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computePi.hpp

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+#pragma once
+
+// ------------------------------------------------------------------
+//
+// Adapted From: http://stackoverflow.com/questions/5905822/function-to-find-the-nth-digit-of-pi
+// Other references:
+//		http://bellard.org/pi/pi_n2/pi_n2.html
+//		https://web.archive.org/web/20150627225748/http://en.literateprograms.org/Pi_with_the_BBP_formula_%28Python%29
+//
+// ------------------------------------------------------------------
+/*
+* Computation of the n'th decimal digit of \pi with very little memory.
+* Written by Fabrice Bellard on January 8, 1997.
+*
+* We use a slightly modified version of the method described by Simon
+* Plouffe in "On the Computation of the n'th decimal digit of various
+* transcendental numbers" (November 1996). We have modified the algorithm
+* to get a running time of O(n^2) instead of O(n^3log(n)^3).
+*
+* This program uses mostly integer arithmetic. It may be slow on some
+* hardwares where integer multiplications and divisons must be done
+* by software. We have supposed that 'int' has a size of 32 bits. If
+* your compiler supports 'long long' integers of 64 bits, you may use
+* the integer version of 'mul_mod' (see HAS_LONG_LONG).
+*/
+
+/* uncomment the following line to use 'long long' integers */
+/* #define HAS_LONG_LONG */
+
+//#ifdef HAS_LONG_LONG
+	#define mul_mod(a,b,m) (( (long long) (a) * (long long) (b) ) % (m))
+//#else
+//	#define mul_mod(a,b,m) std::fmod( (double) a * (double) b, m)
+//#endif
+
+unsigned int computePiDigit(int n);
+unsigned long long piDigitHex(unsigned long long n);