%%
%% %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).
