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Line 65: − + − --[[ − Fold arguments by selectively choosing values (func should return when to choose the current "dominant" value). − ]] − local function binary_fold(func, ...) − local value = fold((function(a, b) if func(a, b) then return a else return b end end), ...) − return value − end − − + − + Line 83:
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Line 113: − + − + − + − + − + − + − + − if not yesno then − yesno = require('Module:Yesno') − end Line 154:
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Line 185: − + − + − − + − + − + − + − + − + + + + + + + + − + − median+ − + − Find the median of set of numbers − − Usage: − {{#invoke:Math | median | number1 | number2 | ...}} − OR − {{#invoke:Math | median }} − ]] − − function wrap.median(args) − return p._median(unpackNumberArgs(args)) − end − − function p._median(...) − local vals = makeArgArray(...) − local count = #vals − table.sort(vals) − − if count == 0 then − return 0 − end − − if p._mod(count, 2) == 0 then − return (vals[count/2] + vals[count/2+1])/2 − else − return vals[math.ceil(count/2)] − end − end − − --[[ − − − + − + − + − + − + + + + + + + + − + − sum+ − + − Finds the sum − − Usage: − {{#invoke:Math| sum | value1 | value2 | ... }} − OR − {{#invoke:Math| sum }} − − Note, any values that do not evaluate to numbers are ignored. − ]] − − function wrap.sum(args) − return p._sum(unpackNumberArgs(args)) − end − − function p._sum(...) − local sums, count = fold((function(a, b) return a + b end), ...) − if not sums then − return 0 − else − return sums − end − end − − --[[ − − − + − + − + − + − + + + + Line 329:
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Line 296: − + − + − + − --[[ − log10 − − returns the log (base 10) of a number − − Usage: − {{#invoke:Math | log10 | x }} − ]] − − function wrap.log10(args) − return math.log10(args[1]) − end − − + − + − + − + Line 387:
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Line 509: − + − + − + − + − + − if not getArgs then + − getArgs = require('Module:Arguments').getArgs+ − end − return wrap[k](getArgs(frame)) -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed. − + − + − return setmetatable(p, mt)+ + + + +
1 revision imported
--[[
--[[
This module provides a number of basic mathematical operations.
This module provides a number of basic mathematical operations.
]]
]]
local yesno, getArgs -- lazily initialized
local yesno = require('Module:Yesno')
local getArgs = require('Module:Arguments').getArgs
local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
--[[
--[[
Helper functions used to avoid redundant code.
Helper functions used to avoid redundant code.
]]
]]
local function err(msg)
local function err(msg)
-- Generates wikitext error messages.
-- Generates wikitext error messages.
return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg)
return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg)
end
end
local function unpackNumberArgs(args)
local function unpackNumberArgs(args)
-- Returns an unpacked list of arguments specified with numerical keys.
-- Returns an unpacked list of arguments specified with numerical keys.
return unpack(ret)
return unpack(ret)
end
end
local function makeArgArray(...)
local function makeArgArray(...)
-- Makes an array of arguments from a list of arguments that might include nils.
-- Makes an array of arguments from a list of arguments that might include nils.
return ret
return ret
end
end
local function fold(func, ...)
local function applyFuncToArgs(func, ...)
-- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters,
-- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters,
-- and must return a number as an output. This number is then supplied as input to the next function call.
-- and must return a number as an output. This number is then supplied as input to the next function call.
local vals = makeArgArray(...)
local vals = makeArgArray(...)
local count = #vals -- The number of valid arguments
local count = #vals -- The number of valid arguments
if count == 0 then return
if count == 0 then return
-- Exit if we have no valid args, otherwise removing the first arg would cause an error.
-- Exit if we have no valid args, otherwise removing the first arg would cause an error.
