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Check in ruler summation experiments
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Justine Tunney
parent
3dab207351
commit
8cdb3e136b
3 changed files with 474 additions and 54 deletions
289
test/libc/tinymath/fdot_test.cc
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289
test/libc/tinymath/fdot_test.cc
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#include "libc/assert.h"
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#include "libc/calls/struct/timespec.h"
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#include "libc/intrin/bsr.h"
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#include "libc/macros.internal.h"
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#include "libc/math.h"
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#include "libc/mem/gc.h"
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#include "libc/mem/leaks.h"
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#include "libc/mem/mem.h"
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#include "libc/runtime/runtime.h"
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#include "libc/stdio/stdio.h"
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#include "libc/x/xasprintf.h"
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#define EXPENSIVE_TESTS 0
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#define CHUNK 8
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#define FASTMATH __attribute__((__optimize__("-O3,-ffast-math")))
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#define PORTABLE __target_clones("avx512f,avx")
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static unsigned long long lcg = 1;
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int rand32(void) {
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/* Knuth, D.E., "The Art of Computer Programming," Vol 2,
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Seminumerical Algorithms, Third Edition, Addison-Wesley, 1998,
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p. 106 (line 26) & p. 108 */
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lcg *= 6364136223846793005;
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lcg += 1442695040888963407;
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return lcg >> 32;
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}
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float float01(unsigned x) { // (0,1)
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return 1.f / 8388608 * ((x >> 9) + .5f);
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}
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float numba(void) { // (-1,1)
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return float01(rand32()) * 2 - 1;
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}
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PORTABLE float fdotf_dubble(const float *A, const float *B, size_t n) {
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double s = 0;
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for (size_t i = 0; i < n; ++i)
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s = fma(A[i], B[i], s);
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return s;
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}
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float fdotf_kahan(const float *A, const float *B, size_t n) {
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size_t i;
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float err, sum, t, y;
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sum = err = 0;
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for (i = 0; i < n; ++i) {
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y = A[i] * B[i] - err;
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t = sum + y;
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err = (t - sum) - y;
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sum = t;
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}
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return sum;
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}
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float fdotf_naive(const float *A, const float *B, size_t n) {
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float s = 0;
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for (size_t i = 0; i < n; ++i)
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s = fmaf(A[i], B[i], s);
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return s;
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}
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#define fdotf_naive_tester(A, B, n, tol) \
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do { \
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float err = fabsf(fdotf_naive(A, B, n) - fdotf_dubble(A, B, n)); \
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if (err > tol) { \
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printf("%s:%d: error: n=%zu failed %g\n", __FILE__, __LINE__, (size_t)n, \
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err); \
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exit(1); \
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} \
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} while (0)
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void test_fdotf_naive(void) {
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float *A = new float[2 * 1024 * 1024 + 1];
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float *B = new float[2 * 1024 * 1024 + 1];
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for (size_t i = 0; i < 2 * 1024 * 1024 + 1; ++i) {
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A[i] = numba();
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B[i] = numba();
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}
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for (size_t n = 0; n < 1024; ++n)
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fdotf_naive_tester(A, B, n, 1e-4);
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#if EXPENSIVE_TESTS
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fdotf_naive_tester(A, B, 128 * 1024, 1e-2);
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fdotf_naive_tester(A, B, 256 * 1024, 1e-2);
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fdotf_naive_tester(A, B, 1024 * 1024, 1e-1);
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fdotf_naive_tester(A, B, 1024 * 1024 - 1, 1e-1);
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fdotf_naive_tester(A, B, 1024 * 1024 + 1, 1e-1);
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fdotf_naive_tester(A, B, 2 * 1024 * 1024, 1e-1);
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fdotf_naive_tester(A, B, 2 * 1024 * 1024 - 1, 1e-1);
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fdotf_naive_tester(A, B, 2 * 1024 * 1024 + 1, 1e-1);
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#endif
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delete[] B;
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delete[] A;
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}
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template <int N>
