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| --[[
| | local z = {} |
|
| |
|
| This module provides a number of basic mathematical operations.
| | -- Generate random number |
| | function z.random( frame ) |
| | first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil |
| | second = tonumber(frame.args[2]) |
|
| |
|
| ]]
| | if first then -- if NaN or nil, will skip down to final return |
| | | if first <= second then -- could match if both nil, but already checked that first is a number in last line |
| local yesno, getArgs -- lazily initialized
| | return math.random(first, second) |
| | | end |
| local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
| | return math.random(first) |
| local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
| | end |
| | | return math.random() |
| --[[
| |
| Helper functions used to avoid redundant code.
| |
| ]]
| |
| | |
| local function err(msg)
| |
| -- Generates wikitext error messages.
| |
| return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg)
| |
| end
| |
| | |
| local function unpackNumberArgs(args)
| |
| -- Returns an unpacked list of arguments specified with numerical keys.
| |
| local ret = {}
| |
| for k, v in pairs(args) do
| |
| if type(k) == 'number' then
| |
| table.insert(ret, v)
| |
| end
| |
| end
| |
| return unpack(ret)
| |
| end
| |
| | |
| local function makeArgArray(...)
| |
| -- Makes an array of arguments from a list of arguments that might include nils.
| |
| local args = {...} -- Table of arguments. It might contain nils or non-number values, so we can't use ipairs.
| |
| local nums = {} -- Stores the numbers of valid numerical arguments.
| |
| local ret = {}
| |
| for k, v in pairs(args) do
| |
| v = p._cleanNumber(v)
| |
| if v then
| |
| nums[#nums + 1] = k
| |
| args[k] = v
| |
| end
| |
| end
| |
| table.sort(nums)
| |
| for i, num in ipairs(nums) do
| |
| ret[#ret + 1] = args[num]
| |
| end
| |
| return ret
| |
| end
| |
| | |
| local function fold(func, ...)
| |
| -- 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.
| |
| local vals = makeArgArray(...)
| |
| local count = #vals -- The number of valid arguments
| |
| if count == 0 then return
| |
| -- Exit if we have no valid args, otherwise removing the first arg would cause an error.
| |
| nil, 0
| |
| end
| |
| local ret = table.remove(vals, 1)
| |
| for _, val in ipairs(vals) do
| |
| ret = func(ret, val)
| |
| end
| |
| return ret, count
| |
| end
| |
| | |
| --[[
| |
| 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
| |
| | |
| --[[ | |
| random
| |
| | |
| Generate a random number
| |
| | |
| Usage:
| |
| {{#invoke: Math | random }}
| |
| {{#invoke: Math | random | maximum value }}
| |
| {{#invoke: Math | random | minimum value | maximum value }}
| |
| ]]
| |
| | |
| function wrap.random(args)
| |
| local first = p._cleanNumber(args[1])
| |
| local second = p._cleanNumber(args[2])
| |
| return p._random(first, second)
| |
| end
| |
| | |
| function p._random(first, second)
| |
| math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
| |
| -- math.random will throw an error if given an explicit nil parameter, so we need to use if statements to check the params.
| |
| if first and second then
| |
| if first <= second then -- math.random doesn't allow the first number to be greater than the second.
