Difference between revisions of "Module:Math/sandbox"
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blackwiki>Mr. Stradivarius (add structure for argument-processing code, convert the random function) |
blackwiki>Mr. Stradivarius (remove spaces inside parentheses so that the module conforms to the style guidelines) |
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| Line 51: | Line 51: | ||
local input_number; | local input_number; | ||
| − | input_number = p._cleanNumber( frame, input_string ); | + | input_number = p._cleanNumber(frame, input_string); |
if input_number == nil then | if input_number == nil then | ||
return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>' | return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>' | ||
else | else | ||
| − | return p._order( input_number ) | + | return p._order(input_number) |
end | end | ||
end | end | ||
| Line 76: | Line 76: | ||
local input_number; | local input_number; | ||
| − | if type( trap_fraction ) == 'string' then | + | if type(trap_fraction) == 'string' then |
trap_fraction = trap_fraction:lower(); | trap_fraction = trap_fraction:lower(); | ||
if trap_fraction == 'false' or trap_fraction == '0' or | if trap_fraction == 'false' or trap_fraction == '0' or | ||
| Line 87: | Line 87: | ||
if trap_fraction then | if trap_fraction then | ||
| − | local pos = string.find( input_string, '/', 1, true ); | + | local pos = string.find(input_string, '/', 1, true); |
if pos ~= nil then | if pos ~= nil then | ||
| − | if string.find( input_string, '/', pos + 1, true ) == nil then | + | if string.find(input_string, '/', pos + 1, true) == nil then |
| − | local denominator = string.sub( input_string, pos+1, -1 ); | + | local denominator = string.sub(input_string, pos+1, -1); |
| − | local denom_value = tonumber( denominator ); | + | local denom_value = tonumber(denominator); |
if denom_value ~= nil then | if denom_value ~= nil then | ||
return math.log10(denom_value); | return math.log10(denom_value); | ||
| Line 99: | Line 99: | ||
end | end | ||
| − | input_number, input_string = p._cleanNumber( frame, input_string ); | + | input_number, input_string = p._cleanNumber(frame, input_string); |
if input_string == nil then | if input_string == nil then | ||
return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>' | return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>' | ||
else | else | ||
| − | return p._precision( input_string ) | + | return p._precision(input_string) |
end | end | ||
end | end | ||
| − | function p._precision( x ) | + | function p._precision(x) |
| − | x = string.upper( x ) | + | x = string.upper(x) |
| − | local decimal = string.find( x, '.', 1, true ) | + | local decimal = string.find(x, '.', 1, true) |
| − | local exponent_pos = string.find( x, 'E', 1, true ) | + | local exponent_pos = string.find(x, 'E', 1, true) |
local result = 0; | local result = 0; | ||
if exponent_pos ~= nil then | if exponent_pos ~= nil then | ||
| − | local exponent = string.sub( x, exponent_pos + 1 ) | + | local exponent = string.sub(x, exponent_pos + 1) |
| − | x = string.sub( x, 1, exponent_pos - 1 ) | + | x = string.sub(x, 1, exponent_pos - 1) |
| − | result = result - tonumber( exponent ) | + | result = result - tonumber(exponent) |
end | end | ||
if decimal ~= nil then | if decimal ~= nil then | ||
| − | result = result + string.len( x ) - decimal | + | result = result + string.len(x) - decimal |
return result | return result | ||
end | end | ||
| − | local pos = string.len( x ); | + | local pos = string.len(x); |
while x:byte(pos) == string.byte('0') do | while x:byte(pos) == string.byte('0') do | ||
pos = pos - 1 | pos = pos - 1 | ||
| Line 149: | Line 149: | ||
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 p.max( frame ) | + | function p.max(frame) |
local args = frame.args; | local args = frame.args; | ||
| Line 160: | Line 160: | ||
local i = 1; | local i = 1; | ||
while args[i] ~= nil do | while args[i] ~= nil do | ||
| − | local val = p._cleanNumber( frame, args[i] ); | + | local val = p._cleanNumber(frame, args[i]); |
if val ~= nil then | if val ~= nil then | ||
