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