Building Abstractions with Functions - Functions and the Processes They Generate - Example: Testing for Primality - Probabilistic methods - applicative-order, process, log, linear
Structure and Interpretation of Computer Programs: JavaScript Edition(Harold Abelson(著)、Gerald Jay Sussman(著)、Julie Sussman(著)、The MIT Press)のChapter 1(Building Abstractions with Functions)、1.2(Functions and the Processes They Generate)、1.2.6(Example: Testing for Primality)、Probabilistic methods、Exercise 1.26の解答を求めてみる。
normal-orderではなくapplicative-orderでは、元のコードだとexpmod(base, exp / 2, m)を計算してからsquareが適用されるから、expmod(base, exp / 2, m)の計算は1回で済むけど、問題のコードだとexp(base, exp / 2, m)の計算が2回計算することになるから。
実際に速度の違いを確認。
コード
function square(x) {
return x * x;
}
function is_even(n) {
return n % 2 === 0;
}
function display(x) {
console.log(x);
}
function get_time() {
// return Date.now();
return performance.now();
}
function math_floor(x) {
return Math.floor(x);
}
function math_random() {
return Math.random();
}
function expmod(base, exp, m) {
return exp === 0 ?
1 :
is_even(exp) ?
square(expmod(base, exp / 2, m)) % m :
(base * expmod(base, exp - 1, m)) % m;
}
function expmod1(base, exp, m) {
return exp === 0 ?
1 :
is_even(exp) ?
(expmod1(base, exp / 2, m) * expmod1(base, exp / 2, m)) % m :
(base * expmod1(base, exp - 1, m))
}
function smallest_divisor(n) {
return find_divisor(n, 2);
}
function next(n) {
return n === 2 ?
3 :
n + 2;
}
function find_divisor(n, test_divisor) {
return square(test_divisor) > n ?
n :
divides(test_divisor, n) ?
test_divisor :
// find_divisor(n, test_divisor + 1);
find_divisor(n, next(test_divisor));
}
function divides(a, b) {
return b % a === 0;
}
function fermat_test(n) {
function try_it(a) {
return expmod(a, n, n) === a;
}
return try_it(1 + math_floor(math_random() * (n - 1)));
}
function fermat_test1(n) {
function try_it(a) {
return expmod1(a, n, n) === a;
}
return try_it(1 + math_floor(math_random() * (n - 1)));
}
function fast_is_prime(n, times) {
return times === 0 ?
true :
fermat_test(n) ?
fast_is_prime(n, times - 1) :
false;
}
function fast_is_prime1(n, times) {
return times === 0 ?
true :
fermat_test1(n) ?
fast_is_prime1(n, times - 1) :
false;
}
function timed_prime_test(n) {
display(n);
return start_prime_test(n, get_time());
}
function timed_prime_test1(n) {
display(n);
return start_prime_test1(n, get_time());
}
function start_prime_test(n, start_time) {
return fast_is_prime(n, 10) ?
report_prime(get_time() - start_time) :
true;
}
function start_prime_test1(n, start_time) {
return fast_is_prime1(n, 10) ?
report_prime(get_time() - start_time) :
true;
}
function report_prime(elapsed_time) {
display(" *** ");
display(`${String(elapsed_time)}`);
}
function search_for_primes(start, stop) {
function iter(n) {
n > stop ?
true :
f(n);
}
function f(n) {
timed_prime_test(n);
iter(n + 2);
}
start % 2 === 0 ?
iter(start + 1) :
iter(start);
}
function search_for_primes1(start, stop) {
function iter(n) {
n > stop ?
true :
f(n);
}
function f(n) {
timed_prime_test1(n);
iter(n + 2);
}
start % 2 === 0 ?
iter(start + 1) :
iter(start);
}
display('log');
search_for_primes(101, 107);
search_for_primes(1001, 1039);
search_for_primes(10001, 10037);
display('linear');
search_for_primes1(101, 107);
search_for_primes1(1001, 1039);
search_for_primes1(10001, 10037);
入出力結果(Terminal, Zsh)
% node answer1.26.js
log
101
***
0.2722399830818176
103
***
0.019895970821380615
105
107
***
0.019631028175354004
1001
1003
1005
1007
1009
***
0.014706015586853027
1011
1013
***
0.019262969493865967
1015
1017
1019
***
0.018829941749572754
1021
***
0.01666104793548584
1023
1025
1027
1029
1031
***
0.034102022647857666
1033
***
0.012418031692504883
1035
1037
1039
***
0.01595902442932129
10001
10003
10005
10007
***
0.018359005451202393
10009
***
0.020741045475006104
10011
10013
10015
10017
10019
10021
10023
10025
10027
10029
10031
10033
10035
10037
***
0.01862400770187378
linear
101
***
0.30984997749328613
103
***
0.22511601448059082
105
107
***
0.23339003324508667
1001
1003
1005
1007
1009
***
1.286895990371704
1011
1013
***
0.5690180063247681
1015
1017
1019
***
0.217989981174469
1021
***
0.2177630066871643
1023
1025
1027
1029
1031
***
0.32638198137283325
1033
***
0.3273810148239136
1035
1037
1039
***
0.323852002620697
10001
10003
10005
10007
***
2.9872609972953796
10009
***
2.789187967777252
10011
10013
10015
10017
10019
10021
10023
10025
10027
10029
10031
10033
10035
10037
***
3.7627260088920593
%