Module:Limits: Difference between revisions
Consistency limits optimisation |
m Temporarily reverting the edit Tag: Undo |
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local p = {} | local p = {} | ||
p.rat = rat | -- multiply the ratio by a power of `equave` so that it lies within [1; equave) | ||
function p.canonical(a, equave) | |||
equave = equave or 2 | |||
if type(a) == 'number' then | |||
a = rat.new(a) | |||
end | |||
local b = rat.copy(a) | |||
while rat.lt(b, 1) do | |||
b = rat.mul(b, equave) | |||
end | |||
while rat.geq(b, equave) do | |||
b = rat.div(b, equave) | |||
end | |||
return b | |||
end | |||
-- compute all positive ratios n/m with n and m <= q modulo powers of equave | -- compute all positive ratios n/m with n and m <= q modulo powers of equave | ||
| Line 11: | Line 25: | ||
for m = 1, q, 2 do | for m = 1, q, 2 do | ||
local a = rat.new(n, m) | local a = rat.new(n, m) | ||
a = | a = p.canonical(a, equave) | ||
local key = rat.as_ratio(a) | local key = rat.as_ratio(a) | ||
ratios[key] = a | ratios[key] = a | ||
| Line 50: | Line 64: | ||
local c_approx = approximate(c) | local c_approx = approximate(c) | ||
c = | c = p.canonical(c, equave) | ||
local c_key = rat.as_ratio(c) | local c_key = rat.as_ratio(c) | ||
if ratios[c_key] then | if ratios[c_key] then | ||