| 1 | (* Copyright (C) 2012 Matthew Fluet. |
| 2 | * Copyright (C) 1999-2006 Henry Cejtin, Matthew Fluet, Suresh |
| 3 | * Jagannathan, and Stephen Weeks. |
| 4 | * Copyright (C) 1997-2000 NEC Research Institute. |
| 5 | * |
| 6 | * MLton is released under a BSD-style license. |
| 7 | * See the file MLton-LICENSE for details. |
| 8 | *) |
| 9 | |
| 10 | structure IEEEReal: IEEE_REAL_EXTRA = |
| 11 | struct |
| 12 | val op + = Int.+ |
| 13 | val op - = Int.- |
| 14 | val op * = Int.* |
| 15 | |
| 16 | exception Unordered |
| 17 | datatype real_order = LESS | EQUAL | GREATER | UNORDERED |
| 18 | |
| 19 | structure Prim = PrimitiveFFI.IEEEReal |
| 20 | |
| 21 | datatype float_class = |
| 22 | INF |
| 23 | | NAN |
| 24 | | NORMAL |
| 25 | | SUBNORMAL |
| 26 | | ZERO |
| 27 | |
| 28 | structure RoundingMode = |
| 29 | struct |
| 30 | datatype t = |
| 31 | TO_NEAREST |
| 32 | | TO_NEGINF |
| 33 | | TO_POSINF |
| 34 | | TO_ZERO |
| 35 | |
| 36 | fun fromInt (i: C_Int.int): t = |
| 37 | let |
| 38 | open Prim.RoundingMode |
| 39 | in |
| 40 | if i = FE_TONEAREST |
| 41 | then TO_NEAREST |
| 42 | else if i = FE_DOWNWARD |
| 43 | then TO_NEGINF |
| 44 | else if i = FE_UPWARD |
| 45 | then TO_POSINF |
| 46 | else if i = FE_TOWARDZERO |
| 47 | then TO_ZERO |
| 48 | else raise Fail "IEEEReal.RoundingMode.fromInt" |
| 49 | end |
| 50 | |
| 51 | fun toInt (m: t): C_Int.int = |
| 52 | let |
| 53 | open Prim.RoundingMode |
| 54 | val i = |
| 55 | case m of |
| 56 | TO_NEAREST => FE_TONEAREST |
| 57 | | TO_NEGINF => FE_DOWNWARD |
| 58 | | TO_POSINF => FE_UPWARD |
| 59 | | TO_ZERO => FE_TOWARDZERO |
| 60 | in |
| 61 | if i = FE_NOSUPPORT |
| 62 | then raise Fail "IEEEReal rounding mode not supported" |
| 63 | else i |
| 64 | end |
| 65 | end |
| 66 | |
| 67 | datatype rounding_mode = datatype RoundingMode.t |
| 68 | |
| 69 | fun setRoundingMode (m: rounding_mode): unit = |
| 70 | if Prim.setRoundingMode (RoundingMode.toInt m) = 0 |
| 71 | then () |
| 72 | else |
| 73 | raise PosixError.raiseSys PosixError.inval |
| 74 | |
| 75 | val getRoundingMode = RoundingMode.fromInt o Prim.getRoundingMode |
| 76 | |
| 77 | fun withRoundingMode (m: rounding_mode, th: unit -> 'a): 'a = |
| 78 | let |
| 79 | val m' = getRoundingMode () |
| 80 | val _ = setRoundingMode m |
| 81 | val res = th () |
| 82 | val _ = setRoundingMode m' |
| 83 | in |
| 84 | res |
| 85 | end |
| 86 | |
| 87 | structure DecimalApprox = |
| 88 | struct |
| 89 | type t = {class: float_class, |
| 90 | digits: int list, |
| 91 | exp: int, |
| 92 | sign: bool} |
| 93 | |
| 94 | val inf: t = {class = INF, |
| 95 | digits = [], |
| 96 | exp = 0, |
| 97 | sign = false} |
| 98 | |
| 99 | val zero: t = {class = ZERO, |
| 100 | digits = [], |
| 101 | exp = 0, |
| 102 | sign = false} |
| 103 | end |
| 104 | |
| 105 | type decimal_approx = DecimalApprox.t |
| 106 | |
| 107 | fun 'a scan reader (state: 'a) = |
| 108 | let |
| 109 | val state = StringCvt.skipWS reader state |
| 110 | fun readc (c, state, f) = |
| 111 | case reader state of |
| 112 | NONE => NONE |
| 113 | | SOME (c', state') => |
| 114 | if c = Char.toLower c' |
| 115 | then f state' |
| 116 | else NONE |
| 117 | fun readString (s, state, failure, success) = |
| 118 | let |
| 119 | val n = String.size s |
| 120 | fun loop (i, state) = |
| 121 | if i = n |
| 122 | then success state |
| 123 | else |
| 124 | case reader state of |
| 125 | NONE => failure () |
| 126 | | SOME (c, state) => |
| 127 | if Char.toLower c = String.sub (s, i) |
| 128 | then loop (i + 1, state) |
| 129 | else failure () |