| |
| return math.random(first, second)
| |
| end
| |
| elseif first then
| |
| return math.random(first)
| |
| else
| |
| return math.random()
| |
| end
| |
| end
| |
| | |
| --[[
| |
| order
| |
| | |
| Determine order of magnitude of a number
| |
| | |
| Usage:
| |
| {{#invoke: Math | order | value }}
| |
| ]]
| |
| | |
| function wrap.order(args)
| |
| local input_string = (args[1] or args.x or '0');
| |
| local input_number = p._cleanNumber(input_string);
| |
| if input_number == nil then
| |
| return err('order of magnitude input appears non-numeric')
| |
| else
| |
| return p._order(input_number)
| |
| end
| |
| end
| |
| | |
| function p._order(x)
| |
| if x == 0 then return 0 end
| |
| return math.floor(math.log10(math.abs(x)))
| |
| end
| |
| | |
| --[[
| |
| precision
| |
| | |
| Detemines the precision of a number using the string representation
| |
| | |
| Usage:
| |
| {{ #invoke: Math | precision | value }}
| |
| ]]
| |
| | |
| function wrap.precision(args)
| |
| local input_string = (args[1] or args.x or '0');
| |
| local trap_fraction = args.check_fraction;
| |
| local input_number;
| |
| | |
| if not yesno then
| |
| yesno = require('Module:Yesno')
| |
| end
| |
| 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);
| |
| if pos ~= nil then
| |
| if string.find(input_string, '/', pos + 1, true) == nil then
| |
| local denominator = string.sub(input_string, pos+1, -1);
| |
| local denom_value = tonumber(denominator);
| |
| if denom_value ~= nil then
| |
| return math.log10(denom_value);
| |
| end
| |
| end
| |
| end
| |
| end
| |
| | |
| input_number, input_string = p._cleanNumber(input_string);
| |
| if input_string == nil then
| |
| return err('precision input appears non-numeric')
| |
| else
| |
| return p._precision(input_string)
| |
| end
| |
| end
| |
| | |
| function p._precision(x)
| |
| if type(x) == 'number' then
| |
| x = tostring(x)
| |
| end
| |
| x = string.upper(x)
| |
| | |
| local decimal = x:find('%.')
| |
| local exponent_pos = x:find('E')
| |
| local result = 0;
| |
| | |
| if exponent_pos ~= nil then
| |
| local exponent = string.sub(x, exponent_pos + 1)
| |
| x = string.sub(x, 1, exponent_pos - 1)
| |
| result = result - tonumber(exponent)
| |
| end
| |
| | |
| if decimal ~= nil then
| |
| result = result + string.len(x) - decimal
| |
| return result
| |
| end
| |
| | |
| local pos = string.len(x);
| |
| while x:byte(pos) == string.byte('0') do
| |
| pos = pos - 1
| |
| result = result - 1
| |
| if pos <= 0 then
| |
| return 0
| |
| end
| |
| end
| |
| | |
| return result
| |
| end
| |
| | |
| | |
| --[[
| |
| max
| |
| | |
| Finds the maximum argument
| |
| | |
| Usage:
| |
| {{#invoke:Math| max | value1 | value2 | ... }}
| |
| | |
| Note, any values that do not evaluate to numbers are ignored.
| |
| ]]
| |
| | |
| function wrap.max(args)
| |
| return p._max(unpackNumberArgs(args))
| |
| end
| |
| | |
| function p._max(...)
| |
| local max_value = binary_fold((function(a, b) return a > b end), ...)
| |
| if max_value then
| |
| return max_value
| |
| end
| |
| end
| |
| | |
| --[[
| |
| 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
| |
| | |
| --[[
| |
| min
| |
| | |
| Finds the minimum argument
| |
| | |
| Usage:
| |
| {{#invoke:Math| min | value1 | value2 | ... }}
| |
| OR
| |
| {{#invoke:Math| min }}
| |
| | |
| When used with no arguments, it takes its input from the parent
| |
| frame. Note, any values that do not evaluate to numbers are ignored.
| |
| ]]
| |
| | |
| function wrap.min(args)
| |
| return p._min(unpackNumberArgs(args))
| |
| end | | end |
|
| |
|
| function p._min(...) | | -- Determine order of magnitude |
| local min_value = binary_fold((function(a, b) return a < b end), ...)
| | function z.order(frame) |
| if min_value then
| | return z._order(tonumber(frame.args[1] or frame.args.x or 0)) |
| return min_value
| |
| end
| |
| end | | end |
| | | function z._order(x) |
| --[[
| | if x == 0 then return 0 end |
| sum
| | return math.floor(math.log10(math.abs(x))) |
| | |
| 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 | | end |
|
| |
|
| function p._sum(...) | | -- Determines precision of a number using the string representation |
| local sums, count = fold((function(a, b) return a + b end), ...)
