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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 | | end |
| | | |
− | local function unpackNumberArgs(args)
| + | -- Determine order of magnitude |
− | -- Returns an unpacked list of arguments specified with numerical keys.
| + | function z.order(frame) |
− | local ret = {}
| + | return z._order(tonumber(frame.args[1] or frame.args.x or 0)) |
− | for k, v in pairs(args) do
| |
− | if type(k) == 'number' then
| |
− | table.insert(ret, v)
| |
− | end
| |
− | end
| |
− | return unpack(ret)
| |
| end | | end |
− | | + | function z._order(x) |
− | local function makeArgArray(...)
| + | if x == 0 then return 0 end |
− | -- Makes an array of arguments from a list of arguments that might include nils.
| + | return math.floor(math.log10(math.abs(x))) |
− | 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 | | end |
| | | |
− | local function fold(func, ...)
| + | -- Determines precision of a number using the string representation |
− | -- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters,
| + | function z.precision( frame ) |
− | -- and must return a number as an output. This number is then supplied as input to the next function call.
| + | return z._precision( frame.args[1] or frame.args.x or '0' ) |
− | 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 | | end |
| + | function z._precision( x ) |
| + | x = string.upper( x ) |
| | | |
− | --[[ | + | -- Remove leading / trailing whitespace |
− | Fold arguments by selectively choosing values (func should return when to choose the current "dominant" value).
| + | x = x:match "^%s*(.-)%s*$"; |
− | ]]
| |
− | 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
| |
| | | |
− | --[[
| + | local decimal = string.find( x, '.', 1, true ) |
− | random
| + | local exponent_pos = string.find( x, 'E', 1, true ) |
− | | + | local result = 0; |
− | Generate a random number
| + | |
− | | + | if exponent_pos ~= nil then |
− | Usage:
| + | local exponent = string.sub( x, exponent_pos + 1 ) |
− | {{#invoke: Math | random }}
| + | x = string.sub( x, 1, exponent_pos - 1 ) |
− | {{#invoke: Math | random | maximum value }}
| + | result = result - tonumber( exponent ) |
− | {{#invoke: Math | random | minimum value | maximum value }}
| + | end |
− | ]]
| + | |
− | | + | if decimal ~= nil then |
− | function wrap.random(args)
| + | result = result + string.len( x ) - decimal |
− | local first = p._cleanNumber(args[1])
| + | return result |
− | local second = p._cleanNumber(args[2])
| + | end |
− | return p._random(first, second)
| + | |
| + | 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 |
| | | |
− | function p._random(first, second) | + | -- Finds maximum argument |
− | math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
| + | function z.max( frame ) |
− | -- math.random will throw an error if given an explicit nil parameter, so we need to use if statements to check the params.
| + | if frame.args[1] == nil then |
− | if first and second then
| + | return '' |
− | if first <= second then -- math.random doesn't allow the first number to be greater than the second.
| + | end |
− | return math.random(first, second)
| + | local max_value = tonumber( frame.args[1] ) |
− | end
| + | |
− | elseif first then
| + | local i = 2; |
− | return math.random(first)
| + | while frame.args[i] ~= nil do |
− | else
| + | local val = tonumber( frame.args[i] ); |
− | return math.random()
| + | if val ~= nil then |
− | end
| + | if val > max_value then |
| + | max_value = val; |
| + | end |
| + | end |
| + | i = i + 1; |
| + | end |
| + | |
| + | return max_value |
| end | | end |
| | | |
− | --[[ | + | -- Finds minimum argument |
− | order
| + | function z.min( frame ) |
− | | + | if frame.args[1] == nil then |
− | Determine order of magnitude of a number
| + | return '' |
− | | + | end |
− | Usage:
| + | local min_value = tonumber( frame.args[1] ) |
− | {{#invoke: Math | order | value }}
| + | |
− | ]] | + | local i = 2; |
− | | + | while frame.args[i] ~= nil do |
− | function wrap.order(args)
| + | local val = tonumber( frame.args[i] ); |
− | local input_string = (args[1] or args.x or '0');
| + | if val ~= nil then |
− | local input_number = p._cleanNumber(input_string);
| + | if val < min_value then |
− | if input_number == nil then
