--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Real/Float.ML Tue Jul 12 21:49:38 2005 +0200
@@ -0,0 +1,519 @@
+(* Title: HOL/Real/Float.ML
+ ID: $Id$
+ Author: Steven Obua
+*)
+
+structure ExactFloatingPoint :
+sig
+ exception Destruct_floatstr of string
+ val destruct_floatstr : (char -> bool) -> (char -> bool) -> string -> bool * string * string * bool * string
+
+ exception Floating_point of string
+
+ type floatrep = IntInf.int * IntInf.int
+ val approx_dec_by_bin : IntInf.int -> floatrep -> floatrep * floatrep
+ val approx_decstr_by_bin : int -> string -> floatrep * floatrep
+end
+=
+struct
+
+fun fst (a,b) = a
+fun snd (a,b) = b
+
+val filter = List.filter;
+
+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
+
+type floatrep = IntInf.int * IntInf.int
+
+exception Floating_point of string;
+
+val ln2_10 = (Math.ln 10.0)/(Math.ln 2.0)
+
+fun intmul a b = IntInf.* (a,b)
+fun intsub a b = IntInf.- (a,b)
+fun intadd a b = IntInf.+ (a,b)
+fun intpow a b = IntInf.pow (a, IntInf.toInt b);
+fun intle a b = IntInf.<= (a, b);
+fun intless a b = IntInf.< (a, b);
+fun intneg a = IntInf.~ a;
+val zero = IntInf.fromInt 0;
+val one = IntInf.fromInt 1;
+val two = IntInf.fromInt 2;
+val ten = IntInf.fromInt 10;
+val five = IntInf.fromInt 5;
+
+fun find_most_significant q r =
+ let
+ fun int2real i =
+ case Real.fromString (IntInf.toString i) of
+ SOME r => r
+ | NONE => raise (Floating_point "int2real")
+ fun subtract (q, r) (q', r') =
+ if intle r r' then
+ (intsub q (intmul q' (intpow ten (intsub r' r))), r)
+ else
+ (intsub (intmul q (intpow ten (intsub r r'))) q', r')
+ fun bin2dec d =
+ if intle zero d then
+ (intpow two d, zero)
+ else
+ (intpow five (intneg d), d)
+
+ val L = IntInf.fromInt (Real.floor (int2real (IntInf.fromInt (IntInf.log2 q)) + (int2real r) * ln2_10))
+ val L1 = intadd L one
+
+ val (q1, r1) = subtract (q, r) (bin2dec L1)
+ in
+ if intle zero q1 then
+ let
+ val (q2, r2) = subtract (q, r) (bin2dec (intadd L1 one))
+ in
+ if intle zero 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 intle zero 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 (intadd acc (intpow two (intsub d d'))) d' ds
+
+ fun seq2bin [] = (zero, zero)
+ | seq2bin (d::ds) = (intadd (addseq zero d ds) one, d)
+
+ fun approx d_seq d0 precision (q,r) =
+ if q = zero then
+ let val x = seq2bin d_seq in
+ (x, x)
+ end
+ else
+ let
+ val (d, (q', r')) = find_most_significant q r
+ in
+ if intless precision (intsub d0 d) then
+ let
+ val d' = intsub d0 precision
+ val x1 = seq2bin (d_seq)
+ val x2 = (intadd (intmul (fst x1) (intpow two (intsub (snd x1) d'))) one, 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 = zero then
+ ((zero, zero), (zero, zero))
+ else
+ let
+ val (d, (q', r')) = find_most_significant q r
+ in
+ if intle precision zero then
+ let
+ val x1 = seq2bin [d]
+ in
+ if q' = zero then
+ (x1, x1)
+ else
