path: root/erts/emulator/test/float_SUITE.erl

%%
%% %CopyrightBegin%
%% 
%% Copyright Ericsson AB 1997-2017. All Rights Reserved.
%% 
%% Licensed under the Apache License, Version 2.0 (the "License");
%% you may not use this file except in compliance with the License.
%% You may obtain a copy of the License at
%%
%%     http://www.apache.org/licenses/LICENSE-2.0
%%
%% Unless required by applicable law or agreed to in writing, software
%% distributed under the License is distributed on an "AS IS" BASIS,
%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
%% See the License for the specific language governing permissions and
%% limitations under the License.
%% 
%% %CopyrightEnd%
%%

-module(float_SUITE).

-include_lib("common_test/include/ct.hrl").

-export([all/0, suite/0, groups/0,
         fpe/1,fp_drv/1,fp_drv_thread/1,denormalized/1,match/1,
         t_mul_add_ops/1,
         bad_float_unpack/1, write/1, cmp_zero/1, cmp_integer/1, cmp_bignum/1]).
-export([otp_7178/1]).
-export([hidden_inf/1]).
-export([arith/1]).

suite() ->
    [{ct_hooks,[ts_install_cth]},
     {timetrap, {minutes, 3}}].

all() -> 
    [fpe, fp_drv, fp_drv_thread, otp_7178, denormalized,
     match, bad_float_unpack, write, {group, comparison}
     ,hidden_inf
     ,arith, t_mul_add_ops].

groups() -> 
    [{comparison, [parallel], [cmp_zero, cmp_integer, cmp_bignum]}].

%%
%% OTP-7178, list_to_float on very small numbers should give 0.0
%% instead of exception, i.e. ignore underflow.
%%
%% test that list_to_float on very small numbers give 0.0
otp_7178(Config) when is_list(Config) ->
    X = list_to_float("1.0e-325"),
    true = (X < 0.00000001) and (X > -0.00000001),
    Y = list_to_float("1.0e-325325325"),
    true = (Y < 0.00000001) and (Y > -0.00000001),
    {'EXIT', {badarg,_}} = (catch list_to_float("1.0e83291083210")),
    ok.

%% Forces floating point exceptions and tests that subsequent, legal,
%% operations are calculated correctly.  Original version by Sebastian
%% Strollo.

fpe(Config) when is_list(Config) ->
    0.0 = math:log(1.0),
    {'EXIT', {badarith, _}} = (catch math:log(-1.0)),
    0.0 = math:log(1.0),
    {'EXIT', {badarith, _}} = (catch math:log(0.0)),
    0.0 = math:log(1.0),
    {'EXIT',{badarith,_}} = (catch 3.23e133 * id(3.57e257)),
    0.0 = math:log(1.0),
    {'EXIT',{badarith,_}} = (catch 5.0/id(0.0)),
    0.0 = math:log(1.0),
    ok.


-define(ERTS_FP_CONTROL_TEST, 0).
-define(ERTS_FP_THREAD_TEST, 1).

fp_drv(Config) when is_list(Config) ->
    fp_drv_test(?ERTS_FP_CONTROL_TEST, proplists:get_value(data_dir, Config)).

fp_drv_thread(Config) when is_list(Config) ->
    %% Run in a separate node since it used to crash the emulator...
    Parent = self(),
    DrvDir = proplists:get_value(data_dir, Config),
    {ok,Node} = start_node(Config),
    Tester = spawn_link(Node,
                        fun () ->
                                Parent !
                                {self(),
                                 fp_drv_test(?ERTS_FP_THREAD_TEST,
                                             DrvDir)}
                        end),
    Result = receive {Tester, Res} -> Res end,
    stop_node(Node),
    Result.

fp_drv_test(Test, DrvDir) ->
    Drv = fp_drv,
    try
        begin
            case erl_ddll:load_driver(DrvDir, Drv) of
                ok ->
                    ok;
                {error, permanent} ->
                    ok;
                {error, LoadError} ->
                    exit({load_error,
                          erl_ddll:format_error(LoadError)});
                LoadError ->
                    exit({load_error, LoadError})
            end,
            case open_port({spawn, Drv}, []) of
                Port when is_port(Port) ->
                    try port_control(Port, Test, "") of
                        "ok" ->
                            0.0 = math:log(1.0),
                            ok;
                        [$s,$k,$i,$p,$:,$ | Reason] ->
                            {skipped, Reason};
                        Error ->
                            exit(Error)
                    after
                        Port ! {self(), close},
                        receive {Port, closed} -> ok end,
                        false = lists:member(Port, erlang:ports()),
                        ok
                    end;
                Error ->
                    exit({open_port_failed, Error})
            end
        end
    catch
        throw:Term -> Term
    after
        erl_ddll:unload_driver(Drv)
    end.

