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Module:Math (edit)

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
m>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)
m>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: Line 4:


]]
]]
local z = {}


local yesno = require('Module:Yesno')
-- Generate random number
local getArgs = require('Module:Arguments').getArgs
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 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
end


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Usage:
Usage:
{{#invoke: Math | order | value }}
    {{#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 == nil then
    input_number = z._cleanNumber( frame, input_string );
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
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
end


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Usage:
Usage:
{{ #invoke: Math | precision | value }}
    {{ #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 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 = trap_fraction:lower();
local pos = string.find(input_string, '/', 1, true);
        if trap_fraction == 'false' or trap_fraction == '0' or
if pos ~= nil then
                trap_fraction == 'no' or trap_fraction == '' then
if string.find(input_string, '/', pos + 1, true) == nil then
            trap_fraction = false;
local denominator = string.sub(input_string, pos+1, -1);
        else
local denom_value = tonumber(denominator);
            trap_fraction = true;
if denom_value ~= nil then
        end
return math.log10(denom_value);
    end
end
   
end                         
    if trap_fraction then
end
        local pos = string.find( input_string, '/', 1, true );
end     
        if pos ~= nil then
 
            if string.find( input_string, '/', pos + 1, true ) == nil then
input_number, input_string = p._cleanNumber(input_string);
                local denominator = string.sub( input_string, pos+1, -1 );
if input_string == nil then
                local denom_value = tonumber( denominator );
return err('precision input appears non-numeric')
                if denom_value ~= nil then
else
                    return math.log10(denom_value);
return p._precision(input_string)
                end
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
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 exponent_pos ~= nil then
    if decimal ~= nil then
local exponent = string.sub(x, exponent_pos + 1)
        result = result + string.len( x ) - decimal
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 = 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
end


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Usage:
Usage:
{{#invoke:Math| max | value1 | value2 | ... }}
    {{#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 function maxOfTwo(a, b)
    end
if a > b then
    local max_value = nil;
return a
   
else
    local i = 1;
return b
    while args[i] ~= nil do
end
        local val = z._cleanNumber( frame, args[i] );
end
        if val ~= nil then
local max_value = applyFuncToArgs(maxOfTwo, ...)
            if max_value == nil or val > max_value then
if max_value then
                max_value = val;
return max_value
            end
end
        end      
        i = i + 1;
    end
 
    return max_value
end
end


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Usage:
Usage:
{{#invoke:Math| min | value1 | value2 | ... }}
    {{#invoke:Math| min | value1 | value2 | ... }}
OR
OR
{{#invoke:Math| min }}
    {{#invoke:Math| min }}


When used with no arguments, it takes its input from the parent
When used with no arguments, it takes its input from the parent
frame.  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.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 function minOfTwo(a, b)
    end
if a < b then
    local min_value = nil;
return a
   
else
    local i = 1;
return b
    while args[i] ~= nil do
end
        local val = z._cleanNumber( frame, args[i] );
end
        if val ~= nil then
local min_value = applyFuncToArgs(minOfTwo, ...)
            if min_value == nil or val < min_value then
if min_value then
                min_value = val;
return min_value
            end
end
        end      
        i = i + 1;
    end
 
    return min_value
end
end


--[[
--[[
average  
average  
 
Finds the average
Finds the average
 
Usage:
Usage:
{{#invoke:Math| average | value1 | value2 | ... }}
    {{#invoke:Math| average | value1 | value2 | ... }}
OR
OR
{{#invoke:Math| average }}
    {{#invoke:Math| average }}
 
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.average( frame )
function wrap.average(args)
    local args = frame.args;
return p._average(unpackNumberArgs(args))
    if args[1] == nil then
end
        local parent = frame:getParent();
 
        args = parent.args;
function p._average(...)
    end
local function getSum(a, b)
    local sum = 0;
return a + b
    local count = 0;
end
local sum, count = applyFuncToArgs(getSum, ...)
    local i = 1;
if not sum then
    while args[i] ~= nil do
return 0
        local val = z._cleanNumber( frame, args[i] );
else
        if val ~= nil then
return sum / count
            sum = sum + val
end
            count = count + 1
        end       
        i = i + 1;
    end
    return (count == 0 and 0 or sum/count)
end
end


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Usage:
Usage:
{{#invoke:Math | round | value | precision }}
    {{#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 z.round(frame)
function wrap.gcd(args)
    local value, precision;
return p._gcd(unpackNumberArgs(args))
   
    value = z._cleanNumber( frame, frame.args[1] or frame.args.value or 0 );
    precision = z._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 );
   
    if value == nil or precision == nil then
        return '<strong class="error">Formatting error: Round input appears non-numeric</strong>'
    else
        return z._round( value, precision );
    end   
end
end
 
function z._round( value, precision )
function p._gcd(...)
    local rescale = math.pow( 10, precision );
local function findGcd(a, b)
    return math.floor( value * rescale + 0.5 ) / rescale;
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
end


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Usage:
Usage:
{{#invoke: Math | precision_format | number | precision }}
    {{#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 );
function p._precision_format(value_string, precision)
        if order + orig_precision >= 14 then
-- For access to Mediawiki built-in formatter.
            precision = 13 - order;         
local lang = mw.getContentLanguage();
        end         
 
    end
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 rounding off, truncate extra digits
if current_precision < precision then
    if precision < current_precision then
local padding
        value = z._round( value, precision );
if current_precision <= 0 then
        current_precision = z._precision( value );
if precision > 0 then
    end   
local zero_sep = lang:formatNum(1.1)
   
formatted_num = formatted_num .. zero_sep:sub(2,2)
    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
                padding = precision;
if padding > 20 then
                if padding > 20 then
padding = 20
                    padding = 20;
end
                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


formatted_num = formatted_num .. string.rep('0', padding)
    -- Add exponential notation, if necessary.
end           
    if order ~= 0 then
else                 
        -- Use proper unary minus sign rather than ASCII default
padding = precision - current_precision
        if order < 0 then
if padding > 20 then
            order = '−' .. lang:formatNum( math.abs(order) );
padding = 20
        else
end
            order = lang:formatNum( order );
formatted_num = formatted_num .. string.rep('0', padding)
        end     
end
       
end
        formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
 
    end
-- Add exponential notation, if necessary.
   
if order ~= 0 then
    return formatted_num;
-- 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


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]]
]]


function p._cleanNumber(number_string)
function z._cleanNumber( frame, number_string )
if type(number_string) == 'number' then
    if number_string == nil or number_string:len() == 0 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 number = tonumber(number_string)
        local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
 
        attempt = tonumber( attempt );
-- If failed, attempt to evaluate input as an expression
        if attempt ~= nil then
if number == nil then
            number = attempt;
local frame = mw.getCurrentFrame()
            number_string = tostring( number );
local attempt = frame:preprocess('{{#expr: ' .. number_string .. '}}')
        else
attempt = tonumber(attempt)
            number = nil;
if attempt ~= nil then
            number_string = nil;
number = attempt
        end
number_string = tostring(number)
    else
else
    -- String is valid but may contain padding, clean it.
number = nil
        number_string = number_string:match( "^%s*(.-)%s*$" );
number_string = nil
    end
end
   
else
    return number, number_string;
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
end


return p
return z
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