diff options
| -rw-r--r-- | lib/stdlib/doc/src/rand.xml | 118 | ||||
| -rw-r--r-- | lib/stdlib/src/rand.erl | 261 | ||||
| -rw-r--r-- | lib/stdlib/test/rand_SUITE.erl | 217 |
3 files changed, 568 insertions, 28 deletions
diff --git a/lib/stdlib/doc/src/rand.xml b/lib/stdlib/doc/src/rand.xml index 89fb858823..21f680a0ee 100644 --- a/lib/stdlib/doc/src/rand.xml +++ b/lib/stdlib/doc/src/rand.xml @@ -133,8 +133,9 @@ variable <c>rand_seed</c> to remember the current state.</p> <p>If a process calls - <seealso marker="#uniform-0"><c>uniform/0</c></seealso> or - <seealso marker="#uniform-1"><c>uniform/1</c></seealso> without + <seealso marker="#uniform-0"><c>uniform/0</c></seealso>, + <seealso marker="#uniform-1"><c>uniform/1</c></seealso> or + <seealso marker="#uniform_real-0"><c>uniform_real/0</c></seealso> without setting a seed first, <seealso marker="#seed-1"><c>seed/1</c></seealso> is called automatically with the default algorithm and creates a non-constant seed.</p> @@ -168,10 +169,17 @@ R3 = rand:uniform(),</pre> S0 = rand:seed_s(exrop), {R4, S1} = rand:uniform_s(S0),</pre> + <p>Textbook basic form Box-Muller standard normal deviate</p> + + <pre> +R5 = rand:uniform_real(), +R6 = rand:uniform(), +SND0 = math:sqrt(-2 * math:log(R5)) * math:cos(math:pi() * R6)</pre> + <p>Create a standard normal deviate:</p> <pre> -{SND0, S2} = rand:normal_s(S1),</pre> +{SND1, S2} = rand:normal_s(S1),</pre> <p>Create a normal deviate with mean -3 and variance 0.5:</p> @@ -414,7 +422,8 @@ tests. We suggest to use a sign test to extract a random Boolean value.</pre> This function may return exactly <c>0.0</c> which can be fatal for certain applications. If that is undesired you can use <c>(1.0 - rand:uniform())</c> to get the - interval <c>0.0 < <anno>X</anno> =< 1.0</c>. + interval <c>0.0 < <anno>X</anno> =< 1.0</c>, or instead use + <seealso marker="#uniform_real-0"><c>uniform_real/0</c></seealso>. </p> <p> If neither endpoint is desired you can test and re-try @@ -432,6 +441,42 @@ end.</pre> </func> <func> + <name name="uniform_real" arity="0"/> + <fsummary>Return a random float.</fsummary> + <desc><marker id="uniform_real-0"/> + <p> + Returns a random float + uniformly distributed in the value range + <c>DBL_MIN =< <anno>X</anno> < 1.0</c> + and updates the state in the process dictionary. + </p> + <p> + Conceptually, a random real number <c>R</c> is generated + from the interval <c>0 =< R < 1</c> and then the + closest rounded down normalized number + in the IEEE 754 Double precision format + is returned. + </p> + <note> + <p> + The generated numbers from this function has got better + granularity for small numbers than the regular + <seealso marker="#uniform-0"><c>uniform/0</c></seealso> + because all bits in the mantissa are random. + This property, in combination with the fact that exactly zero + is never returned is useful for algoritms doing for example + <c>1.0 / <anno>X</anno></c> or <c>math:log(<anno>X</anno>)</c>. + </p> + </note> + <p> + See + <seealso marker="#uniform_real_s-1"><c>uniform_real_s/1</c></seealso> + for more explanation. + </p> + </desc> + </func> + + <func> <name name="uniform" arity="1"/> <fsummary>Return a random integer.</fsummary> <desc><marker id="uniform-1"/> @@ -460,7 +505,8 @@ end.