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Module:Math: Difference between revisions

Module:Math (edit)

Revision as of 00:45, 18 December 2013

2,082 bytes added ,  10 years ago
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>Dragons flight
(add average)
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)
Line 4: 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
end


Line 26: Line 103:


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


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Usage:
Usage:
    {{ #invoke: Math | precision | value }}
{{ #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
 
                local denominator = string.sub( input_string, pos+1, -1 );
input_number, input_string = p._cleanNumber(input_string);
                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
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 decimal ~= nil then
if exponent_pos ~= nil then
        result = result + string.len( x ) - decimal
local exponent = string.sub(x, exponent_pos + 1)
        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
        result = result - 1
return result
        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
end


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Usage:
Usage:
    {{#invoke:Math| max | value1 | value2 | ... }}
{{#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
            if max_value == nil or val > max_value then
local max_value = applyFuncToArgs(maxOfTwo, ...)
                max_value = val;
if max_value then
            end
return max_value
        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 )
 
    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
            if min_value == nil or val < min_value then
local min_value = applyFuncToArgs(minOfTwo, ...)
                min_value = val;
if min_value then
            end
return min_value
        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 }}
 
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 sum = 0;
local function getSum(a, b)
    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
            sum = sum + val
return sum / count
            count = count + 1
end
        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)
 
    local value, precision;
function wrap.gcd(args)
   
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 )
 
    local rescale = math.pow( 10, precision );
function p._gcd(...)
    return math.floor( value * rescale + 0.5 ) / rescale;
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
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 );


    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
function p._precision_format(value_string, precision)
            precision = 13 - order;         
-- For access to Mediawiki built-in formatter.
        end         
local lang = mw.getContentLanguage();
    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


    -- If rounding off, truncate extra digits
-- Pad with zeros, if needed     
    if precision < current_precision then
if current_precision < precision then
        value = z._round( value, precision );
local padding
        current_precision = z._precision( value );
if current_precision <= 0 then
    end   
if precision > 0 then
   
local zero_sep = lang:formatNum(1.1)
    local formatted_num = lang:formatNum( math.abs(value) );
formatted_num = formatted_num .. zero_sep:sub(2,2)
    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


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


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]]
]]


function z._cleanNumber( frame, number_string )
function p._cleanNumber(number_string)
    if number_string == nil or number_string:len() == 0 then
if type(number_string) == 'number' 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 attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
local number = tonumber(number_string)
        attempt = tonumber( attempt );
 
        if attempt ~= nil then
-- If failed, attempt to evaluate input as an expression
            number = attempt;
if number == nil then
            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
end


return z
return p
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