--- a/src/HOL/IsaMakefile Mon May 14 12:52:54 2007 +0200
+++ b/src/HOL/IsaMakefile Mon May 14 12:52:56 2007 +0200
@@ -153,11 +153,12 @@
HOL-Complex: HOL $(OUT)/HOL-Complex
-$(OUT)/HOL-Complex: $(OUT)/HOL Complex/ROOT.ML Library/Zorn.thy \
- Real/ContNotDenum.thy Real/Ferrante_Rackoff.thy Real/float.ML \
+$(OUT)/HOL-Complex: $(OUT)/HOL Complex/ROOT.ML $(SRC)/Pure/General/float.ML \
+ Library/Zorn.thy \
+ Real/ContNotDenum.thy Real/Ferrante_Rackoff.thy Real/float_arith.ML \
Real/Float.thy Real/Lubs.thy Real/PReal.thy Real/RComplete.thy \
Real/ROOT.ML Real/Rational.thy Real/Real.thy Real/RealDef.thy \
- Real/RealPow.thy Real/RealVector.thy Real/ferrante_rackoff_proof.ML \
+ Real/RealPow.thy Real/RealVector.thy Real/ferrante_rackoff_proof.ML \
Real/ferrante_rackoff.ML Real/rat_arith.ML Real/real_arith.ML \
Hyperreal/StarDef.thy Hyperreal/StarClasses.thy \
Hyperreal/EvenOdd.thy Hyperreal/Fact.thy Hyperreal/HLog.thy \
--- a/src/HOL/Matrix/cplex/FloatSparseMatrixBuilder.ML Mon May 14 12:52:54 2007 +0200
+++ b/src/HOL/Matrix/cplex/FloatSparseMatrixBuilder.ML Mon May 14 12:52:56 2007 +0200
@@ -3,182 +3,96 @@
Author: Steven Obua
*)
-structure FloatSparseMatrixBuilder :
+signature FLOAT_SPARSE_MATIRX_BUILDER =
sig
- include MATRIX_BUILDER
-
- structure cplex : CPLEX
+ include MATRIX_BUILDER
- type float = IntInf.int*IntInf.int
- type floatfunc = float -> float
-
+ structure cplex : CPLEX
- val float2cterm : IntInf.int * IntInf.int -> cterm
-
- val approx_value : int -> floatfunc -> string -> cterm * cterm
- val approx_vector : int -> floatfunc -> vector -> cterm * cterm
- val approx_matrix : int -> floatfunc -> matrix -> cterm * cterm
+ type float = Float.float
+ val approx_value : int -> (float -> float) -> string -> term * term
+ val approx_vector : int -> (float -> float) -> vector -> term * term
+ val approx_matrix : int -> (float -> float) -> matrix -> term * term
- val mk_spvec_entry : int -> float -> term
- val empty_spvec : term
- val cons_spvec : term -> term -> term
- val empty_spmat : term
- val mk_spmat_entry : int -> term -> term
- val cons_spmat : term -> term -> term
- val sign_term : term -> cterm
-
- val v_elem_at : vector -> int -> string option
- val m_elem_at : matrix -> int -> vector option
- val v_only_elem : vector -> int option
- val v_fold : (int * string -> 'a -> 'a) -> vector -> 'a -> 'a
- val m_fold : (int * vector -> 'a -> 'a) -> matrix -> 'a -> 'a
+ val mk_spvec_entry : Intt.int -> float -> term
+ val mk_spmat_entry : Intt.int -> term -> term
+ val spvecT: typ
+ val spmatT: typ
+
+ val v_elem_at : vector -> int -> string option
+ val m_elem_at : matrix -> int -> vector option
+ val v_only_elem : vector -> int option
+ val v_fold : (int * string -> 'a -> 'a) -> vector -> 'a -> 'a
+ val m_fold : (int * vector -> 'a -> 'a) -> matrix -> 'a -> 'a
- val transpose_matrix : matrix -> matrix
+ val transpose_matrix : matrix -> matrix
- val cut_vector : int -> vector -> vector
- val cut_matrix : vector -> (int option) -> matrix -> matrix
+ val cut_vector : int -> vector -> vector
+ val cut_matrix : vector -> int option -> matrix -> matrix
- (* cplexProg c A b *)
- val cplexProg : vector -> matrix -> vector -> (cplex.cplexProg * (string -> int))
- (* dual_cplexProg c A b *)
- val dual_cplexProg : vector -> matrix -> vector -> (cplex.cplexProg * (string -> int))
