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Module:Math (view source)

Revision as of 23:27, 31 October 2022

4,700 bytes added ,  1 year ago
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1 revision imported from wikipedia:Module:Math
en>Dragons flight
(Adds comments, slight reordering of functions.)
m (1 revision imported from wikipedia:Module:Math)
 
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Line 4:
 
]]
local z = {}
 
local yesno, getArgs -- lazily initialized
-- 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])
 
local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
if first then -- if NaN or nil, will skip down to final return
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
if first <= second then -- could match if both nil, but already checked that first is a number in last line
 
return math.random(first, second)
--[[
end
Helper functions used to avoid redundant code.
return math.random(first)
]]
end
 
return math.random()
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
 
Line 26 ⟶ 110:
 
Usage:
{{#invoke: Math | order | value }}
]]
 
function z.order(frame)
function wrap.order(args)
local input_string = (frame.args[1] or frame.args.x or '0');
local input_string = (args[1] or args.x or '0');
local input_number;
local input_number = p._cleanNumber(input_string);
if input_number == z._cleanNumber( frame, input_stringnil );then
return err('order of magnitude input appears non-numeric')
if input_number == nil then
else
return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
return p._order(input_number)
else
end
return z._order( input_number )
end
end
 
function z._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
 
Line 50 ⟶ 134:
 
Usage:
{{ #invoke: Math | precision | value }}
]]
 
function z.precision( frame )
function wrap.precision(args)
local input_string = (frame.args[1] or frame.args.x or '0');
local input_string = (args[1] or args.x or '0');
local trap_fraction = frame.args.check_fraction or false;
local trap_fraction = args.check_fraction;
local input_number;
local input_number;
 
if type( trap_fraction ) == 'string' then
if not yesno then
trap_fraction = trap_fraction:lower();
yesno = require('Module:Yesno')
if trap_fraction == 'false' or trap_fraction == '0' or
end
trap_fraction == 'no' or trap_fraction == '' then
if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
trap_fraction = false;
local pos = string.find(input_string, '/', 1, true);
else
if pos ~= nil then
trap_fraction = true;
if string.find(input_string, '/', pos + 1, true) == nil then
end
local denominator = string.sub(input_string, pos+1, -1);
end
local denom_value = tonumber(denominator);
if denom_value ~= nil then
if trap_fraction then
return math.log10(denom_value);
local pos = string.find( input_string, '/', 1, true );
end
if pos ~= nil then
end
if string.find( input_string, '/', pos + 1, true ) == nil then
end
local denominator = string.sub( input_string, pos+1, -1 );
end
local denom_value = tonumber( denominator );
 
if denom_value ~= nil then
input_number, input_string = p._cleanNumber(input_string);
return math.log10(denom_value);
if input_string == nil then
end
return err('precision input appears non-numeric')
end
else
end
return p._precision(input_string)
end
end
input_number, input_string = z._cleanNumber( frame, input_string );
if input_string == nil then
return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>'
else
return z._precision( input_string )
end
end
function z._precision( x )
x = string.upper( x )
 
function p._precision(x)
local decimal = string.find( x, '.', 1, true )
if type(x) == 'number' then
local exponent_pos = string.find( x, 'E', 1, true )
x = tostring(x)
local result = 0;
end
x = string.upper(x)
if exponent_pos ~= nil then
 
local exponent = string.sub( x, exponent_pos + 1 )
local decimal = x:find('%.')
x = string.sub( x, 1, exponent_pos - 1 )
local exponent_pos = x:find('E')
result = result - tonumber( exponent )
local result = 0;
end
 
if decimalexponent_pos ~= nil then
local resultexponent = result + string.lensub( x, )exponent_pos -+ decimal1)
x = string.sub(x, 1, exponent_pos - 1)
return result
result = result - tonumber(exponent)
end
end
 
local pos = string.len( x );
if decimal ~= nil then
while x:byte(pos) == string.byte('0') do
result = result + string.len(x) - decimal
pos = pos - 1
return result = result - 1
end
if pos <= 0 then
 
return 0
local pos = string.len(x);
end
while x:byte(pos) == string.byte('0') do
end
pos = pos - 1
result = result - 1
return result
if pos <= 0 then
return 0
end
end
 
return result
end
 
 
--[[
Line 123 ⟶ 206:
 
Usage:
{{#invoke:Math| max | value1 | value2 | ... }}
OR
{{#invoke:Math| max }}
 
Note, any values that do not evaluate to numbers are ignored.
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 z.max( frame )
function wrap.max(args)
local args = frame.args;
return p._max(unpackNumberArgs(args))
end
if args[1] == nil then
 
local parent = frame:getParent();
function p._max(...)
args = parent.args;
local max_value = binary_fold((function(a, b) return a > b end), ...)
end
local if max_value = nil;then
return max_value
end
local i = 1;
end
while args[i] ~= nil do
 
local val = z._cleanNumber( frame, args[i] );
--[[
if val ~= nil then
median
if max_value == nil or val > max_value then
 
max_value = val;
Find the median of set of numbers
end
 
end
Usage:
i = i + 1;
{{#invoke:Math | median | number1 | number2 | ...}}
end
OR
{{#invoke:Math | median }}
return max_value
]]
 
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 z.min( frame )
function wrap.min(args)
local args = frame.args;
return p._min(unpackNumberArgs(args))
end
if args[1] == nil then
 
local parent = frame:getParent();
function p._min(...)
args = parent.args;
local min_value = binary_fold((function(a, b) return a < b end), ...)
end
local if min_value = nil;then
return min_value
end
local i = 1;
end
while args[i] ~= nil do
 
local val = z._cleanNumber( frame, args[i] );
--[[
if val ~= nil then
sum
if min_value == nil or val < min_value then
 
min_value = val;
Finds the sum
end
 
end
Usage:
i = i + 1;
{{#invoke:Math| sum | value1 | value2 | ... }}
end
OR
{{#invoke:Math| sum }}
return min_value
 
