# Difference between revisions of "Module:Math"

--[[

This module provides a number of basic mathematical operations.

]] local z = {}

-- Generate random number 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])
```
```   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 'Formatting error: Order of magnitude input appears non-numeric'
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 'Formatting error: Precision input appears non-numeric'
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

--[[ 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 z.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 = z._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 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 'Formatting error: Round input appears non-numeric'
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 'Formatting error: invalid input when rounding'
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
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
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;
end

formatted_num = formatted_num .. string.rep( '0', padding );
end
else
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 .. '×10' .. order .. ''
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( 'Expression error: Unrecognized punctuation character "'".' );
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