if max_value == nil or val > max_value then | if max_value == nil or val > max_value then | ||
| Line 185: | Line 185: | ||
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 p.min( frame ) | + | function p.min(frame) |
local args = frame.args; | local args = frame.args; | ||
| Line 196: | Line 196: | ||
local i = 1; | local i = 1; | ||
while args[i] ~= nil do | while args[i] ~= nil do | ||
| − | local val = p._cleanNumber( frame, args[i] ); | + | local val = p._cleanNumber(frame, args[i]); |
if val ~= nil then | if val ~= nil then | ||
if min_value == nil or val < min_value then | if min_value == nil or val < min_value then | ||
| Line 221: | Line 221: | ||
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 p.average( frame ) | + | function p.average(frame) |
local args = frame.args; | local args = frame.args; | ||
if args[1] == nil then | if args[1] == nil then | ||
| Line 232: | Line 232: | ||
local i = 1; | local i = 1; | ||
while args[i] ~= nil do | while args[i] ~= nil do | ||
| − | local val = p._cleanNumber( frame, args[i] ); | + | local val = p._cleanNumber(frame, args[i]); |
if val ~= nil then | if val ~= nil then | ||
sum = sum + val | sum = sum + val | ||
| Line 255: | Line 255: | ||
local value, precision; | local value, precision; | ||
| − | value = p._cleanNumber( frame, frame.args[1] or frame.args.value or 0 ); | + | value = p._cleanNumber(frame, frame.args[1] or frame.args.value or 0); |
| − | precision = p._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 ); | + | precision = p._cleanNumber(frame, frame.args[2] or frame.args.precision or 0); |
if value == nil or precision == nil then | if value == nil or precision == nil then | ||
return '<strong class="error">Formatting error: Round input appears non-numeric</strong>' | return '<strong class="error">Formatting error: Round input appears non-numeric</strong>' | ||
else | else | ||
| − | return p._round( value, precision ); | + | return p._round(value, precision); |
end | end | ||
end | end | ||
| − | function p._round( value, precision ) | + | function p._round(value, precision) |
| − | local rescale = math.pow( 10, precision ); | + | local rescale = math.pow(10, precision); |
| − | return math.floor( value * rescale + 0.5 ) / rescale; | + | return math.floor(value * rescale + 0.5) / rescale; |
end | end | ||
| Line 310: | Line 310: | ||
{{#invoke: Math | precision_format | number | precision }} | {{#invoke: Math | precision_format | number | precision }} | ||
]] | ]] | ||
| − | function p.precision_format( frame ) | + | function p.precision_format(frame) |
-- For access to Mediawiki built-in formatter. | -- For access to Mediawiki built-in formatter. | ||
local lang = mw.getContentLanguage(); | local lang = mw.getContentLanguage(); | ||
local value_string, value, precision; | local value_string, value, precision; | ||
| − | value, value_string = p._cleanNumber( frame, frame.args[1] or 0 ); | + | value, value_string = p._cleanNumber(frame, frame.args[1] or 0); |
| − | precision = p._cleanNumber( frame, frame.args[2] or 0 ); | + | precision = p._cleanNumber(frame, frame.args[2] or 0); |
-- Check for non-numeric input | -- Check for non-numeric input | ||
| Line 323: | Line 323: | ||
end | end | ||
| − | local current_precision = p._precision( value ); | + | local current_precision = p._precision(value); |
| − | local order = p._order( value ); | + | local order = p._order(value); |
-- Due to round-off effects it is neccesary to limit the returned precision under | -- Due to round-off effects it is neccesary to limit the returned precision under | ||
-- some circumstances because the terminal digits will be inaccurately reported. | -- some circumstances because the terminal digits will be inaccurately reported. | ||
if order + precision >= 14 then | if order + precision >= 14 then | ||
| − | orig_precision = p._precision( value_string ); | + | orig_precision = p._precision(value_string); |
if order + orig_precision >= 14 then | if order + orig_precision >= 14 then | ||
precision = 13 - order; | precision = 13 - order; | ||
| Line 338: | Line 338: | ||
