Module:Math
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- --[[
- 引自维基百科(enwp:Module:Math,oldid=613638641)
- This module provides a number of basic mathematical operations.
- ]]
- local yesno, getArgs -- lazily initialized
- 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.
- --[[
- 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 applyFuncToArgs(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
- --[[
- 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 function maxOfTwo(a, b)
- if a > b then
- return a
- else
- return b
- end
- end
- local max_value = applyFuncToArgs(maxOfTwo, ...)
- 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 function minOfTwo(a, b)
- if a < b then
- return a
- else
- return b
- end
- end
- local min_value = applyFuncToArgs(minOfTwo, ...)
- 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 function getSum(a, b)
- return a + b
- end
- local sum, count = applyFuncToArgs(getSum, ...)
- 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 = applyFuncToArgs(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)