+ (* cplexProg c A b *)
+ val cplexProg : vector -> matrix -> vector -> cplex.cplexProg * (string -> int)
+ (* dual_cplexProg c A b *)
+ val dual_cplexProg : vector -> matrix -> vector -> cplex.cplexProg * (string -> int)
+end;
- val real_spmatT : typ
- val real_spvecT : typ
-end
-=
+structure FloatSparseMatrixBuilder : FLOAT_SPARSE_MATIRX_BUILDER =
struct
-
-structure Inttab = TableFun(type key = int val ord = (rev_order o int_ord));
+type float = Float.float
+structure Inttab = TableFun(type key = int val ord = rev_order o int_ord);
type vector = string Inttab.table
type matrix = vector Inttab.table
-type float = IntInf.int*IntInf.int
-type floatfunc = float -> float
-
-val th = theory "FloatSparseMatrix"
-
-fun readtype s = Sign.intern_type th s
-fun readterm s = Sign.intern_const th s
-
-val ty_list = readtype "list"
-val term_Nil = readterm "Nil"
-val term_Cons = readterm "Cons"
-
-val spvec_elemT = HOLogic.mk_prodT (HOLogic.natT, HOLogic.realT)
-val spvecT = Type (ty_list, [spvec_elemT])
-val spmat_elemT = HOLogic.mk_prodT (HOLogic.natT, spvecT)
-val spmatT = Type (ty_list, [spmat_elemT])
-
-val real_spmatT = spmatT
-val real_spvecT = spvecT
-
-val empty_matrix_const = Const (term_Nil, spmatT)
-val empty_vector_const = Const (term_Nil, spvecT)
-
-val Cons_spvec_const = Const (term_Cons, spvec_elemT --> spvecT --> spvecT)
-val Cons_spmat_const = Const (term_Cons, spmat_elemT --> spmatT --> spmatT)
-val float_const = Float.float_const
-
-val zero = IntInf.fromInt 0
-val minus_one = IntInf.fromInt ~1
-val two = IntInf.fromInt 2
-
-val mk_intinf = Float.mk_intinf
-
-val mk_float = Float.mk_float
-
-fun float2cterm (a,b) = cterm_of th (mk_float (a,b))
+val spvec_elemT = HOLogic.mk_prodT (HOLogic.natT, HOLogic.realT);
+val spvecT = HOLogic.listT spvec_elemT;
+val spmat_elemT = HOLogic.mk_prodT (HOLogic.natT, spvecT);
+val spmatT = HOLogic.listT spmat_elemT;
-fun approx_value_term prec f = Float.approx_float prec (fn (x, y) => (f x, f y))
-
-fun approx_value prec pprt value =
- let
- val (flower, fupper) = approx_value_term prec pprt value
- in
- (cterm_of th flower, cterm_of th fupper)
- end
-
-fun sign_term t = cterm_of th t
-
-val empty_spvec = empty_vector_const
-
-val empty_spmat = empty_matrix_const
+fun approx_value prec f =
+ FloatArith.approx_float prec (fn (x, y) => (f x, f y));
fun mk_spvec_entry i f =
- let
- val term_i = mk_intinf HOLogic.natT (IntInf.fromInt i)
- val term_f = mk_float f
- in
- HOLogic.mk_prod (term_i, term_f)
- end
+ HOLogic.mk_prod (HOLogic.mk_number HOLogic.natT i, FloatArith.mk_float f);
fun mk_spmat_entry i e =
- let
- val term_i = mk_intinf HOLogic.natT (IntInf.fromInt i)
- in
- HOLogic.mk_prod (term_i, e)
- end
-
-fun cons_spvec h t = Cons_spvec_const $ h $ t
-
-fun cons_spmat h t = Cons_spmat_const $ h $ t
-
-fun approx_vector_term prec pprt vector =
- let
- fun app (index, s) (vlower, vupper) =
- let
- val (flower, fupper) = approx_value_term prec pprt s
- val index = mk_intinf HOLogic.natT (IntInf.fromInt index)
- val elower = HOLogic.mk_prod (index, flower)
- val eupper = HOLogic.mk_prod (index, fupper)
- in
- (Cons_spvec_const $ elower $ vlower,
- Cons_spvec_const $ eupper $ vupper)
- end
- in
- Inttab.fold app vector (empty_vector_const, empty_vector_const)
- end
