--- a/src/HOL/Real/float_arith.ML Wed Dec 03 09:53:58 2008 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,222 +0,0 @@
-(* Title: HOL/Real/float_arith.ML
- ID: $Id$
- Author: Steven Obua
-*)
-
-signature FLOAT_ARITH =
-sig
- exception Destruct_floatstr of string
- val destruct_floatstr: (char -> bool) -> (char -> bool) -> string -> bool * string * string * bool * string
-
- exception Floating_point of string
- val approx_dec_by_bin: int -> Float.float -> Float.float * Float.float
- val approx_decstr_by_bin: int -> string -> Float.float * Float.float
-
- val mk_float: Float.float -> term
- val dest_float: term -> Float.float
-
- val approx_float: int -> (Float.float * Float.float -> Float.float * Float.float)
- -> string -> term * term
-end;
-
-structure FloatArith : FLOAT_ARITH =
-struct
-
-exception Destruct_floatstr of string;
-
-fun destruct_floatstr isDigit isExp number =
- let
- val numlist = filter (not o Char.isSpace) (String.explode number)
-
- fun countsigns ((#"+")::cs) = countsigns cs
- | countsigns ((#"-")::cs) =
- let
- val (positive, rest) = countsigns cs
- in
- (not positive, rest)
- end
- | countsigns cs = (true, cs)
-
- fun readdigits [] = ([], [])
- | readdigits (q as c::cs) =
- if (isDigit c) then
- let
- val (digits, rest) = readdigits cs
- in
- (c::digits, rest)
- end
- else
- ([], q)
-
- fun readfromexp_helper cs =
- let
- val (positive, rest) = countsigns cs
- val (digits, rest') = readdigits rest
- in
- case rest' of
- [] => (positive, digits)
- | _ => raise (Destruct_floatstr number)
- end
-
- fun readfromexp [] = (true, [])
- | readfromexp (c::cs) =
- if isExp c then
- readfromexp_helper cs
- else
- raise (Destruct_floatstr number)
-
- fun readfromdot [] = ([], readfromexp [])
- | readfromdot ((#".")::cs) =
- let
- val (digits, rest) = readdigits cs
- val exp = readfromexp rest
- in
- (digits, exp)
- end
- | readfromdot cs = readfromdot ((#".")::cs)
-
- val (positive, numlist) = countsigns numlist
- val (digits1, numlist) = readdigits numlist
- val (digits2, exp) = readfromdot numlist
- in
- (positive, String.implode digits1, String.implode digits2, fst exp, String.implode (snd exp))
- end
-
-exception Floating_point of string;
-
-val ln2_10 = Math.ln 10.0 / Math.ln 2.0;
-fun exp5 x = Integer.pow x 5;
-fun exp10 x = Integer.pow x 10;
-fun exp2 x = Integer.pow x 2;
-
-fun find_most_significant q r =
- let
- fun int2real i =
- case (Real.fromString o string_of_int) i of
- SOME r => r
- | NONE => raise (Floating_point "int2real")
- fun subtract (q, r) (q', r') =
- if r <= r' then
- (q - q' * exp10 (r' - r), r)
- else
- (q * exp10 (r - r') - q', r')
- fun bin2dec d =
- if 0 <= d then
- (exp2 d, 0)
- else
- (exp5 (~ d), d)
-
- val L = Real.floor (int2real (IntInf.log2 q) + int2real r * ln2_10)
- val L1 = L + 1
-
- val (q1, r1) = subtract (q, r) (bin2dec L1)
- in
- if 0 <= q1 then
- let
- val (q2, r2) = subtract (q, r) (bin2dec (L1 + 1))
- in
- if 0 <= q2 then
- raise (Floating_point "find_most_significant")
- else
- (L1, (q1, r1))
- end
- else
- let
- val (q0, r0) = subtract (q, r) (bin2dec L)
- in
- if 0 <= q0 then
- (L, (q0, r0))
- else
- raise (Floating_point "find_most_significant")
- end
- end
-
-fun approx_dec_by_bin n (q,r) =
- let
- fun addseq acc d' [] = acc
- | addseq acc d' (d::ds) = addseq (acc + exp2 (d - d')) d' ds
-
- fun seq2bin [] = (0, 0)
- | seq2bin (d::ds) = (addseq 0 d ds + 1, d)
-
- fun approx d_seq d0 precision (q,r) =
- if q = 0 then
- let val x = seq2bin d_seq in
- (x, x)
- end
- else
- let
- val (d, (q', r')) = find_most_significant q r
- in
- if precision < d0 - d then
- let
- val d' = d0 - precision
- val x1 = seq2bin (d_seq)
- val x2 = (fst x1 * exp2 (snd x1 - d') + 1, d') (* = seq2bin (d'::d_seq) *)
- in
- (x1, x2)
- end
- else
- approx (d::d_seq) d0 precision (q', r')
- end
-
- fun approx_start precision (q, r) =
- if q = 0 then
- ((0, 0), (0, 0))
- else
- let
- val (d, (q', r')) = find_most_significant q r
- in
- if precision <= 0 then
- let
- val x1 = seq2bin [d]
- in
- if q' = 0 then
- (x1, x1)
- else
- (x1, seq2bin [d + 1])
- end
- else
- approx [d] d precision (q', r')
- end
- in
- if 0 <= q then
- approx_start n (q,r)
- else
- let
- val ((a1,b1), (a2, b2)) = approx_start n (~ q, r)
- in
- ((~ a2, b2), (~ a1, b1))
- end
- end
-
-fun approx_decstr_by_bin n decstr =
- let
- fun str2int s = the_default 0 (Int.fromString s)
- fun signint p x = if p then x else ~ x
-
- val (p, d1, d2, ep, e) = destruct_floatstr Char.isDigit (fn e => e = #"e" orelse e = #"E") decstr
- val s = size d2
-
- val q = signint p (str2int d1 * exp10 s + str2int d2)
- val r = signint ep (str2int e) - s
- in
- approx_dec_by_bin n (q,r)
- end
-
-fun mk_float (a, b) = @{term "float"} $
- HOLogic.mk_prod (pairself (HOLogic.mk_number HOLogic.intT) (a, b));
-
-fun dest_float (Const ("Float.float", _) $ (Const ("Pair", _) $ a $ b)) =
- pairself (snd o HOLogic.dest_number) (a, b)
- | dest_float t = ((snd o HOLogic.dest_number) t, 0);
-
-fun approx_float prec f value =
- let
- val interval = approx_decstr_by_bin prec value
- val (flower, fupper) = f interval
- in
- (mk_float flower, mk_float fupper)
- end;
-
-end;