Power

ispow2(n::Number) -> Bool

Test whether n is an integer power of two.

See also count_ones, prevpow, nextpow.

Examples

julia> ispow2(4)
true

julia> ispow2(5)
false

julia> ispow2(4.5)
false

julia> ispow2(0.25)
true

julia> ispow2(1//8)
true

prevpow(a, x)

The largest a^n not greater than x, where n is a non-negative integer. a must be greater than 1, and x must not be less than 1.

See also nextpow, isqrt.

Examples

julia> prevpow(2, 7)
4

julia> prevpow(2, 9)
8

julia> prevpow(5, 20)
5

julia> prevpow(4, 16)
16

nextpow(a, x)

The smallest a^n not less than x, where n is a non-negative integer. a must be greater than 1, and x must be greater than 0.

See also prevpow.

Examples

julia> nextpow(2, 7)
8

julia> nextpow(2, 9)
16

julia> nextpow(5, 20)
25

julia> nextpow(4, 16)
16

powermod(x::Integer, p::Integer, m)

Compute $x^p \pmod m$.

Examples

julia> powermod(2, 6, 5)
4

julia> mod(2^6, 5)
4

julia> powermod(5, 2, 20)
5

julia> powermod(5, 2, 19)
6

julia> powermod(5, 3, 19)
11