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Flocq
flocq
Commits
343c7be1
Commit
343c7be1
authored
Jan 13, 2011
by
Guillaume Melquiond
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Beautified term of binary_float_of_bits a bit.
parent
5049b180
Changes
1
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51 additions
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32 deletions
+51
-32
src/Appli/Fappli_IEEE.v
src/Appli/Fappli_IEEE.v
+51
-32
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src/Appli/Fappli_IEEE.v
View file @
343c7be1
...
...
@@ -1140,29 +1140,18 @@ discriminate.
now
apply
Zlt_0_le_0_pred
.
Qed
.
Program
Definition
binary_float_of_bits
(
x
:
Z
)
:=
let
'
(
sx
,
mx
,
ex
)
:=
split_bits
x
in
if
Sumbool
.
sumbool_of_bool
(
Zeq_bool
ex
0
)
then
match
mx
with
|
Z0
=>
B754_zero
prec
emax
sx
|
Zpos
mx
=>
B754_finite
prec
emax
sx
mx
emin
_
|
_
=>
B754_nan
prec
emax
(
*
dummy
*
)
end
else
if
Sumbool
.
sumbool_of_bool
(
Zeq_bool
ex
(
Zpower
2
ew
-
1
))
then
if
Zeq_bool
mx
0
then
B754_infinity
prec
emax
sx
else
B754_nan
prec
emax
else
match
(
mx
+
Zpower
2
mw
)
%
Z
with
|
Zpos
mx
=>
B754_finite
prec
emax
sx
mx
(
ex
+
emin
-
1
)
_
|
_
=>
B754_nan
prec
emax
(
*
dummy
*
)
end
.
Next
Obligation
.
revert
mx0
H2
H
.
intros
mx
Hmx
_.
Lemma
binary_float_of_bits_aux1
:
forall
x
sx
mx
ex
,
split_bits
x
=
(
sx
,
Zpos
mx
,
ex
)
->
bounded
prec
emax
mx
emin
=
true
.
Proof
.
intros
x
sx
mx
ex
Hx
.
injection
Hx
.
intros
Hex
Hmx
_.
assert
(
digits
radix2
(
Zpos
mx
)
<=
mw
)
%
Z
.
apply
digits_le_Zpower
.
simpl
.
rewrite
Hmx
.
rewrite
<-
Hmx
.
eapply
Z_mod_lt
.
apply
Zlt_gt
.
now
apply
(
Zpower_gt_0
radix2
).
...
...
@@ -1188,14 +1177,18 @@ clear -Hew ; omega.
apply
bpow_gt_0
.
Qed
.
Next
Obligation
.
now
split
.
Qed
.
Next
Obligation
.
revert
mx0
H
H0
Heq_anonymous0
.
intros
mx
Hex
Hex
'
Hmx
.
assert
(
prec
=
digits
radix2
(
Zpos
mx
)).
Lemma
binary_float_of_bits_aux2
:
forall
x
sx
mx
ex
px
,
split_bits
x
=
(
sx
,
mx
,
ex
)
->
Zeq_bool
ex
0
=
false
->
Zeq_bool
ex
(
Zpower
2
ew
-
1
)
=
false
->
(
mx
+
Zpower
2
mw
)
%
Z
=
Zpos
px
->
bounded
prec
emax
px
(
ex
+
emin
-
1
)
=
true
.
Proof
.
intros
x
sx
mx
ex
px
Hx
Hex
Hex
'
Hmx
.
injection
Hx
.
intros
Hex
''
Hmx
'
_.
assert
(
prec
=
digits
radix2
(
Zpos
px
)).
rewrite
digits_ln_beta
.
2
:
discriminate
.
apply
sym_eq
.
apply
ln_beta_unique
.
...
...
@@ -1204,7 +1197,8 @@ unfold Zabs.
replace
(
prec
-
1
)
%
Z
with
mw
by
(
unfold
prec
;
ring
).
rewrite
<-
Z2R_Zpower
with
(
1
:=
Hmw
).
rewrite
<-
Z2R_Zpower
.
2
:
now
apply
Zlt_le_weak
.
rewrite
Hmx
.
rewrite
<-
Hmx
.
rewrite
<-
Hmx
'
.
split
.
apply
Z2R_le
.
change
(
radix2
^
mw
)
%
Z
with
(
0
+
2
^
mw
)
%
Z
.