denormalized(Config) when is_list(Config) ->
    Denormalized = 1.0e-307 / 1000,
    roundtrip(Denormalized),
    NegDenormalized = -1.0e-307 / 1000,
    roundtrip(NegDenormalized),
    ok.

roundtrip(N) ->
    N = binary_to_term(term_to_binary(N)),
    N = binary_to_term(term_to_binary(N, [{minor_version,1}])).

match(Config) when is_list(Config) ->
    one = match_1(1.0),
    two = match_1(2.0),
    a_lot = match_1(1000.0),
    {'EXIT',_} = (catch match_1(0.5)),
    ok.

match_1(1.0) -> one;
match_1(2.0) -> two;
match_1(1000.0) -> a_lot.

%% Thanks to Per Gustafsson.

bad_float_unpack(Config) when is_list(Config) ->
    Bin = <<-1:64>>,
    -1 = bad_float_unpack_match(Bin),
    ok.

bad_float_unpack_match(<<F:64/float>>) -> F;
bad_float_unpack_match(<<I:64/integer-signed>>) -> I.

%% Exposes endianness issues.

write(Config) when is_list(Config) ->
    "1.0" = io_lib:write(1.0).

cmp_zero(_Config) ->
    cmp(0.5e-323,0).

cmp_integer(_Config) ->
    Axis = (1 bsl 53)-2.0, %% The point where floating points become unprecise
    span_cmp(Axis,2,200),
    cmp(Axis*Axis,round(Axis)).

cmp_bignum(_Config) ->
    span_cmp((1 bsl 58) - 1.0),%% Smallest bignum float

    %% Test when the big num goes from I to I+1 in size
    [span_cmp((1 bsl (32*I)) - 1.0) || I <- lists:seq(2,30)],

    %% Test bignum greater then largest float
    cmp((1 bsl (64*16)) - 1, (1 bsl (64*15)) * 1.0),
    %% Test when num is much larger then float
    [cmp((1 bsl (32*I)) - 1, (1 bsl (32*(I-2))) * 1.0) || I <- lists:seq(3,30)],
    %% Test when float is much larger than num
    [cmp((1 bsl (64*15)) * 1.0, (1 bsl (32*(I)))) || I <- lists:seq(1,29)],

    %% Test that all int == float works as they should
    [true = 1 bsl N == (1 bsl N)*1.0 || N <- lists:seq(0, 1023)],
    [true = (1 bsl N)*-1 == (1 bsl N)*-1.0 || N <- lists:seq(0, 1023)].

span_cmp(Axis) ->
    span_cmp(Axis, 25).
span_cmp(Axis, Length) ->
    span_cmp(Axis, round(Axis) bsr 52, Length).
span_cmp(Axis, Incr, Length) ->
    [span_cmp(Axis, Incr, Length, 1 bsl (1 bsl I)) || I <- lists:seq(0,6)].
%% This function creates tests around number axis. Both <, > and == is tested
%% for both negative and positive numbers.
%%
%% Axis: The number around which to do the tests eg. (1 bsl 58) - 1.0
%% Incr: How much to increment the test numbers in-between each test.
%% Length: Length/2 is the number of Incr away from Axis to test on the
%%         negative and positive plane.
%% Diff: How much the float and int should differ when comparing
span_cmp(Axis, Incr, Length, Diff) ->
    [begin
         cmp(round(Axis*-1.0)+Diff+I*Incr,Axis*-1.0+I*Incr),
         cmp(Axis*-1.0+I*Incr,round(Axis*-1.0)-Diff+I*Incr)
     end || I <- lists:seq((Length div 2)*-1,(Length div 2))],
    [begin
         cmp(round(Axis)+Diff+I*Incr,Axis+I*Incr),
         cmp(Axis+I*Incr,round(Axis)-Diff+I*Incr)
     end || I <- lists:seq((Length div 2)*-1,(Length div 2))].

