mochiweb-merge / src / mochinum.erl

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333``` ```%% @copyright 2007 Mochi Media, Inc. %% @author Bob Ippolito %% @doc Useful numeric algorithms for floats that cover some deficiencies %% in the math module. More interesting is digits/1, which implements %% the algorithm from: %% http://www.cs.indiana.edu/~burger/fp/index.html %% See also "Printing Floating-Point Numbers Quickly and Accurately" %% in Proceedings of the SIGPLAN '96 Conference on Programming Language %% Design and Implementation. -module(mochinum). -author("Bob Ippolito "). -export([digits/1, frexp/1, int_pow/2, int_ceil/1]). %% IEEE 754 Float exponent bias -define(FLOAT_BIAS, 1022). -define(MIN_EXP, -1074). -define(BIG_POW, 4503599627370496). %% External API %% @spec digits(number()) -> string() %% @doc Returns a string that accurately represents the given integer or float %% using a conservative amount of digits. Great for generating %% human-readable output, or compact ASCII serializations for floats. digits(N) when is_integer(N) -> integer_to_list(N); digits(0.0) -> "0.0"; digits(Float) -> {Frac, Exp} = frexp(Float), Exp1 = Exp - 53, Frac1 = trunc(abs(Frac) * (1 bsl 53)), [Place | Digits] = digits1(Float, Exp1, Frac1), R = insert_decimal(Place, [\$0 + D || D <- Digits]), case Float < 0 of true -> [\$- | R]; _ -> R end. %% @spec frexp(F::float()) -> {Frac::float(), Exp::float()} %% @doc Return the fractional and exponent part of an IEEE 754 double, %% equivalent to the libc function of the same name. %% F = Frac * pow(2, Exp). frexp(F) -> frexp1(unpack(F)). %% @spec int_pow(X::integer(), N::integer()) -> Y::integer() %% @doc Moderately efficient way to exponentiate integers. %% int_pow(10, 2) = 100. int_pow(_X, 0) -> 1; int_pow(X, N) when N > 0 -> int_pow(X, N, 1). %% @spec int_ceil(F::float()) -> integer() %% @doc Return the ceiling of F as an integer. The ceiling is defined as %% F when F == trunc(F); %% trunc(F) when F < 0; %% trunc(F) + 1 when F > 0. int_ceil(X) -> T = trunc(X), case (X - T) of Neg when Neg < 0 -> T; Pos when Pos > 0 -> T + 1; _ -> T end. %% Internal API int_pow(X, N, R) when N < 2 -> R * X; int_pow(X, N, R) -> int_pow(X * X, N bsr 1, case N band 1 of 1 -> R * X; 0 -> R end). insert_decimal(0, S) -> "0." ++ S; insert_decimal(Place, S) when Place > 0 -> L = length(S), case Place - L of 0 -> S ++ ".0"; N when N < 0 -> {S0, S1} = lists:split(L + N, S), S0 ++ "." ++ S1; N when N < 6 -> %% More places than digits S ++ lists:duplicate(N, \$0) ++ ".0"; _ -> insert_decimal_exp(Place, S) end; insert_decimal(Place, S) when Place > -6 -> "0." ++ lists:duplicate(abs(Place), \$0) ++ S; insert_decimal(Place, S) -> insert_decimal_exp(Place, S). insert_decimal_exp(Place, S) -> [C | S0] = S, S1 = case S0 of [] -> "0"; _ -> S0 end, Exp = case Place < 0 of true -> "e-"; false -> "e+" end, [C] ++ "." ++ S1 ++ Exp ++ integer_to_list(abs(Place - 1)). digits1(Float, Exp, Frac) -> Round = ((Frac band 1) =:= 0), case Exp >= 0 of true -> BExp = 1 bsl Exp, case (Frac =/= ?BIG_POW) of true -> scale((Frac * BExp * 2), 2, BExp, BExp, Round, Round, Float); false -> scale((Frac * BExp * 4), 4, (BExp * 2), BExp, Round, Round, Float) end; false -> case (Exp =:= ?MIN_EXP) orelse (Frac =/= ?BIG_POW) of true -> scale((Frac * 2), 1 bsl (1 - Exp), 1, 1, Round, Round, Float); false -> scale((Frac * 4), 1 bsl (2 - Exp), 2, 1, Round, Round, Float) end end. scale(R, S, MPlus, MMinus, LowOk, HighOk, Float) -> Est = int_ceil(math:log10(abs(Float)) - 1.0e-10), %% Note that the scheme implementation uses a 326 element look-up table %% for int_pow(10, N) where we do not. case Est >= 0 of true -> fixup(R, S * int_pow(10, Est), MPlus, MMinus, Est, LowOk, HighOk); false -> Scale = int_pow(10, -Est), fixup(R * Scale, S, MPlus * Scale, MMinus * Scale, Est, LowOk, HighOk) end. fixup(R, S, MPlus, MMinus, K, LowOk, HighOk) -> TooLow = case HighOk of true -> (R + MPlus) >= S; false -> (R + MPlus) > S end, case TooLow of true -> [(K + 1) | generate(R, S, MPlus, MMinus, LowOk, HighOk)]; false -> [K | generate(R * 10, S, MPlus * 10, MMinus * 10, LowOk, HighOk)] end. generate(R0, S, MPlus, MMinus, LowOk, HighOk) -> D = R0 div S, R = R0 rem S, TC1 = case LowOk of true -> R =< MMinus; false -> R < MMinus end, TC2 = case HighOk of true -> (R + MPlus) >= S; false -> (R + MPlus) > S end, case TC1 of false -> case TC2 of false -> [D | generate(R * 10, S, MPlus * 10, MMinus * 10, LowOk, HighOk)]; true -> [D + 1] end; true -> case TC2 of false -> [D]; true -> case R * 2 < S of true -> [D]; false -> [D + 1] end end end. unpack(Float) -> <> = <>, {Sign, Exp, Frac}. frexp1({_Sign, 0, 0}) -> {0.0, 0}; frexp1({Sign, 0, Frac}) -> Exp = log2floor(Frac), <> = <>, {Frac1, -(?FLOAT_BIAS) - 52 + Exp}; frexp1({Sign, Exp, Frac}) -> <> = <>, {Frac1, Exp - ?FLOAT_BIAS}. log2floor(Int) -> log2floor(Int, 0). log2floor(0, N) -> N; log2floor(Int, N) -> log2floor(Int bsr 1, 1 + N). %% %% Tests %% -include_lib("eunit/include/eunit.hrl"). -ifdef(TEST). int_ceil_test() -> 1 = int_ceil(0.0001), 0 = int_ceil(0.0), 1 = int_ceil(0.99), 1 = int_ceil(1.0), -1 = int_ceil(-1.5), -2 = int_ceil(-2.0), ok. int_pow_test() -> 1 = int_pow(1, 1), 1 = int_pow(1, 0), 1 = int_pow(10, 0), 10 = int_pow(10, 1), 100 = int_pow(10, 2), 1000 = int_pow(10, 3), ok. %% XXX arg 02/12/10 %% disabled pending resolution of http://code.google.com/p/mochiweb/issues/detail?id=63 %digits_test_disabled() -> % ?assertEqual("0", % digits(0)), % ?assertEqual("0.0", % digits(0.0)), % ?assertEqual("1.0", % digits(1.0)), % ?assertEqual("-1.0", % digits(-1.0)), % ?assertEqual("0.1", % digits(0.1)), % ?assertEqual("0.01", % digits(0.01)), % ?assertEqual("0.001", % digits(0.001)), % ?assertEqual("1.0e+6", % digits(1000000.0)), % ?assertEqual("0.5", % digits(0.5)), % ?assertEqual("4503599627370496.0", % digits(4503599627370496.0)), % %% small denormalized number % %% 4.94065645841246544177e-324 % <> = <<0,0,0,0,0,0,0,1>>, % ?assertEqual("4.9406564584124654e-324", % digits(SmallDenorm)), % ?assertEqual(SmallDenorm, % list_to_float(digits(SmallDenorm))), % %% large denormalized number % %% 2.22507385850720088902e-308 % <> = <<0,15,255,255,255,255,255,255>>, % ?assertEqual("2.225073858507201e-308", % digits(BigDenorm)), % ?assertEqual(BigDenorm, % list_to_float(digits(BigDenorm))), % %% small normalized number % %% 2.22507385850720138309e-308 % <> = <<0,16,0,0,0,0,0,0>>, % ?assertEqual("2.2250738585072014e-308", % digits(SmallNorm)), % ?assertEqual(SmallNorm, % list_to_float(digits(SmallNorm))), % %% large normalized number % %% 1.79769313486231570815e+308 % <> = <<127,239,255,255,255,255,255,255>>, % ?assertEqual("1.7976931348623157e+308", % digits(LargeNorm)), % ?assertEqual(LargeNorm, % list_to_float(digits(LargeNorm))), % ok. frexp_test() -> %% zero {0.0, 0} = frexp(0.0), %% one {0.5, 1} = frexp(1.0), %% negative one {-0.5, 1} = frexp(-1.0), %% small denormalized number %% 4.94065645841246544177e-324 <> = <<0,0,0,0,0,0,0,1>>, {0.5, -1073} = frexp(SmallDenorm), %% large denormalized number %% 2.22507385850720088902e-308 <> = <<0,15,255,255,255,255,255,255>>, {0.99999999999999978, -1022} = frexp(BigDenorm), %% small normalized number %% 2.22507385850720138309e-308 <> = <<0,16,0,0,0,0,0,0>>, {0.5, -1021} = frexp(SmallNorm), %% large normalized number %% 1.79769313486231570815e+308 <> = <<127,239,255,255,255,255,255,255>>, {0.99999999999999989, 1024} = frexp(LargeNorm), ok. -endif. ```
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