</pre> This function may return exactly <c>0.0</c> which can be fatal for certain applications. If that is undesired you can use <c>(1.0 - rand:uniform(State))</c> to get the - interval <c>0.0 < <anno>X</anno> =< 1.0</c>. + interval <c>0.0 < <anno>X</anno> =< 1.0</c>, or instead use + <seealso marker="#uniform_real_s-1"><c>uniform_real_s/1</c></seealso>. </p> <p> If neither endpoint is desired you can test and re-try @@ -478,6 +524,68 @@ end.</pre> </func> <func> + <name name="uniform_real_s" arity="1"/> + <fsummary>Return a random float.</fsummary> + <desc> + <p> + Returns, for a specified state, a random float + uniformly distributed in the value range + <c>DBL_MIN =< <anno>X</anno> < 1.0</c> + and updates the state in the process dictionary. + </p> + <p> + Conceptually, a random real number <c>R</c> is generated + from the interval <c>0 =< R < 1</c> and then the + closest rounded down normalized number + in the IEEE 754 Double precision format + is returned. + </p> + <note> + <p> + The generated numbers from this function has got better + granularity for small numbers than the regular + <seealso marker="#uniform_s-1"><c>uniform_s/1</c></seealso> + because all bits in the mantissa are random. + This property, in combination with the fact that exactly zero + is never returned is useful for algoritms doing for example + <c>1.0 / <anno>X</anno></c> or <c>math:log(<anno>X</anno>)</c>. + </p> + </note> + <p> + The concept implicates that the probability to get + exactly zero is extremely low; so low that this function + is in fact guaranteed to never return zero. The smallest + number that it might return is <c>DBL_MIN</c>, which is + 2.0^(-1022). + </p> + <p> + The value range stated at the top of this function + description is technically correct, but + <c>0.0 =< <anno>X</anno> < 1.0</c> + is a better description of the generated numbers' + statistical distribution. Except that exactly 0.0 + is never returned, which is not possible to observe + statistically. + </p> + <p> + For example; for all sub ranges + <c>N*2.0^(-53) =< X < (N+1)*2.0^(-53)</c> + where + <c>0 =< integer(N) < 2.0^53</c> + the probability is the same. + Compare that with the form of the numbers generated by + <seealso marker="#uniform_s-1"><c>uniform_s/1</c></seealso>. + </p> + <p> + Having to generate extra random bits for + small numbers costs a little performance. + This function is about 20% slower than the regular + <seealso marker="#uniform_s-1"><c>uniform_s/1</c></seealso> + </p> + </desc> + </func> + + <func> <name name="uniform_s" arity="2"/> <fsummary>Return a random integer.</fsummary> <desc> diff --git a/lib/stdlib/src/rand.erl b/lib/stdlib/src/rand.erl index 7a8a5e6d4a..362e98006e 100644 --- a/lib/stdlib/src/rand.erl +++ b/lib/stdlib/src/rand.erl @@ -21,8 +21,8 @@ %% Multiple PRNG module for Erlang/OTP %% Copyright (c) 2015-2016 Kenji Rikitake %% -%% exrop (xoroshiro116+) added and statistical distribution -%% improvements by the Erlang/OTP team 2017 +%% exrop (xoroshiro116+) added, statistical distribution +%% improvements and uniform_real added by the Erlang/OTP team 2017 %% ===================================================================== -module(rand). @@ -30,10 +30,14 @@ -export([seed_s/1, seed_s/2, seed/1, seed/2, export_seed/0, export_seed_s/1, uniform/0, uniform/1, uniform_s/1, uniform_s/2, + uniform_real/0, uniform_real_s/1, jump/0, jump/1, normal/0, normal/2, normal_s/1, normal_s/3 ]). +%% Debug +-export([make_float/3, float2str/1, bc64/1]). + -compile({inline, [exs64_next/1, exsplus_next/1, exs1024_next/1, exs1024_calc/2, exrop_next/1, exrop_next_s/2, @@ -60,6 +64,10 @@ %% N i evaluated 3 times (?BSL((Bits), (X), (N)) bor ((X) bsr ((Bits)-(N))))). +-define( + BC(V, N), + bc((V), ?BIT((N) - 1), N)). + %%-define(TWO_POW_MINUS53, (math:pow(2, -53))). -define(TWO_POW_MINUS53, 1.11022302462515657e-16). @@ -84,14 +92,21 @@ %% The 'bits' field indicates how many bits the integer %% returned from 'next' has got, i.e 'next' shall return %% an random integer in the range 0..(2^Bits - 1). -%% At least 53 bits is required for the floating point -%% producing fallbacks. This field is only used when -%% the 'uniform' or 'uniform_n' fields are not defined. +%% At least 55 bits is required for the floating point +%% producing fallbacks, but 56 bits would be more future proof. %% %% The fields 'next', 'uniform' and 'uniform_n' -%% implement the algorithm. If 'uniform' or 'uinform_n' +%% implement the algorithm. If 'uniform' or 'uniform_n' %% is not present there is a fallback using 'next' and either -%% 'bits' or the deprecated 'max'. +%% 'bits' or the deprecated 'max'. The 'next' function +%% must generate a word with at least 56 good random bits. +%% +%% The 'weak_low_bits' field indicate how many bits are of +%% lesser quality and they will not be used by the floating point +%% producing functions, nor by the range producing functions +%% when more bits are needed, to avoid weak bits in the middle +%% of the generated bits. The lowest bits from the range +%% functions still have the generator's quality. %% -type alg_handler() :: #{type := alg(), @@ -148,11 +163,7 @@ %% For ranges larger than the algorithm bit size uniform_range(Range, #{next:=Next, bits:=Bits} = Alg, R, V) -> - WeakLowBits = - case Alg of - #{weak_low_bits:=WLB} -> WLB; - #{} -> 0 - end, + WeakLowBits = maps:get(weak_low_bits, Alg, 0), %% Maybe waste the lowest bit(s) when shifting in new bits Shift = Bits - WeakLowBits, ShiftMask = bnot ?MASK(WeakLowBits), @@ -297,7 +308,7 @@ uniform_s({#{bits:=Bits, next:=Next} = Alg, R0}) -> {(V bsr (Bits - 53)) * ?TWO_POW_MINUS53, {Alg, R1}}; uniform_s({#{max:=Max, next:=Next} = Alg, R0}) -> {V, R1} = Next(R0), - %% Old broken algorithm with non-uniform density + %% Old algorithm with non-uniform density {V / (Max + 1), {Alg, R1}}. @@ -317,7 +328,7 @@ uniform_s(N, {#{bits:=Bits, next:=Next} = Alg, R0}) ?uniform_range(N, Alg, R1, V, MaxMinusN, I); uniform_s(N, {#{max:=Max, next:=Next} = Alg, R0}) when is_integer(N), 1 =< N -> - %% Old broken algorithm with skewed probability + %% Old algorithm with skewed probability %% and gap in ranges > Max {V, R1} = Next(R0), if @@ -328,6 +339,189 @@ uniform_s(N, {#{max:=Max, next:=Next} = Alg, R0}) {trunc(F * N) + 1, {Alg, R1}} end. +%% uniform_real/0: returns a random float X where 0.0 < X =< 1.0, +%% updating the state in the process dictionary. + +-spec uniform_real() -> X :: float(). +uniform_real() -> + {X, Seed} = uniform_real_s(seed_get()), + _ = seed_put(Seed), + X. + +%% uniform_real_s/1: given a state, uniform_s/1 +%% returns a random float X where 0.0 < X =< 1.0, +%% and a new state. +%% +%% This function does not use the same form of uniformity +%% as the uniform_s/1 function. +%% +%% Instead, this function does not generate numbers with equal +%% distance in the interval, but rather tries to keep all mantissa +%% bits random also for small numbers, meaning that the distance +%% between possible numbers decreases when the numbers +%% approaches 0.0, as does the possibility for a particular +%% number. Hence uniformity is preserved. +%% +%% To generate 56 bits at the time instead of 53 is actually +%% a speed optimization since the probability to have to +%% generate a second word decreases by 1/2 for every extra bit. +%% +%% This function generates normalized numbers, so the smallest number +%% that can be generated is 2^-1022 with the distance 2^-1074 +%% to the next to smallest number, compared to 2^-53 for uniform_s/1. +%% +%% This concept of uniformity should work better for applications +%% where you need to calculate 1.0/X or math:log(X) since those +%% operations benefits from larger precision approaching 0.0, +%% and that this function does not return 0.0 nor denormalized +%% numbers very close to 0.0. The log() operation in The Box-Muller +%% transformation for normal distribution is an example of this. +%% +%%-define(TWO_POW_MINUS55, (math:pow(2, -55))). +%%-define(TWO_POW_MINUS110, (math:pow(2, -110))). +%%-define(TWO_POW_MINUS55, 2.7755575615628914e-17). +%%-define(TWO_POW_MINUS110, 7.7037197775489436e-34). +%% +-spec uniform_real_s(State :: state()) -> {X :: float(), NewState :: state()}. +uniform_real_s({#{bits:=Bits, next:=Next} = Alg, R0}) -> + %% Generate a 56 bit number without using the weak low bits. + %% + %% Be sure to use only 53 bits when multiplying with + %% math:pow(2.0, -N) to avoid rounding which would make + %% "even" floats more probable than "odd". + %% + {V1, R1} = Next(R0), + M1 = V1 bsr (Bits - 56), + if + ?BIT(55) =< M1 -> + %% We have 56 bits - waste 3 + {(M1 bsr 3) * math:pow(2.0, -53), {Alg, R1}}; + ?BIT(54) =< M1 -> + %% We have 55 bits - waste 2 + {(M1 bsr 2) * math:pow(2.0, -54), {Alg, R1}}; + ?BIT(53) =< M1 -> + %% We have 54 bits - waste 1 + {(M1 bsr 1) * math:pow(2.0, -55), {Alg, R1}}; + ?BIT(52) =< M1 -> + %% We have 53 bits - use all + {M1 * math:pow(2.0, -56), {Alg, R1}}; + true -> + %% Need more bits + {V2, R2} = Next(R1), + uniform_real_s(Alg, Next, M1, -56, R2, V2, Bits) + end; +uniform_real_s({#{max:=_, next:=Next} = Alg, R0}) -> + %% Generate a 56 bit number. + %% Ignore the weak low bits for these old algorithms, + %% just produce something reasonable. + %% + %% Be sure to use only 53 bits when multiplying with + %% math:pow(2.0, -N) to avoid rounding which would make + %% "even" floats more probable than "odd". + %% + {V1, R1} = Next(R0), + M1 = ?MASK(56, V1), + if + ?BIT(55) =< M1 -> + %% We have 56 bits - waste 3 + {(M1 bsr 3) * math:pow(2.0, -53), {Alg, R1}}; + ?BIT(54) =< M1 -> + %% We have 55 bits - waste 2 + {(M1 bsr 2) * math:pow(2.0, -54), {Alg, R1}}; + ?BIT(53) =< M1 -> + %% We