-
-fun approx_matrix_term prec pprt matrix =
- let
- fun app (index, vector) (mlower, mupper) =
- let
- val (vlower, vupper) = approx_vector_term prec pprt vector
- val index = mk_intinf HOLogic.natT (IntInf.fromInt index)
- val elower = HOLogic.mk_prod (index, vlower)
- val eupper = HOLogic.mk_prod (index, vupper)
- in
- (Cons_spmat_const $ elower $ mlower, Cons_spmat_const $ eupper $ mupper)
- end
- val (mlower, mupper) = Inttab.fold app matrix (empty_matrix_const, empty_matrix_const)
- in Inttab.fold app matrix (empty_matrix_const, empty_matrix_const) end;
+ HOLogic.mk_prod (HOLogic.mk_number HOLogic.natT i, e);
fun approx_vector prec pprt vector =
- let
- val (l, u) = approx_vector_term prec pprt vector
- in
- (cterm_of th l, cterm_of th u)
- end
+ let
+ fun app (index, s) (lower, upper) =
+ let
+ val (flower, fupper) = approx_value prec pprt s
+ val index = HOLogic.mk_number HOLogic.natT (Intt.int index)
+ val elower = HOLogic.mk_prod (index, flower)
+ val eupper = HOLogic.mk_prod (index, fupper)
+ in (elower :: lower, eupper :: upper) end;
+ in
+ pairself (HOLogic.mk_list spvecT) (Inttab.fold app vector ([], []))
+ end;
-fun approx_matrix prec pprt matrix =
- let
- val (l, u) = approx_matrix_term prec pprt matrix
- in
- (cterm_of th l, cterm_of th u)
- end
-
+fun approx_matrix prec pprt vector =
+ let
+ fun app (index, v) (lower, upper) =
+ let
+ val (flower, fupper) = approx_vector prec pprt v
+ val index = HOLogic.mk_number HOLogic.natT (Intt.int index)
+ val elower = HOLogic.mk_prod (index, flower)
+ val eupper = HOLogic.mk_prod (index, fupper)
+ in (elower :: lower, eupper :: upper) end;
+ in
+ pairself (HOLogic.mk_list spmatT) (Inttab.fold app vector ([], []))
+ end;
exception Nat_expected of int;
-val zero_interval = approx_value_term 1 I "0"
+val zero_interval = approx_value 1 I "0"
fun set_elem vector index str =
if index < 0 then
raise (Nat_expected index)
- else if (approx_value_term 1 I str) = zero_interval then
+ else if (approx_value 1 I str) = zero_interval then
vector
else
Inttab.update (index, str) vector
--- a/src/HOL/Matrix/cplex/fspmlp.ML Mon May 14 12:52:54 2007 +0200
+++ b/src/HOL/Matrix/cplex/fspmlp.ML Mon May 14 12:52:56 2007 +0200
@@ -9,25 +9,25 @@
type vector = FloatSparseMatrixBuilder.vector
type matrix = FloatSparseMatrixBuilder.matrix
- val y : linprog -> cterm
- val A : linprog -> cterm * cterm
- val b : linprog -> cterm
- val c : linprog -> cterm * cterm
- val r : linprog -> cterm
- val r12 : linprog -> cterm * cterm
+ val y : linprog -> term
+ val A : linprog -> term * term
+ val b : linprog -> term
+ val c : linprog -> term * term
+ val r : linprog -> term
+ val r12 : linprog -> term * term
exception Load of string
val load : string -> int -> bool -> linprog
end
-structure fspmlp : FSPMLP =
+structure Fspmlp : FSPMLP =
struct
type vector = FloatSparseMatrixBuilder.vector
type matrix = FloatSparseMatrixBuilder.matrix
-type linprog = cterm * (cterm * cterm) * cterm * (cterm * cterm) * cterm * (cterm * cterm)
+type linprog = term * (term * term) * term * (term * term) * term * (term * term)
fun y (c1, c2, c3, c4, c5, _) = c1
fun A (c1, c2, c3, c4, c5, _) = c2
@@ -77,8 +77,8 @@
| SOME (NONE, f) => (SOME bound, f)
| SOME (SOME old_bound, f) =>
(SOME ((case btype of
- UPPER => FloatArith.min
