The version of loaded GMP.
# File tmp/rubies/ruby-3.0.5/lib/prime.rb, line 122
def Integer.each_prime(ubound, &block) # :yields: prime
Prime.each(ubound, &block)
end
Iterates the given block over all prime numbers.
See Prime#each for more details.
# File tmp/rubies/ruby-3.0.5/lib/prime.rb, line 22
def Integer.from_prime_division(pd)
Prime.int_from_prime_division(pd)
end
Re-composes a prime factorization and returns the product.
See Prime#int_from_prime_division for more details.
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);
}
}
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.
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);
}
Returns int modulo other.
See Numeric#divmod for more information.
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;
}
Bitwise AND.
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, '*');
}
Performs multiplication: the class of the resulting object depends on the class of numeric.
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;
}
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_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, '+');
}
Performs addition: 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, '-');
}
Performs subtraction: the class of the resulting object depends on the class of numeric.
# File tmp/rubies/ruby-3.0.5/integer.rb, line 6
def -@
Primitive.attr! 'inline'
Primitive.cexpr! 'rb_int_uminus(self)'
end
Returns int, negated.
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;
}
Performs division: the class of the resulting object depends on the class of numeric.
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;
}
Returns true if the value of int is less than that of real.
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;
}
Returns int shifted left count positions, or right if count is negative.
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;
}
Returns true if the value of int is less than or equal to that of real.
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));
}
}
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_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;
}
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
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;
}
Returns true if the value of int is greater than 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;
}
Returns true if the value of int is greater than or equal to that of real.
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;
}
Returns int shifted right count positions, or left if count is negative.
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;
}
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 ifn & ((1 << (j + 1)) - 1)is zero. Otherwise, raises anArgumentError. -
n[...j]is zero ifn & ((1 << j) - 1)is zero. Otherwise, raises anArgumentError.
Note that range operation may exhaust memory. For example, -1[0, 1000000000000] will raise NoMemoryError.
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;
}
Bitwise EXCLUSIVE OR.
# File tmp/rubies/ruby-3.0.5/integer.rb, line 27
def abs
Primitive.attr! 'inline'
Primitive.cexpr! 'rb_int_abs(self)'
end
static VALUE
int_allbits_p(VALUE num, VALUE mask)
{
mask = rb_to_int(mask);
return rb_int_equal(rb_int_and(num, mask), mask);
}
Returns true if all 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;
}
Returns true if any bits of int & mask are 1.
# File tmp/rubies/ruby-3.0.5/integer.rb, line 73
def bit_length
Primitive.attr! 'inline'
Primitive.cexpr! 'rb_int_bit_length(self)'
end
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
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);
}
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_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);
}
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
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);
}
}
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
integer_denominator(VALUE self)
{
return INT2FIX(1);
}
Returns 1.
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;
}
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
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);
}
Performs integer division: returns the integer result of dividing int by numeric.
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;
}
See Numeric#divmod.
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;
}
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!"
# File tmp/rubies/ruby-3.0.5/integer.rb, line 82
def even?
Primitive.attr! 'inline'
Primitive.cexpr! 'rb_int_even_p(self)'
end
Returns true if int is an even number.
VALUE
rb_int_fdiv(VALUE x, VALUE y)
{
if (RB_INTEGER_TYPE_P(x)) {
return DBL2NUM(rb_int_fdiv_double(x, y));
}
return Qnil;
}
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
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);
}
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
VALUE
rb_gcd(VALUE self, VALUE other)
{
other = nurat_int_value(other);
return f_gcd(self, other);
}
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_gcdlcm(VALUE self, VALUE other)
{
other = nurat_int_value(other);
return rb_assoc_new(f_gcd(self, other), f_lcm(self, other));
}
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]
# File tmp/rubies/ruby-3.0.5/integer.rb, line 91
def integer?
return true
end
Since int is already an Integer, this always returns true.
VALUE
rb_lcm(VALUE self, VALUE other)
{
other = nurat_int_value(other);
return f_lcm(self, other);
}
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
# File tmp/rubies/ruby-3.0.5/integer.rb, line 95
def magnitude
Primitive.attr! 'inline'
Primitive.cexpr! 'rb_int_abs(self)'
