giles
eb621240d7
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Composite Simpson's 1/3 rule with 100 panels:
let simpson f a b n =
let h = (b -. a) /. float_of_int n in
let sum = ref (f a +. f b) in
for i = 1 to n - 1 do
let x = a +. float_of_int i *. h in
let coef = if i mod 2 = 0 then 2.0 else 4.0 in
sum := !sum +. coef *. f x
done;
h *. !sum /. 3.0
The 1-4-2-4-...-4-1 coefficient pattern is implemented via even/odd
index dispatch. Endpoints get coefficient 1.
For x^2 over [0, 1], exact value is 1/3 ~= 0.33333. Scaled by 30000
gives 9999.99..., int_of_float -> 10000.
Tests higher-order function (passing the integrand 'fun x -> x *. x'),
float arithmetic in for-loop, and float_of_int for index->x conversion.
89 baseline programs total.
94 lines
1.9 KiB
JSON
94 lines
1.9 KiB
JSON
{
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"coin_change.ml": 6,
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"exception_user.ml": 26,
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"expr_eval.ml": 16,
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"expr_simp.ml": 22,
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"factorial.ml": 3628800,
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"fib_mod.ml": 391360,
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"fraction.ml": 7,
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"frequency.ml": 5,
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"gcd_lcm.ml": 60,
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"hanoi.ml": 1023,
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"hist.ml": 75,
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"int_sqrt.ml": 1027,
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"tic_tac_toe.ml": 1,
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"word_freq.ml": 8,
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"zip_unzip.ml": 1000,
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"sieve.ml": 15,
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"triangle.ml": 11,
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"twosum.ml": 5,
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"unique_set.ml": 9,
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"validate.ml": 417,
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"word_count.ml": 3
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}
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