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Flocq
flocq
Commits
375344c9
Commit
375344c9
authored
Sep 06, 2010
by
BOLDO Sylvie
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Remainder of the division and the square root are in the format
parent
d696276a
Changes
2
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2 changed files
with
38 additions
and
7 deletions
+38
-7
src/Makefile.am
src/Makefile.am
+1
-0
src/Prop/Fprop_div_sqrt_error.v
src/Prop/Fprop_div_sqrt_error.v
+37
-7
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src/Makefile.am
View file @
375344c9
...
...
@@ -21,6 +21,7 @@ FILES = \
Prop/Fprop_mult_error.v
\
Prop/Fprop_plus_error.v
\
Prop/Fprop_relative.v
\
Prop/Fprop_div_sqrt_error.v
\
Prop/Fprop_Sterbenz.v
EXTRA_DIST
=
$(FILES)
...
...
src/Prop/Fprop_div_sqrt_error.v
View file @
375344c9
...
...
@@ -6,23 +6,53 @@ Section Fprop_divsqrt_error.
Variable
beta
:
radix
.
Notation
bpow
e
:=
(
bpow
beta
e
).
Variable
fexp
:
Z
->
Z
.
Hypothesis
prop_exp
:
valid_exp
fexp
.
Notation
format
:=
(
generic_format
beta
fexp
).
Variable
prec
:
Z
.
Variable
Hp
:
Zlt
0
prec
.
Notation
format
:=
(
generic_format
beta
(
FLX_exp
prec
)).
Notation
cexp
:=
(
canonic_exponent
beta
(
FLX_exp
prec
)).
Variable
choice
:
R
->
bool
.
Theorem
format_FLX
:
forall
x
,
(
exists
f
:
float
beta
,
x
=
F2R
f
/
\
(
cexp
x
<=
Fexp
f
)
%
Z
)
->
format
x
.
intros
x
(
f
,
(
H1
,
H2
)).
unfold
generic_format
.
rewrite
H1
at
1
;
unfold
F2R
;
simpl
.
replace
(
Ztrunc
(
scaled_mantissa
beta
(
FLX_exp
prec
)
x
))
with
(
Fnum
f
*
Zpower
(
radix_val
beta
)
(
Fexp
f
-
cexp
x
))
%
Z
.
rewrite
mult_Z2R
.
rewrite
Z2R_Zpower
.
unfold
Zminus
;
rewrite
bpow_add
.
rewrite
Rmult_assoc
;
rewrite
Rmult_assoc
.
rewrite
<-
bpow_add
.
ring_simplify
(
-
cexp
x
+
cexp
x
)
%
Z
.
simpl
;
ring
.
omega
.
unfold
scaled_mantissa
.
replace
(
x
*
bpow
(
-
cexp
x
))
%
R
with
(
Z2R
((
Fnum
f
*
radix_val
beta
^
(
Fexp
f
-
cexp
x
)))).
now
rewrite
Ztrunc_Z2R
.
rewrite
mult_Z2R
.
rewrite
Z2R_Zpower
.
unfold
Zminus
;
rewrite
bpow_add
.
rewrite
H1
at
2
;
unfold
F2R
.
ring
.
omega
.
Qed
.
Theorem
div_error_N
:
forall
x
y
,
format
x
->
format
y
->
format
(
x
-
rounding
beta
fexp
(
ZrndN
choice
)
(
x
/
y
)
*
y
)
%
R
.
format
(
x
-
rounding
beta
(
FLX_exp
prec
)
(
ZrndN
choice
)
(
x
/
y
)
*
y
)
%
R
.
Proof
.
(
*
probablement
seulement
en
FLX
*
)
Admitted
.
(
*
SB
*
)
Theorem
div_error_Z
:
forall
x
y
,
format
x
->
format
y
->
format
(
x
-
rounding
beta
fexp
(
ZrndTZ
)
(
x
/
y
)
*
y
)
%
R
.
format
(
x
-
rounding
beta
(
FLX_exp
prec
)
(
ZrndTZ
)
(
x
/
y
)
*
y
)
%
R
.
Proof
.
(
*
probablement
seulement
en
FLX
*
)
Admitted
.
(
*
SB
*
)
...
...
@@ -31,7 +61,7 @@ Admitted. (* SB *)
Theorem
sqrt_error_N
:
forall
x
,
(
0
<=
x
)
%
R
->
format
x
->
format
(
x
-
Rsqr
(
rounding
beta
fexp
(
ZrndN
choice
)
(
sqrt
x
)))
%
R
.
format
(
x
-
Rsqr
(
rounding
beta
(
FLX_exp
prec
)
(
ZrndN
choice
)
(
sqrt
x
)))
%
R
.
Proof
.
(
*
probablement
seulement
en
FLX
*
)
Admitted
.
(
*
SB
*
)
...
...
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