have 54 bits - waste 1 + {(M1 bsr 1) * math:pow(2.0, -55), {Alg, R1}}; + ?BIT(52) =< M1 -> + %% We have 53 bits - use all + {M1 * math:pow(2.0, -56), {Alg, R1}}; + true -> + %% Need more bits + {V2, R2} = Next(R1), + uniform_real_s(Alg, Next, M1, -56, R2, V2, 56) + end. + +uniform_real_s(Alg, _Next, M0, -1064, R1, V1, Bits) -> % 19*56 + %% This is a very theoretical bottom case. + %% The odds of getting here is about 2^-1008, + %% through a white box test case, or thanks to + %% a malfunctioning PRNG producing 18 56-bit zeros in a row. + %% + %% Fill up to 53 bits, we have at most 52 + B0 = (53 - ?BC(M0, 52)), % Missing bits + {(((M0 bsl B0) bor (V1 bsr (Bits - B0))) * math:pow(2.0, -1064 - B0)), + {Alg, R1}}; +uniform_real_s(Alg, Next, M0, BitNo, R1, V1, Bits) -> + if + %% Optimize the most probable. + %% Fill up to 53 bits. + ?BIT(51) =< M0 -> + %% We have 52 bits in M0 - need 1 + {(((M0 bsl 1) bor (V1 bsr (Bits - 1))) + * math:pow(2.0, BitNo - 1)), + {Alg, R1}}; + ?BIT(50) =< M0 -> + %% We have 51 bits in M0 - need 2 + {(((M0 bsl 2) bor (V1 bsr (Bits - 2))) + * math:pow(2.0, BitNo - 2)), + {Alg, R1}}; + ?BIT(49) =< M0 -> + %% We have 50 bits in M0 - need 3 + {(((M0 bsl 3) bor (V1 bsr (Bits - 3))) + * math:pow(2.0, BitNo - 3)), + {Alg, R1}}; + M0 == 0 -> + M1 = V1 bsr (Bits - 56), + if + ?BIT(55) =< M1 -> + %% We have 56 bits - waste 3 + {(M1 bsr 3) * math:pow(2.0, BitNo - 53), {Alg, R1}}; + ?BIT(54) =< M1 -> + %% We have 55 bits - waste 2 + {(M1 bsr 2) * math:pow(2.0, BitNo - 54), {Alg, R1}}; + ?BIT(53) =< M1 -> + %% We have 54 bits - waste 1 + {(M1 bsr 1) * math:pow(2.0, BitNo - 55), {Alg, R1}}; + ?BIT(52) =< M1 -> + %% We have 53 bits - use all + {M1 * math:pow(2.0, BitNo - 56), {Alg, R1}}; + BitNo =:= -1008 -> + %% Endgame + %% For the last round we can not have 14 zeros or more + %% at the top of M1 because then we will underflow, + %% so we need at least 43 bits + if + ?BIT(42) =< M1 -> + %% We have 43 bits - get the last bits + uniform_real_s(Alg, Next, M1, BitNo - 56, R1); + true -> + %% Would underflow 2^-1022 - start all over + %% + %% We could just crash here since the odds for + %% the PRNG being broken is much higher than + %% for a good PRNG generating this many zeros + %% in a row. Maybe we should write an error + %% report or call this a system limit...? + uniform_real_s({Alg, R1}) + end; + true -> + %% Need more bits + uniform_real_s(Alg, Next, M1, BitNo - 56, R1) + end; + true -> + %% Fill up to 53 bits + B0 = 53 - ?BC(M0, 49), % Number of bits we need to append + {(((M0 bsl B0) bor (V1 bsr (Bits - B0))) + * math:pow(2.0, BitNo - B0)), + {Alg, R1}} + end. +%% +uniform_real_s(#{bits:=Bits} = Alg, Next, M0, BitNo, R0) -> + {V1, R1} = Next(R0), + uniform_real_s(Alg, Next, M0, BitNo, R1, V1, Bits); +uniform_real_s(#{max:=_} = Alg, Next, M0, BitNo, R0) -> + {V1, R1} = Next(R0), + uniform_real_s(Alg, Next, M0, BitNo, R1, ?MASK(56, V1), 56). + %% jump/1: given a state, jump/1 %% returns a new state which is equivalent to that %% after a large number of call defined for each algorithm. @@ -1025,3 +1219,42 @@ normal_fi(Indx) -> 1.0214971439701471e-02,8.6165827693987316e-03,7.0508754713732268e-03, 5.5224032992509968e-03,4.0379725933630305e-03,2.6090727461021627e-03, 