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-rw-r--r--test/Unit/ppc/qmul_test.c793
1 files changed, 793 insertions, 0 deletions
diff --git a/test/Unit/ppc/qmul_test.c b/test/Unit/ppc/qmul_test.c
new file mode 100644
index 000000000..fc5b46d33
--- /dev/null
+++ b/test/Unit/ppc/qmul_test.c
@@ -0,0 +1,793 @@
+#include <stdio.h>
+#include "DD.h"
+
+long double __gcc_qmul(long double x, long double y);
+
+double testAccuracy();
+int testEdgeCases();
+
+int main(int argc, char *argv[]) {
+ if (testEdgeCases())
+ return 1;
+
+ if (testAccuracy() > 2.0)
+ return 1;
+
+ return 0;
+}
+
+struct testVector {
+ double xhi; double xlo;
+ double yhi; double ylo;
+ double rhi; double rlo;
+};
+
+#define INFINITY __builtin_inf()
+#define HUGE 0x1.fffffffffffffp1023
+#define QNAN __builtin_nan("")
+
+const struct testVector edgeCases[] = {
+{ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 },
+{ -0.0, 0.0, 0.0, 0.0, -0.0, 0.0 },
+{ 0.0, 0.0, -0.0, 0.0, -0.0, 0.0 },
+{ -0.0, 0.0, -0.0, 0.0, 0.0, 0.0 },
+
+{ INFINITY, 0.0, 0.0, 0.0, QNAN, 0.0 },
+{ -INFINITY, 0.0, 0.0, 0.0, QNAN, 0.0 },
+{ INFINITY, 0.0, -0.0, 0.0, QNAN, 0.0 },
+{ -INFINITY, 0.0, -0.0, 0.0, QNAN, 0.0 },
+{ INFINITY, 0.0, 1.0, 0.0, INFINITY, 0.0 },
+{ -INFINITY, 0.0, 1.0, 0.0, -INFINITY, 0.0 },
+{ INFINITY, 0.0, -1.0, 0.0, -INFINITY, 0.0 },
+{ -INFINITY, 0.0, -1.0, 0.0, INFINITY, 0.0 },
+{ INFINITY, 0.0, HUGE, 0.0, INFINITY, 0.0 },
+{ -INFINITY, 0.0, HUGE, 0.0, -INFINITY, 0.0 },
+{ INFINITY, 0.0, -HUGE, 0.0, -INFINITY, 0.0 },
+{ -INFINITY, 0.0, -HUGE, 0.0, INFINITY, 0.0 },
+{ INFINITY, 0.0, INFINITY, 0.0, INFINITY, 0.0 },
+{ -INFINITY, 0.0, INFINITY, 0.0, -INFINITY, 0.0 },
+{ INFINITY, 0.0, -INFINITY, 0.0, -INFINITY, 0.0 },
+{ -INFINITY, 0.0, -INFINITY, 0.0, INFINITY, 0.0 },
+{ 0.0, 0.0, INFINITY, 0.0, QNAN, 0.0 },
+{ 0.0, 0.0, -INFINITY, 0.0, QNAN, 0.0 },
+{ -0.0, 0.0, INFINITY, 0.0, QNAN, 0.0 },
+{ -0.0, 0.0, -INFINITY, 0.0, QNAN, 0.0 },
+{ 1.0, 0.0, INFINITY, 0.0, INFINITY, 0.0 },
+{ 1.0, 0.0, -INFINITY, 0.0, -INFINITY, 0.0 },
+{ -1.0, 0.0, INFINITY, 0.0, -INFINITY, 0.0 },
+{ -1.0, 0.0, -INFINITY, 0.0, INFINITY, 0.0 },
+{ HUGE, 0.0, INFINITY, 0.0, INFINITY, 0.0 },
+{ HUGE, 0.0, -INFINITY, 0.0, -INFINITY, 0.0 },
+{ -HUGE, 0.0, INFINITY, 0.0, -INFINITY, 0.0 },
+{ -HUGE, 0.0, -INFINITY, 0.0, INFINITY, 0.0 },