end
# File tmp/rubies/ruby-3.0.5/lib/prime.rb, line 69
def miller_rabin_bases
# Miller-Rabin's complexity is O(k log^3n).
# So we can reduce the complexity by reducing the number of bases tested.
# Using values from https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
i = case
when self < 0xffff then
# For small integers, Miller Rabin can be slower
# There is no mathematical significance to 0xffff
return nil
# when self < 2_047 then 0
when self < 1_373_653 then 1
when self < 9_080_191 then 2
when self < 25_326_001 then 3
when self < 3_215_031_751 then 4
when self < 4_759_123_141 then 5
when self < 1_122_004_669_633 then 6
when self < 2_152_302_898_747 then 7
when self < 3_474_749_660_383 then 8
when self < 341_550_071_728_321 then 9
when self < 3_825_123_056_546_413_051 then 10
when self < 318_665_857_834_031_151_167_461 then 11
when self < 3_317_044_064_679_887_385_961_981 then 12
else return nil
end
MILLER_RABIN_BASES[i]
end
# File tmp/rubies/ruby-3.0.5/lib/prime.rb, line 96
def miller_rabin_test(bases)
return false if even?
r = 0
d = self >> 1
while d.even?
d >>= 1
r += 1
end
self_minus_1 = self-1
bases.each do |a|
x = a.pow(d, self)
next if x == 1 || x == self_minus_1 || a == self
return false if r.times do
x = x.pow(2, self)
break if x == self_minus_1
end
end
true
end
static VALUE
int_nobits_p(VALUE num, VALUE mask)
{
mask = rb_to_int(mask);
return int_zero_p(rb_int_and(num, mask));
}
Returns true if no bits of int & mask are 1.
static VALUE
integer_numerator(VALUE self)
{
return self;
}
Returns self.
# File tmp/rubies/ruby-3.0.5/integer.rb, line 104
def odd?
Primitive.attr! 'inline'
Primitive.cexpr! 'rb_int_odd_p(self)'
end
Returns true if int is an odd number.
# File tmp/rubies/ruby-3.0.5/integer.rb, line 120
def ord
return self
end
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.
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);
}
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
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));
}
Returns the predecessor of int, i.e. the Integer equal to int-1.
1.pred #=> 0 (-1).pred #=> -2
# File tmp/rubies/ruby-3.0.5/lib/prime.rb, line 35
def prime?
return self >= 2 if self <= 3
if (bases = miller_rabin_bases)
return miller_rabin_test(bases)
end
return true if self == 5
return false unless 30.gcd(self) == 1
(7..Integer.sqrt(self)).step(30) do |p|
return false if
self%(p) == 0 || self%(p+4) == 0 || self%(p+6) == 0 || self%(p+10) == 0 ||
self%(p+12) == 0 || self%(p+16) == 0 || self%(p+22) == 0 || self%(p+24) == 0
end
true
end
Returns true if self is a prime number, else returns false. Not recommended for very big integers (> 10**23).
# File tmp/rubies/ruby-3.0.5/lib/prime.rb, line 29
def prime_division(generator = Prime::Generator23.new)
Prime.prime_division(self, generator)
end
Returns the factorization of self.
See Prime#prime_division for more details.
static VALUE
integer_rationalize(int argc, VALUE *argv, VALUE self)
{
rb_check_arity(argc, 0, 1);
return integer_to_r(self);
}
Returns the value as a rational. The optional argument eps is always ignored.
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;
}
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_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);
}
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_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;
}
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
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));
}
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
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;
}
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
# File tmp/rubies/ruby-3.0.5/ext/openssl/lib/openssl/bn.rb, line 37
def to_bn
OpenSSL::BN::new(self)
end
Casts an Integer as an OpenSSL::BN
See ‘man bn` for more info.
# File tmp/rubies/ruby-3.0.5/ext/bigdecimal/lib/bigdecimal/util.rb, line 23
def to_d
BigDecimal(self)
end
Returns the value of int as a BigDecimal.
require 'bigdecimal' require 'bigdecimal/util' 42.to_d # => 0.42e2
See also BigDecimal::new.
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);
}
# File tmp/rubies/ruby-3.0.5/integer.rb, line 130
def to_i
return self
end
# File tmp/rubies/ruby-3.0.5/integer.rb, line 138
def to_int
return self
end
Since int is already an Integer, returns self.
static VALUE
integer_to_r(VALUE self)
{
return rb_rational_new1(self);
}
Returns the value as a rational.
1.to_r #=> (1/1) (1<<64).to_r #=> (18446744073709551616/1)
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);
}
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_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);
}
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_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;
}
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
# File tmp/rubies/ruby-3.0.5/integer.rb, line 146
def zero?
Primitive.attr! 'inline'
Primitive.cexpr! 'rb_int_zero_p(self)'
end
Returns true if int has a zero value.
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;
}
Bitwise OR.
# File tmp/rubies/ruby-3.0.5/integer.rb, line 22
def ~
Primitive.attr! 'inline'
Primitive.cexpr! 'rb_int_comp(self)'
end
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"