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Documentation
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@ -39,13 +39,13 @@ Format.printf "@[<2>shell_b :@ %a@]@;" Cs.pp s_b;
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let shell_pairs =
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Array.mapi (fun i p_a ->
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let c_a = (Cs.coef s_a).(i) in
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let make = make i p_a in
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let make = make p_a in
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Array.mapi (fun j p_b ->
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let c_b = (Cs.coef s_b).(j) in
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let coef = c_a *. c_b in
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assert (coef <> 0.);
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let cutoff = cutoff /. abs_float coef in
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coef, make j p_b cutoff) (Cs.prim s_b)) (Cs.prim s_a)
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coef, make p_b cutoff) (Cs.prim s_b)) (Cs.prim s_a)
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|> Array.to_list
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|> Array.concat
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|> Array.to_list
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@ -15,8 +15,6 @@ type t = {
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totAngMom : AngularMomentum.t;
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shell_a : PrimitiveShell.t;
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shell_b : PrimitiveShell.t;
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(*TODO*)
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i : int; j : int;
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}
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exception Null_contribution
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@ -25,18 +23,20 @@ module Am = AngularMomentum
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module Co = Coordinate
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module Ps = PrimitiveShell
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(** Returns an integer characteristic of a primitive shell pair *)
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let hash a =
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Hashtbl.hash a
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let equivalent a b =
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a = b
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(*
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Hashtbl.hash (a.expo, a.center_a, a.center_ab, a.coef, ContractedShell.totAngMom a.shell_a, ContractedShell.totAngMom a.shell_b)
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*)
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a.expo = b.expo &&
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a.totAngMom = b.totAngMom &&
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a.norm_coef = b.norm_coef &&
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a.center = b.center &&
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a.center_minus_a = b.center_minus_a &&
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a.a_minus_b = b.a_minus_b
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(** Comparison function, used for sorting *)
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let cmp a b =
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hash a - hash b
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@ -63,20 +63,16 @@ let create_make_of p_a p_b =
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Am.( Ps.totAngMom p_a + Ps.totAngMom p_b )
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in
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(* TODO *)
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function i ->
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function p_a ->
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let norm_coef_a =
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Ps.norm_coef p_a
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in
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let alpha_a = (* p_a_expo_center *)
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let alpha_a =
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Co.( Ps.expo p_a |. Ps.center p_a )
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in
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(*TODO *)
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function j ->
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function p_b ->
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let norm_coef =
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@ -113,7 +109,7 @@ let create_make_of p_a p_b =
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in
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Some {
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i ; j ; totAngMom ;
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totAngMom ;
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expo ; expo_inv ; center ; center_minus_a ; a_minus_b ;
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a_minus_b_sq ; norm_coef ; norm_coef_scale ; shell_a = p_a;
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shell_b = p_b }
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@ -126,7 +122,7 @@ let make p_a p_b =
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let f =
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create_make_of p_a p_b
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in
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match f 0 p_a 0 p_b 0. with
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match f p_a p_b 0. with
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| Some result -> result
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| None -> assert false
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@ -22,50 +22,27 @@ where
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\end{align*}
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%}
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Following Ref [1], we define three quantities associated with the shells on centers A and B:
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{%
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\begin{align*}
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\sigma_P & = \frac{1}{\alpha + \beta} \\
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\mathbf{P} & = \left( \alpha \mathbf{A} + \beta \mathbf{B} \right) \, \sigma_P \\
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U_P & = (\pi\,\sigma_P)^{3/2} \exp \left( \alpha \beta \sigma_P |\mathbf{A}-\mathbf{B}|^2 \right)
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\end{align*}
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%}
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{!a_minus_b}, {!a_minus_b_sq} and {!norm_coef_scale} depend only on the
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centering of the two shells, and {!totAngMom} only depends on the angular
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momenta of the two shells. Hence, these quantities need to be computed only
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once when a {!ContractedShellPair.t} is built. Hence, there is the
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{!create_make_of} function which creates a [make] function which is suitable
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for a {!ContractedShellPair.t}.
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References:
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[1] {{:http://dx.doi.org/10.1002/qua.560400604} P.M. Gill, B.G. Johnson, and J.A. Pople, International Journal of Quantum Chemistry 40, 745 (1991)}.
