Ein Anderssono
54d2fecee0
- Added implementations for: bash, brainfuck, c, cpp, crystal, csharp, d, dart, elixir, erlang, fortran, go, haskell, java, javascript, julia, kotlin, objective-c, scala, typescript, lua, nim, odin, perl, php, python, r, ruby, rust, swift, zig, assembly, vimscript, wolfram - All implementations use Machin's formula: π/4 = 4*arctan(1/5) - arctan(1/239) - Build system with ./build.sh, test system with ./test.sh - Performance testing with ./run_all.sh - Comprehensive README.md explaining performance differences - Test framework verifies correctness against known π values
120 lines
2.9 KiB
C
120 lines
2.9 KiB
C
#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <gmp.h>
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// Calculate arctan(1/x) using Taylor series
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// arctan(1/x) = 1/x - 1/(3*x^3) + 1/(5*x^5) - ...
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void arctan(mpz_t result, unsigned long x, unsigned long decimals) {
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mpz_t term, x_squared, contrib;
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mpz_init(term);
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mpz_init(x_squared);
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mpz_init(contrib);
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// Scale factor: 10^(decimals + 10) for precision
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mpz_t scale;
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mpz_init(scale);
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mpz_ui_pow_ui(scale, 10, decimals + 10);
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// x_squared = x * x
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mpz_set_ui(x_squared, x);
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mpz_mul_ui(x_squared, x_squared, x);
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// term = scale / x (first term: 1/x)
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mpz_fdiv_q_ui(term, scale, x);
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// result = 0
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mpz_set_ui(result, 0);
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// Iterate through Taylor series
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unsigned long n = 0;
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int sign = 1;
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while (mpz_cmp_ui(term, 0) != 0 && n < decimals * 3) {
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// Divide by (2n+1)
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mpz_fdiv_q_ui(contrib, term, 2 * n + 1);
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if (sign > 0) {
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mpz_add(result, result, contrib);
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} else {
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mpz_sub(result, result, contrib);
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}
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// Next term: divide by x^2
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mpz_fdiv_q(term, term, x_squared);
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// Alternate sign
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sign = -sign;
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n++;
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// Stop when term becomes negligible
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if (n > decimals * 2) break;
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}
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mpz_clear(term);
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mpz_clear(x_squared);
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mpz_clear(contrib);
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mpz_clear(scale);
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}
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void calculate_pi(mpz_t result, unsigned long decimals) {
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mpz_t arctan_1_5, arctan_1_239;
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mpz_init(arctan_1_5);
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mpz_init(arctan_1_239);
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// Calculate arctan(1/5)
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arctan(arctan_1_5, 5, decimals);
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// Calculate arctan(1/239)
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arctan(arctan_1_239, 239, decimals);
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// pi/4 = 4*arctan(1/5) - arctan(1/239)
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// pi = 16*arctan(1/5) - 4*arctan(1/239)
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mpz_mul_ui(arctan_1_5, arctan_1_5, 16);
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mpz_mul_ui(arctan_1_239, arctan_1_239, 4);
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mpz_sub(result, arctan_1_5, arctan_1_239);
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mpz_clear(arctan_1_5);
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mpz_clear(arctan_1_239);
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}
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int main(int argc, char *argv[]) {
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unsigned long decimals = 100;
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if (argc > 1) {
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decimals = strtoul(argv[1], NULL, 10);
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if (decimals == 0) {
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decimals = 100;
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}
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}
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mpz_t pi;
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mpz_init(pi);
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calculate_pi(pi, decimals);
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// Convert to string
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char *pi_str = mpz_get_str(NULL, 10, pi);
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size_t len = strlen(pi_str);
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// Print with decimal point
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if (len > 0) {
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putchar('3');
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if (decimals > 0) {
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putchar('.');
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// Print decimals, skipping the leading "3"
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size_t start = 1;
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size_t end = start + decimals;
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if (end > len) end = len;
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for (size_t i = start; i < end && i < len; i++) {
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putchar(pi_str[i]);
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}
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}
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putchar('\n');
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}
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free(pi_str);
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mpz_clear(pi);
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return 0;
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} |