+
+{ QNAN, 0.0, 0.0, 0.0, QNAN, 0.0 },
+{ -QNAN, 0.0, 0.0, 0.0, QNAN, 0.0 },
+{ QNAN, 0.0, -0.0, 0.0, QNAN, 0.0 },
+{ -QNAN, 0.0, -0.0, 0.0, QNAN, 0.0 },
+{ QNAN, 0.0, 1.0, 0.0, QNAN, 0.0 },
+{ -QNAN, 0.0, 1.0, 0.0, QNAN, 0.0 },
+{ QNAN, 0.0, -1.0, 0.0, QNAN, 0.0 },
+{ -QNAN, 0.0, -1.0, 0.0, QNAN, 0.0 },
+{ QNAN, 0.0, HUGE, 0.0, QNAN, 0.0 },
+{ -QNAN, 0.0, HUGE, 0.0, QNAN, 0.0 },
+{ QNAN, 0.0, -HUGE, 0.0, QNAN, 0.0 },
+{ -QNAN, 0.0, -HUGE, 0.0, QNAN, 0.0 },
+{ QNAN, 0.0, INFINITY, 0.0, QNAN, 0.0 },
+{ -QNAN, 0.0, INFINITY, 0.0, QNAN, 0.0 },
+{ QNAN, 0.0, -INFINITY, 0.0, QNAN, 0.0 },
+{ -QNAN, 0.0, -INFINITY, 0.0, QNAN, 0.0 },
+{ QNAN, 0.0, QNAN, 0.0, QNAN, 0.0 },
+{ -QNAN, 0.0, QNAN, 0.0, QNAN, 0.0 },
+{ QNAN, 0.0, -QNAN, 0.0, QNAN, 0.0 },
+{ -QNAN, 0.0, -QNAN, 0.0, QNAN, 0.0 },
+{ 0.0, 0.0, QNAN, 0.0, QNAN, 0.0 },
+{ 0.0, 0.0, -QNAN, 0.0, QNAN, 0.0 },
+{ -0.0, 0.0, QNAN, 0.0, QNAN, 0.0 },
+{ -0.0, 0.0, -QNAN, 0.0, QNAN, 0.0 },
+{ 1.0, 0.0, QNAN, 0.0, QNAN, 0.0 },
+{ 1.0, 0.0, -QNAN, 0.0, QNAN, 0.0 },
+{ -1.0, 0.0, QNAN, 0.0, QNAN, 0.0 },
+{ -1.0, 0.0, -QNAN, 0.0, QNAN, 0.0 },
+{ HUGE, 0.0, QNAN, 0.0, QNAN, 0.0 },
+{ HUGE, 0.0, -QNAN, 0.0, QNAN, 0.0 },
+{ -HUGE, 0.0, QNAN, 0.0, QNAN, 0.0 },
+{ -HUGE, 0.0, -QNAN, 0.0, QNAN, 0.0 },
+{ INFINITY, 0.0, QNAN, 0.0, QNAN, 0.0 },
+{ INFINITY, 0.0, -QNAN, 0.0, QNAN, 0.0 },
+{ -INFINITY, 0.0, QNAN, 0.0, QNAN, 0.0 },
+{ -INFINITY, 0.0, -QNAN, 0.0, QNAN, 0.0 },
+};
+
+const int numEdgeCases = sizeof(edgeCases) / sizeof(struct testVector);
+
+
+int testEdgeCases() {
+ int i;
+ DD a, b, c, r;
+ for (i=0; i<numEdgeCases; ++i) {
+ a.hi = edgeCases[i].xhi;
+ a.lo = edgeCases[i].xlo;
+ b.hi = edgeCases[i].yhi;
+ b.lo = edgeCases[i].ylo;
+ r.hi = edgeCases[i].rhi;
+ r.lo = edgeCases[i].rlo;
+
+ int error;
+
+ DD c = { .ld = __gcc_qmul(a.ld, b.ld) };
+
+ if (r.hi != r.hi) {
+ if (c.hi == c.hi)
+ error = 1;
+ else if (c.lo != 0.0)
+ error = 1;
+ else
+ error = 0;
+ }
+
+ else if (r.hi == 0.0)
+ error = memcmp(&c, &r, sizeof(DD));
+
+ else
+ error = ((c.hi != r.hi) || (c.lo != r.lo));
+
+ if (error) {
+ printf("Error on edge case %a x %a: expected (%a, %a), got (%a, %a).\n", a.hi, b.hi, r.hi, r.lo, c.hi, c.lo);
+ return 1;
+ }
+ }
+
+ return 0;
+}
+
+
+/*
+
+ Code for generating the test cases, requires the mpfr package to run.
