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
124 lines
3.3 KiB
Objective-C
124 lines
3.3 KiB
Objective-C
// Pi calculation using Machin's formula
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// pi/4 = 4*arctan(1/5) - arctan(1/239)
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#import <Foundation/Foundation.h>
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#include <gmp.h>
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// Calculate arctan(1/x) using Taylor series with arbitrary precision
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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 scale, term, x_squared, temp;
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mpz_init(scale);
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mpz_init(term);
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mpz_init(x_squared);
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mpz_init(temp);
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// scale = 10^(decimals + 10)
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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_ui_pow_ui(x_squared, x, 2);
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// term = scale / 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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int sign = 1;
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unsigned long n = 1;
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while (mpz_cmp_ui(term, 0) > 0) {
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// result += sign * term / n
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mpz_fdiv_q_ui(temp, term, n);
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if (sign > 0) {
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mpz_add(result, result, temp);
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} else {
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mpz_sub(result, result, temp);
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}
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// term = term / x²
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mpz_fdiv_q(term, term, x_squared);
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n += 2;
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sign = -sign;
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}
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mpz_clear(scale);
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mpz_clear(term);
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mpz_clear(x_squared);
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mpz_clear(temp);
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}
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// Calculate pi using Machin's formula
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NSString* calculatePi(int decimals) {
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if (decimals < 1) {
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decimals = 100;
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}
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mpz_t arctan5, arctan239, pi;
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mpz_init(arctan5);
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mpz_init(arctan239);
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mpz_init(pi);
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// Machin's formula: pi/4 = 4*arctan(1/5) - arctan(1/239)
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arctan(arctan5, 5, decimals);
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arctan(arctan239, 239, decimals);
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// pi = 16*arctan(1/5) - 4*arctan(1/239)
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mpz_mul_ui(arctan5, arctan5, 16);
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mpz_mul_ui(arctan239, arctan239, 4);
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mpz_sub(pi, arctan5, arctan239);
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// Convert to string
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char* piStr = mpz_get_str(NULL, 10, pi);
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NSString* result = [NSString stringWithUTF8String:piStr];
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free(piStr);
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// Format output
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if (decimals == 0) {
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return @"3";
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}
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// Pad with zeros if needed
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NSString* padded = result;
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if ([result length] < decimals + 1) {
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NSUInteger zerosNeeded = decimals + 1 - [result length];
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padded = [@"0" stringByPaddingToLength:zerosNeeded withString:@"0" startingAtIndex:0];
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padded = [padded stringByAppendingString:result];
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}
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// Insert decimal point
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NSString* beforeDecimal = [padded substringWithRange:NSMakeRange(0, 1)];
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NSString* afterDecimal = [padded substringWithRange:NSMakeRange(1, [padded length] - 1)];
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// Pad or truncate to desired length
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if ([afterDecimal length] < decimals) {
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afterDecimal = [afterDecimal stringByPaddingToLength:decimals withString:@"0" startingAtIndex:0];
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} else {
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afterDecimal = [afterDecimal substringWithRange:NSMakeRange(0, decimals)];
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}
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mpz_clear(arctan5);
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mpz_clear(arctan239);
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mpz_clear(pi);
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return [NSString stringWithFormat:@"%@.%@", beforeDecimal, afterDecimal];
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}
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int main(int argc, const char* argv[]) {
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@autoreleasepool {
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int decimals = 100;
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if (argc > 1) {
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decimals = atoi(argv[1]);
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if (decimals < 1) {
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decimals = 100;
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}
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}
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NSString* pi = calculatePi(decimals);
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printf("%s\n", [pi UTF8String]);
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}
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return 0;
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} |