Module:Math
De Histoire de l'IST
La documentation pour ce module peut être créée à Module:Math/doc
--[[
This module provides a number of basic mathematical operations.
]]
local z = {}
-- Generate random number
function z.random( frame )
local first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil
local second = tonumber(frame.args[2])
if first then -- if NaN or nil, will skip down to final return
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
return math.random(first)
end
return math.random()
end
--[[
order
Determine order of magnitude of a number
Usage:
{{#invoke: Math | order | value }}
]]
function z.order(frame)
local input_string = (frame.args[1] or frame.args.x or '0');
local input_number;
input_number = z._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 z._order( input_number )
end
end
function z._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 z.precision( frame )
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 = 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 )
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 z.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 = z._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 z.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 = z._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
--[[
round
Rounds a number to specified precision
Usage:
{{#invoke:Math | round | value | precision }}
--]]
function z.round(frame)
local value, precision;
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
function z._round( value, precision )
local rescale = math.pow( 10, precision );
return math.floor( value * rescale + 0.5 ) / rescale;
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 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 );
-- 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
local orig_precision = z._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 = 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);
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 z._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
else
-- String is valid but may contain padding, clean it.
number_string = number_string:match( "^%s*(.-)%s*$" );
end
return number, number_string;
end
return z
