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Module:Q-odd-limit intervals: Difference between revisions

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m There were a few issues it seems
Update (generate monzo lists instead of hard coding)
Line 1: Line 1:
bit32 = require( 'bit32' )
bit32 = require ('bit32')
utils = require ('Module:Utils')


local p = {}
local p = {}


local PRIME_LIST = {2, 3, 5, 7, 11, 13, 17, 19}
local PRIME_LIST = {2, 3, 5, 7, 11, 13, 17, 19, 23}
 
local function get_monzo_list (limit)
local monzo_list = {}
if limit >= 3 then
table.insert (monzo_list, {-1, 1, 0, 0, 0, 0, 0, 0})
end if limit >= 5 then
table.insert (monzo_list, {-2, 0, 1, 0, 0, 0, 0, 0})
table.insert (monzo_list, {0, -1, 1, 0, 0, 0, 0, 0})
end if limit >= 7 then
table.insert (monzo_list, {-2, 0, 0, 1, 0, 0, 0, 0})
table.insert (monzo_list, {-1, -1, 0, 1, 0, 0, 0, 0})
table.insert (monzo_list, {0, 0, -1, 1, 0, 0, 0, 0})
end if limit >= 9 then
table.insert (monzo_list, {-3, 2, 0, 0, 0, 0, 0, 0})
table.insert (monzo_list, {0, 2, -1, 0, 0, 0, 0, 0})
table.insert (monzo_list, {0, 2, 0, -1, 0, 0, 0, 0})
end if limit >= 11 then
table.insert (monzo_list, {-3, 0, 0, 0, 1, 0, 0, 0})
table.insert (monzo_list, {-1, -1, 0, 0, 1, 0, 0, 0})
table.insert (monzo_list, {0, -2, 0, 0, 1, 0, 0, 0})
table.insert (monzo_list, {-1, 0, -1, 0, 1, 0, 0, 0})
table.insert (monzo_list, {0, 0, 0, -1, 1, 0, 0, 0})
end if limit >= 13 then
table.insert (monzo_list, {-3, 0, 0, 0, 0, 1, 0, 0})
table.insert (monzo_list, {-2, -1, 0, 0, 0, 1, 0, 0})
table.insert (monzo_list, {0, -2, 0, 0, 0, 1, 0, 0})
table.insert (monzo_list, {-1, 0, -1, 0, 0, 1, 0, 0})
table.insert (monzo_list, {0, 0, 0, -1, 0, 1, 0, 0})
table.insert (monzo_list, {0, 0, 0, 0, -1, 1, 0, 0})
end if limit >= 15 then
table.insert (monzo_list, {-3, 1, 1, 0, 0, 0, 0, 0})
table.insert (monzo_list, {-1, 1, 1, -1, 0, 0, 0, 0})
table.insert (monzo_list, {0, 1, 1, 0, -1, 0, 0, 0})
table.insert (monzo_list, {0, 1, 1, 0, 0, -1, 0, 0})
end if limit >= 17 then
table.insert (monzo_list, {-4, 0, 0, 0, 0, 0, 1, 0})
table.insert (monzo_list, {-2, -1, 0, 0, 0, 0, 1, 0})
table.insert (monzo_list, {0, -2, 0, 0, 0, 0, 1, 0})
table.insert (monzo_list, {-1, 0, -1, 0, 0, 0, 1, 0})
table.insert (monzo_list, {-1, 0, 0, -1, 0, 0, 1, 0})
table.insert (monzo_list, {0, 0, 0, 0, -1, 0, 1, 0})
table.insert (monzo_list, {0, 0, 0, 0, 0, -1, 1, 0})
table.insert (monzo_list, {0, -1, -1, 0, 0, 0, 1, 0})
end if limit >= 19 then
table.insert (monzo_list, {-4, 0, 0, 0, 0, 0, 0, 1})
table.insert (monzo_list, {-2, -1, 0, 0, 0, 0, 0, 1})
table.insert (monzo_list, {-1, -2, 0, 0, 0, 0, 0, 1})
table.insert (monzo_list, {-1, 0, -1, 0, 0, 0, 0, 1})
table.insert (monzo_list, {-1, 0, 0, -1, 0, 0, 0, 1})
table.insert (monzo_list, {0, 0, 0, 0, -1, 0, 0, 1})
table.insert (monzo_list, {0, 0, 0, 0, 0, -1, 0, 1})
table.insert (monzo_list, {0, 0, 0, 0, 0, 0, -1, 1})
table.insert (monzo_list, {0, -1, -1, 0, 0, 0, 1, 0})
end if limit >= 21 then
table.insert (monzo_list, {-4, 1, 0, 1, 0, 0, 0, 0})
table.insert (monzo_list, {-2, 1, -1, 1, 0, 0, 0, 0})
table.insert (monzo_list, {0, 1, 0, 1, -1, 0, 0, 0})
table.insert (monzo_list, {0, 1, 0, 1, 0, -1, 0, 0})
table.insert (monzo_list, {0, 1, 0, 1, 0, 0, -1, 0})
table.insert (monzo_list, {0, 1, 0, 1, 0, 0, 0, -1})
end
return monzo_list
end
 
