### In Files

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

Quicksearch

# Integer

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

GMP_VERSION

### 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`.

```
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

Comparisonâ€”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 Referenceâ€”Returns the `n`th 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
{
}
```
anybits?(mask) → true or false click to toggle source

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

```
static VALUE
{
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`.

â€śNumber of bitsâ€ť 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)
else if (base < 2)
}
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`.

```
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
{
}
```
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
```