mode math algorithms to math folder

2026-04-04 02:59:43 +08:00 · 2020-05-27 19:00:20 -04:00
parent a53ba4b856
commit e480c049be
4 changed files with 0 additions and 0 deletions
--- a/math/fibonacci_large.cpp
+++ b/math/fibonacci_large.cpp
@@ -0,0 +1,84 @@
+/**
+ * @file
+ * @brief Computes N^th Fibonacci number given as
+ * input argument. Uses custom build arbitrary integers library
+ * to perform additions and other operations.
+ *
+ * Took 0.608246 seconds to compute 50,000^th Fibonacci
+ * number that contains 10450 digits!
+ *
+ * @see fibonacci.cpp, fibonacci_fast.cpp
+ */
+
+#include <cinttypes>
+#include <ctime>
+#include <iostream>
+
+#include "./large_number.h"
+
+/** Compute fibonacci numbers using the relation
+ * \f[f(n)=f(n-1)+f(n-2)\f]
+ * and returns the result as a large_number type.
+ */
+large_number fib(uint64_t n) {
+    large_number f0(1);
+    large_number f1(1);
+
+    do {
+        large_number f2 = f1;
+        f1 += f0;
+        f0 = f2;
+        n--;
+    } while (n > 2);  // since we start from 2
+
+    return f1;
+}
+
+int main(int argc, char *argv[]) {
+    uint64_t N;
+    if (argc == 2) {
+        N = strtoull(argv[1], NULL, 10);
+    } else {
+        std::cout << "Enter N: ";
+        std::cin >> N;
+    }
+
+    clock_t start_time = std::clock();
+    large_number result = fib(N);
+    clock_t end_time = std::clock();
+    double time_taken = static_cast<double>(end_time - start_time) /
+                        static_cast<double>(CLOCKS_PER_SEC);
+
+    std::cout << std::endl
+              << N << "^th Fibonacci number: " << result << std::endl
+              << "Number of digits: " << result.num_digits() << std::endl
+              << "Time taken: " << std::scientific << time_taken << " s"
+              << std::endl;
+
+    N = 5000;
+    if (fib(N) ==
+        large_number(
+            "387896845438832563370191630832590531208212771464624510616059721489"
+            "555013904403709701082291646221066947929345285888297381348310200895"
+            "498294036143015691147893836421656394410691021450563413370655865623"
+            "825465670071252592990385493381392883637834751890876297071203333705"
+            "292310769300851809384980180384781399674888176555465378829164426891"
+            "298038461377896902150229308247566634622492307188332480328037503913"
+            "035290330450584270114763524227021093463769910400671417488329842289"
+            "149127310405432875329804427367682297724498774987455569190770388063"
+            "704683279481135897373999311010621930814901857081539785437919530561"
+            "751076105307568878376603366735544525884488624161921055345749367589"
+            "784902798823435102359984466393485325641195222185956306047536464547"
+            "076033090242080638258492915645287629157575914234380914230291749108"
+            "898415520985443248659407979357131684169286803954530954538869811466"
+            "508206686289742063932343848846524098874239587380197699382031717420"
+            "893226546887936400263079778005875912967138963421425257911687275560"
+            "0360311370547754724604639987588046985178408674382863125"))
+        std::cout << "Test for " << N << "^th Fibonacci number passed!"
+                  << std::endl;
+    else
+        std::cerr << "Test for " << N << "^th Fibonacci number failed!"
+                  << std::endl;
+
+    return 0;
+}