Routines (alphabetical) > Routines: A > ALOG2

# ALOG2

The ALOG2 function returns the logarithm to the base 2 of X.

For input of a complex number, Z = X + iY, the complex number can be rewritten as Z = R exp(iq), where R = abs(Z) and q = atan(y,x). The complex log base 2 is then given by,

alog2(Z) = alog2(R) + i q/alog(2)

In the above formula, the use of the two-argument arctangent separates the solutions at Y = 0 and takes into account the branch-cut discontinuity along the real axis from -∞ to 0, and ensures that 2^(alog2(Z)) is equal to Z 1. For details see formulas 4.4.1-3 in Abramowitz, M. and Stegun, I.A., 1964: Handbook of Mathematical Functions (Washington: National Bureau of Standards).

## Examples

Find the base 2 logarithm of 100 and print the result by entering:

PRINT, ALOG2(100)

IDL prints:

6.64386

## Syntax

Result = ALOG2(X)

## Return Value

Returns the logarithm to the base 2 of X.

## Arguments

### X

The value for which the base 2 log is desired. For real input, X should be greater than or equal to zero. If X is double-precision floating or complex, the result is of the same type. All other types are converted to single-precision floating-point and yield floating-point results. If X is an array, the result has the same dimensions, with each element containing the base 2 log of the corresponding element of X.

## Keywords

### Thread Pool Keywords

This routine is written to make use of IDL’s thread pool, which can increase execution speed on systems with multiple CPUs. The values stored in the !CPU system variable control whether IDL uses the thread pool for a given computation. In addition, you can use the thread pool keywords TPOOL_MAX_ELTS, TPOOL_MIN_ELTS, and TPOOL_NOTHREAD to override the defaults established by !CPU for a single invocation of this routine. See Thread Pool Keywords for details.

## Version History

8.4 | Introduced

## See Also

ALOG, ALOG10, ATAN