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Module:Math (view source)

Revision as of 04:06, 18 December 2013

2,082 bytes removed ,  10 years ago
Undid revision 586573269 by Mr. Stradivarius (talk) the code refactor broke some existing modules - revert for now while I work out the extent of the problem
en>Mr. Stradivarius
(add a gcd function per edit request by User:Mxn, add a mod function, alter existing functions to allow access from Lua without calling a frame object, use Module:Arguments to process arguments, p._cleanNumber improvements)
en>Mr. Stradivarius
(Undid revision 586573269 by Mr. Stradivarius (talk) the code refactor broke some existing modules - revert for now while I work out the extent of the problem)
Line 4:
 
]]
local z = {}
 
-- Generate random number
local yesno = require('Module:Yesno')
function z.random( frame )
local getArgs = require('Module:Arguments').getArgs
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
local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
if first <= second then -- could match if both nil, but already checked that first is a number in last line
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
return math.random(first, second)
 
end
--[[
return math.random(first)
Helper functions used to avoid redundant code.
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 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
 
Line 103 ⟶ 26:
 
Usage:
{{#invoke: Math | order | value }}
]]
function z.order(frame)
 
local input_string = (frame.args[1] or frame.args.x or '0');
function wrap.order(args)
local input_number;
local input_string = (args[1] or args.x or '0');
local input_number = p._cleanNumber(input_string);
if input_number == nilz._cleanNumber( frame, input_string then);
if input_number == nil then
return err('order of magnitude input appears non-numeric')
return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
else
else
return p._order(input_number)
return z._order( input_number )
end
end
end
function z._order(x)
 
if x == 0 then return 0 end
function p._order(x)
return math.floor(math.log10(math.abs(x)))
if x == 0 then return 0 end
return math.floor(math.log10(math.abs(x)))
end
 
Line 127 ⟶ 50:
 
Usage:
{{ #invoke: Math | precision | value }}
]]
function z.precision( frame )
 
local input_string = (frame.args[1] or frame.args.x or '0');
function wrap.precision(args)
local trap_fraction = frame.args.check_fraction or false;
local input_string = (args[1] or args.x or '0');
local input_number;
local trap_fraction = args.check_fraction;
local input_number;
if type( trap_fraction ) == 'string' then
 
trap_fraction = trap_fraction:lower();
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 trap_fraction == 'false' or trap_fraction == '0' or
local pos = string.find(input_string, '/', 1, true);
trap_fraction == 'no' or trap_fraction == '' then
if pos ~= nil then
trap_fraction = false;
if string.find(input_string, '/', pos + 1, true) == nil then
else
local denominator = string.sub(input_string, pos+1, -1);
trap_fraction = true;
local denom_value = tonumber(denominator);
end
if denom_value ~= nil then
end
return math.log10(denom_value);
end
if trap_fraction then
end
local pos = string.find( input_string, '/', 1, true );
end
if pos ~= nil then
end
if string.find( input_string, '/', pos + 1, true ) == nil then
 
input_number, input_string local denominator = pstring._cleanNumbersub( input_string, pos+1, -1 );
local denom_value = tonumber( denominator );
if input_string == nil then
if denom_value ~= nil then
return err('precision input appears non-numeric')
return math.log10(denom_value);
else
end
return p._precision(input_string)
end
end
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 )
 
local decimal = string.find( x, '.', 1, true )
function p._precision(x)
local exponent_pos = string.find( x, 'E', 1, true )
if type(x) == 'number' then
local result = 0;
x = tostring(x)
end
if exponent_pos ~= nil then
x = string.upper(x)
local exponent = string.sub( x, exponent_pos + 1 )
 
x = string.sub( x, 1, exponent_pos - 1 )
local decimal = x:find('%.')
result = result - tonumber( exponent )
local exponent_pos = x:find('E')
end
local result = 0;
 
if exponent_posdecimal ~= nil then
local exponent result = result + string.sublen( x, exponent_pos) +- 1)decimal
return result
x = string.sub(x, 1, exponent_pos - 1)
end
result = result - tonumber(exponent)
end
local pos = string.len( x );
 
while x:byte(pos) == string.byte('0') do
if decimal ~= nil then
pos = pos - 1
result = result + string.len(x) - decimal
return result = result - 1
if pos <= 0 then
end
return 0
 
end
local pos = string.len(x);
end
while x:byte(pos) == string.byte('0') do
pos = pos - 1
return result
result = result - 1
if pos <= 0 then
return 0
end
end
 
return result
end
 
Line 195 ⟶ 123:
 
Usage:
{{#invoke:Math| max | value1 | value2 | ... }}
OR
{{#invoke:Math| max }}
 
When used with no arguments, it takes its input from the parent
Note, any values that do not evaluate to numbers are ignored.
frame. Note, any values that do not evaluate to numbers are ignored.
]]
function z.max( frame )
 
local args = frame.args;
function wrap.max(args)
return p._max(unpackNumberArgs(args))
if args[1] == nil then
end
local parent = frame:getParent();
 
args = parent.args;
function p._max(...)
end
local function maxOfTwo(a, b)
local max_value = nil;
if a > b then
return a
local i = 1;
else
while args[i] ~= nil do
return b
local val = z._cleanNumber( frame, args[i] );
end
if val ~= nil then
end
local if max_value == applyFuncToArgs(maxOfTwo,nil or val > max_value ...)then
if max_value then= val;
end
return max_value
end
end
i = i + 1;
end
return max_value
end
 
Line 224 ⟶ 159:
 