| | function z.precision( frame ) |
| if not sums then
| | return z._precision( frame.args[1] or frame.args.x or '0' ) |
| return 0
| |
| else
| |
| return sums
| |
| end
| |
| end | | end |
| | function z._precision( x ) |
| | x = string.upper( x ) |
|
| |
|
| --[[ | | -- Remove leading / trailing whitespace |
| average
| | x = x:match "^%s*(.-)%s*$"; |
| | |
| Finds the average
| |
| | |
| Usage:
| |
| {{#invoke:Math| average | value1 | value2 | ... }}
| |
| OR
| |
| {{#invoke:Math| average }}
| |
| | |
| Note, any values that do not evaluate to numbers are ignored.
| |
| ]]
| |
| | |
| function wrap.average(args)
| |
| return p._average(unpackNumberArgs(args))
| |
| end
| |
|
| |
|
| function p._average(...)
| | local decimal = string.find( x, '.', 1, true ) |
| local sum, count = fold((function(a, b) return a + b end), ...)
| | local exponent_pos = string.find( x, 'E', 1, true ) |
| if not sum then
| | local result = 0; |
| return 0
| | |
| else
| | if exponent_pos ~= nil then |
| return sum / count
| | local exponent = string.sub( x, exponent_pos + 1 ) |
| end
| | x = string.sub( x, 1, exponent_pos - 1 ) |
| | result = result - tonumber( exponent ) |
| | end |
| | |
| | if decimal ~= nil then |
| | result = result + string.len( x ) - decimal |
| | return result |
| | end |
| | |
| | local pos = string.len( x ); |
| | while x:byte(pos) == string.byte('0') do |
| | pos = pos - 1 |
| | result = result - 1 |
| | if pos <= 0 then |
| | return 0 |
| | end |
| | end |
| | |
| | return result |
| end | | end |
|
| |
|
| --[[ | | -- Finds maximum argument |
| round
| | function z.max( frame ) |
| | | if frame.args[1] == nil then |
| Rounds a number to specified precision
| | return '' |
| | | end |
| Usage:
| | local max_value = tonumber( frame.args[1] ) |
| {{#invoke:Math | round | value | precision }}
| | |
| | | local i = 2; |
| --]]
| | while frame.args[i] ~= nil do |
| | | local val = tonumber( frame.args[i] ); |
| function wrap.round(args)
| | if val ~= nil then |
| local value = p._cleanNumber(args[1] or args.value or 0)
| | if val > max_value then |
| local precision = p._cleanNumber(args[2] or args.precision or 0)
| | max_value = val; |
| if value == nil or precision == nil then
| | end |
| return err('round input appears non-numeric')
| | end |
| else
| | i = i + 1; |
| return p._round(value, precision)
| | end |
| end
| | |
| | return max_value |
| end | | end |
|
| |
|
| function p._round(value, precision) | | -- Finds minimum argument |
| local rescale = math.pow(10, precision or 0);
| | function z.min( frame ) |
| return math.floor(value * rescale + 0.5) / rescale;
| | if frame.args[1] == nil then |
| | return '' |
| | end |
| | local min_value = tonumber( frame.args[1] ) |
| | |
| | local i = 2; |
| | while frame.args[i] ~= nil do |
| | local val = tonumber( frame.args[i] ); |
| | if val ~= nil then |
| | if val < min_value then |
| | min_value = val; |
| | end |
| | end |
| | i = i + 1; |
| | end |
| | |
| | return min_value |
| end | | end |
|
| |
|
| --[[ | | -- Rounds a number to the specified precision and formats according to rules |
| log10
| | -- originally used for {{template:Rnd}} |
| | function z.round( frame ) |
| | -- For access to Mediawiki built-in formatter. |
| | local lang = mw.getContentLanguage(); |
| | |
| | local value = tonumber( frame.args[1] or 0 ); |
| | local precision = tonumber( frame.args[2] or 0 ); |
| | local current_precision = z._precision( value ); |
| | |
| | -- If rounding off, truncate extra digits |
| | if precision < current_precision then |
| | local rescale = math.pow( 10, precision ); |
| | value = math.floor( value * rescale + 0.5 ) / rescale; |