+ (x1, seq2bin [intadd d one])
+ end
+ else
+ approx [d] d precision (q', r')
+ end
+ in
+ if intle zero q then
+ approx_start n (q,r)
+ else
+ let
+ val ((a1,b1), (a2, b2)) = approx_start n (intneg q, r)
+ in
+ ((intneg a2, b2), (intneg a1, b1))
+ end
+ end
+
+fun approx_decstr_by_bin n decstr =
+ let
+ fun str2int s = case IntInf.fromString s of SOME x => x | NONE => zero
+ fun signint p x = if p then x else intneg x
+
+ val (p, d1, d2, ep, e) = destruct_floatstr Char.isDigit (fn e => e = #"e" orelse e = #"E") decstr
+ val s = IntInf.fromInt (size d2)
+
+ val q = signint p (intadd (intmul (str2int d1) (intpow ten s)) (str2int d2))
+ val r = intsub (signint ep (str2int e)) s
+ in
+ approx_dec_by_bin (IntInf.fromInt n) (q,r)
+ end
+
+end;
+
+structure FloatArith =
+struct
+
+type float = IntInf.int * IntInf.int
+
+val izero = IntInf.fromInt 0
+val ione = IntInf.fromInt 1
+val imone = IntInf.fromInt ~1
+val itwo = IntInf.fromInt 2
+fun imul a b = IntInf.* (a,b)
+fun isub a b = IntInf.- (a,b)
+fun iadd a b = IntInf.+ (a,b)
+
+val floatzero = (izero, izero)
+
+fun positive_part (a,b) =
+ (if IntInf.< (a,izero) then izero else a, b)
+
+fun negative_part (a,b) =
+ (if IntInf.< (a,izero) then a else izero, b)
+
+fun is_negative (a,b) =
+ if IntInf.< (a, izero) then true else false
+
+fun is_positive (a,b) =
+ if IntInf.< (izero, a) then true else false
+
+fun is_zero (a,b) =
+ if a = izero then true else false
+
+fun ipow2 a = IntInf.pow ((IntInf.fromInt 2), IntInf.toInt a)
+
+fun add (a1, b1) (a2, b2) =
+ if IntInf.< (b1, b2) then
+ (iadd a1 (imul a2 (ipow2 (isub b2 b1))), b1)
+ else
+ (iadd (imul a1 (ipow2 (isub b1 b2))) a2, b2)
+
+fun sub (a1, b1) (a2, b2) =
+ if IntInf.< (b1, b2) then
+ (isub a1 (imul a2 (ipow2 (isub b2 b1))), b1)
+ else
+ (isub (imul a1 (ipow2 (isub b1 b2))) a2, b2)
+
+fun neg (a, b) = (IntInf.~ a, b)
+
+fun is_equal a b = is_zero (sub a b)
+
+fun is_less a b = is_negative (sub a b)
+
+fun max a b = if is_less a b then b else a
+
+fun min a b = if is_less a b then a else b
+
+fun abs a = if is_negative a then neg a else a
+
+fun mul (a1, b1) (a2, b2) = (imul a1 a2, iadd b1 b2)
+
+end;
+
+
+structure Float:
+sig
+ type float = FloatArith.float
+ type floatfunc = float * float -> float * float
+
+ val mk_intinf : typ -> IntInf.int -> term
+ val mk_float : float -> term
+
+ exception Dest_intinf;
+ val dest_intinf : term -> IntInf.int
+ val dest_nat : term -> IntInf.int
+
+ exception Dest_float;
+ val dest_float : term -> float
+
+ val float_const : term
+
+ val float_add_const : term
+ val float_diff_const : term
+ val float_uminus_const : term
+ val float_pprt_const : term
+ val float_nprt_const : term
+ val float_abs_const : term
+ val float_mult_const : term
+ val float_le_const : term
+
+ val nat_le_const : term
+ val nat_less_const : term
+ val nat_eq_const : term
+
+ val approx_float : int -> floatfunc -> string -> term * term
