Implement smoothstep table generation.

Check in a generated smootherstep table as smoothstep.h rather than
generating it at configure time, since not all systems (e.g. Windows)
have dc.

1 files changed, 106 insertions, 0 deletions

diff --git a/test/unit/smoothstep.c b/test/unit/smoothstep.c
new file mode 100644
index 0000000..4cfb213
--- /dev/null
+++ b/test/unit/smoothstep.c
@@ -0,0 +1,106 @@
+#include "test/jemalloc_test.h"
+
+static const uint64_t smoothstep_tab[] = {
+#define	STEP(step, h, x, y) \
+	h,
+	SMOOTHSTEP
+#undef STEP
+};
+
+TEST_BEGIN(test_smoothstep_integral)
+{
+	uint64_t sum, min, max;
+	unsigned i;
+
+	/*
+	 * The integral of smoothstep in the [0..1] range equals 1/2.  Verify
+	 * that the fixed point representation's integral is no more than
+	 * rounding error distant from 1/2.  Regarding rounding, each table
+	 * element is rounded down to the nearest fixed point value, so the
+	 * integral may be off by as much as SMOOTHSTEP_NSTEPS ulps.
+	 */
+	sum = 0;
+	for (i = 0; i < SMOOTHSTEP_NSTEPS; i++)
+		sum += smoothstep_tab[i];
+
+	max = (KQU(1) << (SMOOTHSTEP_BFP-1)) * (SMOOTHSTEP_NSTEPS+1);
+	min = max - SMOOTHSTEP_NSTEPS;
+
+	assert_u64_ge(sum, min,
+	    "Integral too small, even accounting for truncation");
+	assert_u64_le(sum, max, "Integral exceeds 1/2");
+	if (false) {
+		malloc_printf("%"FMTu64" ulps under 1/2 (limit %d)\n",
+		    max - sum, SMOOTHSTEP_NSTEPS);
+	}
+}
+TEST_END
+
+TEST_BEGIN(test_smoothstep_monotonic)
+{
+	uint64_t prev_h;
+	unsigned i;
+
+	/*
+	 * The smoothstep function is monotonic in [0..1], i.e. its slope is
+	 * non-negative.  In practice we want to parametrize table generation
+	 * such that piecewise slope is greater than zero, but do not require
+	 * that here.
+	 */
+	prev_h = 0;
+	for (i = 0; i < SMOOTHSTEP_NSTEPS; i++) {
+		uint64_t h = smoothstep_tab[i];
+		assert_u64_ge(h, prev_h, "Piecewise non-monotonic, i=%u", i);
+		prev_h = h;
+	}
+	assert_u64_eq(smoothstep_tab[SMOOTHSTEP_NSTEPS-1],
+	    (KQU(1) << SMOOTHSTEP_BFP), "Last step must equal 1");
+}
+TEST_END
+
+TEST_BEGIN(test_smoothstep_slope)
+{
+	uint64_t prev_h, prev_delta;
+	unsigned i;
+
+	/*
+	 * The smoothstep slope strictly increases until x=0.5, and then
+	 * strictly decreases until x=1.0.  Verify the slightly weaker
+	 * requirement of monotonicity, so that inadequate table precision does
+	 * not cause false test failures.
+	 */
+	prev_h = 0;
+	prev_delta = 0;
+	for (i = 0; i < SMOOTHSTEP_NSTEPS / 2 + SMOOTHSTEP_NSTEPS % 2; i++) {
+		uint64_t h = smoothstep_tab[i];
+		uint64_t delta = h - prev_h;
+		assert_u64_ge(delta, prev_delta,
+		    "Slope must monotonically increase in 0.0 <= x <= 0.5, "
+		    "i=%u", i);
+		prev_h = h;
+		prev_delta = delta;
+	}
+
+	prev_h = KQU(1) << SMOOTHSTEP_BFP;
+	prev_delta = 0;
+	for (i = SMOOTHSTEP_NSTEPS-1; i >= SMOOTHSTEP_NSTEPS / 2; i--) {
+		uint64_t h = smoothstep_tab[i];
+		uint64_t delta = prev_h - h;
+		assert_u64_ge(delta, prev_delta,
+		    "Slope must monotonically decrease in 0.5 <= x <= 1.0, "
+		    "i=%u", i);
+		prev_h = h;
+		prev_delta = delta;
+	}
+}
+TEST_END
+
+int
+main(void)
+{
+
+	return (test(
+	    test_smoothstep_integral,
+	    test_smoothstep_monotonic,
+	    test_smoothstep_slope));
+}