| 130 | in |
| 131 | loop (0, state) |
| 132 | end |
| 133 | fun charToDigit c = Char.ord c - Char.ord #"0" |
| 134 | fun digitStar (ds: int list, state) = |
| 135 | let |
| 136 | fun done () = (rev ds, state) |
| 137 | in |
| 138 | case reader state of |
| 139 | NONE => done () |
| 140 | | SOME (c, state) => |
| 141 | if Char.isDigit c |
| 142 | then digitStar (charToDigit c :: ds, state) |
| 143 | else done () |
| 144 | end |
| 145 | fun digitPlus (state, failure, success) = |
| 146 | case reader state of |
| 147 | NONE => failure () |
| 148 | | SOME (c, state) => |
| 149 | if Char.isDigit c |
| 150 | then success (digitStar ([charToDigit c], state)) |
| 151 | else failure () |
| 152 | (* [+~-]?[0-9]+ *) |
| 153 | type exp = {digits: int list, negate: bool} |
| 154 | fun 'b afterE (state: 'a, |
| 155 | failure: unit -> 'b, |
| 156 | success: exp * 'a -> 'b) : 'b = |
| 157 | case reader state of |
| 158 | NONE => failure () |
| 159 | | SOME (c, state) => |
| 160 | let |
| 161 | fun neg () = |
| 162 | digitPlus (state, failure, |
| 163 | fn (ds, state) => |
| 164 | success ({digits = ds, negate = true}, |
| 165 | state)) |
| 166 | in |
| 167 | case c of |
| 168 | #"+" => digitPlus (state, failure, |
| 169 | fn (ds, state) => |
| 170 | success ({digits = ds, |
| 171 | negate = false}, |
| 172 | state)) |
| 173 | | #"~" => neg () |
| 174 | | #"-" => neg () |
| 175 | | _ => |
| 176 | if Char.isDigit c |
| 177 | then |
| 178 | let |
| 179 | val (ds, state) = |
| 180 | digitStar ([charToDigit c], state) |
| 181 | in |
| 182 | success ({digits = ds, negate = false}, |
| 183 | state) |
| 184 | end |
| 185 | else failure () |
| 186 | end |
| 187 | (* e[+~-]?[0-9]+)? *) |
| 188 | fun exp (state: 'a, failure, success) = |
| 189 | case reader state of |
| 190 | NONE => failure () |
| 191 | | SOME (c, state) => |
| 192 | case Char.toLower c of |
| 193 | #"e" => afterE (state, failure, success) |
| 194 | | _ => failure () |
| 195 | (* (\.[0-9]+)(e[+~-]?[0-9]+)? *) |
| 196 | fun 'b afterDot (state: 'a, |
| 197 | failure: unit -> 'b, |
| 198 | success: int list * exp * 'a -> 'b) = |
| 199 | digitPlus (state, failure, |
| 200 | fn (frac, state) => |
| 201 | exp (state, |
| 202 | fn () => success (frac, |
| 203 | {digits = [], negate = false}, |
| 204 | state), |
| 205 | fn (e, state) => success (frac, e, state))) |
| 206 | fun stripLeadingZeros (ds: int list): int * int list = |
| 207 | let |
| 208 | fun loop (i, ds) = |
| 209 | case ds of |
| 210 | [] => (i, []) |
| 211 | | d :: ds' => |
| 212 | if d = 0 |
| 213 | then loop (i + 1, ds') |
| 214 | else (i, ds) |
| 215 | in |
| 216 | loop (0, ds) |
| 217 | end |
| 218 | fun stripTrailingZeros ds = |
| 219 | case ds of |
| 220 | [] => [] |
| 221 | | _ => |
| 222 | case List.last ds of |
| 223 | 0 => rev (#2 (stripLeadingZeros (rev ds))) |
| 224 | | _ => ds |
| 225 | fun done (whole: int list, |
| 226 | frac: int list, |
| 227 | {digits: int list, negate: bool}, |
| 228 | state: 'a) = |
| 229 | let |
| 230 | val (_, il) = stripLeadingZeros whole |
| 231 | val fl = stripTrailingZeros frac |
| 232 | datatype exp = |
| 233 | Int of int |
| 234 | | Overflow of DecimalApprox.t |
| 235 | val exp = |
| 236 | case (SOME (let |
| 237 | val i = |
| 238 | List.foldl (fn (d, n) => n * 10 + d) |
| 239 | 0 digits |
| 240 | in |
| 241 | if negate then Int.~ i else i |
| 242 | end) |
| 243 | handle General.Overflow => NONE) of |
| 244 | NONE => Overflow (if negate |
| 245 | then DecimalApprox.zero |
| 246 | else DecimalApprox.inf) |
| 247 | | SOME i => Int i |
