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4.8.1 Exponential and logarithmic functions

`cl_R exp (const cl_R& x)`
`cl_N exp (const cl_N& x)`

Returns the exponential function of `x`. This is `e^x` where `e` is the base of the natural logarithms. The range of the result is the entire complex plane excluding 0.

`cl_R ln (const cl_R& x)`

`x` must be > 0. Returns the (natural) logarithm of x.

`cl_N log (const cl_N& x)`

Returns the (natural) logarithm of x. If `x` is real and positive, this is `ln(x)`. In general, `log(x) = log(abs(x)) + i*phase(x)`. The range of the result is the strip in the complex plane `-pi < imagpart(log(x)) <= pi`.

`cl_R phase (const cl_N& x)`

Returns the angle part of `x` in its polar representation as a complex number. That is, `phase(x) = atan(realpart(x),imagpart(x))`. This is also the imaginary part of `log(x)`. The range of the result is the interval `-pi < phase(x) <= pi`. The result will be an exact number only if `zerop(x)` or if `x` is real and positive.

`cl_R log (const cl_R& a, const cl_R& b)`

`a` and `b` must be > 0. Returns the logarithm of `a` with respect to base `b`. `log(a,b) = ln(a)/ln(b)`. The result can be exact only if `a = 1` or if `a` and `b` are both rational.

`cl_N log (const cl_N& a, const cl_N& b)`

Returns the logarithm of `a` with respect to base `b`. `log(a,b) = log(a)/log(b)`.

`cl_N expt (const cl_N& x, const cl_N& y)`

Exponentiation: Returns `x^y = exp(y*log(x))`.

The constant e = exp(1) = 2.71828… is returned by the following functions:

`cl_F exp1 (float_format_t f)`

Returns e as a float of format `f`.

`cl_F exp1 (const cl_F& y)`

Returns e in the float format of `y`.

`cl_F exp1 (void)`

Returns e as a float of format `default_float_format`.

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