-- If rounding off, truncate extra digits | -- If rounding off, truncate extra digits | ||
if precision < current_precision then | if precision < current_precision then | ||
| − | value = p._round( value, precision ); | + | value = p._round(value, precision); |
| − | current_precision = p._precision( value ); | + | current_precision = p._precision(value); |
end | end | ||
| − | local formatted_num = lang:formatNum( math.abs(value) ); | + | local formatted_num = lang:formatNum(math.abs(value)); |
local sign; | local sign; | ||
| Line 353: | Line 353: | ||
-- Handle cases requiring scientific notation | -- Handle cases requiring scientific notation | ||
| − | if string.find( formatted_num, 'E', 1, true ) ~= nil or math.abs(order) >= 9 then | + | if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then |
| − | value = value * math.pow( 10, -order ); | + | value = value * math.pow(10, -order); |
current_precision = current_precision + order; | current_precision = current_precision + order; | ||
precision = precision + order; | precision = precision + order; | ||
| − | formatted_num = lang:formatNum( math.abs(value) ); | + | formatted_num = lang:formatNum(math.abs(value)); |
else | else | ||
order = 0; | order = 0; | ||
| Line 368: | Line 368: | ||
if current_precision <= 0 then | if current_precision <= 0 then | ||
if precision > 0 then | if precision > 0 then | ||
| − | local zero_sep = lang:formatNum( 1.1 ); | + | local zero_sep = lang:formatNum(1.1); |
formatted_num = formatted_num .. zero_sep:sub(2,2); | formatted_num = formatted_num .. zero_sep:sub(2,2); | ||
| Line 376: | Line 376: | ||
end | end | ||
| − | formatted_num = formatted_num .. string.rep( '0', padding ); | + | formatted_num = formatted_num .. string.rep('0', padding); |
end | end | ||
else | else | ||
| Line 383: | Line 383: | ||
padding = 20; | padding = 20; | ||
end | end | ||
| − | formatted_num = formatted_num .. string.rep( '0', padding ); | + | formatted_num = formatted_num .. string.rep('0', padding); |
end | end | ||
end | end | ||
| Line 391: | Line 391: | ||
-- Use proper unary minus sign rather than ASCII default | -- Use proper unary minus sign rather than ASCII default | ||
if order < 0 then | if order < 0 then | ||
| − | order = '−' .. lang:formatNum( math.abs(order) ); | + | order = '−' .. lang:formatNum(math.abs(order)); |
else | else | ||
| − | order = lang:formatNum( order ); | + | order = lang:formatNum(order); |
end | end | ||
| Line 408: | Line 408: | ||
]] | ]] | ||
| − | function p._cleanNumber( frame, number_string ) | + | function p._cleanNumber(frame, number_string) |
if number_string == nil or number_string:len() == 0 then | if number_string == nil or number_string:len() == 0 then | ||
return nil, nil; | return nil, nil; | ||
| Line 414: | Line 414: | ||
-- Attempt basic conversion | -- Attempt basic conversion | ||
| − | local number = tonumber( number_string ) | + | local number = tonumber(number_string) |
-- If failed, attempt to evaluate input as an expression | -- If failed, attempt to evaluate input as an expression | ||
if number == nil then | if number == nil then | ||
| − | local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' ); | + | local attempt = frame:preprocess('{{#expr: ' .. number_string .. '}}'); |
| − | attempt = tonumber( attempt ); | + | attempt = tonumber(attempt); |
if attempt ~= nil then | if attempt ~= nil then | ||
number = attempt; | number = attempt; | ||
| − | number_string = tostring( number ); | + | number_string = tostring(number); |
else | else | ||
number = nil; | number = nil; | ||
| Line 432: | Line 432: | ||
else | else | ||
-- String is valid but may contain padding, clean it. | -- String is valid but may contain padding, clean it. | ||
| − | number_string = number_string:match( "^%s*(.-)%s*$" ); | + | number_string = number_string:match("^%s*(.-)%s*$"); |
end | end | ||
Revision as of 12:41, 5 December 2013
Documentation for this module may be created at Module:Math/sandbox/doc
--[[
This module provides a number of basic mathematical operations.
]]
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.