| 248 | val da = |
| 249 | case il of |
| 250 | [] => |
| 251 | (case fl of |
| 252 | [] => DecimalApprox.zero |
| 253 | | _ => |
| 254 | case exp of |
| 255 | Int e => |
| 256 | let |
| 257 | val (m, fl) = stripLeadingZeros fl |
| 258 | in |
| 259 | {class = NORMAL, |
| 260 | digits = fl, |
| 261 | exp = e - m, |
| 262 | sign = false} |
| 263 | end |
| 264 | | Overflow da => da) |
| 265 | | _ => |
| 266 | case exp of |
| 267 | Int e => |
| 268 | {class = NORMAL, |
| 269 | digits = stripTrailingZeros (il @ fl), |
| 270 | exp = e + length il, |
| 271 | sign = false} |
| 272 | | Overflow da => da |
| 273 | in |
| 274 | SOME (da, state) |
| 275 | end |
| 276 | fun normal' (c, state) = |
| 277 | case Char.toLower c of |
| 278 | #"i" => readc (#"n", state, fn state => |
| 279 | readc (#"f", state, fn state => |
| 280 | let |
| 281 | fun res state = |
| 282 | SOME ({class = INF, |
| 283 | digits = [], |
| 284 | exp = 0, |
| 285 | sign = false}, |
| 286 | state) |
| 287 | in |
| 288 | readString ("inity", state, |
| 289 | fn () => res state, |
| 290 | res) |
| 291 | end)) |
| 292 | | #"n" => readc (#"a", state, fn state => |
| 293 | readc (#"n", state, fn state => |
| 294 | SOME ({class = NAN, |
| 295 | digits = [], |
| 296 | exp = 0, |
| 297 | sign = false}, |
| 298 | state))) |
| 299 | (* (([0-9]+(\.[0-9]+)?)|(\.[0-9]+))(e[+~-]?[0-9]+)? *) |
| 300 | | #"." => afterDot (state, |
| 301 | fn () => NONE, |
| 302 | fn (frac, exp, state) => |
| 303 | done ([], frac, exp, state)) |
| 304 | | _ => |
| 305 | if Char.isDigit c |
| 306 | then |
| 307 | (* ([0-9]+(\.[0-9]+)?)(e[+~-]?[0-9]+)? *) |
| 308 | let |
| 309 | val (whole, state) = |
| 310 | digitStar ([charToDigit c], state) |
| 311 | fun no () = done (whole, [], |
| 312 | {digits = [], negate = false}, |
| 313 | state) |
| 314 | in |
| 315 | case reader state of |
| 316 | NONE => no () |
| 317 | | SOME (c, state) => |
| 318 | case Char.toLower c of |
| 319 | #"." => |
| 320 | afterDot (state, no, |
| 321 | fn (frac, e, state) => |
| 322 | done (whole, frac, e, state)) |
| 323 | | #"e" => |
| 324 | afterE (state, no, |
| 325 | fn (e, state) => |
| 326 | done (whole, [], e, state)) |
| 327 | | _ => no () |
| 328 | end |
| 329 | else NONE |
| 330 | fun normal state = |
| 331 | case reader state of |
| 332 | NONE => NONE |
| 333 | | SOME z => normal' z |
| 334 | fun negate state = |
| 335 | case normal state of |
| 336 | NONE => NONE |
| 337 | | SOME ({class, digits, exp, ...}, state) => |
| 338 | SOME ({class = class, |
| 339 | digits = digits, |
| 340 | exp = exp, |
| 341 | sign = true}, |
| 342 | state) |
| 343 | in |
| 344 | case reader state of |
| 345 | NONE => NONE |
| 346 | | SOME (c, state) => |
| 347 | case c of |
| 348 | #"~" => negate state |
| 349 | | #"-" => negate state |
| 350 | | #"+" => normal state |
| 351 | | _ => normal' (c, state) |
| 352 | end |
| 353 | |
| 354 | fun fromString s = StringCvt.scanString scan s |
| 355 | |
| 356 | fun toString {class, sign, digits, exp}: string = |
| 357 | let |
| 358 | fun digitStr () = implode (map StringCvt.digitToChar digits) |
| 359 | fun norm () = |
| 360 | let val num = "0." ^ digitStr() |
| 361 | in if exp = 0 |
| 362 | then num |
| 363 | else concat [num, "E", Int.toString exp] |
| 364 | end |
| 365 | val num = |
| 366 | case class of |
| 367 | ZERO => "0.0" |
| 368 | | NORMAL => norm () |
| 369 | | SUBNORMAL => norm () |
| 370 | | INF => "inf" |
| 371 | | NAN => "nan" |
| 372 | in if sign |
| 373 | then "~" ^ num |
| 374 | else num |
| 375 | end |
| 376 | end |