| + | min_value = val; |
− | return err('order of magnitude input appears non-numeric')
| + | end |
− | else
| + | end |
− | return p._order(input_number)
| + | i = i + 1; |
− | end
| + | end |
| + | |
| + | return min_value |
| end | | end |
| | | |
− | function p._order(x) | + | -- Rounds a number to specified precision |
− | if x == 0 then return 0 end
| + | function z.round(frame) |
− | return math.floor(math.log10(math.abs(x)))
| + | local value = tonumber(frame.args[1] or frame.args.value or 0); |
| + | local precision = tonumber(frame.args[2] or frame.args.precision or 0); |
| + | return z._round( value, precision ); |
| end | | end |
− | | + | function z._round( value, precision ) |
− | --[[
| + | local rescale = math.pow( 10, precision ); |
− | precision
| + | return math.floor( value * rescale + 0.5 ) / rescale; |
− | | |
− | 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 | | end |
| | | |
− | function p._precision(x) | + | -- Rounds a number to the specified precision and formats according to rules |
− | if type(x) == 'number' then
| + | -- originally used for {{template:Rnd}}. Output is a string. |
− | x = tostring(x)
| + | function z.precision_format( frame ) |
− | end
| + | -- For access to Mediawiki built-in formatter. |
− | x = string.upper(x)
| + | local lang = mw.getContentLanguage(); |
− | | + | |
− | local decimal = x:find('%.')
| + | local value = tonumber( frame.args[1] or 0 ); |
− | local exponent_pos = x:find('E')
| + | local precision = tonumber( frame.args[2] or 0 ); |
− | local result = 0;
| + | local current_precision = z._precision( value ); |
− | | |
− | 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
| + | local order = z._order( value ); |
− | result = result + string.len(x) - decimal
| + | |
− | return result
| + | -- Due to round-off effects it is neccesary to limit the returned precision under |
− | end
| + | -- some circumstances because the terminal digits will be inaccurately reported. |
| + | if order + precision >= 14 then |
| + | precision = 13 - order; |
| + | end |
| | | |
− | local pos = string.len(x);
| + | -- If rounding off, truncate extra digits |
− | while x:byte(pos) == string.byte('0') do
| + | if precision < current_precision then |
− | pos = pos - 1
| + | value = z._round( value, precision ); |
− | result = result - 1
| + | current_precision = z._precision( value ); |
− | if pos <= 0 then
| + | end |
− | return 0
| + | |
− | end
| + | local formatted_num = lang:formatNum( math.abs(value) ); |
− | end
| + | 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 |
| + | 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 |
| | | |
− | return result
| + | -- 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 | | end |
| | | |
− | | + | return z |
− | --[[
| |
− | 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
| |
− | | |
− | --[[
| |
− | 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
| |
− | | |
− | function p._min(...)
| |
− | local min_value = binary_fold((function(a, b) return a < b end), ...)
| |
− | if min_value then
| |
− | return min_value
| |
− | end
| |
− | end
| |
− | | |
− | --[[
| |
− | average
| |
− | | |
− | 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 sum, count = fold((function(a, b) return a + b end), ...)
| |
− | if not sum then
| |
− | return 0
| |
− | else
| |
− | return sum / count
| |
− | end
| |
− | end
| |
− | | |
− | --[[
| |
− | round
| |
− | | |
− | Rounds a number to specified precision
| |
− | | |
− | Usage:
| |
− | {{#invoke:Math | round | value | precision }}
| |
− | | |
− | --]]
| |
− | | |
− | function wrap.round(args)
| |
− | local value = p._cleanNumber(args[1] or args.value or 0)
| |
− | local precision = p._cleanNumber(args[2] or args.precision or 0)
| |
− | if value == nil or precision == nil then
| |
− | return err('round input appears non-numeric')
| |
− | else
| |
− | return p._round(value, precision)
| |
− | end
| |
− | end
| |
− | | |
− | function p._round(value, precision)
| |
− | local rescale = math.pow(10, precision or 0);
| |
− | return math.floor(value * rescale + 0.5) / rescale;
| |
− | end
| |
− | | |
− | --[[
| |
− | mod
| |
− | | |
− | 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
| |
− | | |
− | function p._mod(x, y)
| |
− | 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)
| |