1.2602859304985975e-03}). + +%%%bitcount64(0) -> 0; +%%%bitcount64(V) -> 1 + bitcount(V, 64). +%%% +%%%-define( +%%% BITCOUNT(V, N), +%%% bitcount(V, N) -> +%%% if +%%% (1 bsl ((N) bsr 1)) =< (V) -> +%%% ((N) bsr 1) + bitcount((V) bsr ((N) bsr 1), ((N) bsr 1)); +%%% true -> +%%% bitcount((V), ((N) bsr 1)) +%%% end). +%%%?BITCOUNT(V, 64); +%%%?BITCOUNT(V, 32); +%%%?BITCOUNT(V, 16); +%%%?BITCOUNT(V, 8); +%%%?BITCOUNT(V, 4); +%%%?BITCOUNT(V, 2); +%%%bitcount(_, 1) -> 0. + +bc64(V) -> ?BC(V, 64). + +%% Linear from high bit - higher probability first gives faster execution +bc(V, B, N) when B =< V -> N; +bc(V, B, N) -> bc(V, B bsr 1, N - 1). + +make_float(S, E, M) -> + <<F/float>> = <<S:1, E:11, M:52>>, + F. + +float2str(N) -> + <<S:1, E:11, M:52>> = <<(float(N))/float>>, + lists:flatten( + io_lib:format( + "~c~c.~13.16.0bE~b", + [case S of 1 -> $-; 0 -> $+ end, + case E of 0 -> $0; _ -> $1 end, + M, E - 16#3ff])). diff --git a/lib/stdlib/test/rand_SUITE.erl b/lib/stdlib/test/rand_SUITE.erl index f69d42551e..ef4f9faad9 100644 --- a/lib/stdlib/test/rand_SUITE.erl +++ b/lib/stdlib/test/rand_SUITE.erl @@ -29,11 +29,14 @@ basic_stats_uniform_1/1, basic_stats_uniform_2/1, basic_stats_standard_normal/1, basic_stats_normal/1, + uniform_real_conv/1, plugin/1, measure/1, reference_jump_state/1, reference_jump_procdict/1]). -export([test/0, gen/1]). +-export([uniform_real_gen/1, uniform_gen/2]). + -include_lib("common_test/include/ct.hrl"). -define(LOOP, 1000000). @@ -46,7 +49,7 @@ all() -> [seed, interval_int, interval_float, api_eq, reference, - {group, basic_stats}, + {group, basic_stats}, uniform_real_conv, plugin, measure, {group, reference_jump} ]. @@ -101,7 +104,7 @@ seed_1(Alg) -> _ = rand:uniform(), S00 = get(rand_seed), erase(), - _ = rand:uniform(), + _ = rand:uniform_real(), false = S00 =:= get(rand_seed), %% hopefully %% Choosing algo and seed @@ -228,11 +231,13 @@ interval_float(Config) when is_list(Config) -> interval_float_1(0) -> ok; interval_float_1(N) -> X = rand:uniform(), + Y = rand:uniform_real(), if - 0.0 =< X, X < 1.0 -> + 0.0 =< X, X < 1.0, 0.0 < Y, Y < 1.0 -> ok; true -> - io:format("X=~p 0=<~p<1.0~n", [X,X]), + io:format("X=~p 0.0=<~p<1.0~n", [X,X]), + io:format("Y=~p 0.0<~p<1.0~n", [Y,Y]), exit({X, rand:export_seed()}) end, interval_float_1(N-1). @@ -334,7 +339,13 @@ basic_stats_normal(Config) when is_list(Config) -> IntendedMeanVariancePairs). basic_uniform_1(N, S0, Sum, A0) when N > 0 -> - {X,S} = rand:uniform_s(S0), + {X,S} = + case N band 1 of + 0 -> + rand:uniform_s(S0); + 1 -> + rand:uniform_real_s(S0) + end, I = trunc(X*100), A = array:set(I, 1+array:get(I,A0), A0), basic_uniform_1(N-1, S, Sum+X, A); @@ -400,6 +411,137 @@ normal_s(Mean, Variance, State0) -> rand:normal_s(Mean, Variance, State0). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% White box test of the conversion to float + +uniform_real_conv(Config) when is_list(Config) -> + [begin +%% ct:pal("~13.16.0bx~3.16.0b: ~p~n", [M,E,Gen]), + uniform_real_conv_check(M, E, Gen) + end || {M, E, Gen} <- uniform_real_conv_data()], + uniform_real_scan(0), + uniform_real_scan(3). + +uniform_real_conv_data() -> + [{16#fffffffffffff, -1, [16#3ffffffffffffff]}, + {16#fffffffffffff, -1, [16#3ffffffffffffe0]}, + {16#ffffffffffffe, -1, [16#3ffffffffffffdf]}, + %% + {16#0000000000000, -1, [16#200000000000000]}, + {16#fffffffffffff, -2, [16#1ffffffffffffff]}, + {16#fffffffffffff, -2, [16#1fffffffffffff0]}, + {16#ffffffffffffe, -2, [16#1ffffffffffffef]}, + %% + {16#0000000000000, -2, [16#100000000000000]}, + {16#fffffffffffff, -3, [16#0ffffffffffffff]}, + {16#fffffffffffff, -3, [16#0fffffffffffff8]}, + {16#ffffffffffffe, -3, [16#0fffffffffffff7]}, + %% + {16#0000000000000, -3, [16#080000000000000]}, + {16#fffffffffffff, -4, [16#07fffffffffffff]}, + {16#fffffffffffff, -4, [16#07ffffffffffffc]}, + {16#ffffffffffffe, -4, [16#07ffffffffffffb]}, + %% + {16#0000000000000, -4, [16#040000000000000]}, + {16#fffffffffffff, -5, [16#03fffffffffffff,16#3ffffffffffffff]}, + {16#fffffffffffff, -5, [16#03ffffffffffffe,16#200000000000000]}, + {16#ffffffffffffe, -5, [16#03fffffffffffff,16#1ffffffffffffff]}, + {16#ffffffffffffe, -5, [16#03fffffffffffff,16#100000000000000]}, + %% + {16#0000000000001, -56, [16#000000000000007,16#00000000000007f]}, + {16#0000000000001, -56, [16#000000000000004,16#000000000000040]}, + {16#0000000000000, -57, [16#000000000000003,16#20000000000001f]}, + {16#0000000000000, -57, [16#000000000000000,16#200000000000000]}, + {16#fffffffffffff, -58, [16#000000000000003,16#1ffffffffffffff]}, + {16#fffffffffffff, -58, [16#000000000000000,16#1fffffffffffff0]}, + {16#ffffffffffffe, -58, [16#000000000000000,16#1ffffffffffffef]}, + {16#ffffffffffffe, -58, [16#000000000000000,16#1ffffffffffffe0]}, + %% + {16#0000000000000, -58, [16#000000000000000,16#10000000000000f]}, + {16#0000000000000, -58, [16#000000000000000,16#100000000000000]}, + {2#11001100000000000000000000000000000000000011000000011, % 53 bits + -1022, + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, % 18 zeros + 2#1100110000000000000000000000000000000000001 bsl 2, % 43 bits + 2#1000000011 bsl (56-10+2)]}, % 10 bits + {0, -1, % 0.5 after retry + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, % 18 zeros + 2#111111111111111111111111111111111111111111 bsl 2, % 42 bits - retry + 16#200000000000003]}]. % 0.5 + +-define(UNIFORM_REAL_SCAN_PATTERN, (16#19000000000009)). % 53 bits +-define(UNIFORM_REAL_SCAN_NUMBER, (1021)). + +uniform_real_scan_template(K) -> + <<0:?UNIFORM_REAL_SCAN_NUMBER, + ?UNIFORM_REAL_SCAN_PATTERN:53,K:2,0:1>>. + +uniform_real_scan(K) -> + Templ = uniform_real_scan_template(K), + N = ?UNIFORM_REAL_SCAN_NUMBER, + uniform_real_scan(Templ, N, K). + +uniform_real_scan(Templ, N, K) when 0 =< N -> + <<_:N/bits,T/bits>> = Templ, + Data = uniform_real_scan_data(T, K), + uniform_real_conv_check( + ?UNIFORM_REAL_SCAN_PATTERN, N - 1 - ?UNIFORM_REAL_SCAN_NUMBER, Data), + uniform_real_scan(Templ, N - 1, K); +uniform_real_scan(_, _, _) -> + ok. + +uniform_real_scan_data(Templ, K) -> + case Templ of + <<X:56, T/bits>> -> + B = rand:bc64(X), + [(X bsl 2) bor K | + if + 53 =< B -> + []; + true -> + uniform_real_scan_data(T, K) + end]; + _ -> + <<X:56, _/bits>> = <<Templ/bits, 0:56>>, + [(X bsl 2) bor K] + end. + +uniform_real_conv_check(M, E, Gen) -> + <<F/float>> = <<0:1, (E + 16#3ff):11, M:52>>, + try uniform_real_gen(Gen) of + F -> F; + FF -> + ct:pal( + "~s =/= ~s: ~s~n", + [rand:float2str(FF), rand:float2str(F), + [["16#",integer_to_list(G,16),$\s]||G<-Gen]]), + ct:fail({neq, FF, F}) + catch + Error:Reason -> + ct:pal( + "~w:~p ~s: ~s~n", + [Error, Reason, rand:float2str(F), + [["16#",integer_to_list(G,16),$\s]||G<-Gen]]), + ct:fail({Error, Reason, F, erlang:get_stacktrace()}) + end. + + +uniform_real_gen(Gen) -> + State = rand_state(Gen), + {F, {#{type := rand_SUITE_list},[]}} = rand:uniform_real_s(State), + F. + +uniform_gen(Range, Gen) -> + State = rand_state(Gen), + {N, {#{type := rand_SUITE_list},[]}} = rand:uniform_s(Range, State), + N. + +%% Loaded dice for white box tests +rand_state(Gen) -> + {#{type => rand_SUITE_list, bits => 58, weak_low_bits => 1, + next => fun ([H|T]) -> {H, T} end}, + Gen}. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Test that the user can write algorithms. plugin(Config) when is_list(Config) -> @@ -520,6 +662,21 @@ do_measure(_Config) -> end, Algs), %% + ct:pal("~nRNG uniform integer half range performance~n",[]), + _ = + measure_1( + fun (State) -> half_range(State) end, + fun (State, Range, Mod) -> + measure_loop( + fun (St0) -> + ?CHECK_UNIFORM_RANGE( + Mod:uniform_s(Range, St0), Range, + X, St1) + end, + State) + end, + Algs), + %% ct:pal("~nRNG uniform integer half range + 1 performance~n",[]), _ = measure_1( @@ -630,7 +787,8 @@ do_measure(_Config) -> Algs), %% ct:pal("~nRNG uniform float performance~n",[]), - _ = measure_1( + _ = + measure_1( fun (_) -> 0 end, fun (State, _, Mod) -> measure_loop( @@ -641,8 +799,22 @@ do_measure(_Config) -> end, Algs), %% + ct:pal("~nRNG uniform_real float performance~n",[]), + _ = + measure_1( + fun (_) -> 0 end, + fun (State, _, Mod) -> + measure_loop( + fun (St0) -> + ?CHECK_UNIFORM(Mod:uniform_real_s(St0), X, St) + end, + State) + end, + Algs), + %% ct:pal("~nRNG normal float performance~n",[]), - _ = measure_1( + [TMarkNormalFloat|_] = + measure_1( fun (_) -> 0 end, fun (State, _, Mod) -> measure_loop( @@ -652,10 +824,36 @@ do_measure(_Config) -> State) end, Algs), + %% Just for fun try an implementation of the Box-Muller + %% transformation for creating normal distribution floats + %% to compare with our Ziggurat implementation. + %% Generates two numbers per call that we add so they + %% will not be optimized away. Hence the benchmark time + %% is twice what it should be. + TwoPi = 2 * math:pi(), + _ = + measure_1( + fun (_) -> 0 end, + fun (State, _, Mod) -> + measure_loop( + fun (State0) -> + {U1, State1} = Mod:uniform_real_s(State0), + {U2, State2} = Mod:uniform_s(State1), + R = math:sqrt(-2.0 * math:log(U1)), + T = TwoPi * U2, + Z0 = R * math:cos(T), + Z1 = R * math:sin(T), + ?CHECK_NORMAL({Z0 + Z1, State2}, X, State3) + end, + State) + end, + exrop, TMarkNormalFloat), ok. +-define(LOOP_MEASURE, (?LOOP div 5)). + measure_loop(Fun, State) -> - measure_loop(Fun, State, ?LOOP). + measure_loop(Fun, State, ?LOOP_MEASURE). %% measure_loop(Fun, State, N) when 0 < N -> measure_loop(Fun, Fun(State), N-1); @@ -693,7 +891,8 @@ measure_1(RangeFun, Fun, Alg, TMark) -> end, io:format( "~.12w: ~p ns ~p% [16#~.16b]~n", - [Alg, (Time * 1000 + 500) div ?LOOP, Percent, Range]), + [Alg, (Time * 1000 + 500) div ?LOOP_MEASURE, + Percent, Range]), Parent ! {self(), Time}, normal end), |