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Reworked the number formatting system. Will now attempt to generate the shortest possible representation of the given number.

This commit is contained in:
Jon Michael Aanes 2017-04-03 20:01:36 +02:00
parent e5e23422ef
commit ae73cc9b64
4 changed files with 297 additions and 190 deletions

View File

@ -20,6 +20,17 @@ local function factorial (n)
return a
end
local function inverse_factorial (n)
-- Returns the inverse factorial of n.
-- That is some m, where n = m!
local a, i = 1, 1
while a < n do
i = i + 1
a = a * i
end
return (a == n) and i or nil
end
local function calculate_fraction (n)
-- Returns x and y such that x/y = n. If none could be found, returns nil.
local a, b = 1, n % 1
@ -35,84 +46,129 @@ local function calculate_fraction (n)
end
end
local MATH_SHORTHAND = {
-- Only used if options.math_shorthand = true
['0/0'] = 'nan',
['1/0'] = '',
['-1/0'] = '-∞',
['math.pi'] = 'π',
['math.exp(1)'] = 'e',
local UNICODE_SUPERSCRIPT = {
['0'] = '', ['1'] = '¹', ['2'] = '²', ['3'] = '³', ['4'] = '',
['5'] = '', ['6'] = '', ['7'] = '', ['8'] = '', ['9'] = '',
['-'] = '', ['+'] = '', ['='] = '', ['('] = '', [')'] = '',
}
local function to_superscript (n)
return tostring(n):gsub('.', function (a) return UNICODE_SUPERSCRIPT[a] end)
end
local UNICODE_CHAR_PATTERN = '[\01-\127\192-\255][\128-\191]*'
local function unicode_len (str)
local len = 0
for char in str:gmatch(UNICODE_CHAR_PATTERN) do len = len + 1 end
return len
end
--------------------------------------------------------------------------------
local SPECIAL_NUMBER = {
-- x = ∞
{ est = function (...) return ... end,
real = function (a) return math.huge end,
repr = function (a) return '1/0' end,
short = function (a) return '' end,
},
-- Factorial
{ est = function (n) return inverse_factorial(n) end,
real = function (a) return factorial(a) end,
repr = function (a) return ('fac(%i)'):format(a) end,
short = function (a) return a..'!' end,
},
-- x = 2^a
{ est = function (n) return math.log(n)/math.log(2) end,
real = function (a) return 2^a end,
repr = function (a) return '2^'..a end,
short = function (a) return '2'..to_superscript(a) end,
},
-- x = 10^a
{ est = function (n) return math.log(n)/math.log(10) end,
real = function (a) return 10^a end,
repr = function (a) return '10^'..a end,
short = function (a) return '10'..to_superscript(a) end,
},
-- x = 1/√a
{ est = function (n) return 1/(n^2) end,
real = function (a) return 1/math.sqrt(a) end,
repr = function (a) return ('1/math.sqrt(%i)'):format(a) end,
short = function (a) return '1/√'..a end,
},
-- x = lg a
{ est = function (n) return math.exp(n) end,
real = function (a) return math.log(a) end,
repr = function (a) return ('math.log(%i)'):format(a) end,
short = function (a) return ('lg(%i)'):format(a) end,
},
-- x = ^a
{ est = function (n) return math.log(n) end,
real = function (a) return math.exp(a) end,
repr = function (a) return ('math.exp(%i)'):format(a) end,
short = function (a) return a == 1 and '' or ''..to_superscript(a) end,
},
-- x = aπ
{ est = function (n) return n/math.pi end,
real = function (a) return a*math.pi end,
repr = function (a) return a == 1 and 'math.pi' or a..'*math.pi' end,
short = function (a) return (a == 1 and '' or a)..'π' end,
},
-- x = sqrt(a)
{ est = function (n) return n^2 end,
