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Author: garyexplains

leibniz_fixedpoint.c

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+// Copyright (C) <2024>, Gary Sims
+// All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// 1. Redistributions of source code must retain the above copyright notice, this
+//   list of conditions and the following disclaimer.
+// 2. Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+// WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+// DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
+// ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+// (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+// LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+// ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
+
+#include <stdio.h>
+#include <stdint.h>
+
+#define FIXED_FACTOR 1000000000000000000
+#define FIXED_PLACES 18
+
+void print_fixed_point_r(uint64_t n, int i) {
+    uint64_t num = n;
+    int c;
+
+    c = num % 10;
+    num = num / 10;
+    if((i<FIXED_PLACES) || (num>0))
+        print_fixed_point_r(num, i + 1);
+    if (i == FIXED_PLACES) {
+        if(num==0)
+            printf("0");
+        printf(".");
+    }
+    printf("%c", c + '0');
+}
+
+void print_fixed_point(uint64_t n) {
+    print_fixed_point_r(n, 1);
+}
+
+uint64_t set_fixed_point_int(uint64_t n) {
+    return n * FIXED_FACTOR;
+}
+
+// decimal expansion for positive fixed point rational numbers
+uint64_t fixed_point_dec_expansion(uint64_t dividend, uint64_t divisor) {
+    uint64_t result = 0;
+    if (divisor == 0)
+        return 0;
+
+    uint64_t quotient = dividend / divisor;
+    result = result + quotient;
+    result = result * 10;
+
+    // Start calculating the fractional part
+    uint64_t remainder = dividend % divisor;
+    
+    for (int i = 0; i < FIXED_PLACES-1; i++) {
+        // Multiply the remainder by 10 for the next digit
+        remainder = remainder * 10;
+        int digit = remainder / divisor;
+        result = result + digit;
+        result = result * 10;
+        remainder = remainder % divisor;
+    }
+    return result;
+}
+
+#define ITERATIONS 10000000
+
+void main(void) {
+    uint64_t pi = set_fixed_point_int(1);
+
+    int series = 3;
+    for(int i=0;i<ITERATIONS;i++) {
+        pi = pi - fixed_point_dec_expansion(1, series);
+        pi = pi + fixed_point_dec_expansion(1, series+2);
+        series = series + 4;
+    }
+
+    print_fixed_point(pi*4); printf("\n");
+}