Data commit

Task/Safe-addition/C/safe-addition-1.c

@@ -0,0 +1,50 @@
+#include <fenv.h>	/* fegetround(), fesetround() */
+#include <stdio.h>	/* printf() */
+
+/*
+ * Calculates an interval for a + b.
+ *   interval[0] <= a + b
+ *   a + b <= interval[1]
+ */
+void
+safe_add(volatile double interval[2], volatile double a, volatile double b)
+{
+#pragma STDC FENV_ACCESS ON
+	unsigned int orig;
+
+	orig = fegetround();
+	fesetround(FE_DOWNWARD);	/* round to -infinity */
+	interval[0] = a + b;
+	fesetround(FE_UPWARD);		/* round to +infinity */
+	interval[1] = a + b;
+	fesetround(orig);
+}
+
+int
+main()
+{
+	const double nums[][2] = {
+		{1, 2},
+		{0.1, 0.2},
+		{1e100, 1e-100},
+		{1e308, 1e308},
+	};
+	double ival[2];
+	int i;
+
+	for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) {
+		/*
+		 * Calculate nums[i][0] + nums[i][1].
+		 */
+		safe_add(ival, nums[i][0], nums[i][1]);
+
+		/*
+		 * Print the result. %.17g gives the best output.
+		 * %.16g or plain %g gives not enough digits.
+		 */
+		printf("%.17g + %.17g =\n", nums[i][0], nums[i][1]);
+		printf("    [%.17g, %.17g]\n", ival[0], ival[1]);
+		printf("    size %.17g\n\n", ival[1] - ival[0]);
+	}
+	return 0;
+}

Task/Safe-addition/C/safe-addition-2.c

@@ -0,0 +1,49 @@
+#include <float.h>	/* _controlfp() */
+#include <stdio.h>	/* printf() */
+
+/*
+ * Calculates an interval for a + b.
+ *   interval[0] <= a + b
+ *   a + b <= interval[1]
+ */
+void
+safe_add(volatile double interval[2], volatile double a, volatile double b)
+{
+	unsigned int orig;
+
+	orig = _controlfp(0, 0);
+	_controlfp(_RC_DOWN, _MCW_RC);	/* round to -infinity */
+	interval[0] = a + b;
+	_controlfp(_RC_UP, _MCW_RC);	/* round to +infinity */
+	interval[1] = a + b;
+	_controlfp(orig, _MCW_RC);
+}
+
+int
+main()
+{
+	const double nums[][2] = {
+		{1, 2},
+		{0.1, 0.2},
+		{1e100, 1e-100},
+		{1e308, 1e308},
+	};
+	double ival[2];
+	int i;
+
+	for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) {
+		/*
+		 * Calculate nums[i][0] + nums[i][1].
+		 */
+		safe_add(ival, nums[i][0], nums[i][1]);
+
+		/*
+		 * Print the result. %.17g gives the best output.
+		 * %.16g or plain %g gives not enough digits.
+		 */
+		printf("%.17g + %.17g =\n", nums[i][0], nums[i][1]);
+		printf("    [%.17g, %.17g]\n", ival[0], ival[1]);
+		printf("    size %.17g\n\n", ival[1] - ival[0]);
+	}
+	return 0;
+}

Task/Safe-addition/C/safe-addition-3.c

@@ -0,0 +1,49 @@
+#include <ieeefp.h>	/* fpsetround() */
+#include <stdio.h>	/* printf() */
+
+/*
+ * Calculates an interval for a + b.
+ *   interval[0] <= a + b
+ *   a + b <= interval[1]
+ */
+void
+safe_add(volatile double interval[2], volatile double a, volatile double b)
+{
+	fp_rnd orig;
+
+	orig = fpsetround(FP_RM);	/* round to -infinity */
+	interval[0] = a + b;
+	fpsetround(FP_RP);		/* round to +infinity */
+	interval[1] = a + b;
+	fpsetround(orig);
+}
+
+int
+main()
+{
+	const double nums[][2] = {
+		{1, 2},
+		{0.1, 0.2},
+		{1e100, 1e-100},
+		{1e308, 1e308},
+	};
+	double ival[2];
+	int i;
+
+	for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) {
+		/*
+		 * Calculate nums[i][0] + nums[i][1].
+		 */
+		safe_add(ival, nums[i][0], nums[i][1]);
+
+		/*
+		 * Print the result. With OpenBSD libc, %.17g gives
+		 * the best output; %.16g or plain %g gives not enough
+		 * digits.
+		 */
+		printf("%.17g + %.17g =\n", nums[i][0], nums[i][1]);
+		printf("    [%.17g, %.17g]\n", ival[0], ival[1]);
+		printf("    size %.17g\n\n", ival[1] - ival[0]);
+	}
+	return 0;
+}