| | end |
| | |
| | local formatted_num = lang:formatNum( math.abs(value) ); |
| | local sign; |
| | |
| | -- Use proper unary minus sign rather than ASCII default |
| | if value < 0 then |
| | sign = '−'; |
| | else |
| | sign = ''; |
| | end |
| | |
| | local order; |
| | |
| | -- Handle cases requiring scientific notation |
| | order = z._order( value ); |
| | if string.find( formatted_num, 'E', 1, true ) ~= nil or math.abs(order) >= 9 then |
| | value = value * math.pow( 10, -order ); |
| | current_precision = current_precision + order; |
| | precision = precision + order; |
| | formatted_num = lang:formatNum( value ); |
| | else |
| | order = 0; |
| | end |
| | formatted_num = sign .. formatted_num; |
| | |
| | -- Pad with zeros, if needed |
| | if current_precision < precision then |
| | if current_precision <= 0 then |
| | if precision > 0 then |
| | local zero_sep = lang:formatNum( 1.1 ); |
| | formatted_num = formatted_num .. zero_sep:sub(2,2); |
| | formatted_num = formatted_num .. string.rep( '0', precision ); |
| | end |
| | else |
| | formatted_num = formatted_num .. string.rep( '0', precision - current_precision ); |
| | end |
| | end |
|
| |
|
| returns the log (base 10) of a number
| | -- Add exponential notation, if necessary. |
| | | if order ~= 0 then |
| Usage:
| | -- Use proper unary minus sign rather than ASCII default |
| {{#invoke:Math | log10 | x }}
| | if order < 0 then |
| ]]
| | order = '−' .. lang:formatNum( math.abs(order) ); |
| | | else |
| function wrap.log10(args)
| | order = lang:formatNum( order ); |
| return math.log10(args[1])
| | end |
| end
| | |
| | | formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>' |
| --[[
| | end |
| mod
| | |
| | | return formatted_num; |
| Implements the modulo operator
| |
| | |
| Usage:
| |
| {{#invoke:Math | mod | x | y }}
| |
| | |
| --]]
| |
| | |
| function wrap.mod(args)
| |
| local x = p._cleanNumber(args[1])
| |
| local y = p._cleanNumber(args[2])
| |
| if not x then
| |
| return err('first argument to mod appears non-numeric')
| |
| elseif not y then
| |
| return err('second argument to mod appears non-numeric')
| |
| else
| |
| return p._mod(x, y)
| |
| end
| |
| end | | end |
|
| |
|
| function p._mod(x, y)
| | return z |
| local ret = x % y
| |
| if not (0 <= ret and ret < y) then
| |
| ret = 0
| |
| end
| |
| return ret
| |
| end
| |
| | |
| --[[
| |
| gcd
| |
| | |
| Calculates the greatest common divisor of multiple numbers
| |
| | |
| Usage:
| |
| {{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}
| |
| --]]
| |
| | |
| function wrap.gcd(args)
| |
| return p._gcd(unpackNumberArgs(args))
| |
| end
| |
| | |
| function p._gcd(...)
| |
| local function findGcd(a, b)
| |
| local r = b
| |
| local oldr = a
| |
| while r ~= 0 do
| |
| local quotient = math.floor(oldr / r)
| |
| oldr, r = r, oldr - quotient * r
| |
| end
| |
| if oldr < 0 then
| |
| oldr = oldr * -1
| |
| end
| |
| return oldr
| |
| end
| |
| local result, count = fold(findGcd, ...)
| |
| return result
| |
| end
| |
| | |
| --[[
| |
| precision_format
| |
| | |
| Rounds a number to the specified precision and formats according to rules
| |
| originally used for {{template:Rnd}}. Output is a string.
| |
| | |
| Usage:
| |
| {{#invoke: Math | precision_format | number | precision }}
| |
| ]]
| |
| | |
| function wrap.precision_format(args)
| |
| local value_string = args[1] or 0
| |
| local precision = args[2] or 0
| |
| return p._precision_format(value_string, precision)
| |
| end
| |
| | |
| function p._precision_format(value_string, precision)
| |
| -- For access to Mediawiki built-in formatter.
