**10 - 1).size   #=> 10
(256**20 - 1).size   #=> 20
(256**40 - 1).size   #=> 40

 
               static VALUE
int_size(VALUE num)
{
    if (FIXNUM_P(num)) {
        return fix_size(num);
    }
    else if (RB_TYPE_P(num, T_BIGNUM)) {
        return rb_big_size_m(num);
    }
    return Qnil;
}

succ → integer click to toggle source

Returns the successor of int, i.e. the Integer equal to int+1.

1.next      #=> 2
(-1).next   #=> 0
1.succ      #=> 2
(-1).succ   #=> 0

 
               VALUE
rb_int_succ(VALUE num)
{
    if (FIXNUM_P(num)) {
        long i = FIX2LONG(num) + 1;
        return LONG2NUM(i);
    }
    if (RB_TYPE_P(num, T_BIGNUM)) {
        return rb_big_plus(num, INT2FIX(1));
    }
    return num_funcall1(num, '+', INT2FIX(1));
}

times {|i| block } → self click to toggle source

times → an_enumerator

Iterates the given block int times, passing in values from zero to int - 1.

If no block is given, an Enumerator is returned instead.

5.times {|i| print i, " " }   #=> 0 1 2 3 4

 
               static VALUE
int_dotimes(VALUE num)
{
    RETURN_SIZED_ENUMERATOR(num, 0, 0, int_dotimes_size);

    if (FIXNUM_P(num)) {
        long i, end;

        end = FIX2LONG(num);
        for (i=0; i<end; i++) {
            rb_yield_1(LONG2FIX(i));
        }
    }
    else {
        VALUE i = INT2FIX(0);

        for (;;) {
            if (!RTEST(rb_funcall(i, '<', 1, num))) break;
            rb_yield(i);
            i = rb_funcall(i, '+', 1, INT2FIX(1));
        }
    }
    return num;
}

Also aliased as: each

to_f → float click to toggle source

Converts int to a Float. If int doesn't fit in a Float, the result is infinity.

 
               static VALUE
int_to_f(VALUE num)
{
    double val;

    if (FIXNUM_P(num)) {
        val = (double)FIX2LONG(num);
    }
    else if (RB_TYPE_P(num, T_BIGNUM)) {
        val = rb_big2dbl(num);
    }
    else {
        rb_raise(rb_eNotImpError, "Unknown subclass for to_f: %s", rb_obj_classname(num));
    }

    return DBL2NUM(val);
}

to_i → integer click to toggle source

Since int is already an Integer, returns self.

to_int is an alias for to_i.

 
               # File integer.rb, line 130
def to_i
  return self
end

to_int → integer click to toggle source

Since int is already an Integer, returns self.

 
               # File integer.rb, line 138
def to_int
  return self
end

to_r → rational click to toggle source

Returns the value as a rational.

1.to_r        #=> (1/1)
(1<<64).to_r  #=> (18446744073709551616/1)

 
               static VALUE
integer_to_r(VALUE self)
{
    return rb_rational_new1(self);
}

to_s(base=10) → string click to toggle source

Returns a string containing the place-value representation of int with radix base (between 2 and 36).

12345.to_s       #=> "12345"
12345.to_s(2)    #=> "11000000111001"
12345.to_s(8)    #=> "30071"
12345.to_s(10)   #=> "12345"
12345.to_s(16)   #=> "3039"
12345.to_s(36)   #=> "9ix"
78546939656932.to_s(36)  #=> "rubyrules"

 
               static VALUE
int_to_s(int argc, VALUE *argv, VALUE x)
{
    int base;

    if (rb_check_arity(argc, 0, 1))
        base = NUM2INT(argv[0]);
    else
        base = 10;
    return rb_int2str(x, base);
}

Also aliased as: inspect

truncate([ndigits]) → integer or float click to toggle source

Returns int truncated (toward zero) to a precision of ndigits decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least ndigits.abs trailing zeros.

Returns self when ndigits is zero or positive.

1.truncate           #=> 1
1.truncate(2)        #=> 1
18.truncate(-1)      #=> 10
(-18).truncate(-1)   #=> -10

 
               static VALUE
int_truncate(int argc, VALUE* argv, VALUE num)
{
    int ndigits;

    if (!rb_check_arity(argc, 0, 1)) return num;
    ndigits = NUM2INT(argv[0]);
    if (ndigits >= 0) {
        return num;
    }
    return rb_int_truncate(num, ndigits);
}

upto(limit) {|i| block } → self click to toggle source

upto(limit) → an_enumerator

Iterates the given block, passing in integer values from int up to and including limit.

If no block is given, an Enumerator is returned instead.

5.upto(10) {|i| print i, " " }   #=> 5 6 7 8 9 10

 
               static VALUE
int_upto(VALUE from, VALUE to)
{
    RETURN_SIZED_ENUMERATOR(from, 1, &to, int_upto_size);
    if (FIXNUM_P(from) && FIXNUM_P(to)) {
        long i, end;

        end = FIX2LONG(to);
        for (i = FIX2LONG(from); i <= end; i++) {
            rb_yield(LONG2FIX(i));
        }
    }
    else {
        VALUE i = from, c;

        while (!(c = rb_funcall(i, '>', 1, to))) {
            rb_yield(i);
            i = rb_funcall(i, '+', 1, INT2FIX(1));
        }
        ensure_cmp(c, i, to);
    }
    return from;
}

zero? → true or false click to toggle source

Returns true if int has a zero value.

 
               # File integer.rb, line 146
def zero?
  Primitive.attr! 'inline'
  Primitive.cexpr! 'rb_int_zero_p(self)'
end

int | other_int → integer click to toggle source

Bitwise OR.

 
               static VALUE
int_or(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_or(x, y);
    }
    else if (RB_TYPE_P(x, T_BIGNUM)) {
        return rb_big_or(x, y);
    }
    return Qnil;
}

~int → integer click to toggle source

One’s complement: returns a number where each bit is flipped.

Inverts the bits in an Integer. As integers are conceptually of infinite length, the result acts as if it had an infinite number of one bits to the left. In hex representations, this is displayed as two periods to the left of the digits.

sprintf("%X", ~0x1122334455)    #=> "..FEEDDCCBBAA"

 
               # File integer.rb, line 22
def ~
  Primitive.attr! 'inline'
  Primitive.cexpr! 'rb_int_comp(self)'
end

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