nil, 0
nil, 0
end
end
local ret = table.remove(vals, 1)
local ret = table.remove(vals, 1)
for _, val in ipairs(vals) do
for _, val in ipairs(vals) do
return ret, count
return ret, count
end
end
--[[
--[[
random
random
Generate a random number
Generate a random number
Usage:
Usage:
{{#invoke: Math | random }}
{{#invoke: Math | random }}
{{#invoke: Math | random | minimum value | maximum value }}
{{#invoke: Math | random | minimum value | maximum value }}
]]
]]
function wrap.random(args)
function wrap.random(args)
local first = p._cleanNumber(args[1])
local first = p._cleanNumber(args[1])
return p._random(first, second)
return p._random(first, second)
end
end
function p._random(first, second)
function p._random(first, second)
math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
end
end
end
end
--[[
--[[
order
order
Determine order of magnitude of a number
Determine order of magnitude of a number
Usage:
Usage:
{{#invoke: Math | order | value }}
{{#invoke: Math | order | value }}
]]
]]
function wrap.order(args)
function wrap.order(args)
local input_string = (args[1] or args.x or '0');
local input_string = (args[1] or args.x or '0');
else
else
return p._order(input_number)
return p._order(input_number)
end
end
end
end
function p._order(x)
function p._order(x)
if x == 0 then return 0 end
if x == 0 then return 0 end
return math.floor(math.log10(math.abs(x)))
return math.floor(math.log10(math.abs(x)))
end
end
--[[
--[[
precision
precision
Detemines the precision of a number using the string representation
Detemines the precision of a number using the string representation
Usage:
Usage:
{{ #invoke: Math | precision | value }}
{{ #invoke: Math | precision | value }}
]]
]]
function wrap.precision(args)
function wrap.precision(args)
local input_string = (args[1] or args.x or '0');
local input_string = (args[1] or args.x or '0');
local trap_fraction = args.check_fraction;
local trap_fraction = args.check_fraction;
local input_number;
local input_number;
if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
local pos = string.find(input_string, '/', 1, true);
local pos = string.find(input_string, '/', 1, true);
return math.log10(denom_value);
return math.log10(denom_value);
end
end
end
end
end
end
end
end
input_number, input_string = p._cleanNumber(input_string);
input_number, input_string = p._cleanNumber(input_string);
if input_string == nil then
if input_string == nil then
else
else
return p._precision(input_string)
return p._precision(input_string)
end
end
end
end
function p._precision(x)
function p._precision(x)
if type(x) == 'number' then
if type(x) == 'number' then
end
end
x = string.upper(x)
x = string.upper(x)
local decimal = x:find('%.')
local decimal = x:find('%.')
local exponent_pos = x:find('E')
local exponent_pos = x:find('E')
local result = 0;
local result = 0;
if exponent_pos ~= nil then
if exponent_pos ~= nil then
local exponent = string.sub(x, exponent_pos + 1)
local exponent = string.sub(x, exponent_pos + 1)
x = string.sub(x, 1, exponent_pos - 1)
x = string.sub(x, 1, exponent_pos - 1)
result = result - tonumber(exponent)
result = result - tonumber(exponent)
end
end
if decimal ~= nil then
if decimal ~= nil then
result = result + string.len(x) - decimal
result = result + string.len(x) - decimal
return result
return result
end
end
local pos = string.len(x);
local pos = string.len(x);
while x:byte(pos) == string.byte('0') do
while x:byte(pos) == string.byte('0') do
end
end
end
end
return result
return result
end
end
--[[
--[[
max
max
Finds the maximum argument
Finds the maximum argument
Usage:
Usage:
{{#invoke:Math| max | value1 | value2 | ... }}
{{#invoke:Math| max | value1 | value2 | ... }}
Note, any values that do not evaluate to numbers are ignored.
Note, any values that do not evaluate to numbers are ignored.
]]
]]
function wrap.max(args)
function wrap.max(args)
return p._max(unpackNumberArgs(args))
return p._max(unpackNumberArgs(args))
end
end
function p._max(...)
function p._max(...)
local max_value = binary_fold((function(a, b) return a > b end), ...)
local function maxOfTwo(a, b)
if a > b then
return a
else
return b
end
end
local max_value = applyFuncToArgs(maxOfTwo, ...)
if max_value then
if max_value then
return max_value
return max_value
end
end
end
end
--[[
--[[
min
min
Finds the minimum argument
Finds the minimum argument
Usage:
Usage:
{{#invoke:Math| min | value1 | value2 | ... }}
{{#invoke:Math| min | value1 | value2 | ... }}
OR
OR
{{#invoke:Math| min }}
{{#invoke:Math| min }}
When used with no arguments, it takes its input from the parent
When used with no arguments, it takes its input from the parent
frame. Note, any values that do not evaluate to numbers are ignored.
frame. Note, any values that do not evaluate to numbers are ignored.
