--- a/src/HOL/Real/float.ML Wed Dec 13 15:45:30 2006 +0100
+++ b/src/HOL/Real/float.ML Wed Dec 13 15:45:31 2006 +0100
@@ -13,35 +13,35 @@
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
+end
=
struct
exception Destruct_floatstr of string;
-fun destruct_floatstr isDigit isExp number =
+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
+ | 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
+ | readdigits (q as c::cs) =
+ if (isDigit c) then
let
val (digits, rest) = readdigits cs
in
(c::digits, rest)
end
else
- ([], q)
+ ([], q)
fun readfromexp_helper cs =
let
@@ -51,27 +51,27 @@
case rest' of
[] => (positive, digits)
| _ => raise (Destruct_floatstr number)
- end
+ end
fun readfromexp [] = (true, [])
- | readfromexp (c::cs) =
+ | readfromexp (c::cs) =
if isExp c then
readfromexp_helper cs
- else
- raise (Destruct_floatstr number)
+ else
+ raise (Destruct_floatstr number)
fun readfromdot [] = ([], readfromexp [])
- | readfromdot ((#".")::cs) =
- let
+ | readfromdot ((#".")::cs) =
+ let
val (digits, rest) = readdigits cs
val exp = readfromexp rest
in
(digits, exp)
- end
+ end
| readfromdot cs = readfromdot ((#".")::cs)
-
- val (positive, numlist) = countsigns numlist
- val (digits1, numlist) = readdigits numlist
+
+ 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))
@@ -82,10 +82,10 @@
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 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);
@@ -96,33 +96,33 @@
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') =
+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
+ 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))
+ (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)
+ val (q1, r1) = subtract (q, r) (bin2dec L1)
in
- if intle zero q1 then
+ if intle zero q1 then
let
val (q2, r2) = subtract (q, r) (bin2dec (intadd L1 one))
in
- if intle zero q2 then
+ if intle zero q2 then
raise (Floating_point "find_most_significant")
else
(L1, (q1, r1))
@@ -135,76 +135,76 @@
(L, (q0, r0))
else
raise (Floating_point "find_most_significant")
- end
+ end
end
fun approx_dec_by_bin n (q,r) =
- let
+ 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
+ fun approx d_seq d0 precision (q,r) =
+ if q = zero then
let val x = seq2bin d_seq in
(x, x)
end
- else
- let
+ else
+ let
val (d, (q', r')) = find_most_significant q r
- in
- if intless precision (intsub d0 d) then
- let
+ 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) *)
+ 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
-
+ approx (d::d_seq) d0 precision (q', r')
+ end
+
fun approx_start precision (q, r) =
- if q = zero then
+ if q = zero then
((zero, zero), (zero, zero))
else
- let
+ let
val (d, (q', r')) = find_most_significant q r
- in
- if intle precision zero then
+ in
+ if intle precision zero then
let
val x1 = seq2bin [d]
in
- if q' = zero then
+ if q' = zero then
(x1, x1)
else
(x1, seq2bin [intadd d one])
end
else
approx [d] d precision (q', r')
- end
+ end
in
- if intle zero q then
+ if intle zero q then
approx_start n (q,r)
else
- let
- val ((a1,b1), (a2, b2)) = approx_start n (intneg q, r)
+ let
+ val ((a1,b1), (a2, b2)) = approx_start n (intneg q, r)
in
((intneg a2, b2), (intneg a1, b1))
- end
+ end
end
fun approx_decstr_by_bin n decstr =
- let
- fun str2int s = case IntInf.fromString s of SOME x => x | NONE => zero
+ 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
@@ -213,10 +213,10 @@
end;
-structure FloatArith =
+structure FloatArith =
struct
-type float = IntInf.int * IntInf.int
+type float = IntInf.int * IntInf.int
val izero = IntInf.fromInt 0
val ione = IntInf.fromInt 1
@@ -228,30 +228,30 @@
val floatzero = (izero, izero)
-fun positive_part (a,b) =
+fun positive_part (a,b) =
(if IntInf.< (a,izero) then izero else a, b)
-fun negative_part (a,b) =
+fun negative_part (a,b) =
(if IntInf.< (a,izero) then a else izero, b)
-fun is_negative (a,b) =
+fun is_negative (a,b) =
if IntInf.< (a, izero) then true else false
-fun is_positive (a,b) =
+fun is_positive (a,b) =
if IntInf.< (izero, a) then true else false
-fun is_zero (a,b) =
+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) =
+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) =
+fun sub (a1, b1) (a2, b2) =
if IntInf.< (b1, b2) then
(isub a1 (imul a2 (ipow2 (isub b2 b1))), b1)
else
@@ -285,7 +285,7 @@
exception Dest_intinf;
val dest_intinf : term -> IntInf.int
val dest_nat : term -> IntInf.int
-
+
exception Dest_float;
val dest_float : term -> float
@@ -297,7 +297,7 @@
val float_pprt_const : term
val float_nprt_const : term
val float_abs_const : term
- val float_mult_const : term
+ val float_mult_const : term
val float_le_const : term
val nat_le_const : term
@@ -314,8 +314,8 @@
val invoke_float_op : term -> thm
val invoke_nat_op : term -> thm*)
-end
-=
+end
+=
struct
structure Inttab = TableFun(type key = int val ord = (rev_order o int_ord));
@@ -337,64 +337,31 @@
val nat_le_const = Const ("Orderings.less_eq", HOLogic.natT --> HOLogic.natT --> HOLogic.boolT)
val nat_less_const = Const ("Orderings.less", 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.B0_const else HOLogic.B1_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)
- in
- HOLogic.bit_const $ bin_of q $ mk_bit r
- end
- in
- HOLogic.number_of_const ty $ (bin_of n)
- end
+fun mk_intinf ty n = HOLogic.number_of_const ty $ HOLogic.mk_numeral n;
-fun dest_intinf n =
- let
- fun dest_bit n =
- case n of
- Const ("Numeral.bit.B0", _) => FloatArith.izero
- | Const ("Numeral.bit.B1", _) => 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
+val dest_intinf = snd o HOLogic.dest_number
-fun mk_float (a,b) =
+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
+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
+fun dest_nat n =
+ let
val v = dest_intinf n
in
if IntInf.< (v, FloatArith.izero) then
@@ -403,7 +370,7 @@
v
end
-fun approx_float prec f value =
+fun approx_float prec f value =
let
val interval = ExactFloatingPoint.approx_decstr_by_bin prec value
val (flower, fupper) = f interval
@@ -415,26 +382,26 @@
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
+ 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')
+ 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')
+ 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
+ else raise exn
end
- | f $ a =>
+ | f $ a =>
let
val a' = dest_float a
in
@@ -454,7 +421,7 @@
val th = ref ([]: theory list)
val sg = ref ([]: Sign.sg list)
-fun invoke_float_op c =
+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))
@@ -466,10 +433,10 @@
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
+ case t of
+ f $ a $ b =>
+ let
+ val a' = dest_nat a
val b' = dest_nat b
in
if f = nat_le_const then
@@ -478,7 +445,7 @@
else
HOLogic.false_const)
else if f = nat_eq_const then
- (if a' = b' then
+ (if a' = b' then
HOLogic.true_const
else
HOLogic.false_const)
@@ -487,12 +454,13 @@
HOLogic.true_const
else
HOLogic.false_const)
- else
- raise exn
+ else
+ raise exn
+
end
| _ => raise exn)
-fun invoke_nat_op c =
+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))