cmp(Big,Small) when is_float(Big) ->
    BigGtSmall = lists:flatten(
                   io_lib:format("~f > ~p",[Big,Small])),
    BigLtSmall = lists:flatten(
                   io_lib:format("~f < ~p",[Big,Small])),
    BigEqSmall = lists:flatten(
                   io_lib:format("~f == ~p",[Big,Small])),
    SmallGtBig = lists:flatten(
                   io_lib:format("~p > ~f",[Small,Big])),
    SmallLtBig = lists:flatten(
                   io_lib:format("~p < ~f",[Small,Big])),
    SmallEqBig = lists:flatten(
                   io_lib:format("~p == ~f",[Small,Big])),
    cmp(Big,Small,BigGtSmall,BigLtSmall,SmallGtBig,SmallLtBig,
        SmallEqBig,BigEqSmall);
cmp(Big,Small) when is_float(Small) ->
    BigGtSmall = lists:flatten(
                   io_lib:format("~p > ~f",[Big,Small])),
    BigLtSmall = lists:flatten(
                   io_lib:format("~p < ~f",[Big,Small])),
    BigEqSmall = lists:flatten(
                   io_lib:format("~p == ~f",[Big,Small])),
    SmallGtBig = lists:flatten(
                   io_lib:format("~f > ~p",[Small,Big])),
    SmallLtBig = lists:flatten(
                   io_lib:format("~f < ~p",[Small,Big])),
    SmallEqBig = lists:flatten(
                   io_lib:format("~f == ~p",[Small,Big])),
    cmp(Big,Small,BigGtSmall,BigLtSmall,SmallGtBig,SmallLtBig,
        SmallEqBig,BigEqSmall).

cmp(Big,Small,BigGtSmall,BigLtSmall,SmallGtBig,SmallLtBig,
    SmallEqBig,BigEqSmall) ->
    {_,_,_,true} = {Big,Small,BigGtSmall,
                    Big > Small},
    {_,_,_,false} = {Big,Small,BigLtSmall,
                     Big < Small},
    {_,_,_,false} = {Big,Small,SmallGtBig,
                     Small > Big},
    {_,_,_,true} = {Big,Small,SmallLtBig,
                    Small < Big},
    {_,_,_,false} = {Big,Small,SmallEqBig,
                     Small == Big},
    {_,_,_,false} = {Big,Small,BigEqSmall,
                     Big == Small}.

id(I) -> I.

start_node(Config) when is_list(Config) ->
    Pa = filename:dirname(code:which(?MODULE)),
    Name = list_to_atom(atom_to_list(?MODULE)
                        ++ "-"
                        ++ atom_to_list(proplists:get_value(testcase, Config))
                        ++ "-"
                        ++ integer_to_list(erlang:system_time(second))
                        ++ "-"
                        ++ integer_to_list(erlang:unique_integer([positive]))),
    test_server:start_node(Name, slave, [{args, "-pa "++Pa}]).

stop_node(Node) ->
    test_server:stop_node(Node).


%% Test that operations that might hide infinite intermediate results
%% do not supress the badarith.
hidden_inf(Config) when is_list(Config) ->
    ZeroP = 0.0,
    ZeroN = id(ZeroP) * (-1),
    [hidden_inf_1(A, B, Z, 9.23e307)
     || A <- [1.0, -1.0, 3.1415, -0.00001000131, 3.57e257, ZeroP, ZeroN],
        B <- [1.0, -1.0, 3.1415, -0.00001000131, 3.57e257, ZeroP, ZeroN],
        Z <- [ZeroP, ZeroN]],
    ok.

hidden_inf_1(A, B, Zero, Huge) ->
    {'EXIT',{badarith,_}} = (catch (B / (A / Zero))),
    {'EXIT',{badarith,_}} = (catch (B * (A / Zero))),
    {'EXIT',{badarith,_}} = (catch (B / (Huge * Huge))),
    {'EXIT',{badarith,_}} = (catch (B * (Huge * Huge))),
    {'EXIT',{badarith,_}} = (catch (B / (Huge + Huge))),
    {'EXIT',{badarith,_}} = (catch (B * (Huge + Huge))),
    {'EXIT',{badarith,_}} = (catch (B / (-Huge - Huge))),
    {'EXIT',{badarith,_}} = (catch (B * (-Huge - Huge))).