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*)
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type t = {
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expo : float; (* alpha + beta *)
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expo_inv : float; (* 1/(alpha + beta) *)
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center : Coordinate.t; (* P = (alpha * A + beta B)/(alpha+beta) *)
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center_minus_a : Coordinate.t; (* P - A *)
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a_minus_b : Coordinate.t; (* A - B *)
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a_minus_b_sq : float; (* |A-B|^2 *)
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norm_coef_scale : float array lazy_t;
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norm_coef : float; (* norm_coef_a * norm_coef_b * g, with
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g = (pi/(alpha+beta))^(3/2) exp (-|A-B|^2 * alpha*beta/(alpha+beta)) *)
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totAngMom : AngularMomentum.t;
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shell_a : PrimitiveShell.t;
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shell_b : PrimitiveShell.t;
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i : int; (*TODO remove *)
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j : int; (*TODO remove *)
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}
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type t
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val make : PrimitiveShell.t -> PrimitiveShell.t -> t
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(** Creates a primitive shell pair using two primitive shells. *)
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val create_make_of : PrimitiveShell.t -> PrimitiveShell.t ->
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(int -> PrimitiveShell.t -> int -> PrimitiveShell.t -> float -> t option)
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(* TODO
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(PrimitiveShell.t -> PrimitiveShell.t -> float -> t option)
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*)
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(** Creates a make function [PrimitiveShell.t -> PrimitiveShell.t -> float -> t] in which
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all the quantities common to the shell and independent of the exponent
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are pre-computed.
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@ -75,30 +52,39 @@ val create_make_of : PrimitiveShell.t -> PrimitiveShell.t ->
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*)
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val equivalent : t -> t -> bool
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val hash : t -> int
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val cmp : t -> t -> int
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val monocentric : t -> bool
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val center : t -> Coordinate.t
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(** Coordinates of the center {%$\mathbf{P}$%}. *)
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val norm_coef_scale : t -> float array
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val expo : t -> float
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(** {% \\[ \alpha + \beta \\] %}*)
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val expo_inv : t -> float
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(** {% \\[ \frac{1}{\alpha + \beta} \\] %}*)
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val totAngMom : t -> AngularMomentum.t
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(** Total angular momentum of the shell pair: sum of the angular momenta of
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the shells.
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the shells. *)
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val center : t -> Coordinate.t
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(** Coordinates of the center {% $\mathbf{P}$ %}. *)
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val monocentric : t -> bool
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(** True if both shells of the pair have the same center. *)
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val shell_a : t -> PrimitiveShell.t
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(** Returns the first primitive shell that was used to build the shell pair. *)
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val shell_b : t -> PrimitiveShell.t
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(** Returns the second primitive shell that was used to build the shell pair. *)
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val norm_coef : t -> float
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(** Normalization coefficient of the shell pair. *)
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val norm_coef_scale : t -> float array
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(** Normalization factor, characteristic of the powers of x, y and z of
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both shells of the pair. It is the outer product of the 2
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{!PrimitiveShell.norm_coef_scale} arrays of the shells consituting the
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pair.
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*)
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val expo : t -> float
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(** Exponent of the Gaussian output of the Gaussian product : {% \\[ \alpha + \beta \\] %}*)
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val expo_inv : t -> float
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(** Inverse of the exponent : {% \\[ \sigma_P = \frac{1}{\alpha + \beta} \\] %}*)
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val a_minus_b : t -> Coordinate.t
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(** {% $\mathbf{A}-\mathbf{B}$ %} *)
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@ -108,12 +94,13 @@ val a_minus_b_sq : t -> float
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val center_minus_a : t -> Coordinate.t
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(** {% $\mathbf{P}-\mathbf{A}$ %} *)
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val norm_coef : t -> float
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(** Normalization coefficient of the shell pair. *)
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val shell_a : t -> PrimitiveShell.t
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(** Returns the first primitive shell that was used to build the shell pair. *)
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val equivalent : t -> t -> bool
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(** True if two primitive shell pairs are equivalent. *)
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val shell_b : t -> PrimitiveShell.t
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(** Returns the second primitive shell that was used to build the shell pair. *)
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val hash : t -> int
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(** Returns an integer characteristic of the shell pair. *)
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val cmp : t -> t -> int
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(** Arbitray comparison function for sorting. *)
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