%% The MIT License %% Copyright (c) 2010 Alisdair Sullivan %% Permission is hereby granted, free of charge, to any person obtaining a copy %% of this software and associated documentation files (the "Software"), to deal %% in the Software without restriction, including without limitation the rights %% to use, copy, modify, merge, publish, distribute, sublicense, and/or sell %% copies of the Software, and to permit persons to whom the Software is %% furnished to do so, subject to the following conditions: %% The above copyright notice and this permission notice shall be included in %% all copies or substantial portions of the Software. %% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR %% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, %% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE %% AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER %% LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, %% OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN %% THE SOFTWARE. %% conversion of floats to 'nice' decimal output. erlang's float implementation %% is almost but not quite ieee 754. it converts negative zero to plain zero %% silently, and throws exceptions for any operations that would produce NaN %% or infinity. as far as I can tell that is. trying to match against NaN or %% infinity binary patterns produces nomatch exceptions, and arithmetic %% operations produce badarg exceptions. with that in mind, this function %% makes no attempt to handle special values (except for zero) -module(nicefloats). -export([format/1]). -ifdef(TEST). -include_lib("eunit/include/eunit.hrl"). -endif. -spec format(Float::float()) -> string(). format(Float) when is_float(Float) -> nice_decimal(Float). %% algorithm from "Printing FLoating-Point Numbers Quickly and Accurately" by %% Burger & Dybvig nice_decimal(0.0) -> "0.0"; nice_decimal(Num) -> {F, E} = extract(<>), {R, S, MP, MM} = initial_vals(F, E), K = ceiling(math:log10(abs(Num)) - 1.0e-10), Round = F band 1 =:= 0, {Dpoint, Digits} = scale(R, S, MP, MM, K, Round), if Num >= 0 -> format(Dpoint, Digits) ; Num < 0 -> "-" ++ format(Dpoint, Digits) end. extract(<<_:1, 0:11, Frac:52>>) -> {Frac, -1074}; extract(<<_:1, Exp:11, Frac:52>>) -> {Frac + (1 bsl 52), Exp - 1075}. ceiling(X) -> Y = trunc(X), case X - Y of Z when Z > 0 -> Y + 1 ; _ -> Y end. initial_vals(F, E) when E >= 0, F /= 1 bsl 52 -> BE = 1 bsl E, {F * BE * 2, 2, BE, BE}; initial_vals(F, E) when E >= 0 -> BE = 1 bsl E, {F * BE * 4, 4, BE * 2, BE}; initial_vals(F, E) when E == -1074; F /= 1 bsl 52 -> {F * 2, 1 bsl (-E + 1), 1, 1}; initial_vals(F, E) -> {F * 4, 1 bsl (-E + 2), 2, 1}. scale(R, S, MP, MM, K, Round) -> case K >= 0 of true -> fixup(R, S * pow(10, K), MP, MM, K, Round) ; false -> Scale = pow(10, -1 * K), fixup(R * Scale, S, MP * Scale, MM * Scale, K, Round) end. fixup(R, S, MP, MM, K, true) -> case (R + MP >= S) of true -> {K + 1, generate(R, S, MP, MM, true)} ; false -> {K, generate(R * 10, S, MP * 10, MM * 10, true)} end; fixup(R, S, MP, MM, K, false) -> case (R + MP > S) of true -> {K + 1, generate(R, S, MP, MM, true)} ; false -> {K, generate(R * 10, S, MP * 10, MM * 10, true)} end. generate(RT, S, MP, MM, Round) -> D = RT div S, R = RT rem S, TC1 = case Round of true -> (R =< MM); false -> (R < MM) end, TC2 = case Round of true -> (R + MP >= S); false -> (R + MP > S) end, case TC1 of false -> case TC2 of false -> [D | generate(R * 10, S, MP * 10, MM * 10, Round)] ; true -> [D + 1] end ; true -> case TC2 of false -> [D] ; true -> case R * 2 < S of true -> [D] ; false -> [D + 1] end end end. %% this is not efficient at all and should be replaced with a lookup table %% probably pow(_B, 0) -> 1; pow(B, E) when E > 0 -> pow(B, E, 1). pow(B, E, Acc) when E < 2 -> B * Acc; pow(B, E, Acc) when E band 1 == 1 -> pow(B * B, E bsr 1, B * Acc); pow(B, E, Acc) -> pow(B * B, E bsr 1, Acc). format(0, Digits) -> format(Digits, ignore, ".0"); format(Dpoint, Digits) when Dpoint =< length(Digits), Dpoint > 0 -> format(Digits, Dpoint, []); format(Dpoint, Digits) when Dpoint > 0 -> Pad = Dpoint - length(Digits), case Pad of X when X > 6 -> format(Digits, 1, []) ++ "e" ++ integer_to_list(Dpoint - 1) ; _ -> format(Digits ++ [ 0 || _ <- lists:seq(1, Pad)], Dpoint, []) end; format(Dpoint, Digits) when Dpoint < 0 -> format(Digits, 1, []) ++ "e" ++ integer_to_list(Dpoint - 1). format([], 0, Acc) -> lists:reverse("0." ++ Acc); format([], ignore, Acc) -> lists:reverse(Acc); format(Digits, 0, Acc) -> format(Digits, ignore, "." ++ Acc); format([Digit|Digits], Dpoint, Acc) -> format(Digits, case Dpoint of ignore -> ignore; X -> X - 1 end, to_ascii(Digit) ++ Acc ). to_ascii(X) -> [X + 48]. %% ascii "1" is [49], "2" is [50], etc... %% eunit tests -ifdef(TEST). nice_decimal_test_() -> [ {"0.0", ?_assert(nice_decimal(0.0) =:= "0.0")}, {"1.0", ?_assert(nice_decimal(1.0) =:= "1.0")}, {"-1.0", ?_assert(nice_decimal(-1.0) =:= "-1.0")}, {"3.1234567890987654321", ?_assert( nice_decimal(3.1234567890987654321) =:= "3.1234567890987655") }, {"1.0e23", ?_assert(nice_decimal(1.0e23) =:= "1.0e23")}, {"0.3", ?_assert(nice_decimal(3.0/10.0) =:= "0.3")}, {"0.0001", ?_assert(nice_decimal(0.0001) =:= "1.0e-4")}, {"0.00000001", ?_assert(nice_decimal(0.00000001) =:= "1.0e-8")}, {"1.0e-323", ?_assert(nice_decimal(1.0e-323) =:= "1.0e-323")}, {"1.0e308", ?_assert(nice_decimal(1.0e308) =:= "1.0e308")}, {"min normalized float", ?_assert( nice_decimal(math:pow(2, -1022)) =:= "2.2250738585072014e-308" ) }, {"max normalized float", ?_assert( nice_decimal((2 - math:pow(2, -52)) * math:pow(2, 1023)) =:= "1.7976931348623157e308" ) }, {"min denormalized float", ?_assert(nice_decimal(math:pow(2, -1074)) =:= "5.0e-324") }, {"max denormalized float", ?_assert( nice_decimal((1 - math:pow(2, -52)) * math:pow(2, -1022)) =:= "2.225073858507201e-308" ) } ]. -endif.