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
 
--[[
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
 
Line 195 ⟶ 336:
 
Usage:
{{#invoke:Math | round | value | precision }}
 
--]]
 
function z.round(frame)
function wrap.round(args)
local value, precision;
local value = p._cleanNumber(args[1] or args.value or 0)
local valueprecision = zp._cleanNumber( frame, frame.args[12] or frame.args.valueprecision or 0 );
if value precision == z._cleanNumber( frame, frame.args[2]nil or frame.args.precision or== 0nil );then
return err('round input appears non-numeric')
else
if value == nil or precision == nil then
return p._round(value, precision)
return '<strong class="error">Formatting error: Round input appears non-numeric</strong>'
end
else
return z._round( value, precision );
end
end
 
function z._round( value, precision )
function local rescale = mathp.pow_round( 10value, precision );
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
 
--[[
log10
 
returns the log (base 10) of a number
 
Usage:
{{#invoke:Math | log10 | x }}
]]
 
function wrap.log10(args)
return math.log10(args[1])
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
 
Line 218 ⟶ 431:
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 z.precision_format( frame )
-- For access to Mediawiki built-in formatter.
local lang = mw.getContentLanguage();
local value_string, value, precision;
value, value_string = z._cleanNumber( frame, frame.args[1] or 0 );
precision = z._cleanNumber( frame, frame.args[2] or 0 );
-- Check for non-numeric input
if value == nil or precision == nil then
return '<strong class="error">Formatting error: invalid input when rounding</strong>'
end
local current_precision = z._precision( value );
 
function wrap.precision_format(args)
local order = z._order( value );
local value_string = args[1] or 0
local precision = args[2] or 0
-- Due to round-off effects it is neccesary to limit the returned precision under
return p._precision_format(value_string, precision)
-- some circumstances because the terminal digits will be inaccurately reported.
end
if order + precision >= 14 then
orig_precision = z._precision( value_string );
if order + orig_precision >= 14 then
precision = 13 - order;
end
end
 
function p._precision_format(value_string, precision)
-- If rounding off, truncate extra digits
-- For access to Mediawiki built-in formatter.
if precision < current_precision then
local lang = mw.getContentLanguage();
value = z._round( value, precision );
current_precision = z._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);
 
local value
padding = precision;
value, value_string = p._cleanNumber(value_string)
if padding > 20 then
precision = p._cleanNumber(precision)
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
 
-- Check for non-numeric input
-- Add exponential notation, if necessary.
if value == nil ifor orderprecision ~== 0nil then
return err('invalid input when rounding')
-- Use proper unary minus sign rather than ASCII default
end
if order < 0 then
 
order = '−' .. lang:formatNum( math.abs(order) );
local current_precision = p._precision(value)
else
local order = lang:formatNump._order( order value);
 
end
-- Due to round-off effects it is neccesary to limit the returned precision under
-- some circumstances because the terminal digits will be inaccurately reported.
formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
if order + precision >= 14 then
end
if order + p._precision(value_string) >= 14 then
precision = 13 - order;
return formatted_num;
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
 
--[[
divide
Helper function that interprets the input numerically. If the
 
Implements the division operator
 
Usage:
{{#invoke:Math | divide | x | y | round= | precision= }}
 
--]]
function wrap.divide(args)
local x = args[1]
local y = args[2]
local round = args.round
local precision = args.precision
if not yesno then
yesno = require('Module:Yesno')
end
return p._divide(x, y, yesno(round), precision)
end
 
function p._divide(x, y, round, precision)
if y == nil or y == "" then
return err("Empty divisor")
elseif not tonumber(y) then
if type(y) == 'string' and string.sub(y, 1, 1) == '<' then
return y
else
return err("Not a number: " .. y)
end
elseif x == nil or x == "" then
return err("Empty dividend")
elseif not tonumber(x) then
if type(x) == 'string' and string.sub(x, 1, 1) == '<' then
return x
else
return err("Not a number: " .. x)
end
else
local z = x / y
if round then
return p._round(z, 0)
elseif precision then
return p._round(z, precision)
else
return z
end
end
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 zp._cleanNumber( frame, number_string )
if type(number_string == nil or number_string:len() == 0'number' then
-- We were passed a number, so we don't need to do any processing.
return nil, nil;
return number_string, tostring(number_string)
end
elseif type(number_string) ~= 'string' or not number_string:find('%S') then
-- We were passed a non-string or a blank string, so exit.
-- Attempt basic conversion
return nil, nil;
local number = tonumber( number_string )
end
 
-- If failed, attempt to evaluate input as an expression
-- Attempt basic conversion
if number == nil then
local attemptnumber = frame:preprocesstonumber( '{{#expr: ' .. number_string .. '}}' );
 
attempt = tonumber( attempt );
-- If failed, attempt to evaluate input as an expression
if attempt ~= nil then
if number == nil attempt;then
local success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
number_string = tostring( number );
if success then
else
number = nil;tonumber(result)
number_string = nil;tostring(number)
else
end
number = nil
else
number_string = nil
-- String is valid but may contain padding, clean it.
end
number_string = number_string:match( "^%s*(.-)%s*$" );
else
end
number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it.
number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs.
return number, number_string;
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
 
--[[
return z
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)
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