- | LOWER => FloatArith.max)
+ UPPER => Float.min
+ | LOWER => Float.max)
old_bound bound), f)
in
VarGraph.update (key, x) g
@@ -125,16 +125,16 @@
fun calc_sure_bound_from_sources g (key as (_, btype)) =
let
fun mult_upper x (lower, upper) =
- if FloatArith.is_negative x then
- FloatArith.mul x lower
+ if Float.cmp_zero x = LESS then
+ Float.mult x lower
else
- FloatArith.mul x upper
+ Float.mult x upper
fun mult_lower x (lower, upper) =
- if FloatArith.is_negative x then
- FloatArith.mul x upper
+ if Float.cmp_zero x = LESS then
+ Float.mult x upper
else
- FloatArith.mul x lower
+ Float.mult x lower
val mult_btype = case btype of UPPER => mult_upper | LOWER => mult_lower
@@ -146,7 +146,7 @@
| SOME x =>
(case get_sure_bound g src_key of
NONE => NONE
- | SOME src_sure_bound => SOME (FloatArith.add x (mult_btype src_sure_bound coeff)))
+ | SOME src_sure_bound => SOME (Float.add x (mult_btype src_sure_bound coeff)))
in
case fold add_src_bound sources (SOME row_bound) of
NONE => sure_bound
@@ -155,8 +155,8 @@
NONE => new_sure_bound
| SOME old_bound =>
SOME (case btype of
- UPPER => FloatArith.min old_bound new_bound
- | LOWER => FloatArith.max old_bound new_bound))
+ UPPER => Float.min old_bound new_bound
+ | LOWER => Float.max old_bound new_bound))
end
in
case VarGraph.lookup g key of
@@ -187,6 +187,15 @@
exception Load of string;
+(*val empty_spvec = @ {term "Nil :: (nat * real) list"};
+fun cons_spvec x xs = @ {term "Cons :: nat * real => nat * real => (nat * real) list"} $ x $ xs;
+val empty_spmat = @ {term "Nil :: (nat * (nat * real) list) list"};
+fun cons_spmat x xs = @ {term "Cons :: nat * (nat * real) list => (nat * (nat * real) list) list => (nat * (nat * real) list) list"} $ x $ xs;*)
+val empty_spvec = Bound 0
+fun cons_spvec x xs = Bound 0
+val empty_spmat = Bound 0
+fun cons_spmat x xs = Bound 0
+
fun calcr safe_propagation xlen names prec A b =
let
val empty = Inttab.empty
@@ -198,17 +207,17 @@
fun test_1 (lower, upper) =
if lower = upper then
- (if FloatArith.is_equal lower (IntInf.fromInt ~1, FloatArith.izero) then ~1
- else if FloatArith.is_equal lower (IntInf.fromInt 1, FloatArith.izero) then 1
+ (if Float.eq (lower, (Intt.int ~1, Intt.zero)) then ~1
+ else if Float.eq (lower, (Intt.int 1, Intt.zero)) then 1
else 0)
else 0
fun calcr (row_index, a) g =
let
val b = FloatSparseMatrixBuilder.v_elem_at b row_index
- val (_, b2) = ExactFloatingPoint.approx_decstr_by_bin prec (case b of NONE => "0" | SOME b => b)
+ val (_, b2) = FloatArith.approx_decstr_by_bin prec (case b of NONE => "0" | SOME b => b)
val approx_a = FloatSparseMatrixBuilder.v_fold (fn (i, s) => fn l =>
- (i, ExactFloatingPoint.approx_decstr_by_bin prec s)::l) a []
+ (i, FloatArith.approx_decstr_by_bin prec s)::l) a []
fun fold_dest_nodes (dest_index, dest_value) g =
let
@@ -219,7 +228,7 @@
else let
val (dest_key as (_, dest_btype), row_bound) =
if dest_test = ~1 then
- ((dest_index, LOWER), FloatArith.neg b2)
+ ((dest_index, LOWER), Float.neg b2)
else
((dest_index, UPPER), b2)
@@ -228,10 +237,10 @@
else
let
val coeff = case dest_btype of
- UPPER => (FloatArith.neg src_upper, FloatArith.neg src_lower)
+ UPPER => (Float.neg src_upper, Float.neg src_lower)
| LOWER => src_value
in
- if FloatArith.is_negative src_lower then
+ if Float.cmp_zero src_lower = LESS then