+
+ #include <stdio.h>
+ #include <stdlib.h>
+ #include <mpfr.h>
+ #include <math.h>
+
+ #ifdef __x86_64__
+ #define randlength 2
+ #else
+ #define randlength 4
+ #endif
+
+ void printTest(mpfr_t a, mpfr_t b, mpfr_t c) {
+ static const double INFINITYD = __builtin_INFINITY();
+
+ MPFR_DECL_INIT(tmp, 53);
+
+ double ahi = mpfr_get_d(a, GMP_RNDN);
+ mpfr_set_d(tmp, ahi, GMP_RNDN);
+ mpfr_sub(tmp, a, tmp, GMP_RNDN);
+ double alo = mpfr_get_d(tmp, GMP_RNDN);
+ printf("{%0.13a, %0.13a, ", ahi, alo);
+
+ double bhi = mpfr_get_d(b, GMP_RNDN);
+ mpfr_set_d(tmp, bhi, GMP_RNDN);
+ mpfr_sub(tmp, b, tmp, GMP_RNDN);
+ double blo = mpfr_get_d(tmp, GMP_RNDN);
+ printf("%0.13a, %0.13a, ", bhi, blo);
+
+ double chi = mpfr_get_d(c, GMP_RNDN);
+ mpfr_set_d(tmp, chi, GMP_RNDN);
+ mpfr_sub(tmp, c, tmp, GMP_RNDN);
+ double clo = isINFINITY(chi) ? 0.0 : mpfr_get_d(tmp, GMP_RNDN);
+ printf("%0.13a, %0.13a},\n", chi, clo);
+ }
+
+ int main(int argc, char *argv[]) {
+
+ MPFR_DECL_INIT(a, 106);
+ MPFR_DECL_INIT(b, 106);
+ MPFR_DECL_INIT(c, 106);
+
+ int exponent_range = atoi(argv[1]);
+
+ int i;
+ for (i=0; i<128; ++i) {
+ mpfr_random2(a, randlength, exponent_range);
+ mpfr_random2(b, randlength, exponent_range);
+ mpfr_mul(c, a, b, GMP_RNDN);
+ printTest(a, b, c);
+
+ mpfr_neg(b, b, GMP_RNDN);
+ mpfr_mul(c, a, b, GMP_RNDN);
+ printTest(a, b, c);
+
+ mpfr_neg(a, a, GMP_RNDN);
+ mpfr_neg(b, b, GMP_RNDN);
+ mpfr_mul(c, a, b, GMP_RNDN);
+ printTest(a, b, c);
+
+ mpfr_neg(b, b, GMP_RNDN);
+ mpfr_mul(c, a, b, GMP_RNDN);
+ printTest(a, b, c);
+ }
+ return 0;
+ }
+
+ */
+
+const struct testVector accuracyTests[] = {
+{0x1.00001ffffff00p-784, 0x1.fffff83ff8000p-839, 0x1.00ffc00ffff00p-771, 0x1.fe0007fffff00p-827, 0x0.0000000000000p+0, 0x0.0000000000000p+0},
+{0x1.00001ffffff00p-784, 0x1.fffff83ff8000p-839, -0x1.00ffc00ffff00p-771, -0x1.fe0007fffff00p-827, -0x0.0000000000000p+0, -0x0.0000000000000p+0},
+{-0x1.00001ffffff00p-784, -0x1.fffff83ff8000p-839, 0x1.00ffc00ffff00p-771, 0x1.fe0007fffff00p-827, -0x0.0000000000000p+0, -0x0.0000000000000p+0},
+{-0x1.00001ffffff00p-784, -0x1.fffff83ff8000p-839, -0x1.00ffc00ffff00p-771, -0x1.fe0007fffff00p-827, 0x0.0000000000000p+0, 0x0.0000000000000p+0},
+{0x1.00001fffff800p-705, 0x1.fffffffe00000p-779, 0x1.3fffffff80000p+666, 0x1.ffffffff00000p+593, 0x1.400027ff7f5ffp-39, 0x1.e0001ffe80000p-111},