real = function (a) return math.sqrt(a) end,
repr = function (a) return ('math.sqrt(%i)'):format(a) end,
short = function (a) return ''..a end,
},
-- a = x
{ est = function (n) return n end,
real = function (a) return a end,
repr = function (a) return ('%i'):format(a) end,
short = function (a) return ('%i'):format(a) end,
},
}
--------------------------------------------------------------------------------
-- Generate special number table
-- TODO: Restructure this.
local LONG_ASS_CONSTANT = '___________________________________________________'
local SPECIAL_NUMBER = {}
do
SPECIAL_NUMBER[ 1/0] = '1/0'
SPECIAL_NUMBER[math.pi] = 'math.pi'
SPECIAL_NUMBER[math.exp(1)] = 'math.exp(1)'
for i = -10, -6 do
SPECIAL_NUMBER[math.pow(10, i)] = '10^'..i
end
for i = -15, -7 do
SPECIAL_NUMBER[math.pow( 2, i)] = '2^'..i
local function format_number (n, shorthand)
if n ~= n then return shorthand and 'NaN' or '0/0'
elseif n < 0 then return '-' .. format_number(-n, shorthand)
end
for i = 5, 308 do
SPECIAL_NUMBER[math.pow(10, i)] = '10^'..i
-- Finding the shortest
local shortest, length = LONG_ASS_CONSTANT, unicode_len(LONG_ASS_CONSTANT)
local function alternative_repr (repr)
local repr_len = unicode_len(repr)
if repr_len < length then shortest, length = repr, repr_len end
end
for i = 17, 1023 do
SPECIAL_NUMBER[math.pow( 2, i) ] = '2^'..i
--SPECIAL_NUMBER[math.pow( 2, i) - 1] = '2^'..i..'-1'
--SPECIAL_NUMBER[math.pow( 2, i) + 1] = '2^'..i..'+1'
-- Maybe it's a "special" number?
for _, special_number_tests in pairs(SPECIAL_NUMBER) do
local a = special_number_tests.est(n)
if a then
local a_near = math.floor(a + 0.5)
if n == special_number_tests.real(a_near) then
alternative_repr( special_number_tests[shorthand and 'short' or 'repr'](a_near) )
end
for i = 9, 170 do
SPECIAL_NUMBER[factorial(i)] = i..'!'
end
for i = 1, 100 do
local sqrt = math.sqrt(i)
if not is_integer(sqrt) then
SPECIAL_NUMBER[1/sqrt] = '1/math.sqrt('..i..')'
SPECIAL_NUMBER[sqrt] = 'math.sqrt('..i..')'
end
end
for i = 1, 100 do
local log = math.log(i)
if not is_integer(log) then
SPECIAL_NUMBER[log] = 'math.log('..i..')'
end
end
end
--------------------------------------------------------------------------------
local function format_number (n)
-- Returns a string of n formatted as to allow easy back into a lua interpreter.
if n ~= n then return '0/0'
elseif n < 0 then return '-' .. format_number(-n)
elseif SPECIAL_NUMBER[n] then return SPECIAL_NUMBER[n]
end
-- Maybe it's an integer?
if is_integer(n) then return tostring(n) end
-- Maybe it's a fraction?
-- Maybe it's a fractional number?
do
local numerator, denumberator = calculate_fraction(n)
if numerator then
return format_number(numerator)..'/'..format_number(denumberator)
if numerator and denumberator ~= 1 then
alternative_repr( format_number(numerator)..'/'..format_number(denumberator) )
end
return ( tostring(n):gsub('e%+?', '*10^') ) -- Parantheses to return first result.
end
-- Maybe it's a decimal number?
alternative_repr( tostring(n):gsub('([^e]+)e%+?(%-?)0+', function(a, b) return (a == '1' and '' or a..'*')..'10^'..b end))
-- Well, this is not a pretty number!
return shortest
end
return function (value, options, depth, l)
l[#l+1] = format_number(value)
if options.math_shorthand then
l[#l] = MATH_SHORTHAND[ l[#l] ]
end
l[#l+1] = format_number(value, options.math_shorthand)
end

