/**
 * float/1 emulator.
 *
 * Warranty & Liability
 * To the extent permitted by applicable law and unless explicitly
 * otherwise agreed upon, XLOG Technologies AG make_bdds no warranties
 * regarding the provided information. XLOG Technologies AG assumes
 * no liability that any problems might be solved with the information
 * provided by XLOG Technologies AG.
 *
 * Rights & License
 * All industrial property rights regarding the information - copyright
 * and patent rights in particular - are the sole property of XLOG
 * Technologies AG. If the company was not the originator of some
 * excerpts, XLOG Technologies AG has at least obtained the right to
 * reproduce, change and translate the information.
 *
 * Reproduction is restricted to the whole unaltered document. Reproduction
 * of the information is only allowed for non-commercial uses. Selling,
 * giving away or letting of the execution of the library is prohibited.
 * The library can be distributed as part of your applications and libraries
 * for execution provided this comment remains unchanged.
 *
 * Restrictions
 * Only to be distributed with programs that add significant and primary
 * functionality to the library. Not to be distributed with additional
 * software intended to replace any components of the library.
 *
 * Trademarks
 * Jekejeke is a registered trademark of XLOG Technologies AG.
 */

/**
 * float_half_even(X, Y):
 * Succeeds in Y with float(X) using rounding mode HALF_EVEN.
 */
% float_half_even(+Integer, -Float)
float_half_even(X, Y) :-
    X < 0, !, H is -X,
    M is msb(H), float_half_even(M, H, J), Y is -J.
float_half_even(X, Y) :-
    M is msb(X), float_half_even(M, X, Y).

float_half_even(M, X,Y) :-
    (M < 53;
     getbit(X, M-53) =:= 0;
     getbit(X, M-52) =:= 0, M-53 =:= lsb(X)), !, mpz_get_d(X,Y).
float_half_even(_, X,Y) :-
    mpz_get_d(X,H), Y is nexttoward(H, 1E300).

/**
 * mpz_get(X, Y):
 * Succeeds in Y with float(X) using rounding mode DOWN.
 */
% mpz_get_d(+Integer, -Float)
mpz_get_d(X, Y) :-
    M is msb(X), mpz_get_d(M, X, Y).

% mpz_get_d(+Integer, +Integer, -Float)
mpz_get_d(M, X, Y) :-
    M < 53, !, Y is float(X).
mpz_get_d(M, X, Y) :-
    K is M-52, Y is float(X>>K)*(1<<K).

% ?- case(N, X, Y), float_half_even(X,Z), Y =\= Z.
% fail.

% ?- case2(N, X, Y), float_half_even(X,Z), Y =\= Z.
% fail.