Annotation of /trunk/src/common/float-lit.sml

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1 :	jhr	26	(* float-lit.sml
2 :			*
3 :			* COPYRIGHT (c) 2010 The Diderot Project (http://diderot.cs.uchicago.edu)
4 :			* All rights reserved.
5 :			*
6 :			* Internal representation of floating-point literals with limited
7 :			* support for arithmetic.
8 :			*)
9 :
10 :			structure FloatLit :> sig
11 :
12 :			type float
13 :
14 :			val isZero : float -> bool
15 :
16 :			(* return the representation of +/-0.0 *)
17 :			val zero : bool ->float
18 :
19 :			(* plus and minus one *)
20 :			val one : float
21 :			val m_one : float
22 :
23 :			(* negate a float *)
24 :			val negate : float -> float
25 :
26 :			(* equality, comparisons, and hashing functions *)
27 :			val same : (float * float) -> bool
28 :	jhr	42	val compare : (float * float) -> order (* not ordering on reals *)
29 :	jhr	26	val hash : float -> word
30 :
31 :	jhr	42	(* special floats *)
32 :			val nan : float (* some quiet NaN *)
33 :			val posInf : float (* positive infinity *)
34 :			val negInf : float (* negative infinity *)
35 :
36 :	jhr	26	(* create a float from pieces: isNeg is true if the number is negative, whole
37 :			* is the whole-number part, frac is the fractional part, and exp is the
38 :			* exponent. This function may raise Overflow, when the exponent of the
39 :			* normalized representation is too small or too large.
40 :			*)
41 :			val float : {isNeg : bool, whole : string, frac : string, exp : int} -> float
42 :			val toString : float -> string
43 :
44 :			(* external representation (for pickling) *)
45 :			val toBytes : float -> Word8Vector.vector
46 :			val fromBytes : Word8Vector.vector -> float
47 :
48 :			end = struct
49 :
50 :			structure SS = Substring
51 :			structure W = Word
52 :			structure W8V = Word8Vector
53 :
54 :			(* The value {isNeg, digits=[d0, ..., dn], exp} represents the number
55 :			*
56 :			* [+/-] 0.d0...dn * 10^exp
57 :			*
58 :			* where the sign is negative if isNeg is true.
59 :			*)
60 :	jhr	42	datatype float
61 :			= PosInf (* positive infinity *)
62 :			| NegInf (* negative infinity *)
63 :			| NaN (* some quiet NaN *)
64 :			| Flt of {isNeg : bool, digits : int list, exp : int}
65 :	jhr	26
66 :	jhr	42	(* special floats *)
67 :			val nan = NaN
68 :			val posInf = PosInf
69 :			val negInf = NegInf
70 :
71 :			fun isZero (Flt{isNeg, digits=[0], exp}) = true
72 :	jhr	26	| isZero _ = false
73 :
74 :	jhr	42	fun zero isNeg = Flt{isNeg = isNeg, digits = [0], exp = 0}
75 :	jhr	26
76 :	jhr	42	val one = Flt{isNeg = false, digits = [1], exp = 1}
77 :			val m_one = Flt{isNeg = true, digits = [1], exp = 1}
78 :	jhr	26
79 :			(* negate a float *)
80 :	jhr	42	fun negate PosInf = NegInf
81 :			| negate NegInf = PosInf
82 :			| negate NaN = raise Fail "negate nan"
83 :			| negate (Flt{isNeg, digits, exp}) =
84 :			Flt{isNeg = not isNeg, digits = digits, exp = exp}
85 :	jhr	26
86 :			(* equality, comparisons, and hashing functions *)
87 :	jhr	42	fun same (NegInf, NegInf) = true
88 :			| same (PosInf, PosInf) = true
89 :			| same (NaN, NaN) = true
90 :			| same (Flt f1, Flt f2) =
91 :	jhr	26	(#isNeg f1 = #isNeg f2) andalso (#exp f1 = #exp f2)
92 :			andalso (#digits f1 = #digits f2)
93 :	jhr	42	| same _ = false
94 :	jhr	26
95 :	jhr	42	fun compare (NegInf, NegInf) = EQUAL
96 :			| compare (NegInf, _) = LESS
97 :			| compare (_, NegInf) = GREATER
98 :			| compare (PosInf, PosInf) = EQUAL
99 :			| compare (PosInf, _) = LESS
100 :			| compare (_, PosInf) = GREATER
101 :			| compare (NaN, NaN) = EQUAL
102 :			| compare (NaN, _) = LESS
103 :			| compare (_, NaN) = GREATER
104 :			| compare (Flt f1, Flt f2) = (case (#isNeg f1, #isNeg f2)
105 :	jhr	26	of (false, true) => GREATER
106 :			| (true, false) => LESS
107 :			| _ => (case Int.compare(#exp f1, #exp f2)
108 :			of EQUAL => let
109 :			fun cmp ([], []) = EQUAL
110 :			| cmp ([], _) = LESS
111 :			| cmp (_, []) = GREATER
112 :			| cmp (d1::r1, d2::r2) = (case Int.compare(d1, d2)
113 :			of EQUAL => cmp(r1, r2)
114 :			| order => order
115 :			(* end case *))