]]
]]
function wrap.min(args)
function wrap.min(args)
return p._min(unpackNumberArgs(args))
return p._min(unpackNumberArgs(args))
end
end
function p._min(...)
function p._min(...)
local min_value = binary_fold((function(a, b) return a < b end), ...)
local function minOfTwo(a, b)
if a < b then
return a
else
return b
end
end
local min_value = applyFuncToArgs(minOfTwo, ...)
if min_value then
if min_value then
return min_value
return min_value
end
end
end
end
--[[
--[[
average
average
Finds the average
Finds the average
Usage:
Usage:
{{#invoke:Math| average | value1 | value2 | ... }}
{{#invoke:Math| average | value1 | value2 | ... }}
OR
OR
{{#invoke:Math| average }}
{{#invoke:Math| average }}
Note, any values that do not evaluate to numbers are ignored.
Note, any values that do not evaluate to numbers are ignored.
]]
]]
function wrap.average(args)
function wrap.average(args)
return p._average(unpackNumberArgs(args))
return p._average(unpackNumberArgs(args))
end
end
function p._average(...)
function p._average(...)
local sum, count = fold((function(a, b) return a + b end), ...)
local function getSum(a, b)
return a + b
end
local sum, count = applyFuncToArgs(getSum, ...)
if not sum then
if not sum then
return 0
return 0
end
end
end
end
--[[
--[[
round
round
Rounds a number to specified precision
Rounds a number to specified precision
Usage:
Usage:
{{#invoke:Math | round | value | precision }}
{{#invoke:Math | round | value | precision }}
--]]
--]]
function wrap.round(args)
function wrap.round(args)
local value = p._cleanNumber(args[1] or args.value or 0)
local value = p._cleanNumber(args[1] or args.value or 0)
else
else
return p._round(value, precision)
return p._round(value, precision)
end
end
end
end
function p._round(value, precision)
function p._round(value, precision)
local rescale = math.pow(10, precision or 0);
local rescale = math.pow(10, precision or 0);
return math.floor(value * rescale + 0.5) / rescale;
return math.floor(value * rescale + 0.5) / rescale;
end
end
--[[
--[[
mod
mod
Implements the modulo operator
Implements the modulo operator
Usage:
Usage:
{{#invoke:Math | mod | x | y }}
{{#invoke:Math | mod | x | y }}
--]]
--]]
function wrap.mod(args)
function wrap.mod(args)
local x = p._cleanNumber(args[1])
local x = p._cleanNumber(args[1])
else
else
return p._mod(x, y)
return p._mod(x, y)
end
end
end
end
function p._mod(x, y)
function p._mod(x, y)
local ret = x % y
local ret = x % y
return ret
return ret
end
end
--[[
--[[
gcd
gcd
Calculates the greatest common divisor of multiple numbers
Calculates the greatest common divisor of multiple numbers
Usage:
Usage:
{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}
{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}
--]]
--]]
function wrap.gcd(args)
function wrap.gcd(args)
return p._gcd(unpackNumberArgs(args))
return p._gcd(unpackNumberArgs(args))
end
end
function p._gcd(...)
function p._gcd(...)
local function findGcd(a, b)
local function findGcd(a, b)
return oldr
return oldr
end
end
local result, count = fold(findGcd, ...)
local result, count = applyFuncToArgs(findGcd, ...)
return result
return result
end
end
--[[
--[[
precision_format
precision_format
Rounds a number to the specified precision and formats according to rules
Rounds a number to the specified precision and formats according to rules
originally used for {{template:Rnd}}. Output is a string.
originally used for {{template:Rnd}}. Output is a string.
Usage:
Usage:
{{#invoke: Math | precision_format | number | precision }}
{{#invoke: Math | precision_format | number | precision }}
]]
]]
function wrap.precision_format(args)
function wrap.precision_format(args)
local value_string = args[1] or 0
local value_string = args[1] or 0
return p._precision_format(value_string, precision)
return p._precision_format(value_string, precision)
end
end
function p._precision_format(value_string, precision)
function p._precision_format(value_string, precision)
-- For access to Mediawiki built-in formatter.