local function round (n)
return math.floor (n + 0.5)
end


local function is_in (v, t)
local function is_in (v, t)
Line 88: Line 22:
end
end
return t
return t
end
local function gcd (a, b)
if b ~= 0 then
return gcd (b, a % b)
else
return math.abs (a)
end
end
end


Line 109: Line 51:
end
end
return {num = num, den = den}
return {num = num, den = den}
end
local function ratio2monzo (ratio, subgroup)
local monzo = {}
for i = 1, #subgroup do
monzo[i] = 0
while ratio.num % subgroup[i] == 0 do
monzo[i] = monzo[i] + 1
ratio.num = ratio.num / subgroup[i]
end while ratio.den % subgroup[i] == 0 do
monzo[i] = monzo[i] - 1
ratio.den = ratio.den / subgroup[i]
end
end
return monzo
end
end


Line 114: Line 71:
local jip = {}
local jip = {}
for i = 1, #subgroup do
for i = 1, #subgroup do
jip[i] = 1200*math.log (subgroup[i]) / math.log (2)
jip[i] = 1200*utils._log (subgroup[i], 2)
end
end
return inner_product (jip, monzo)
return inner_product (jip, monzo)
end
local function ratio_8ve_reduction (ratio)
local oct = math.floor (utils._log (ratio.num/ratio.den, 2))
if oct > 0 then
ratio.den = ratio.den * 2^oct
elseif oct < 0 then
ratio.num = ratio.num * 2^(-oct)
end
return ratio
end
local function odd_limit_monzo_list_gen (limit)
local monzo_list = {}
local subgroup = table_filter (PRIME_LIST, limit)
for num = 1, limit, 2 do
for den = 1, num, 2 do
if gcd (num, den) == 1 then
ratio = ratio_8ve_reduction ({num = num, den = den})
table.insert (monzo_list, ratio2monzo (ratio, subgroup))
end
end
end
return monzo_list
end
end


Line 147: Line 128:
local val = {}
local val = {}
for i = 1, #subgroup do
for i = 1, #subgroup do
val[i] = round (steps*math.log (subgroup[i])/math.log (2))
val[i] = utils._round_dec (steps*utils._log (subgroup[i], 2))
end
end
error_list = find_error (val, subgroup, monzo_list)
error_list = find_error (val, subgroup, monzo_list)
Line 189: Line 170:
end
end
local subgroup = table_filter (PRIME_LIST, limit)
local subgroup = table_filter (PRIME_LIST, limit)
local monzo_list = get_monzo_list (limit)
local monzo_list = odd_limit_monzo_list_gen (limit)


return approx (steps, subgroup, monzo_list, title)
return approx (steps, subgroup, monzo_list, title)
Retrieved from "https://en.xen.wiki/w/Module:Q-odd-limit_intervals"