1:- encoding(utf8).
    2:- module(
    3  math_ext,
    4  [
    5    avg_list/2,           % +Numbers, -Avg
    6    between/4,            % +Low, +High, +Interval, ?Value
    7    decimal_parts/3,      % ?Decimal, ?Integer, ?Fractorial
    8    fractional_integer/2, % +Number, -Fractorial
    9    fractional_weights/2, % ?Fractional, ?Weights
   10    inf_max/3,            % +X, +Y, -Z
   11    inf_min/3,            % +X, +Y, -Z
   12    integer_weights/2,    % ?Integer, ?Weights
   13    integer_weights/3     % ?Integer, +Base, ?Weights
   14  ]
   15).

   21:- use_module(library(aggregate)).   22:- use_module(library(clpfd)).   23:- use_module(library(error)).   24:- use_module(library(lists)).   25:- use_module(library(plunit)).

 avg_list(+Numbers:list(number), +Avg:number) is semidet

avg_list(+Numbers:list(number), -Avg:number) is det

Examples

?- avg_list([1 rdiv 3, 1 rdiv 6], X).
X = 1 rdiv 4.

Special cases

Avg is the integer 0 in case Numbers is the empty list. This is in line with how sum_list/2 works.

throws

- instantiation_error if Numbers is non-ground.

   48avg_list([], 0):- !.
   49avg_list(L, Avg):-
   50  aggregate(count+sum(X), member(X, L), Len+Sum),
   51  Avg is Sum / Len.

 between(+Low:integer, +High:integer, +Interval:integer, +Value:integer) is semidet

between(+Low:integer, +High:integer, +Interval:integer, -Value:integer) is nondet

   60between(Low, _, _, Low).
   61between(Low1, High, Interval, Value):-
   62  Low2 is Low1 + Interval,
   63  (High == ∞ -> true ; Low2 =< High),  between(Low2, High, Interval, Value).

 decimal_parts(+Decimal:number, -Integer:integer, -Frac:nonneg) is det

decimal_parts(-Decimal:number, +Integer:integer, +Frac:nonneg) is det

throws

- instantation_error

- type_error

   74decimal_parts(N, Int, Frac):-
   75  ground(N),
   76  must_be(number, N), !,
   77  Int is floor(float_integer_part(N)),
   78  fractional_integer(N, Frac).
   79decimal_parts(N, Int, Frac):-
   80  must_be(integer, Int),
   81  must_be(nonneg, Frac),
   82  number_length(Frac, Length),
   83  N is copysign(abs(Int) + (Frac rdiv (10 ^ Length)), Int).

 fractional_integer(+Frac:number, -Int:integer) is det

Variant of float_fractional_part/2 where the integer value instead of the fractional part is returned.

   92fractional_integer(Frac, _) :-
   93  \+ ground(Frac), !,
   94  instantiation_error(Frac).
   95fractional_integer(Frac, Int) :-
   96  Frac = A rdiv B, !,
   97  FloatFrac is A / B,
   98  fractional_integer(FloatFrac, Int).
   99fractional_integer(Frac, Int) :-
  100  atom_number(FracAtom, Frac),
  101  % We assume that there is at most one occurrence of `.'.
  102  sub_atom(FracAtom, IndexOfDot, 1, _, .), !,
  103  Skip is IndexOfDot + 1,
  104  sub_atom(FracAtom, Skip, _, 0, IntAtom),
  105  atom_number(IntAtom, Int).
  106fractional_integer(_, 0).