| |
| local lang = mw.getContentLanguage();
| |
| | |
| local value
| |
| value, value_string = p._cleanNumber(value_string)
| |
| precision = p._cleanNumber(precision)
| |
| | |
| -- Check for non-numeric input
| |
| if value == nil or precision == nil then
| |
| return err('invalid input when rounding')
| |
| end
| |
| | |
| local current_precision = p._precision(value)
| |
| local order = p._order(value)
| |
| | |
| -- Due to round-off effects it is neccesary to limit the returned precision under
| |
| -- some circumstances because the terminal digits will be inaccurately reported.
| |
| if order + precision >= 14 then
| |
| orig_precision = p._precision(value_string)
| |
| if order + orig_precision >= 14 then
| |
| precision = 13 - order;
| |
| end
| |
| end
| |
| | |
| -- If rounding off, truncate extra digits
| |
| if precision < current_precision then
| |
| value = p._round(value, precision)
| |
| current_precision = p._precision(value)
| |
| end
| |
| | |
| local formatted_num = lang:formatNum(math.abs(value))
| |
| local sign
| |
| | |
| -- Use proper unary minus sign rather than ASCII default
| |
| if value < 0 then
| |
| sign = '−'
| |
| else
| |
| sign = ''
| |
| end
| |
| | |
| -- Handle cases requiring scientific notation
| |
| if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then
| |
| value = value * math.pow(10, -order)
| |
| current_precision = current_precision + order
| |
| precision = precision + order
| |
| formatted_num = lang:formatNum(math.abs(value))
| |
| else
| |
| order = 0;
| |
| end
| |
| formatted_num = sign .. formatted_num
| |
| | |
| -- Pad with zeros, if needed
| |
| if current_precision < precision then
| |
| local padding
| |
| if current_precision <= 0 then
| |
| if precision > 0 then
| |
| local zero_sep = lang:formatNum(1.1)
| |
| formatted_num = formatted_num .. zero_sep:sub(2,2)
| |
| | |
| padding = precision
| |
| if padding > 20 then
| |
| padding = 20
| |
| end
| |
| | |
| formatted_num = formatted_num .. string.rep('0', padding)
| |
| end
| |
| else
| |
| padding = precision - current_precision
| |
| if padding > 20 then
| |
| padding = 20
| |
| end
| |
| formatted_num = formatted_num .. string.rep('0', padding)
| |
| end
| |
| end
| |
| | |
| -- Add exponential notation, if necessary.
| |
| if order ~= 0 then
| |
| -- Use proper unary minus sign rather than ASCII default
| |
| if order < 0 then
| |
| order = '−' .. lang:formatNum(math.abs(order))
| |
| else
| |
| order = lang:formatNum(order)
| |
| end
| |
| | |
| formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
| |
| end
| |
| | |
| return formatted_num
| |
| end
| |
| | |
| --[[
| |
| Helper function that interprets the input numerically. If the
| |
| input does not appear to be a number, attempts evaluating it as
| |
| a parser functions expression.
| |
| ]]
| |
| | |
| function p._cleanNumber(number_string)
| |
| if type(number_string) == 'number' then
| |
| -- We were passed a number, so we don't need to do any processing.
| |
| return number_string, tostring(number_string)
| |
| elseif type(number_string) ~= 'string' or not number_string:find('%S') then
| |
| -- We were passed a non-string or a blank string, so exit.
| |
| return nil, nil;
| |
| end
| |
| | |
| -- Attempt basic conversion
| |
| local number = tonumber(number_string)
| |
| | |
| -- If failed, attempt to evaluate input as an expression
| |
| if number == nil then
| |
| local success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
| |
| if success then
| |
| number = tonumber(result)
| |
| number_string = tostring(number)
| |
| else
| |
| number = nil
| |
| number_string = nil
| |
| end
| |
| else
| |
| number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it.
| |
| number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs.
| |
| if number_string:find('^%-?0[xX]') then
| |
| -- Number is using 0xnnn notation to indicate base 16; use the number that Lua detected instead.
| |
| number_string = tostring(number)
| |
| end
| |
| end
| |
| | |
| return number, number_string
| |
| end
| |
| | |
| --[[
| |
| 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.
| |
| ]]
| |
| | |
| local mt = { __index = function(t, k)
| |
| return function(frame)
| |
| 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.
| |
| end
| |
| end }
| |
| | |
| return setmetatable(p, mt)
| |