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-rw-r--r--memory/jemalloc/src/test/unit/smoothstep.c106
1 files changed, 106 insertions, 0 deletions
diff --git a/memory/jemalloc/src/test/unit/smoothstep.c b/memory/jemalloc/src/test/unit/smoothstep.c
new file mode 100644
index 000000000..4cfb21343
--- /dev/null
+++ b/memory/jemalloc/src/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));
+}