natural package:integer-logarithms

Deprecated: It is no faster than (^)

Calculate the integer logarithm of an Integer to base 10. The argument must be not zero, otherwise an error is thrown.

Calculate the natural logarithm of an Natural to base 2. The argument must be non-zero, otherwise an error is thrown.

Cacluate the integer logarithm for an arbitrary base. The base must be greater than 1, the second argument, the number whose logarithm is sought, must be positive, otherwise an error is thrown. If base == 2, the specialised version is called, which is more efficient than the general algorithm. Satisfies:

base ^ integerLogBase base m <= m < base ^ (integerLogBase base m + 1)

for base > 1 and m > 0.

Power of an Natural by the left-to-right repeated squaring algorithm. This needs two multiplications in each step while the right-to-left algorithm needs only one multiplication for 0-bits, but here the two factors always have approximately the same size, which on average gains a bit when the result is large. For small results, it is unlikely to be any faster than (^), quite possibly slower (though the difference shouldn't be large), and for exponents with few bits set, the same holds. But for exponents with many bits set, the speedup can be significant. Warning: No check for the negativity of the exponent is performed, a negative exponent is interpreted as a large positive exponent.

Same as naturalPower, but for exponents of type Word.