floating-point-approximation-ii

Floating-point Approximation (II)

Given

• a semi-inclusive interval I = [l, u) (l is in interval I but u is not) l and u being floating numbers (0 <= l < u),

• an integer n (n > 0)

• a function f: x (float number) -> f(x) (float number)

we want to return as a list the n values:

f(l), f(l + 1 * d), ..., f(u -d) where d = (u - l) / n

or as a string (Bash, Nim):

"f(l), f(l + 1 * d), ..., f(u -d)" where d = (u - l) / n

Call this function interp:

interp(f, l, u, n) -> [f(l), f(l + 1 * d), ..., f(u - d)]

The n resulting values f(l), f(l + 1 * d), ..., f(u - d) will be floored to two decimals ( except Shell and Nim: see below).

For that you can use: floor(y * 100.0) / 100.0.

Examples:
interp(x -> x, 0.0, 0.9, 3) -> [0.0; 0.3; 0.6]
interp(x -> x, 0.0, 0.9, 4) -> [0.0; 0.22; 0.45; 0.67]
interp(x -> x, 0.0, 1.0, 4) -> [0.0; 0.25; 0.5; 0.75]
interp(x -> sin x, 0.0, 0.9, 3)  -> [0.0; 0.29; 0.56]