rlogc

func F ¶

func F(n float64) float64

This function increments n logarithmically.

This function computes (in a mathematical sense):

f(n) = log(exp(n)+1)

However, to prevent floating point overflows, this function, its implementation exploits the following rule:

f(n) = n + f(-n)

Which can be proven as follows:

f(n) = log(exp(n)+1)
f(n) = log(exp(n)+exp(0))
f(n) = log(exp(n-n)+exp(0-n))+n
f(n) = log(exp(0)+exp(-n))+n
f(n) = log(1+exp(-n))+n
f(n) = n + log(exp(-n)+1)
f(n) = n + f(-n)

The function is implemented as

f(n) = max(0,n) + log(exp(-abs(n))+1)

Which is correct because:

max(0,n) = 0 IF n<0
-abs(n)  = n IF n<0

max(0,n) = n IF n>0
-abs(n) = -n IF n>0

max(0,n) = -abs(n) = 0 IF n = 0

func GetDecayFromHalfLife ¶

func GetDecayFromHalfLife(HL int64) float64

Calculates the decay value for a given Half-life time.

Half-life (symbol t½) is the time required for a quantity to reduce to half of its initial value. See also: https://en.wikipedia.org/wiki/Half-life

The time unit of HL is the same as the time unit of the Timer in use.

For example, if you want to have a Half-life time of one hour, and your Timer increments once every second - thus the time unit of your Timer is one second - you must specify the number of seconds of this hour: 3600. However, if your Timer's time unit is one millisecond, you must specify the number of milliseconds within an hour (3600000) in order to get a Half-life time of one hour.