179
test/test_number.lua Normal file
View File

@ -0,0 +1,179 @@
local SUITE = require('TestSuite').new('number')
SUITE:setEnviroment{
format = require('pretty')
}
local function format_test (t)
SUITE:addTest(t.expect, function ()
assert_equal(t.expect, format(t.input, t.options))
end)
end
local function number_test (t)
SUITE:addTest(t.expect, function ()
assert_equal(t.expect, format(t.input, {}))
end)
SUITE:addTest(t.shorthand or (t.expect .. ' shorthand'), function ()
assert_equal(t.shorthand or t.expect, format(t.input, { math_shorthand = true }))
end)
end
--------------------------------------------------------------------------------
-- Integers
number_test {
input = 0,
expect = '0',
}
number_test {
input = -0,
expect = '0',
}
number_test {
input = 2000,
expect = '2000',
}
number_test {
input = -2000,
expect = '-2000',
}
--------------------------------------------------------------------------------
-- Exponents
number_test {
input = 10^5,
expect = '10^5',
shorthand = '10⁵',
}
number_test {
input = 10^-6,
expect = '10^-6',
shorthand = '10⁻⁶',
}
number_test {
input = 2^17,
expect = '2^17',
shorthand = '2¹⁷',
}
number_test {
input = 2^-7,
expect = '2^-7',
shorthand = '2⁻⁷',
}
--------------------------------------------------------------------------------
-- Decimal numbers
number_test {
input = 0.1,
expect = '0.1',
}
number_test {
input = 0.65,
expect = '0.65',
}
--------------------------------------------------------------------------------
-- Fractions
number_test {
input = 1/3,
expect = '1/3',
}
number_test {
input = 9/17,
expect = '9/17',
}
--------------------------------------------------------------------------------
-- Squareroots, logarithms, and other fine functions
number_test {
input = math.sqrt(8),
expect = 'math.sqrt(8)',
shorthand = '√8',
}
number_test {
input = 1/math.sqrt(8),
expect = '1/math.sqrt(8)',
shorthand = '1/√8',
}
number_test {
input = math.log(8),
expect = 'math.log(8)',
shorthand = 'lg(8)',
}
number_test {
input = 6227020800,
expect = 'fac(13)',
shorthand = '13!',
}
--------------------------------------------------------------------------------
-- Constants, and multiples of constants
number_test {
input = math.pi,
expect = 'math.pi',
shorthand = 'π',
}
number_test {
input = 7*math.pi,
expect = '7*math.pi',
shorthand = '',
}
number_test {
input = math.exp(1),
expect = 'math.exp(1)',
shorthand = '',
}
number_test {
input = math.exp(10),
expect = 'math.exp(10)',
shorthand = 'ℯ¹⁰',
}
number_test {
input = 1/0,
expect = '1/0',
shorthand = ''
}
number_test {
input = -1/0,
expect = '-1/0',
shorthand = '-∞'
}
number_test {
input = 0/0,
expect = '0/0',
shorthand = 'NaN',
}
--------------------------------------------------------------------------------
format_test {
input = { 1/2, 1/3, 1/4, 1/5 },
expect = '{ 1/2, 1/3, 1/4, 1/5 }',
}
--------------------------------------------------------------------------------
return SUITE

View File

@ -106,135 +106,6 @@ format_test {
expect = '\'ø\'',
}
--------------------------------------------------------------------------------
-- Numbers
format_test {
input = 0,
expect = '0',
}
format_test {
input = 2000,
expect = '2000',
}
format_test {
input = -2000,
expect = '-2000',
}
--------------------------------------------------------------------------------
-- Numbers, Other formats
format_test {
input = 10^5,
expect = '10^5',
}
format_test {
input = 10^-6,
expect = '10^-6',
}
format_test {
input = 2^17,
expect = '2^17',
}
format_test {
input = 2^-7,
expect = '2^-7',
}
format_test {
input = 1/3,
expect = '1/3',
}
format_test {
input = 9/17,
expect = '9/17',
}
format_test {
input = math.sqrt(2),
expect = 'math.sqrt(2)',
}
format_test {
input = 1/math.sqrt(2),
expect = '1/math.sqrt(2)',
}
format_test {
input = math.log(2),
expect = 'math.log(2)',
}
--------------------------------------------------------------------------------
-- Numbers, Constants
format_test {
input = math.pi,
expect = 'math.pi',
}
format_test {
input = math.exp(1),
expect = 'math.exp(1)',
}
format_test {
input = 1/0, -- Same as math.huge
expect = '1/0',
}
format_test {
input = -1/0, -- Same as -math.huge
expect = '-1/0',
}
format_test {
input = 0/0, -- Same as nan
expect = '0/0',
}
format_test {
input = 1/0, -- Same as math.huge
options = { math_shorthand = true },
expect = '',
}
format_test {
input = -1/0, -- Same as -math.huge
options = { math_shorthand = true },
expect = '-∞',
}
format_test {
input = 0/0, -- Same as nan
options = { math_shorthand = true },
expect = 'nan',
}
format_test {
input = math.pi,
options = { math_shorthand = true },
expect = 'π',
}
format_test {
input = math.exp(1),
options = { math_shorthand = true },
expect = 'e',
}
format_test {
input = { 1/2, 1/3, 1/4, 1/5 },
expect = '{ 1/2, 1/3, 1/4, 1/5 }',
}
--------------------------------------------------------------------------------
-- Primitive types

View File

@ -3,4 +3,5 @@ package.path = package.path .. ';./test/?.lua;./src/?.lua'
local TEST_SUITE = require("TestSuite").new('pretty')
TEST_SUITE:addModules('test/test_*')
TEST_SUITE:setOptions(...)
TEST_SUITE:runTests()