add_edge g (src_index, UPPER) dest_key row_index coeff
else
add_edge g (src_index, LOWER) dest_key row_index coeff
@@ -248,7 +257,7 @@
val atest = test_1 a
in
if atest = ~1 then
- update_sure_bound g (u, LOWER) (FloatArith.neg b2)
+ update_sure_bound g (u, LOWER) (Float.neg b2)
else if atest = 1 then
update_sure_bound g (u, UPPER) b2
else
@@ -264,28 +273,28 @@
fun add_row_entry m index value =
let
- val vec = FloatSparseMatrixBuilder.cons_spvec (FloatSparseMatrixBuilder.mk_spvec_entry 0 value) FloatSparseMatrixBuilder.empty_spvec
+ val vec = cons_spvec (FloatSparseMatrixBuilder.mk_spvec_entry 0 value) empty_spvec
in
- FloatSparseMatrixBuilder.cons_spmat (FloatSparseMatrixBuilder.mk_spmat_entry index vec) m
+ cons_spmat (FloatSparseMatrixBuilder.mk_spmat_entry index vec) m
end
fun abs_estimate i r1 r2 =
if i = 0 then
- let val e = FloatSparseMatrixBuilder.empty_spmat in (e, (e, e)) end
+ let val e = empty_spmat in (e, (e, e)) end
else
let
val index = xlen-i
val (r, (r12_1, r12_2)) = abs_estimate (i-1) r1 r2
val b1 = case Inttab.lookup r1 index of NONE => raise (Load ("x-value not bounded from below: "^(names index))) | SOME x => x
val b2 = case Inttab.lookup r2 index of NONE => raise (Load ("x-value not bounded from above: "^(names index))) | SOME x => x
- val abs_max = FloatArith.max (FloatArith.neg (FloatArith.negative_part b1)) (FloatArith.positive_part b2)
+ val abs_max = Float.max (Float.neg (Float.negative_part b1)) (Float.positive_part b2)
+ val i' = Intt.int index
in
- (add_row_entry r index abs_max, (add_row_entry r12_1 index b1, add_row_entry r12_2 index b2))
+ (add_row_entry r i' abs_max, (add_row_entry r12_1 i' b1, add_row_entry r12_2 i' b2))
end
- val sign = FloatSparseMatrixBuilder.sign_term
val (r, (r1, r2)) = abs_estimate xlen r1 r2
in
- (sign r, (sign r1, sign r2))
+ (r, (r1, r2))
end
fun load filename prec safe_propagation =
@@ -304,7 +313,7 @@
val v = FloatSparseMatrixBuilder.set_vector FloatSparseMatrixBuilder.empty_matrix 0 v
val b = FloatSparseMatrixBuilder.transpose_matrix (FloatSparseMatrixBuilder.set_vector FloatSparseMatrixBuilder.empty_matrix 0 b)
val c = FloatSparseMatrixBuilder.set_vector FloatSparseMatrixBuilder.empty_matrix 0 c
- val (y1, _) = FloatSparseMatrixBuilder.approx_matrix prec FloatArith.positive_part v
+ val (y1, _) = FloatSparseMatrixBuilder.approx_matrix prec Float.positive_part v
val A = FloatSparseMatrixBuilder.approx_matrix prec id A
val (_,b2) = FloatSparseMatrixBuilder.approx_matrix prec id b
val c = FloatSparseMatrixBuilder.approx_matrix prec id c
--- a/src/HOL/Matrix/cplex/matrixlp.ML Mon May 14 12:52:54 2007 +0200
+++ b/src/HOL/Matrix/cplex/matrixlp.ML Mon May 14 12:52:56 2007 +0200
@@ -23,13 +23,13 @@
([(certT (TVar (hd (term_tvars (prop_of thm)))), certT HOLogic.realT)], []) thm)
end
-val spm_mult_le_dual_prts_no_let = thm "SparseMatrix.spm_mult_le_dual_prts_no_let"
+val spm_mult_le_dual_prts_no_let = thm "SparseMatrix.spm_mult_le_dual_prts_no_let";
+val cert = cterm_of (Thm.theory_of_thm spm_mult_le_dual_prts_no_let);
fun lp_dual_estimate_prt_primitive (y, (A1, A2), (c1, c2), b, (r1, r2)) =
let
- val cert = cterm_of (Thm.theory_of_thm spm_mult_le_dual_prts_no_let)
val th = inst_real spm_mult_le_dual_prts_no_let
- fun var s x = (cert (Var ((s,0), FloatSparseMatrixBuilder.real_spmatT)), x)