116 :			in
117 :			cmp (#digits f1, #digits f2)
118 :			end
119 :			| order => order
120 :			(* end case *))
121 :			(* end case *))
122 :
123 :	jhr	42	fun hash PosInf = 0w1
124 :			| hash NegInf = 0w3
125 :			| hash NaN = 0w5
126 :			| hash (Flt{isNeg, digits, exp}) = let
127 :	jhr	26	fun hashDigits ([], h, _) = h
128 :			| hashDigits (d::r, h, i) =
129 :			hashDigits (r, W.<<(W.fromInt d, i+0w4), W.andb(i+0w1, 0wxf))
130 :			in
131 :			hashDigits(digits, W.fromInt exp, 0w0)
132 :			end
133 :
134 :			fun float {isNeg, whole, frac, exp} = let
135 :			fun cvtDigit (c, l) = (Char.ord c - Char.ord #"0") :: l
136 :			fun isZero #"0" = true | isZero _ = false
137 :			(* whole digits with leading zeros removed *)
138 :			val whole = SS.dropl isZero (SS.full whole)
139 :			(* fractional digits with trailing zeros removed *)
140 :			val frac = SS.dropr isZero (SS.full frac)
141 :			(* normalize by stripping leading zero digits *)
142 :			fun normalize {isNeg, digits=[], exp} = zero isNeg
143 :			| normalize {isNeg, digits=0::r, exp} =
144 :			normalize {isNeg=isNeg, digits=r, exp=exp-1}
145 :	jhr	42	| normalize flt = Flt flt
146 :	jhr	26	in
147 :			case SS.foldr cvtDigit (SS.foldr cvtDigit [] frac) whole
148 :			of [] => zero isNeg
149 :			| digits => normalize {
150 :			isNeg = isNeg,
151 :			digits = digits,
152 :			exp = exp + SS.size whole
153 :			}
154 :			(* end case *)
155 :			end
156 :
157 :	jhr	42	fun toString PosInf = "+inf"
158 :			| toString NegInf = "-inf"
159 :			| toString NaN = "nan"
160 :			| toString (Flt{isNeg, digits, exp}) = let
161 :	jhr	26	val s = if isNeg then "-0." else "0."
162 :			val e = if exp < 0
163 :			then ["e-", Int.toString(~exp)]
164 :			else ["e", Int.toString exp]
165 :			in
166 :			concat(s :: List.foldr (fn (d, ds) => Int.toString d :: ds) e digits)
167 :			end
168 :
169 :
170 :
171 :			(***** external representation (for pickling) *****
172 :			*
173 :			* The representation we use is a sequence of bytes:
174 :			*
175 :			* [sign, d0, ..., dn, exp0, ..., exp3]
176 :			*
177 :			* where
178 :			* sign == 0 or 1
179 :			* di == ith digit
180 :			* expi == ith byte of exponent (exp0 is lsb, exp3 is msb).
181 :			*
182 :	jhr	42	* we encode Infs and NaNs using the sign byte:
183 :			*
184 :			* 2 == PosInf
185 :			* 3 == NegInf
186 :			* 4 == NaN
187 :			*
188 :	jhr	26	* NOTE: we could pack the sign and digits into 4-bit nibbles, but we are keeping
189 :			* things simple for now.
190 :			*)
191 :
192 :	jhr	42	fun toBytes PosInf = Word8Vector.fromList [0w2]
193 :			| toBytes NegInf = Word8Vector.fromList [0w3]
194 :			| toBytes NaN = Word8Vector.fromList [0w4]
195 :			| toBytes (Flt{isNeg, digits, exp}) = let
196 :	jhr	26	val sign = if isNeg then 0w1 else 0w0
197 :			val digits = List.map Word8.fromInt digits
198 :			val exp' = W.fromInt exp
199 :			fun byte i = Word8.fromLargeWord(W.toLargeWord((W.>>(exp', 0w8*i))))
200 :			val exp = [byte 0w0, byte 0w1, byte 0w2, byte 0w3]
201 :			in
202 :			Word8Vector.fromList(sign :: (digits @ exp))
203 :			end
204 :
205 :			fun fromBytes v = let
206 :			fun error () = raise Fail "Bogus float pickle"
207 :	jhr	42	val len = W8V.length v
208 :			in
209 :			if (len = 1)
210 :			then (case W8V.sub(v, 0) (* special float value *)
211 :			of 0w2 => PosInf
212 :			| 0w3 => NegInf
213 :			| 0w4 => NaN
214 :	jhr	26	| _ => error()
215 :			(* end case *))
216 :	jhr	42	else let
217 :			val ndigits = W8V.length v - 5
218 :			val _ = if (ndigits < 1) then error() else ()
219 :			val isNeg = (case W8V.sub(v, 0)
220 :			of 0w0 => false
221 :			| 0w1 => true
222 :			| _ => error()
223 :			(* end case *))
224 :			fun digit i = Word8.toInt(W8V.sub(v, i+1))
225 :			fun byte i = W.<<(
226 :			W.fromLargeWord(Word8.toLargeWord(W8V.sub(v, ndigits+1+i))),
227 :			W.fromInt(8*i))
228 :			val exp = W.toIntX(W.orb(byte 3, W.orb(byte 2, W.orb(byte 1, byte 0))))
229 :			in
230 :			Flt{isNeg = isNeg, digits = List.tabulate(ndigits, digit), exp = exp}
231 :			end
232 :	jhr	26	end
233 :
234 :			end
235 :

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