 fractional_weights(-Frac:number, +Weights:list(between(0,9))) is det

fractional_weights(+Frac:number, -Weights:list(between(0,9))) is det

  113fractional_weights(Frac, Weights):-
  114  ground(Weights), !,
  115  aggregate_all(
  116    sum(N),
  117    (
  118      nth1(Position, Weights, Weight),
  119      N is Weight rdiv (10 ^ Position)
  120    ),
  121    Frac
  122  ).
  123fractional_weights(Frac, Weights):-
  124  ground(Frac), !,
  125  fractional_integer(Frac, Int),
  126  integer_weights(Int, Weights).
  127fractional_weights(_, _):-
  128  instantiation_error(_).
  129
  130
  131
  132%! inf_max(+X, +Y, -Z) is det.
  133
  134inf_max(∞, _, ∞) :- !.
  135inf_max(_, ∞, ∞) :- !.
  136inf_max(-∞, Y, Y) :- !.
  137inf_max(X, -∞, X) :- !.
  138inf_max(X, Y, Z) :-
  139  Z is max(X, Y).
  140
  141
  142
  143%! inf_min(+X, +Y, -Z) is det.
  144
  145inf_min(-∞, _, -∞) :- !.
  146inf_min(_, -∞, -∞) :- !.
  147inf_min(∞, Y, Y) :- !.
  148inf_min(X, ∞, X) :- !.
  149inf_min(X, Y, Z) :-
  150  Z is min(X, Y).

 integer_weights(+Int:nonneg, +Weights:list(between(0,9))) is semidet

integer_weights(-Int:nonneg, +Weights:list(between(0,9))) is det

integer_weights(+Int:nonneg, -Weights:list(between(0,9))) is det

  158integer_weights(Int, Weights):-
  159  integer_weights(Int, 10, Weights).

 integer_weights(+Int:nonneg, +Base:nonneg, +Weights:list(between(0,9))) is semidet

integer_weights(-Int:nonneg, +Base:nonneg, +Weights:list(between(0,9))) is det

integer_weights(+Int:nonneg, +Base:nonneg, -Weights:list(between(0,9))) is det

See also

- http://stackoverflow.com/questions/4192063/reversible-binary-to-number-predicate/28442760#28442760

  168integer_weights(Int, Base, Weights):-
  169  (nonvar(Int), nonvar(Base) ; nonvar(Weights)), !,
  170  integer_weights0(Int, Base, Weights, 0, Int).
  171
  172integer_weights0(Int, _, [], Int, _) :- !.
  173integer_weights0(Int, Base, [Weight|Weights], Int0, M):-
  174  in_base(Weight, Base),
  175  Int1 #= Weight + Base * Int0,
  176  M #>= Int1,
  177  integer_weights0(Int, Base, Weights, Int1, M).
  178
  179in_base(Weight, Base):-
  180  Base #= Max + 1,
  181  Weight in 0..Max.
  182
  183:- begin_tests('integer_weights/3').  184
  185test(
  186  'integer_weights(+,+,+) is semidet. TRUE',
  187  [forall(integer_weights_test(Int,Base,Weights))]
  188):-
  189  integer_weights(Int, Base, Weights).
  190test(
  191  'integer_weights(+,+,-) is multi. TRUE',
  192  [forall(integer_weights_test(Int,Base,Weights)),nondet]
  193):-
  194  integer_weights(Int, Base, Weights0),
  195  Weights0 = Weights.
  196test(
  197  'integer_weights(-,+,+) is multi. TRUE',
  198  [forall(integer_weights_test(Int, Base, Weights)),nondet]
  199):-
  200  integer_weights(Int, Base, Weights0),
  201  Weights0 = Weights.
  202
  203integer_weights_test(1226, 10, [1,2,2,6]).
  204integer_weights_test(120, 60, [2,0]).
  205
  206:- end_tests('integer_weights/3').

 number_length(+Number:number, -Length:integer) is det

 number_length(+Number:number, +Radix:integer, -Length:integer) is det

Returns the length of the given number ‘before the dot’.

Arguments:

An	- integer representing a decimal number.
Radix	- An integer representing the radix used. Common values are 2.0 (binary), 8.0 (octal), 10.0 (decimal, used by number_length/2, and 16.0 (hexadecimal).
Length	- An integer representing the number of digits in the given number.

  224number_length(M, L):-
  225  number_length(M, 10.0, L).
  226
  227
  228number_length(N1, Radix, L1):-
  229  N2 is N1 / Radix,
  230  N2 >= 1.0, !,
  231  number_length(N2, Radix, L2),
  232  L1 is L2 + 1.
  233number_length(_N, _Radix, 1):- !