+ fun var s x = (cert (Var ((s,0), FloatSparseMatrixBuilder.spmatT)), x)
val th = Thm.instantiate ([], [var "A1" A1, var "A2" A2, var "y" y, var "c1" c1, var "c2" c2,
var "r1" r1, var "r2" r2, var "b" b]) th
in th end
@@ -38,10 +38,10 @@
let
val certificate =
let
- open fspmlp
+ open Fspmlp
val l = load lptfile prec false
in
- (y l, A l, c l, b l, r12 l)
+ (y l |> cert, A l |> pairself cert, c l |> pairself cert, b l |> cert, r12 l |> pairself cert)
end
in
lp_dual_estimate_prt_primitive certificate
@@ -55,7 +55,7 @@
check (concl_of th)
end
-fun prep ths = (Library.filter is_meta_eq ths) @ (map (standard o mk_meta_eq) (Library.filter (not o is_meta_eq) ths))
+fun prep ths = filter is_meta_eq ths @ map (standard o mk_meta_eq) (filter_out is_meta_eq ths)
fun inst_tvar ty thm =
let
@@ -71,8 +71,8 @@
val matrix_compute =
let
- val spvecT = FloatSparseMatrixBuilder.real_spvecT
- val spmatT = FloatSparseMatrixBuilder.real_spmatT
+ val spvecT = FloatSparseMatrixBuilder.spvecT
+ val spmatT = FloatSparseMatrixBuilder.spmatT
val spvecT_elem = HOLogic.mk_prodT (HOLogic.natT, HOLogic.realT)
val spmatT_elem = HOLogic.mk_prodT (HOLogic.natT, spvecT)
val case_compute = map thm ["list_case_compute", "list_case_compute_empty", "list_case_compute_cons"]
@@ -86,7 +86,7 @@
@ (map (inst_tvar HOLogic.realT) (thms "MatrixLP.sparse_row_matrix_arith_simps"))
@ (thms "MatrixLP.boolarith")
@ (inst_tvars [HOLogic.natT, HOLogic.realT] [thm "fst_compute", thm "snd_compute"])
- @ (inst_tvars [HOLogic.natT, FloatSparseMatrixBuilder.real_spvecT] [thm "fst_compute", thm "snd_compute"])
+ @ (inst_tvars [HOLogic.natT, FloatSparseMatrixBuilder.spvecT] [thm "fst_compute", thm "snd_compute"])
@ (inst_tvars [HOLogic.boolT, spmatT_elem] case_compute)
@ (inst_tvars [HOLogic.boolT, spvecT_elem] case_compute)
@ (inst_tvars [HOLogic.boolT, HOLogic.realT] case_compute)
--- a/src/HOL/Real/Float.thy Mon May 14 12:52:54 2007 +0200
+++ b/src/HOL/Real/Float.thy Mon May 14 12:52:56 2007 +0200
@@ -7,7 +7,7 @@
theory Float
imports Real Parity
-uses ("float.ML")
+uses "~~/src/Pure/General/float.ML" ("float_arith.ML")
begin
definition
@@ -526,6 +526,6 @@
(* for use with the compute oracle *)
lemmas arith = binarith intarith intarithrel natarith powerarith floatarith not_false_eq_true not_true_eq_false
-use "float.ML";
+use "float_arith.ML";
end
--- a/src/HOL/Real/float.ML Mon May 14 12:52:54 2007 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,373 +0,0 @@
-(* 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
-
-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
-
-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 float_const = Const ("Float.float", HOLogic.mk_prodT (HOLogic.intT, HOLogic.intT) --> HOLogic.realT)
-
-val float_add_const = Const ("HOL.plus", HOLogic.realT --> HOLogic.realT --> HOLogic.realT)
-val float_diff_const = Const ("HOL.minus", HOLogic.realT --> HOLogic.realT --> HOLogic.realT)
-val float_mult_const = Const ("HOL.times", HOLogic.realT --> HOLogic.realT --> HOLogic.realT)
-val float_uminus_const = Const ("HOL.uminus", HOLogic.realT --> HOLogic.realT)
-val float_abs_const = Const ("HOL.abs", HOLogic.realT --> HOLogic.realT)
-val float_le_const = Const ("Orderings.less_eq", 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 ("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 = HOLogic.number_of_const ty $ HOLogic.mk_numeral n;