-- For access to Mediawiki built-in formatter.
local lang = mw.getContentLanguage();
local lang = mw.getContentLanguage();
local value
local value
value, value_string = p._cleanNumber(value_string)
value, value_string = p._cleanNumber(value_string)
precision = p._cleanNumber(precision)
precision = p._cleanNumber(precision)
-- Check for non-numeric input
-- Check for non-numeric input
if value == nil or precision == nil then
if value == nil or precision == nil then
return err('invalid input when rounding')
return err('invalid input when rounding')
end
end
local current_precision = p._precision(value)
local current_precision = p._precision(value)
local order = p._order(value)
local order = p._order(value)
-- Due to round-off effects it is neccesary to limit the returned precision under
-- Due to round-off effects it is neccesary to limit the returned precision under
-- some circumstances because the terminal digits will be inaccurately reported.
-- some circumstances because the terminal digits will be inaccurately reported.
if order + precision >= 14 then
if order + precision >= 14 then
orig_precision = p._precision(value_string)
precision = 13 - order;
if order + orig_precision >= 14 then
end
precision = 13 - order;
end
end
end
-- If rounding off, truncate extra digits
-- If rounding off, truncate extra digits
if precision < current_precision then
if precision < current_precision then
value = p._round(value, precision)
value = p._round(value, precision)
current_precision = p._precision(value)
current_precision = p._precision(value)
end
end
local formatted_num = lang:formatNum(math.abs(value))
local formatted_num = lang:formatNum(math.abs(value))
local sign
local sign
-- Use proper unary minus sign rather than ASCII default
-- Use proper unary minus sign rather than ASCII default
if value < 0 then
if value < 0 then
else
else
sign = ''
sign = ''
end
end
-- Handle cases requiring scientific notation
-- Handle cases requiring scientific notation
if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then
if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then
formatted_num = lang:formatNum(math.abs(value))
formatted_num = lang:formatNum(math.abs(value))
else
else
order = 0;
order = 0;
end
end
formatted_num = sign .. formatted_num
formatted_num = sign .. formatted_num
-- Pad with zeros, if needed
-- Pad with zeros, if needed
if current_precision < precision then
if current_precision < precision then
local padding
local padding
local zero_sep = lang:formatNum(1.1)
local zero_sep = lang:formatNum(1.1)
formatted_num = formatted_num .. zero_sep:sub(2,2)
formatted_num = formatted_num .. zero_sep:sub(2,2)
padding = precision
padding = precision
if padding > 20 then
if padding > 20 then
padding = 20
padding = 20
end
end
formatted_num = formatted_num .. string.rep('0', padding)
formatted_num = formatted_num .. string.rep('0', padding)
end
end
else
else
padding = precision - current_precision
padding = precision - current_precision
if padding > 20 then
if padding > 20 then
end
end
end
end
-- Add exponential notation, if necessary.
-- Add exponential notation, if necessary.
if order ~= 0 then
if order ~= 0 then
else
else
order = lang:formatNum(order)
order = lang:formatNum(order)
end
end
formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
end
end
return formatted_num
return formatted_num
end
end
--[[
--[[
Helper function that interprets the input numerically. If the
Helper function that interprets the input numerically. If the
input does not appear to be a number, attempts evaluating it as
input does not appear to be a number, attempts evaluating it as
a parser functions expression.
a parser functions expression.
]]
]]
function p._cleanNumber(number_string)
function p._cleanNumber(number_string)
if type(number_string) == 'number' then
if type(number_string) == 'number' then
return nil, nil;
return nil, nil;
end
end
-- Attempt basic conversion
-- Attempt basic conversion
local number = tonumber(number_string)
local number = tonumber(number_string)
-- If failed, attempt to evaluate input as an expression
-- If failed, attempt to evaluate input as an expression
if number == nil then
if number == nil then
local success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
local frame = mw.getCurrentFrame()
if success then
local attempt = frame:callParserFunction('#expr', number_string)
number = tonumber(result)
attempt = tonumber(attempt)
if attempt ~= nil then
number = attempt
number_string = tostring(number)
number_string = tostring(number)
else
else
end
end
end
end
return number, number_string
return number, number_string
end
end
--[[
--[[
Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the current
Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the current
frame or the parent frame, and it also trims whitespace for all arguments and removes blank arguments.
frame or the parent frame, and it also trims whitespace for all arguments and removes blank arguments.
]]
]]
local mt = { __index = function(t, k)
local function makeWrapper(funcName)
return function(frame)
return function (frame)
local args = getArgs(frame) -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.
return wrap[funcName](args)
end
end
end }
end
for funcName in pairs(wrap) do
p[funcName] = makeWrapper(funcName)
end
return p