%% Improve code coverage in our different arithmetic functions
%% and make sure they yield consistent results.
arith(_Config) ->
    _TAG_IMMED1_SIZE = 4,

    <<FLOAT_MAX/float>> = <<0:1, 16#7fe:11, -1:52>>,
    <<FLOAT_MIN/float>> = <<0:1, 0:11, 1:52>>,
    <<FloatNegZero/float>> = <<1:1, 0:11, 0:52>>,

    WORD_BITS = erlang:system_info(wordsize) * 8,
    SMALL_BITS = (WORD_BITS - _TAG_IMMED1_SIZE),
    SMALL_MAX = (1 bsl (SMALL_BITS-1)) - 1,
    SMALL_MIN = -(1 bsl (SMALL_BITS-1)),
    BIG1_MAX = (1 bsl WORD_BITS) - 1,
    BIG2_MAX = (1 bsl (WORD_BITS*2)) - 1,

    fixnum = erts_internal:term_type(SMALL_MAX),
    fixnum = erts_internal:term_type(SMALL_MIN),
    bignum = erts_internal:term_type(SMALL_MAX + 1),
    bignum = erts_internal:term_type(SMALL_MIN - 1),

    L = [0, 0.0, FloatNegZero, 1, 1.0, 17, 17.0, 0.17,
         FLOAT_MIN, FLOAT_MAX,
         SMALL_MAX, SMALL_MAX+1,
         SMALL_MIN, SMALL_MIN-1,
         BIG1_MAX, BIG1_MAX+1,
         BIG2_MAX, BIG2_MAX+1,
         trunc(FLOAT_MAX), trunc(FLOAT_MAX)+1, trunc(FLOAT_MAX)*2,
         immed_badarg,
         "list badarg",
         {"boxed badarg"}],

    foreach_pair(fun(A,B) -> do_bin_ops(A,B) end, L).

foreach_pair(F, L) ->
    lists:foreach(
      fun(A) -> lists:foreach(fun(B) -> F(A,B) end, L) end,
      L).

do_bin_ops(A, B) ->
    Fun = fun(Op) ->
                  Op(A,B),
                  is_number(A) andalso Op(-A,B),
                  is_number(B) andalso Op(A,-B),
                  is_number(A) andalso is_number(B) andalso Op(-A,-B)
          end,
    lists:foreach(Fun,
                  [fun op_add/2, fun op_sub/2, fun op_mul/2, fun op_div/2]).

op_add(A, B) ->
    Info = [A,B],
    R = unify(catch A + B, Info),
    R = unify(my_apply(erlang,'+',[A,B]), Info),
    case R of
        _ when A + B =:= element(1,R) -> ok;
        {{'EXIT',badarith}, Info} -> ok
    end.

op_sub(A, B) ->
    Info = [A,B],
    R = unify(catch A - B, Info),
    R = unify(my_apply(erlang,'-',[A,B]), Info),
    case R of
        _ when A - B =:= element(1,R) -> ok;
        {{'EXIT',badarith}, Info} -> ok
    end.

op_mul(A, B) ->
    Info = [A,B],
    R = unify(catch A * B, Info),
    R = unify(my_apply(erlang,'*',[A,B]), Info),
    case R of
        _ when A * B =:= element(1,R) -> ok;
        {{'EXIT',badarith}, Info} -> ok
    end.

op_div(A, B) ->
    Info = [A,B],
    R = unify(catch A / B, Info),
    R = unify(my_apply(erlang,'/',[A,B]), Info),
    case R of
        _ when A / B =:= element(1,R) -> ok;
        {{'EXIT',badarith}, Info} -> ok
    end.

my_apply(M, F, A) ->
    catch apply(id(M), id(F), A).

% Unify exceptions be removing stack traces.
% and add argument info to make it easer to debug failed matches.
unify({'EXIT',{Reason,_Stack}}, Info) ->
    {{'EXIT', Reason}, Info};
unify(Other, Info) ->
    {Other, Info}.


-define(epsilon, 1.0e-20).
check_epsilon(R,Val) ->
    if erlang:abs(R-Val) < ?epsilon -> ok;
       true -> ct:fail({R,Val})
    end.

t_mul_add_ops(Config) when is_list(Config) ->
    check_epsilon(op_mul_add(1, 2.0, 1.0, 0.0), 1.0),
    check_epsilon(op_mul_add(2, 2.0, 1.0, 0.0), 3.0),
    check_epsilon(op_mul_add(3, 2.0, 1.0, 0.0), 7.0),
    check_epsilon(op_mul_add(4, 2.0, 1.0, 0.0), 15.0),
    check_epsilon(op_mul_add(5, 2.0, 1.0, 0.0), 31.0),
    check_epsilon(op_mul_add(6, 2.0, 1.0, 0.0), 63.0),
    check_epsilon(op_mul_add(6, 2.0, 1.3, 0.0), 81.9),
    check_epsilon(op_mul_add(6, 2.03, 1.3, 0.0), 87.06260151458997),
    ok.


op_mul_add(0, _, _, R) -> R;
op_mul_add(N, A, B, R) when is_float(A), is_float(B), is_float(R) ->
    op_mul_add(N - 1, A, B, R * A + B).