-
-val dest_intinf = snd o HOLogic.dest_number
-
-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
-
-end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Real/float_arith.ML Mon May 14 12:52:56 2007 +0200
@@ -0,0 +1,226 @@
+(* Title: HOL/Real/Float.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: Intt.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;
+val exp5 = Intt.pow (Intt.int 5);
+val exp10 = Intt.pow (Intt.int 10);
+
+fun intle a b = not (Intt.cmp (a, b) = GREATER);
+fun intless a b = Intt.cmp (a, b) = LESS;
+
+fun find_most_significant q r =
+ let
+ fun int2real i =
+ case (Real.fromString o Intt.string_of_int) i of
+ SOME r => r
+ | NONE => raise (Floating_point "int2real")
+ fun subtract (q, r) (q', r') =
+ if intle r r' then
+ (Intt.sub q (Intt.mult q' (exp10 (Intt.sub r' r))), r)
+ else
+ (Intt.sub (Intt.mult q (exp10 (Intt.sub r r'))) q', r')
+ fun bin2dec d =
+ if intle Intt.zero d then
+ (Intt.exp d, Intt.zero)
+ else
+ (exp5 (Intt.neg d), d)
+
+ val L = Intt.int (Real.floor (int2real (Intt.log q) + int2real r * ln2_10))
+ val L1 = Intt.inc L
+
+ val (q1, r1) = subtract (q, r) (bin2dec L1)
+ in
+ if intle Intt.zero q1 then
+ let
+ val (q2, r2) = subtract (q, r) (bin2dec (Intt.inc L1))
+ in
+ if intle Intt.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 Intt.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 (Intt.add acc (Intt.exp (Intt.sub d d'))) d' ds
+
+ fun seq2bin [] = (Intt.zero, Intt.zero)
+ | seq2bin (d::ds) = (Intt.inc (addseq Intt.zero d ds), d)
+
+ fun approx d_seq d0 precision (q,r) =
+ if q = Intt.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 (Intt.sub d0 d) then
+ let
+ val d' = Intt.sub d0 precision
+ val x1 = seq2bin (d_seq)
+ val x2 = (Intt.inc
+ (Intt.mult (fst x1)
+ (Intt.exp (Intt.sub (snd x1) d'))), 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 = Intt.zero then
+ ((Intt.zero, Intt.zero), (Intt.zero, Intt.zero))
+ else
+ let
+ val (d, (q', r')) = find_most_significant q r
+ in
+ if intle precision Intt.zero then
+ let
+ val x1 = seq2bin [d]
+ in
+ if q' = Intt.zero then
+ (x1, x1)
+ else
+ (x1, seq2bin [Intt.inc d])
+ end
+ else
+ approx [d] d precision (q', r')
+ end
+ in
+ if intle Intt.zero q then
+ approx_start n (q,r)
+ else
+ let
+ val ((a1,b1), (a2, b2)) = approx_start n (Intt.neg q, r)
+ in
+ ((Intt.neg a2, b2), (Intt.neg a1, b1))
+ end
+ end
+
+fun approx_decstr_by_bin n decstr =
+ let
+ fun str2int s = the_default Intt.zero (Intt.int_of_string s);
+ fun signint p x = if p then x else Intt.neg x
+
+ val (p, d1, d2, ep, e) = destruct_floatstr Char.isDigit (fn e => e = #"e" orelse e = #"E") decstr
+ val s = Intt.int (size d2)
+
+ val q = signint p (Intt.add (Intt.mult (str2int d1) (exp10 s)) (str2int d2))
+ val r = Intt.sub (signint ep (str2int e)) s
+ in
+ approx_dec_by_bin (Intt.int 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, Intt.zero);
+
+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;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/General/float.ML Mon May 14 12:52:56 2007 +0200
@@ -0,0 +1,60 @@
+(* Title: Pure/General/float.ML
+ ID: $Id$
+ Author: Steven Obua, Florian Haftmann, TU Muenchen
+
+Implementation of real numbers as mantisse-exponent pairs.
