First version of Axpy

src/Appli/Axpy.v

+Require Import Fcore.
+
+Section Axpy.
+
+Variable beta : radix.
+Notation bpow e := (bpow beta e).
+
+Variable prec : Z.
+Variable Hp : Zlt 0 prec.
+
+(* FLX ou FLT ? *)
+
+Notation format := (generic_format beta (FLX_exp prec)).
+Notation cexp := (canonic_exponent beta (FLX_exp prec)).
+
+Variable choice : R -> bool.
+
+Variable a1 x1 y1 a x y:R.
+
+Hypothesis Ha: format a.
+Hypothesis Hx: format x.
+Hypothesis Hy: format y.
+
+Notation t := (rounding beta (FLX_exp prec) (ZrndN choice) (a*x)).
+Notation u := (rounding beta (FLX_exp prec) (ZrndN choice) (t+y)).
+Notation MinOrMax x f := 
+   ((f = rounding beta (FLX_exp prec) ZrndUP x) 
+     \/ (f = rounding beta (FLX_exp prec) ZrndDN x)).
+
+
+Theorem Axpy_opt :
+  (6 <= prec)%Z ->
+ ((bpow 1 +1 + bpow (4-prec))* Rabs (a*x) <= Rabs y)%R ->
+   (Rabs (y1 - y + a1 * x1 - a * x) <=
+      bpow (1-prec) / (6*bpow 1) * Rabs y)%R ->
+         (MinOrMax (a1 * x1 + y1) u).
+Admitted.