+
+ val sign_term : term -> cterm
+
+(* exception Float_op_oracle_data of term
+ exception Nat_op_oracle_data of term
+
+ val float_op_oracle : Sign.sg * exn -> term
+ val nat_op_oracle : Sign.sg * exn -> term
+
+ val invoke_float_op : term -> thm
+ val invoke_nat_op : term -> thm*)
+end
+=
+struct
+
+structure Inttab = TableFun(type key = int val ord = (rev_order o int_ord));
+
+type float = IntInf.int*IntInf.int
+type floatfunc = float*float -> float*float
+
+val th = theory "Float"
+val sg = sign_of th
+
+val float_const = Const ("Float.float", HOLogic.mk_prodT (HOLogic.intT, HOLogic.intT) --> HOLogic.realT)
+
+val float_add_const = Const ("op +", HOLogic.realT --> HOLogic.realT --> HOLogic.realT)
+val float_diff_const = Const ("op -", HOLogic.realT --> HOLogic.realT --> HOLogic.realT)
+val float_mult_const = Const ("op *", HOLogic.realT --> HOLogic.realT --> HOLogic.realT)
+val float_uminus_const = Const ("uminus", HOLogic.realT --> HOLogic.realT)
+val float_abs_const = Const ("HOL.abs", HOLogic.realT --> HOLogic.realT)
+val float_le_const = Const ("op <=", HOLogic.realT --> HOLogic.realT --> HOLogic.boolT)
+val float_pprt_const = Const ("OrderedGroup.pprt", HOLogic.realT --> HOLogic.realT)
+val float_nprt_const = Const ("OrderedGroup.nprt", HOLogic.realT --> HOLogic.realT)
+
+val nat_le_const = Const ("op <=", HOLogic.natT --> HOLogic.natT --> HOLogic.boolT)
+val nat_less_const = Const ("op <", HOLogic.natT --> HOLogic.natT --> HOLogic.boolT)
+val nat_eq_const = Const ("op =", HOLogic.natT --> HOLogic.natT --> HOLogic.boolT)
+
+val zero = FloatArith.izero
+val minus_one = FloatArith.imone
+val two = FloatArith.itwo
+
+exception Dest_intinf;
+exception Dest_float;
+
+fun mk_intinf ty n =
+ let
+ fun mk_bit n = if n = zero then HOLogic.false_const else HOLogic.true_const
+
+ fun bin_of n =
+ if n = zero then HOLogic.pls_const
+ else if n = minus_one then HOLogic.min_const
+ else
+ let
+ (*val (q,r) = IntInf.divMod (n, two): doesn't work in SML 10.0.7, but in newer versions!!!*)
+ val q = IntInf.div (n, two)
+ val r = IntInf.mod (n, two)
+ in
+ HOLogic.bit_const $ bin_of q $ mk_bit r
+ end
+ in
+ HOLogic.number_of_const ty $ (bin_of n)
+ end
+
+fun dest_intinf n =
+ let
+ fun dest_bit n =
+ case n of
+ Const ("False", _) => FloatArith.izero
+ | Const ("True", _) => FloatArith.ione
+ | _ => raise Dest_intinf
+
+ fun int_of n =
+ case n of
+ Const ("Numeral.Pls", _) => FloatArith.izero
+ | Const ("Numeral.Min", _) => FloatArith.imone
+ | Const ("Numeral.Bit", _) $ q $ r => FloatArith.iadd (FloatArith.imul (int_of q) FloatArith.itwo) (dest_bit r)
+ | _ => raise Dest_intinf
+ in
+ case n of
+ Const ("Numeral.number_of", _) $ n' => int_of n'
+ | Const ("Numeral0", _) => FloatArith.izero
+ | Const ("Numeral1", _) => FloatArith.ione
+ | _ => raise Dest_intinf
+ end
+
+fun mk_float (a,b) =