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forceinline float hdot(const float *A, const float *B) {
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return hdot<N / 2>(A, B) + hdot<N / 2>(A + N / 2, B + N / 2);
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}
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template <>
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forceinline float hdot<1>(const float *A, const float *B) {
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return A[0] * B[0];
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}
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float fdotf_recursive(const float *A, const float *B, size_t n) {
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if (n > 32) {
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float x, y;
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x = fdotf_recursive(A, B, n / 2);
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y = fdotf_recursive(A + n / 2, B + n / 2, n - n / 2);
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return x + y;
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} else {
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float s;
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size_t i;
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for (s = i = 0; i < n; ++i)
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s = fmaf(A[i], B[i], s);
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return s;
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}
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}
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FASTMATH float fdotf_ruler(const float *A, const float *B, size_t n) {
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int rule, step = 2;
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size_t chunk, sp = 0;
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float stack[bsr(n / CHUNK + 1) + 1];
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for (chunk = 0; chunk + CHUNK * 4 <= n; chunk += CHUNK * 4, step += 2) {
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float sum = 0;
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for (size_t elem = 0; elem < CHUNK * 4; ++elem)
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sum += A[chunk + elem] * B[chunk + elem];
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for (rule = bsr(step & -step); --rule;)
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sum += stack[--sp];
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stack[sp++] = sum;
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}
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float res = 0;
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while (sp)
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res += stack[--sp];
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for (; chunk < n; ++chunk)
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res += A[chunk] * B[chunk];
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return res;
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}
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#define fdotf_ruler_tester(A, B, n, tol) \
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do { \
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float err = fabsf(fdotf_ruler(A, B, n) - fdotf_dubble(A, B, n)); \
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if (err > tol) { \
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printf("%s:%d: error: n=%zu failed %g\n", __FILE__, __LINE__, (size_t)n, \
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err); \
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exit(1); \
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} \
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} while (0)
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void test_fdotf_ruler(void) {
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float *A = new float[10 * 1024 * 1024 + 1];
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float *B = new float[10 * 1024 * 1024 + 1];
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for (size_t i = 0; i < 10 * 1024 * 1024 + 1; ++i) {
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A[i] = numba();
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B[i] = numba();
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}
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fdotf_ruler_tester(A, B, 96, 1e-6);
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for (size_t n = 0; n < 4096; ++n)
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fdotf_ruler_tester(A, B, n, 1e-5);
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#if EXPENSIVE_TESTS
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fdotf_ruler_tester(A, B, 128 * 1024, 1e-4);
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fdotf_ruler_tester(A, B, 256 * 1024, 1e-4);
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fdotf_ruler_tester(A, B, 1024 * 1024, 1e-3);
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fdotf_ruler_tester(A, B, 1024 * 1024 - 1, 1e-3);
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fdotf_ruler_tester(A, B, 1024 * 1024 + 1, 1e-3);
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fdotf_ruler_tester(A, B, 2 * 1024 * 1024, 1e-3);
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fdotf_ruler_tester(A, B, 2 * 1024 * 1024 - 1, 1e-3);
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fdotf_ruler_tester(A, B, 2 * 1024 * 1024 + 1, 1e-3);
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fdotf_ruler_tester(A, B, 8 * 1024 * 1024, 1e-3);
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fdotf_ruler_tester(A, B, 10 * 1024 * 1024, 1e-3);
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#endif
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delete[] B;
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delete[] A;
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}
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PORTABLE float fdotf_hefty(const float *A, const float *B, size_t n) {
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unsigned i, par, len = 0;
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float sum, res[n / CHUNK + 1];
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for (res[0] = i = 0; i + CHUNK <= n; i += CHUNK)
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res[len++] = hdot<CHUNK>(A + i, B + i);
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if (i < n) {
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for (sum = 0; i < n; i++)
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sum = fmaf(A[i], B[i], sum);
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res[len++] = sum;
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}
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for (par = len >> 1; par; par >>= 1, len >>= 1) {
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for (i = 0; i < par; ++i)
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res[i] += res[par + i];
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if (len & 1)
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res[par - 1] += res[len - 1];