--[[
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 = tonumber(args[1])
local second = tonumber(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 = (frame.args[1] or frame.args.x or '0');
local input_number;
input_number = p._cleanNumber(frame, input_string);
if input_number == nil then
return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
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 = (frame.args[1] or frame.args.x or '0');
local trap_fraction = frame.args.check_fraction or false;
local input_number;
if type(trap_fraction) == 'string' then
trap_fraction = trap_fraction:lower();
if trap_fraction == 'false' or trap_fraction == '0' or
trap_fraction == 'no' or trap_fraction == '' then
trap_fraction = false;
else
trap_fraction = true;
end
end
if trap_fraction then
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(frame, input_string);
if input_string == nil then
return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>'
else
return p._precision(input_string)
end
end
function p._precision(x)
x = string.upper(x)
local decimal = string.find(x, '.', 1, true)
local exponent_pos = string.find(x, 'E', 1, true)
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 | ... }}
OR
{{#invoke:Math| max }}
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 p.max(frame)
local args = frame.args;
if args[1] == nil then
local parent = frame:getParent();
args = parent.args;
end
local max_value = nil;
local i = 1;
while args[i] ~= nil do
local val = p._cleanNumber(frame, args[i]);
if val ~= nil then
if max_value == nil or val > max_value then
max_value = val;
end
end
i = i + 1;
end
return max_value
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 p.min(frame)
local args = frame.args;
if args[1] == nil then
local parent = frame:getParent();
args = parent.args;
end
local min_value = nil;
local i = 1;
while args[i] ~= nil do
local val = p._cleanNumber(frame, args[i]);
if val ~= nil then
if min_value == nil or val < min_value then
min_value = val;
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
frame. Note, any values that do not evaluate to numbers are ignored.
]]
function p.average(frame)
local args = frame.args;
if args[1] == nil then
local parent = frame:getParent();
args = parent.args;
end
local sum = 0;
local count = 0;
local i = 1;
while args[i] ~= nil do
local val = p._cleanNumber(frame, args[i]);
if val ~= nil then
sum = sum + val
count = count + 1
end
i = i + 1;
end
return (count == 0 and 0 or sum/count)
end
--[[
round
Rounds a number to specified precision
Usage:
{{#invoke:Math | round | value | precision }}
--]]
function p.round(frame)
local value, precision;
value = p._cleanNumber(frame, frame.args[1] or frame.args.value or 0);
precision = p._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 p._round(value, precision);
end
end
function p._round(value, precision)
local rescale = math.pow(10, precision);
return math.floor(value * rescale + 0.5) / rescale;
end
--[=[
gcd
Calculates the [[greatest common divisor]] of two numbers according to the [[extended Euclidean algorithm]].
Usage:
{{#invoke:Math | gcd | value 1 | value 2 }}
]=]
function p.gcd(frame)
local args = frame.args
if args[1] == nil then
local parent = frame:getParent()
args = parent.args
end
local a = p._cleanNumber(frame, args[1])
local b = p._cleanNumber(frame, args[2])
if not a or not b then return end
local r = b
local oldr = a
while r ~= 0 do
local quotient = math.floor(oldr / r)
oldr, r = r, oldr - quotient * r
end
if a == 0 and b < 0 or b == 0 and a < 0 then oldr = oldr * -1 end
return oldr
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 p.precision_format(frame)
-- For access to Mediawiki built-in formatter.
local lang = mw.getContentLanguage();
local value_string, value, precision;
value, value_string = p._cleanNumber(frame, frame.args[1] or 0);
precision = p._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 = 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(frame, number_string)
if number_string == nil or number_string:len() == 0 then
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 attempt = frame:preprocess('{{#expr: ' .. number_string .. '}}');
attempt = tonumber(attempt);
if attempt ~= nil then
number = attempt;
number_string = tostring(number);
else
number = nil;
number_string = nil;
end
elseif type(number_string) == 'number' then
-- We were passed a number, so we need to convert number_string to a string.
number_string = tostring(number)
else
-- String is valid but may contain padding, clean it.
number_string = number_string:match("^%s*(.-)%s*$");
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)
-- If called via #invoke, use the args passed into the invoking template, or the args passed to #invoke if any exist.
-- Otherwise assume args are being passed directly in from the debug console or from another Lua module.
local origArgs
if frame == mw.getCurrentFrame() then
origArgs = frame:getParent().args
for k, v in pairs(frame.args) do
origArgs = frame.args
break
end
else
origArgs = frame
end
-- Trim whitespace and remove blank arguments.
local args = {}
for k, v in pairs(origArgs) do
if type(v) == 'string' then
v = mw.text.trim(v)
end
if v ~= '' then
args[k] = v
end
end
return wrap[funcName](args)
end
end
local funcNames = {'random', 'order', 'precision', 'max', 'min', 'average', 'round', 'gcd'}
for _, funcName in ipairs(funcNames) do
p[funcName] = makeWrapper(funcName)
end
return p