/*
* 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;
expect_u64_ge(sum, min,
"Integral too small, even accounting for truncation");
expect_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
/*
* 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];
expect_u64_ge(h, prev_h, "Piecewise non-monotonic, i=%u", i);
prev_h = h;
}
expect_u64_eq(smoothstep_tab[SMOOTHSTEP_NSTEPS-1],
(KQU(1) << SMOOTHSTEP_BFP), "Last step must equal 1");
}
TEST_END
/*
* 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;
expect_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;
expect_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);
}