...
...
@@ -1226,13 +1220,14 @@ unfold canonic, canonic_exponent.
rewrite
ln_beta_F2R_digits
.
2
:
discriminate
.
unfold
Fexp
,
FLT_exp
.
rewrite
<-
H
.
replace
(
prec
+
(
(
x
/
2
^
mw
)
mod
2
^
ew
+
emin
-
1
)
-
prec
)
%
Z
with
((
x
/
2
^
mw
)
mod
2
^
ew
+
emin
-
1
)
%
Z
by
ring
.
replace
(
prec
+
(
ex
+
emin
-
1
)
-
prec
)
%
Z
with
(
ex
+
emin
-
1
)
%
Z
by
ring
.
apply
sym_eq
.
apply
Zmax_left
.
generalize
(
Zeq_bool_neq
_
_
Hex
).
cut
(
0
<=
(
x
/
2
^
mw
)
mod
2
^
ew
)
%
Z
.
cut
(
0
<=
ex
)
%
Z
.
unfold
emin
.
clear
;
intros
H1
H2
;
omega
.
rewrite
<-
Hex
''
.
eapply
Z_mod_lt
.
apply
Zlt_gt
.
apply
(
Zpower_gt_0
radix2
).
...
...
@@ -1248,7 +1243,7 @@ unfold emin.
apply
Zplus_lt_reg_r
with
(
emax
-
1
)
%
Z
.
ring_simplify
.
generalize
(
Zeq_bool_neq
_
_
Hex
'
).
cut
(
(
x
/
2
^
mw
)
mod
2
^
ew
<
2
^
ew
)
%
Z
.
cut
(
ex
<
2
^
ew
)
%
Z
.
replace
(
2
^
ew
)
%
Z
with
(
2
*
emax
)
%
Z
.
clear
;
intros
H1
H2
;
omega
.
replace
ew
with
(
1
+
(
ew
-
1
))
%
Z
by
ring
.
...
...
@@ -1256,6 +1251,7 @@ rewrite Zpower_exp.
apply
refl_equal
.
discriminate
.
clear
-
Hew
;
omega
.
rewrite
<-
Hex
''
.
eapply
Z_mod_lt
.
apply
Zlt_gt
.
apply
(
Zpower_gt_0
radix2
).
...
...
@@ -1263,4 +1259,27 @@ now apply Zlt_le_weak.
apply
bpow_gt_0
.
Qed
.
Definition
binary_float_of_bits
(
x
:
Z
)
:=
match
split_bits
x
as
v1
return
split_bits
x
=
v1
->
binary_float
with
|
(
sx
,
mx
,
ex
)
=>
match
Zeq_bool
ex
0
as
v2
return
_
=
v2
->
_
->
binary_float
with
|
true
=>
fun
_
=>
match
mx
as
v3
return
split_bits
x
=
(
sx
,
v3
,
ex
)
->
binary_float
with
|
Zpos
px
=>
fun
H1
=>
B754_finite
prec
emax
sx
px
emin
(
binary_float_of_bits_aux1
x
sx
px
ex
H1
)
|
Z0
=>
fun
_
=>
B754_zero
prec
emax
sx
|
_
=>
fun
_
=>
B754_nan
prec
emax
(
*
dummy
*
)
end
|
false
=>
fun
H2
=>
match
Zeq_bool
ex
(
Zpower
2
ew
-
1
)
as
v3
return
_
=
v3
->
_
->
binary_float
with
|
true
=>
fun
_
_
=>
if
Zeq_bool
mx
0
then
B754_infinity
prec
emax
sx
else
B754_nan
prec
emax
|
false
=>
fun
H3
H1
=>
match
(
mx
+
Zpower
2
mw
)
%
Z
as
v4
return
_
=
v4
->
binary_float
with
|
Zpos
px
=>
fun
H4
=>
B754_finite
prec
emax
sx
px
_
(
binary_float_of_bits_aux2
x
sx
mx
ex
px
H1
H2
H3
H4
)
|
_
=>
fun
_
=>
B754_nan
prec
emax
(
*
dummy
*
)
end
(
refl_equal
_
)
end
(
refl_equal
_
)
end
(
refl_equal
_
)
end
(
refl_equal
_
).
End
Binary_Bits
.
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