jemalloc/test/unit/smoothstep.c

#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));
}