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 )
 
local args = frame.args;
function wrap.min(args)
return p._min(unpackNumberArgs(args))
if args[1] == nil then
end
local parent = frame:getParent();
 
args = parent.args;
function p._min(...)
end
local function minOfTwo(a, b)
local min_value = nil;
if a < b then
return a
local i = 1;
else
while args[i] ~= nil do
return b
local val = z._cleanNumber( frame, args[i] );
end
if val ~= nil then
end
local if min_value == applyFuncToArgs(minOfTwo,nil or val < min_value ...)then
if min_value then= val;
end
return min_value
end
end
i = i + 1;
end
return min_value
end
 
--[[
average
 
Finds the average
 
Usage:
{{#invoke:Math| average | value1 | value2 | ... }}
OR
{{#invoke:Math| average }}
 
When used with no arguments, it takes its input from the parent
Note, any values that do not evaluate to numbers are ignored.
frame. Note, any values that do not evaluate to numbers are ignored.
]]
function z.average( frame )
 
local args = frame.args;
function wrap.average(args)
if args[1] == nil then
return p._average(unpackNumberArgs(args))
local parent = frame:getParent();
end
args = parent.args;
 
end
function p._average(...)
local functionsum getSum(a,= b)0;
local count = 0;
return a + b
end
local i = 1;
local sum, count = applyFuncToArgs(getSum, ...)
while args[i] ~= nil do
if not sum then
local val = z._cleanNumber( frame, args[i] );
return 0
if val ~= nil then
else
return sum = sum /+ countval
count = count + 1
end
end
i = i + 1;
end
return (count == 0 and 0 or sum/count)
end
 
Line 285 ⟶ 230:
 
Usage:
{{#invoke:Math | round | value | precision }}
 
--]]
function z.round(frame)
 
local value, precision;
function wrap.round(args)
local value = p._cleanNumber(args[1] or args.value or 0)
local precision value = pz._cleanNumber( frame, frame.args[21] or frame.args.precisionvalue or 0 );
if value = precision = nilz._cleanNumber( frame, frame.args[2] or frame.args.precision ==or nil0 then);
return err('round input appears non-numeric')
if value == nil or precision == nil then
else
return '<strong class="error">Formatting error: Round input appears non-numeric</strong>'
return p._round(value, precision)
end else
return z._round( value, precision );
end
end
function z._round( value, precision )
 
function p local rescale = math._roundpow(value 10, precision );
return math.floor( value * rescale + 0.5 ) / rescale;
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
 
Line 371 ⟶ 257:
 
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 );
 
local order = z._order( value );
function wrap.precision_format(args)
local value_string = args[1] or 0
-- Due to round-off effects it is neccesary to limit the returned precision under
local precision = args[2] or 0
-- some circumstances because the terminal digits will be inaccurately reported.
return p._precision_format(value_string, precision)
if order + precision >= 14 then
end
orig_precision = z._precision( value_string );
if order + orig_precision >= 14 then
precision = 13 - order;
end
end
 
-- If rounding off, truncate extra digits
function p._precision_format(value_string, precision)
if precision < current_precision then
-- For access to Mediawiki built-in formatter.
value = z._round( value, precision );
local lang = mw.getContentLanguage();
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);
 
padding = precision;
local value
if padding > 20 then
value, value_string = p._cleanNumber(value_string)
padding = 20;
precision = p._cleanNumber(precision)
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.
-- Check for non-numeric input
if value == nil orif precisionorder =~= nil0 then
-- Use proper unary minus sign rather than ASCII default
return err('invalid input when rounding')
if order < 0 then
end
order = '−' .. lang:formatNum( math.abs(order) );
 
else
local current_precision = p._precision(value)
local order = p._orderlang:formatNum(value order );
end
 
-- Due to round-off effects it is neccesary to limit the returned precision under
formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
-- some circumstances because the terminal digits will be inaccurately reported.
end
if order + precision >= 14 then
orig_precision = p._precision(value_string)
return formatted_num;
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
 
Line 477 ⟶ 357:
]]
 
function pz._cleanNumber( frame, number_string )
if type(number_string == nil or number_string:len() == 'number'0 then
return nil, nil;
-- We were passed a number, so we don't need to do any processing.
end
return number_string, tostring(number_string)
elseif type(number_string) ~= 'string' or not number_string:find('%S') then
-- Attempt basic conversion
-- We were passed a non-string or a blank string, so exit.
local number = tonumber( number_string )
return nil, nil;
end
-- If failed, attempt to evaluate input as an expression
 
if number == nil then
-- Attempt basic conversion
local numberattempt = tonumberframe:preprocess( '{{#expr: ' .. number_string .. '}}' );
attempt = tonumber( attempt );
 
if attempt ~= nil then
-- If failed, attempt to evaluate input as an expression
if number == nil thenattempt;
number_string = tostring( number );
local frame = mw.getCurrentFrame()
else
local attempt = frame:preprocess('{{#expr: ' .. number_string .. '}}')
number = nil;
attempt = tonumber(attempt)
number_string = nil;
if attempt ~= nil then
end
number = attempt
else
number_string = tostring(number)
-- String is valid but may contain padding, clean it.
else
number_string = number_string:match( "^%s*(.-)%s*$" );
number = nil
end
number_string = nil
end
return number, number_string;
else
number_string = number_string:match("^%s*(.-)%s*$") -- 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 function makeWrapper(funcName)
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
 
for funcName in pairs(wrap) do
p[funcName] = makeWrapper(funcName)
end
 
return pz
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