+ float_const $ (HOLogic.mk_prod ((mk_intinf HOLogic.intT a), (mk_intinf HOLogic.intT b)))
+
+fun dest_float f =
+ case f of
+ (Const ("Float.float", _) $ (Const ("Pair", _) $ a $ b)) => (dest_intinf a, dest_intinf b)
+ | Const ("Numeral.number_of",_) $ a => (dest_intinf f, 0)
+ | Const ("Numeral0", _) => (FloatArith.izero, FloatArith.izero)
+ | Const ("Numeral1", _) => (FloatArith.ione, FloatArith.izero)
+ | _ => raise Dest_float
+
+fun dest_nat n =
+ let
+ val v = dest_intinf n
+ in
+ if IntInf.< (v, FloatArith.izero) then
+ FloatArith.izero
+ else
+ v
+ end
+
+fun approx_float prec f value =
+ let
+ val interval = ExactFloatingPoint.approx_decstr_by_bin prec value
+ val (flower, fupper) = f interval
+ in
+ (mk_float flower, mk_float fupper)
+ end
+
+fun sign_term t = cterm_of sg t
+
+(*exception Float_op_oracle_data of term;
+
+fun float_op_oracle (sg, exn as Float_op_oracle_data t) =
+ Logic.mk_equals (t,
+ case t of
+ f $ a $ b =>
+ let
+ val a' = dest_float a
+ val b' = dest_float b
+ in
+ if f = float_add_const then
+ mk_float (FloatArith.add a' b')
+ else if f = float_diff_const then
+ mk_float (FloatArith.sub a' b')
+ else if f = float_mult_const then
+ mk_float (FloatArith.mul a' b')
+ else if f = float_le_const then
+ (if FloatArith.is_less b' a' then
+ HOLogic.false_const
+ else
+ HOLogic.true_const)
+ else raise exn
+ end
+ | f $ a =>
+ let
+ val a' = dest_float a
+ in
+ if f = float_uminus_const then
+ mk_float (FloatArith.neg a')
+ else if f = float_abs_const then
+ mk_float (FloatArith.abs a')
+ else if f = float_pprt_const then
+ mk_float (FloatArith.positive_part a')
+ else if f = float_nprt_const then
+ mk_float (FloatArith.negative_part a')
+ else
+ raise exn
+ end
+ | _ => raise exn
+ )
+val th = ref ([]: Theory.theory list)
+val sg = ref ([]: Sign.sg list)
+
+fun invoke_float_op c =
+ let
+ val th = (if length(!th) = 0 then th := [theory "MatrixLP"] else (); hd (!th))
+ val sg = (if length(!sg) = 0 then sg := [sign_of th] else (); hd (!sg))
+ in
+ invoke_oracle th "float_op" (sg, Float_op_oracle_data c)
+ end
+
+exception Nat_op_oracle_data of term;
+
+fun nat_op_oracle (sg, exn as Nat_op_oracle_data t) =
+ Logic.mk_equals (t,
+ case t of
+ f $ a $ b =>
+ let
+ val a' = dest_nat a
+ val b' = dest_nat b
+ in
+ if f = nat_le_const then
+ (if IntInf.<= (a', b') then
+ HOLogic.true_const
+ else
+ HOLogic.false_const)
+ else if f = nat_eq_const then
+ (if a' = b' then
+ HOLogic.true_const
+ else
+ HOLogic.false_const)
+ else if f = nat_less_const then
+ (if IntInf.< (a', b') then
+ HOLogic.true_const
+ else
+ HOLogic.false_const)
+ else
+ raise exn
+ end
+ | _ => raise exn)
+
+fun invoke_nat_op c =
+ let
+ val th = (if length (!th) = 0 then th := [theory "MatrixLP"] else (); hd (!th))
+ val sg = (if length (!sg) = 0 then sg := [sign_of th] else (); hd (!sg))
+ in
+ invoke_oracle th "nat_op" (sg, Nat_op_oracle_data c)
+ end
+*)
+end;
\ No newline at end of file