+{0x1.00001fffff800p-705, 0x1.fffffffe00000p-779, -0x1.3fffffff80000p+666, -0x1.ffffffff00000p+593, -0x1.400027ff7f5ffp-39, -0x1.e0001ffe80000p-111},
+{-0x1.00001fffff800p-705, -0x1.fffffffe00000p-779, 0x1.3fffffff80000p+666, 0x1.ffffffff00000p+593, -0x1.400027ff7f5ffp-39, -0x1.e0001ffe80000p-111},
+{-0x1.00001fffff800p-705, -0x1.fffffffe00000p-779, -0x1.3fffffff80000p+666, -0x1.ffffffff00000p+593, 0x1.400027ff7f5ffp-39, 0x1.e0001ffe80000p-111},
+{0x1.0000000800000p-800, -0x1.0000000000000p-872, 0x1.000003fffc002p-916, -0x1.0000000000000p-1021, 0x0.0000000000000p+0, 0x0.0000000000000p+0},
+{0x1.0000000800000p-800, -0x1.0000000000000p-872, -0x1.000003fffc002p-916, 0x1.0000000000000p-1021, -0x0.0000000000000p+0, -0x0.0000000000000p+0},
+{-0x1.0000000800000p-800, 0x1.0000000000000p-872, 0x1.000003fffc002p-916, -0x1.0000000000000p-1021, -0x0.0000000000000p+0, -0x0.0000000000000p+0},
+{-0x1.0000000800000p-800, 0x1.0000000000000p-872, -0x1.000003fffc002p-916, 0x1.0000000000000p-1021, 0x0.0000000000000p+0, 0x0.0000000000000p+0},
+{0x1.000003ffffffep-19, -0x1.ffe0080000000p-103, 0x1.0800000000000p-211, -0x1.0000000000000p-307, 0x1.0800041fffffep-230, -0x1.00000020fef08p-286},
+{0x1.000003ffffffep-19, -0x1.ffe0080000000p-103, -0x1.0800000000000p-211, 0x1.0000000000000p-307, -0x1.0800041fffffep-230, 0x1.00000020fef08p-286},
+{-0x1.000003ffffffep-19, 0x1.ffe0080000000p-103, 0x1.0800000000000p-211, -0x1.0000000000000p-307, -0x1.0800041fffffep-230, 0x1.00000020fef08p-286},
+{-0x1.000003ffffffep-19, 0x1.ffe0080000000p-103, -0x1.0800000000000p-211, 0x1.0000000000000p-307, 0x1.0800041fffffep-230, -0x1.00000020fef08p-286},
+{0x1.0000007fffc00p-464, 0x1.efe0000000000p-558, 0x1.007fffffe0000p+756, 0x0.0000000000000p+0, 0x1.008000801fbfep+292, -0x1.fffeffff07900p+231},
+{0x1.0000007fffc00p-464, 0x1.efe0000000000p-558, -0x1.007fffffe0000p+756, 0x0.0000000000000p+0, -0x1.008000801fbfep+292, 0x1.fffeffff07900p+231},
+{-0x1.0000007fffc00p-464, -0x1.efe0000000000p-558, 0x1.007fffffe0000p+756, 0x0.0000000000000p+0, -0x1.008000801fbfep+292, 0x1.fffeffff07900p+231},
+{-0x1.0000007fffc00p-464, -0x1.efe0000000000p-558, -0x1.007fffffe0000p+756, 0x0.0000000000000p+0, 0x1.008000801fbfep+292, -0x1.fffeffff07900p+231},
+{0x1.3fe0000100000p-20, -0x1.0000000000000p-93, 0x1.3fffffffffe00p-397, 0x1.fe00040000000p-472, 0x1.8fd800013fd80p-417, 0x1.ffffc7d404500p-472},
+{0x1.3fe0000100000p-20, -0x1.0000000000000p-93, -0x1.3fffffffffe00p-397, -0x1.fe00040000000p-472, -0x1.8fd800013fd80p-417, -0x1.ffffc7d404500p-472},
