57 lines
1.2 KiB
C
57 lines
1.2 KiB
C
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#include <stdio.h>
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#include <math.h>
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/* Naive approach using the definition
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* of γ as the difference between log(n)
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* and the Rieman sum of its derivative (1/n).
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*
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* The result is:
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*
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* approx: 0.57721 56648 77325
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* true: 0.57721 56649 01533
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* diff: 0.00000 00000 24207
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*
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* The convergence is logarithmic and so
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* slow that the double precision runs out
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* at the 10th decimal digit.
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*
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*/
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double exact = 0.577215664901532860;
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double partial_sum(size_t n) {
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double sum = 0;
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for (double k = 1; k <= n; k++) {
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sum += 1/k;
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}
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return sum - log(n);
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}
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int main () {
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size_t prev_n, n = 2;
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double prev_diff, diff=1;
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double approx;
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/* Compute the approximation
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* and the difference from the true value.
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* Stop when the difference starts increasing
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* due to roundoff errors.
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*
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*/
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do {
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prev_n = n;
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n *= 10;
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prev_diff = diff;
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approx = partial_sum(n);
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diff = fabs(exact - approx);
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printf("n:\t%.0e\t", (double)n);
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printf("diff:\t%e\n", diff);
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} while (diff < prev_diff);
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printf("n:\t%.0e\n", (double)prev_n);
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printf("approx:\t%.15f\n", approx);
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printf("true:\t%.15f\n", exact);
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printf("diff:\t%.15f\n", prev_diff);
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printf("\t 123456789_12345\n");
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}
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