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

number.lua

@@ -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 = {
+local UNICODE_SUPERSCRIPT = {
-	-- Only used if options.math_shorthand = true
+	['0'] = '⁰', ['1'] = '¹', ['2'] = '²', ['3'] = '³', ['4'] = '⁴',
-	['0/0']          =  'nan',
+	['5'] = '⁵', ['6'] = '⁶', ['7'] = '⁷', ['8'] = '⁸', ['9'] = '⁹',
-	['1/0']          =   '∞',
+	['-'] = '⁻', ['+'] = '⁺', ['='] = '⁼', ['('] = '⁽', [')'] = '⁾',
-	['-1/0']         =  '-∞',
+}
-	['math.pi']      =   'π',
+local function to_superscript (n)
-	['math.exp(1)']  =   'e',
+	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 = ℯ^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 'ℯ' or 'ℯ'..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 = {}
+local function format_number (n, shorthand)
-do
+	if     n ~= n   then  return shorthand and 'NaN' or '0/0'
-	SPECIAL_NUMBER[ 1/0]         =  '1/0'
+	elseif n <  0   then  return '-' .. format_number(-n, shorthand)
-	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
 	end
 
-	for i = 5, 308 do
+	-- Finding the shortest
-		SPECIAL_NUMBER[math.pow(10, i)] = '10^'..i
+	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
+	-- Maybe it's a "special" number?
-		SPECIAL_NUMBER[math.pow( 2, i)    ] =  '2^'..i
+	for _, special_number_tests in pairs(SPECIAL_NUMBER) do
-		--SPECIAL_NUMBER[math.pow( 2, i) - 1] =  '2^'..i..'-1'
+		local a = special_number_tests.est(n)
-		--SPECIAL_NUMBER[math.pow( 2, i) + 1] =  '2^'..i..'+1'
+		if a then
-	end
+			local a_near = math.floor(a + 0.5)
-
+			if n == special_number_tests.real(a_near) then
-	for i = 9, 170 do
+				alternative_repr( special_number_tests[shorthand and 'short' or 'repr'](a_near) )
-		SPECIAL_NUMBER[factorial(i)] = i..'!'
+			end
-	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
+	-- Maybe it's a fractional number?
-		local log = math.log(i)
+	do
-		if not is_integer(log) then
+		local numerator, denumberator = calculate_fraction(n)
-			SPECIAL_NUMBER[log] = 'math.log('..i..')'
+		if numerator and denumberator ~= 1 then
+			alternative_repr( format_number(numerator)..'/'..format_number(denumberator) )
 		end
 	end
-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))
 
-local function format_number (n)
+	-- Well, this is not a pretty number!
-	-- Returns a string of n formatted as to allow easy back into a lua interpreter.
+	return shortest
-	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?
-	local numerator, denumberator = calculate_fraction(n)
-	if numerator then
-		return format_number(numerator)..'/'..format_number(denumberator)
-	end
-	return ( tostring(n):gsub('e%+?', '*10^') )  -- Parantheses to return first result.
 end
 
 return function (value, options, depth, l)
-	l[#l+1] = format_number(value)
+	l[#l+1] = format_number(value, options.math_shorthand)
-	if options.math_shorthand then
-		l[#l] = MATH_SHORTHAND[ l[#l] ]
-	end
 end

test/test_number.lua

@@ -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 = '7π',
+}
+
+number_test {
+    input     =  math.exp(1),
+    expect    = 'math.exp(1)',
+    shorthand = 'ℯ',
+}
+
+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

test/test_pretty.lua

@@ -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
 

test/tests.lua

@@ -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()