Class: Integer

Inherits:
Numeric show all
Defined in:
numeric.c,
numeric.c

Overview

******************************************************************

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

Constant Summary collapse

GMP_VERSION =

The version of loaded GMP.

rb_sprintf("GMP %s", gmp_version)

Class Method Summary collapse

Instance Method Summary collapse

Methods inherited from Numeric

#+@, #-@, #abs, #abs2, #angle, #arg, #clone, #conj, #conjugate, #dup, #eql?, #finite?, #i, #imag, #imaginary, #infinite?, #integer?, #magnitude, #negative?, #nonzero?, #phase, #polar, #positive?, #quo, #real, #real?, #rect, #rectangular, #singleton_method_added, #step, #to_c, #to_int, #zero?

Methods included from Comparable

#between?, #clamp

Class Method Details

.sqrt(n) ⇒ Integer

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.

Returns:



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# File 'numeric.c', line 5353

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);
    }
}

Instance Method Details

#%(other) ⇒ Object #modulo(other) ⇒ Object

Returns int modulo other.

See Numeric#divmod for more information.



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# File 'numeric.c', line 3872

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);
}

#&(other_int) ⇒ Integer

Bitwise AND.

Returns:



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# File 'numeric.c', line 4435

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;
}

#*(numeric) ⇒ Object

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



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# File 'numeric.c', line 3685

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, '*');
}

#**(numeric) ⇒ Object

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)



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# File 'numeric.c', line 4087

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;
}

#+(numeric) ⇒ Object

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



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# File 'numeric.c', line 3596

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, '+');
}

#-(numeric) ⇒ Object

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



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# File 'numeric.c', line 3635

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, '-');
}

#/(numeric) ⇒ Object

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



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# File 'numeric.c', line 3802

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;
}

#<(real) ⇒ Boolean

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

Returns:

  • (Boolean) 


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# File 'numeric.c', line 4313

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;
}

#<<(count) ⇒ Integer

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

Returns:



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# File 'numeric.c', line 4551

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;
}

#<=(real) ⇒ Boolean

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

Returns:

  • (Boolean) 


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# File 'numeric.c', line 4353

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;
}

#<=>(numeric) ⇒ -1, ...

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.

Returns:

  • (-1, 0, +1, nil) 


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# File 'numeric.c', line 4195

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));
    }
}

#==(other) ⇒ Boolean

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

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

Returns:

  • (Boolean) 


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# File 'numeric.c', line 4146

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;
}

#===(y) ⇒ Object 



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# File 'numeric.c', line 4146

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;
}

#>(real) ⇒ Boolean

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

Returns:

  • (Boolean) 


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# File 'numeric.c', line 4235

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;
}

#>=(real) ⇒ Boolean

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

Returns:

  • (Boolean) 


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# File 'numeric.c', line 4275

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;
}

#>>(count) ⇒ Integer

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

Returns:



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# File 'numeric.c', line 4598

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;
}

#[](n) ⇒ 0, 1 #[](n, m) ⇒ Numeric #[](range) ⇒ Numeric

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.

Overloads:



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# File 'numeric.c', line 4758

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;
}

#^(other_int) ⇒ Integer

Bitwise EXCLUSIVE OR.

Returns:



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# File 'numeric.c', line 4505

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;
}

#allbits?(mask) ⇒ Boolean

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

Returns:

  • (Boolean) 


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# File 'numeric.c', line 3285

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) ⇒ Boolean

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

Returns:

  • (Boolean) 


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# File 'numeric.c', line 3299

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;
}

#ceil([ndigits]) ⇒ Integer, Float

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

Returns:



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# File 'numeric.c', line 5239

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

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"

Returns:



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# File 'numeric.c', line 3412

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

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]

Returns:



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# File 'bignum.c', line 6745

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

Returns 1.

Returns:

  • (1) 


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# File 'rational.c', line 2059

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

#digits ⇒ Array #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

Overloads:



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# File 'numeric.c', line 4965

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

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

Returns:



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# File 'numeric.c', line 3829

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

See Numeric#divmod.

Returns:



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# File 'numeric.c', line 3949

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| ... } ⇒ self #downto(limit) ⇒ Object

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!"

Overloads:

  • #downto(limit) {|i| ... } ⇒ self

    Yields:

    • (i)

    Returns:

    • (self) 


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# File 'numeric.c', line 5065

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;
}

#fdiv(numeric) ⇒ Float

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

Returns:



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# File 'numeric.c', line 3747

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, Float

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

Returns:



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# File 'numeric.c', line 5207

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

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

Returns:



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# File 'rational.c', line 1888

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

#gcdlcm(other_int) ⇒ Array

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]

Returns:



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# File 'rational.c', line 1926

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

#lcm(other_int) ⇒ Integer

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

Returns:



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# File 'rational.c', line 1907

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

#%(other) ⇒ Object #modulo(other) ⇒ Object

Returns int modulo other.

See Numeric#divmod for more information.



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# File 'numeric.c', line 3872

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 #succ ⇒ Integer

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

Overloads:

#nobits?(mask) ⇒ Boolean

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

Returns:

  • (Boolean) 


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# File 'numeric.c', line 3313

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

Returns self.

Returns:

  • (self) 


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# File 'rational.c', line 2047

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

#pow(numeric) ⇒ Numeric #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

Overloads:



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# File 'bignum.c', line 7107

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 ⇒ Object

#rationalize([eps]) ⇒ Object

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



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# File 'rational.c', line 2157

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

#remainder(numeric) ⇒ Object

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.



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# File 'numeric.c', line 3901

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, Float

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

Returns:



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# File 'numeric.c', line 5172

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 ⇒ Integer

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

Returns:



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# File 'numeric.c', line 4857

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;
}

#next ⇒ Integer #succ ⇒ Integer

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

Overloads:

#times {|i| ... } ⇒ self #times ⇒ Object

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

Overloads:

  • #times {|i| ... } ⇒ self

    Yields:

    • (i)

    Returns:

    • (self) 


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# File 'numeric.c', line 5115

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;
}

#to_f ⇒ Float

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

Returns:



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# File 'numeric.c', line 4779

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_r ⇒ Object

Returns the value as a rational.

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



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# File 'rational.c', line 2144

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

#to_s(base = 10) ⇒ String Also known as: inspect

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"

Returns:



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# File 'numeric.c', line 3536

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);
}

#truncate([ndigits]) ⇒ Integer, Float

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

Returns:



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# File 'numeric.c', line 5271

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| ... } ⇒ self #upto(limit) ⇒ Object

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

Overloads:

  • #upto(limit) {|i| ... } ⇒ self

    Yields:

    • (i)

    Returns:

    • (self) 


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# File 'numeric.c', line 5019

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;
}

#|(other_int) ⇒ Integer

Bitwise OR.

Returns:



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# File 'numeric.c', line 4470

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;
}