diff options
Diffstat (limited to 'theories/Numbers/Cyclic/Int31/Int31.v')
| -rw-r--r-- | theories/Numbers/Cyclic/Int31/Int31.v | 18 |
1 files changed, 9 insertions, 9 deletions
diff --git a/theories/Numbers/Cyclic/Int31/Int31.v b/theories/Numbers/Cyclic/Int31/Int31.v index 20f750f6..f414663a 100644 --- a/theories/Numbers/Cyclic/Int31/Int31.v +++ b/theories/Numbers/Cyclic/Int31/Int31.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -117,12 +117,12 @@ Definition iszero : int31 -> bool := Eval compute in It seems to work, but later "unfold iszero" takes forever. *) -(** [base] is [2^31], obtained via iterations of [Zdouble]. +(** [base] is [2^31], obtained via iterations of [Z.double]. It can also be seen as the smallest b > 0 s.t. phi_inv b = 0 (see below) *) Definition base := Eval compute in - iter_nat size Z Zdouble 1%Z. + iter_nat size Z Z.double 1%Z. (** * Recursors *) @@ -155,11 +155,11 @@ Definition recr := recr_aux size. (** * Conversions *) -(** From int31 to Z, we simply iterates [Zdouble] or [Zdouble_plus_one]. *) +(** From int31 to Z, we simply iterates [Z.double] or [Z.succ_double]. *) Definition phi : int31 -> Z := recr Z (0%Z) - (fun b _ => match b with D0 => Zdouble | D1 => Zdouble_plus_one end). + (fun b _ => match b with D0 => Z.double | D1 => Z.succ_double end). (** From positive to int31. An abstract definition could be : [ phi_inv (2n) = 2*(phi_inv n) /\ @@ -293,13 +293,13 @@ Notation "n '*c' m" := (mul31c n m) (at level 40, no associativity) : int31_scop (** Division of a double size word modulo [2^31] *) Definition div3121 (nh nl m : int31) := - let (q,r) := Zdiv_eucl (phi2 nh nl) (phi m) in + let (q,r) := Z.div_eucl (phi2 nh nl) (phi m) in (phi_inv q, phi_inv r). (** Division modulo [2^31] *) Definition div31 (n m : int31) := - let (q,r) := Zdiv_eucl (phi n) (phi m) in + let (q,r) := Z.div_eucl (phi n) (phi m) in (phi_inv q, phi_inv r). Notation "n / m" := (div31 n m) : int31_scope. @@ -391,7 +391,7 @@ Eval lazy delta [On In Twon] in | Lt => iter31_sqrt 31 (fun i j => j) i (fst (i/Twon)) end. -Definition v30 := Eval compute in (addmuldiv31 (phi_inv (Z_of_nat size - 1)) In On). +Definition v30 := Eval compute in (addmuldiv31 (phi_inv (Z.of_nat size - 1)) In On). Definition sqrt312_step (rec: int31 -> int31 -> int31 -> int31) (ih il j: int31) := @@ -452,7 +452,7 @@ Definition positive_to_int31 (p:positive) := p2i size p. It is used as default answer for numbers of zeros in [head0] and [tail0] *) -Definition T31 : int31 := Eval compute in phi_inv (Z_of_nat size). +Definition T31 : int31 := Eval compute in phi_inv (Z.of_nat size). Definition head031 (i:int31) := recl _ (fun _ => T31) |