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Flocq
flocq
Commits
4964a0d0
Commit
4964a0d0
authored
Oct 07, 2010
by
Guillaume Melquiond
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Plain Diff
Simplified proof.
parent
4bb89f65
Changes
2
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2 changed files
with
15 additions
and
22 deletions
+15
-22
src/Core/Fcore_generic_fmt.v
src/Core/Fcore_generic_fmt.v
+11
-0
src/Core/Fcore_ulp.v
src/Core/Fcore_ulp.v
+4
-22
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src/Core/Fcore_generic_fmt.v
View file @
4964a0d0
...
...
@@ -209,6 +209,17 @@ rewrite <- opp_F2R.
now
apply
f_equal
.
Qed
.
Theorem
generic_format_abs
:
forall
x
,
generic_format
x
->
generic_format
(
Rabs
x
).
Proof
.
intros
x
Hx
.
unfold
generic_format
.
rewrite
scaled_mantissa_abs
,
canonic_exponent_abs
.
rewrite
Ztrunc_abs
.
rewrite
<-
abs_F2R
.
now
apply
f_equal
.
Qed
.
Theorem
canonic_exponent_fexp
:
forall
x
ex
,
(
bpow
(
ex
-
1
)
<=
Rabs
x
<
bpow
ex
)
%
R
->
...
...
src/Core/Fcore_ulp.v
View file @
4964a0d0
...
...
@@ -54,7 +54,6 @@ unfold ulp.
now
rewrite
canonic_exponent_abs
.
Qed
.
Theorem
ulp_le_pos
:
forall
x
,
(
0
<
x
)
%
R
->
...
...
@@ -74,7 +73,6 @@ apply F2R_gt_0_reg with beta (canonic_exponent beta fexp x).
now
rewrite
<-
Fx
.
Qed
.
Theorem
ulp_le_abs
:
forall
x
,
(
x
<>
0
)
%
R
->
...
...
@@ -82,28 +80,12 @@ Theorem ulp_le_abs:
(
ulp
x
<=
Rabs
x
)
%
R
.
Proof
.
intros
x
Zx
Fx
.
case
(
Rdichotomy
_
_
Zx
);
intros
Sx
.
(
*
*
)
rewrite
<-
(
Rmult_1_l
(
ulp
x
)).
pattern
x
at
2
;
rewrite
Fx
.
rewrite
abs_F2R
.
unfold
F2R
,
ulp
;
simpl
.
apply
Rmult_le_compat_r
.
apply
bpow_ge_0
.
replace
1
%
R
with
(
Z2R
(
Zsucc
0
))
by
reflexivity
.
apply
Z2R_le
.
apply
Zlt_le_succ
.
apply
F2R_gt_0_reg
with
beta
(
canonic_exponent
beta
fexp
x
).
rewrite
<-
abs_F2R
,
<-
Fx
.
rewrite
Rabs_left1
;
auto
with
real
.
(
*
*
)
rewrite
Rabs_right
.
now
apply
ulp_le_pos
.
now
apply
Rgt_ge
.
rewrite
<-
ulp_abs
.
apply
ulp_le_pos
.
now
apply
Rabs_pos_lt
.
now
apply
generic_format_abs
.
Qed
.
Theorem
ulp_DN_UP
:
forall
x
,
~
F
x
->
round
beta
fexp
rndUP
x
=
(
round
beta
fexp
rndDN
x
+
ulp
x
)
%
R
.
...
...
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