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}
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return res[0];
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}
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#define fdotf_hefty_tester(A, B, n, tol) \
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do { \
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float err = fabsf(fdotf_hefty(A, B, n) - fdotf_dubble(A, B, n)); \
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if (err > tol) { \
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printf("%s:%d: error: n=%zu failed %g\n", __FILE__, __LINE__, (size_t)n, \
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err); \
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exit(1); \
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} \
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} while (0)
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void test_fdotf_hefty(void) {
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float *A = new float[10 * 1024 * 1024 + 1];
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float *B = new float[10 * 1024 * 1024 + 1];
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for (size_t i = 0; i < 10 * 1024 * 1024 + 1; ++i) {
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A[i] = numba();
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B[i] = numba();
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}
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for (size_t n = 0; n < 1024; ++n)
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fdotf_hefty_tester(A, B, n, 1e-5);
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#if EXPENSIVE_TESTS
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fdotf_hefty_tester(A, B, 128 * 1024, 1e-4);
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fdotf_hefty_tester(A, B, 256 * 1024, 1e-4);
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fdotf_hefty_tester(A, B, 1024 * 1024, 1e-3);
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fdotf_hefty_tester(A, B, 1024 * 1024 - 1, 1e-3);
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fdotf_hefty_tester(A, B, 1024 * 1024 + 1, 1e-3);
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fdotf_hefty_tester(A, B, 2 * 1024 * 1024, 1e-3);
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fdotf_hefty_tester(A, B, 2 * 1024 * 1024 - 1, 1e-3);
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fdotf_hefty_tester(A, B, 2 * 1024 * 1024 + 1, 1e-3);
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fdotf_hefty_tester(A, B, 8 * 1024 * 1024, 1e-3);
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fdotf_hefty_tester(A, B, 10 * 1024 * 1024, 1e-3);
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#endif
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delete[] B;
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delete[] A;
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}
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float nothing(float x) {
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return x;
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}
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float (*barrier)(float) = nothing;
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#define BENCH(ITERATIONS, WORK_PER_RUN, CODE) \
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do { \
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struct timespec start = timespec_real(); \
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for (int __i = 0; __i < ITERATIONS; ++__i) { \
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asm volatile("" ::: "memory"); \
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CODE; \
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} \
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long long work = (WORK_PER_RUN) * (ITERATIONS); \
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long nanos = \
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(timespec_tonanos(timespec_sub(timespec_real(), start)) + work - 1) / \
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(double)work; \
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printf("%8ld ns %2dx %s\n", nanos, (ITERATIONS), #CODE); \
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} while (0)
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int main() {
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ShowCrashReports();
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#if EXPENSIVE_TESTS
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size_t n = 512 * 1024;
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#else
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size_t n = 1024;
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#endif
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float *A = new float[n];
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float *B = new float[n];
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for (size_t i = 0; i < n; ++i) {
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A[i] = numba();
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B[i] = numba();
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}
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float kahan, naive, dubble, recursive, hefty, ruler;
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test_fdotf_naive();
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test_fdotf_hefty();
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test_fdotf_ruler();
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BENCH(20, 1, (kahan = barrier(fdotf_kahan(A, B, n))));
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BENCH(20, 1, (dubble = barrier(fdotf_dubble(A, B, n))));
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BENCH(20, 1, (naive = barrier(fdotf_naive(A, B, n))));
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BENCH(20, 1, (recursive = barrier(fdotf_recursive(A, B, n))));
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BENCH(20, 1, (ruler = barrier(fdotf_ruler(A, B, n))));
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BENCH(20, 1, (hefty = barrier(fdotf_hefty(A, B, n))));
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printf("dubble = %f (%g)\n", dubble, fabs(dubble - dubble));
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printf("kahan = %f (%g)\n", kahan, fabs(kahan - dubble));
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printf("naive = %f (%g)\n", naive, fabs(naive - dubble));
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printf("recursive = %f (%g)\n", recursive, fabs(recursive - dubble));
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printf("ruler = %f (%g)\n", ruler, fabs(ruler - dubble));
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printf("hefty = %f (%g)\n", hefty, fabs(hefty - dubble));
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delete[] B;
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delete[] A;
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CheckForMemoryLeaks();
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}
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