+*)
+
+signature FLOAT =
+sig
+ type float = Intt.int * Intt.int
+ val zero: float
+ val eq: float * float -> bool
+ val cmp: float * float -> order
+ val cmp_zero: float -> order
+ val min: float -> float -> float
+ val max: float -> float -> float
+ val add: float -> float -> float
+ val sub: float -> float -> float
+ val neg: float -> float
+ val mult: float -> float -> float
+ val positive_part: float -> float
+ val negative_part: float -> float
+end;
+
+structure Float : FLOAT =
+struct
+
+type float = Intt.int * Intt.int;
+
+val zero = (Intt.zero, Intt.zero);
+
+fun add (a1, b1) (a2, b2) =
+ if Intt.cmp (b1, b2) = LESS then
+ (Intt.add a1 (Intt.mult a2 (Intt.exp (Intt.sub b2 b1))), b1)
+ else
+ (Intt.add (Intt.mult a1 (Intt.exp (Intt.sub b1 b2))) a2, b2);
+
+fun sub (a1, b1) (a2, b2) =
+ if Intt.cmp (b1, b2) = LESS then
+ (Intt.sub a1 (Intt.mult a2 (Intt.exp (Intt.sub b2 b1))), b1)
+ else
+ (Intt.sub (Intt.mult a1 (Intt.exp (Intt.sub b1 b2))) a2, b2);
+
+fun neg (a, b) = (Intt.neg a, b);
+
+fun mult (a1, b1) (a2, b2) = (Intt.mult a1 a2, Intt.add b1 b2);
+
+fun cmp_zero (a, b) = Intt.cmp_zero a;
+
+fun cmp (r, s) = cmp_zero (sub r s);
+
+fun eq (r, s) = cmp (r, s) = EQUAL;
+
+fun min r s = case cmp (r, s) of LESS => r | _ => s;
+fun max r s = case cmp (r, s) of LESS => s | _ => r;
+
+fun positive_part (a, b) = (Intt.max Intt.zero a, b);
+fun negative_part (a, b) = (Intt.min Intt.zero a, b);
+
+end;
--- a/src/Pure/General/int.ML Mon May 14 12:52:54 2007 +0200
+++ b/src/Pure/General/int.ML Mon May 14 12:52:56 2007 +0200
@@ -19,6 +19,9 @@
val cmp: int * int -> order
val le: int -> int -> bool
val cmp_zero: int -> order
+ val min: int -> int -> int
+ val max: int -> int -> int
+ val inc: int -> int
val add: int -> int -> int
val sub: int -> int -> int
val mult: int -> int -> int
@@ -27,6 +30,8 @@
val mod: int -> int -> int
val neg: int -> int
val exp: int -> int
+ val log: int -> int
+ val pow: int -> int -> int (* exponent -> base -> result *)
end;
structure Intt: INTT =
@@ -34,29 +39,35 @@
open IntInf;
-val int = IntInf.fromInt;
+val int = fromInt;
val zero = int 0;
val one = int 1;
val two = int 2;
-val machine_int = IntInf.toInt;
-val string_of_int = IntInf.toString;
-val int_of_string = IntInf.fromString;
+val machine_int = toInt;
+val string_of_int = toString;
+val int_of_string = fromString;
-val eq = op =;
+val eq = op = : int * int -> bool;
val cmp = compare;
val le = curry (op <=);
val cmp_zero = curry cmp zero;
+
+val min = curry min;
+val max = curry max;
+
+val inc = curry (op +) one;
+
val add = curry (op +);
val sub = curry (op -);
val mult = curry ( op * );
val divmod = curry divMod;
-nonfix div
-val div = curry div;
-nonfix mod
-val mod = curry mod;
-val neg = IntInf.~;
-fun exp n = pow (2, IntInf.toInt n);
+nonfix div val div = curry div;
+nonfix mod val mod = curry mod;
+val neg = ~;
+val pow = fn k => fn l => pow (l, toInt k);
+fun exp k = pow k two;
+val log = int o log2;
end;