From 11da511c784eca003deb90c23570f0873954e0de Mon Sep 17 00:00:00 2001
From: Duncan Wilkie <antigravityd@gmail.com>
Date: Sat, 18 Nov 2023 06:11:09 -0600
Subject: Initial commit.

---
 ic-reals-6.3/math-lib/pi.c | 151 +++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 151 insertions(+)
 create mode 100644 ic-reals-6.3/math-lib/pi.c

(limited to 'ic-reals-6.3/math-lib/pi.c')

diff --git a/ic-reals-6.3/math-lib/pi.c b/ic-reals-6.3/math-lib/pi.c
new file mode 100644
index 0000000..15c32d2
--- /dev/null
+++ b/ic-reals-6.3/math-lib/pi.c
@@ -0,0 +1,151 @@
+/*
+ * Copyright (C) 2000, Imperial College
+ *
+ * This file is part of the Imperial College Exact Real Arithmetic Library.
+ * See the copyright notice included in the distribution for conditions
+ * of use.
+ */
+
+#include <stdio.h>
+#include "real.h"
+#include "real-impl.h"
+
+static mpz_t k;
+
+Real Pi;
+
+static void piCont();
+static void nextMatrix(Tensor, int);
+
+void
+initPi()
+{
+	Real sq, cls;
+	DigsX *digsX;
+	TenXY *tenXY;
+	static int doneInit;
+	void force_To_DigsX_From_TenXY_Entry();
+
+	if (!doneInit) {
+		registerForceFunc(piCont, "piCont", 2);
+		doneInit++;
+	}
+
+	mpz_init_set_str(k, "10939058860032000", 10);
+
+	sq = sqrt_QInt(10005, 1);
+	cls = (Real) allocCls(piCont, (void *) 0);
+	cls->gen.tag.isSigned = FALSE;
+
+	tenXY = (TenXY *) div_R_R(sq, cls);
+	tenXY->forceY = piCont;
+
+	digsX = allocDigsX();
+	digsX->x = (Real) tenXY;
+	digsX->force = force_To_DigsX_From_TenXY_Entry;
+
+#ifdef DAVINCI
+		beginGraphUpdate();
+		newEdgeToOnlyChild(digsX, tenXY);
+		endGraphUpdate();
+#endif
+
+	Pi = (Real) digsX;
+}
+
+/*
+ * It might be possible compute the next matrix in the sequence
+ * in terms of the previous matrix. This would mean having much more
+ * state but presumably much quicker.
+ */
+static void
+piCont()
+{
+	TenXY *tenXY;
+	Cls *cls;
+	int digitsNeeded;
+	int n;
+
+	tenXY = (TenXY *) POP;
+	digitsNeeded = (int) POP;
+
+	cls = (Cls *) tenXY->y;
+	n = (int) cls->userData;
+
+	/*
+	 * The two constants below have been determined empirically. The second
+	 * may be off by one (ie 47) in some circumstances.
+	 */
+	while (digitsNeeded > 0) {
+		nextMatrix(tenXY->ten, n);
+		if (n == 0)
+			digitsNeeded -= 27;
+		else
+			digitsNeeded -= 46;
+		n +=1;
+	}
+	cls->userData = (void *) n;
+}
+
+static void
+nextMatrix(Tensor ten, int n)
+{
+	SmallMatrix smallMat;
+
+	if (n == 0) {
+		smallMat[0][0] = 6795705;
+		smallMat[0][1] = 213440;
+		smallMat[1][0] = 6795704;
+		smallMat[1][1] = 213440;
+		multVectorPairTimesSmallMatrix(ten[0], ten[1], smallMat);
+		multVectorPairTimesSmallMatrix(ten[2], ten[3], smallMat);
+	}
+	else {
+		/* b = 2n - 1 */
+		mpz_set_ui(tmpb_z, n);
+		mpz_mul_2exp(tmpb_z, tmpb_z, 1);
+		mpz_sub_ui(tmpb_z, tmpb_z, 1);
+	
+		/* tmp = 6n - 5, tmpf_z = 6n */
+		mpz_set_ui(tmpa_z, n);
+		mpz_mul_ui(tmpa_z, tmpa_z, 6);
+		mpz_set(tmpf_z, tmpa_z);
+		mpz_sub_ui(tmpa_z, tmpa_z, 5);
+	
+		/* tmpf_z = 6n - 1 */
+		mpz_sub_ui(tmpf_z, tmpf_z, 1);
+	
+		/* b = (2n - 1) * (6n - 5) * (6n - 1) */
+		mpz_mul(tmpb_z, tmpb_z, tmpa_z);
+		mpz_mul(tmpb_z, tmpb_z, tmpf_z);
+	
+		/* c = b*(545140134n + 13591409) */
+		mpz_set_ui(tmpa_z, 545140134);
+		mpz_mul_ui(tmpa_z, tmpa_z, n);
+		mpz_add_ui(tmpa_z, tmpa_z, 13591409);
+		mpz_mul(tmpc_z, tmpb_z, tmpa_z);
+	
+		/* d = b * (n + 1) */
+		mpz_set_ui(tmpd_z, n + 1);
+		mpz_mul(tmpd_z, tmpd_z, tmpb_z);
+	
+		/* e = 10939058860032000*n^4 */
+		mpz_set_ui(tmpe_z, n);
+		mpz_mul(tmpe_z, tmpe_z, tmpe_z);
+		mpz_mul(tmpe_z, tmpe_z, tmpe_z);
+		mpz_mul(tmpe_z, tmpe_z, k);
+	
+		mpz_sub(bigTmpMat[0][0], tmpe_z, tmpd_z);
+		mpz_set(bigTmpMat[1][1], bigTmpMat[0][0]);
+		mpz_add(bigTmpMat[0][1], tmpe_z, tmpd_z);
+		mpz_set(bigTmpMat[1][0], bigTmpMat[0][1]);
+	
+		mpz_sub(bigTmpMat[0][0], bigTmpMat[0][0], tmpc_z);
+		mpz_add(bigTmpMat[0][1], bigTmpMat[0][1], tmpc_z);
+		mpz_sub(bigTmpMat[1][0], bigTmpMat[1][0], tmpc_z);
+		mpz_add(bigTmpMat[1][1], bigTmpMat[1][1], tmpc_z);
+	
+		multVectorPairTimesMatrix(ten[0], ten[1], bigTmpMat);
+		multVectorPairTimesMatrix(ten[2], ten[3], bigTmpMat);
+	}
+}
-- 
cgit v1.2.3