+{-0x1.3fe0000100000p-20, 0x1.0000000000000p-93, 0x1.3fffffffffe00p-397, 0x1.fe00040000000p-472, -0x1.8fd800013fd80p-417, -0x1.ffffc7d404500p-472},
+{-0x1.3fe0000100000p-20, 0x1.0000000000000p-93, -0x1.3fffffffffe00p-397, -0x1.fe00040000000p-472, 0x1.8fd800013fd80p-417, 0x1.ffffc7d404500p-472},
+{0x1.0001fff800000p-371, 0x1.ffffff0000ffep-425, 0x1.00ff000000800p-806, -0x1.0000000800000p-872, 0x0.0000000000000p+0, 0x0.0000000000000p+0},
+{0x1.0001fff800000p-371, 0x1.ffffff0000ffep-425, -0x1.00ff000000800p-806, 0x1.0000000800000p-872, -0x0.0000000000000p+0, -0x0.0000000000000p+0},
+{-0x1.0001fff800000p-371, -0x1.ffffff0000ffep-425, 0x1.00ff000000800p-806, -0x1.0000000800000p-872, -0x0.0000000000000p+0, -0x0.0000000000000p+0},
+{-0x1.0001fff800000p-371, -0x1.ffffff0000ffep-425, -0x1.00ff000000800p-806, 0x1.0000000800000p-872, 0x0.0000000000000p+0, 0x0.0000000000000p+0},
+{0x1.0000800000000p-723, -0x1.ffffffe400000p-786, 0x1.000001ffffffap-94, -0x1.ffe1f80400000p-169, 0x1.0000820000ffap-817, -0x1.0c100109bfa00p-879},
+{0x1.0000800000000p-723, -0x1.ffffffe400000p-786, -0x1.000001ffffffap-94, 0x1.ffe1f80400000p-169, -0x1.0000820000ffap-817, 0x1.0c100109bfa00p-879},
+{-0x1.0000800000000p-723, 0x1.ffffffe400000p-786, 0x1.000001ffffffap-94, -0x1.ffe1f80400000p-169, -0x1.0000820000ffap-817, 0x1.0c100109bfa00p-879},
+{-0x1.0000800000000p-723, 0x1.ffffffe400000p-786, -0x1.000001ffffffap-94, 0x1.ffe1f80400000p-169, 0x1.0000820000ffap-817, -0x1.0c100109bfa00p-879},
+{0x1.0000010000000p-343, -0x1.0000000000000p-448, 0x1.007fffffffc00p-425, 0x1.fffffc0000000p-496, 0x1.008001007fc00p-768, -0x1.e000002004000p-835},
+{0x1.0000010000000p-343, -0x1.0000000000000p-448, -0x1.007fffffffc00p-425, -0x1.fffffc0000000p-496, -0x1.008001007fc00p-768, 0x1.e000002004000p-835},
+{-0x1.0000010000000p-343, 0x1.0000000000000p-448, 0x1.007fffffffc00p-425, 0x1.fffffc0000000p-496, -0x1.008001007fc00p-768, 0x1.e000002004000p-835},
+{-0x1.0000010000000p-343, 0x1.0000000000000p-448, -0x1.007fffffffc00p-425, -0x1.fffffc0000000p-496, 0x1.008001007fc00p-768, -0x1.e000002004000p-835},
+{0x1.0080000000000p-417, -0x1.0000000000000p-490, 0x1.001ffffffc000p-985, 0x1.0000000000000p-1039, 0x0.0000000000000p+0, 0x0.0000000000000p+0},
+{0x1.0080000000000p-417, -0x1.0000000000000p-490, -0x1.001ffffffc000p-985, -0x1.0000000000000p-1039, -0x0.0000000000000p+0, -0x0.0000000000000p+0},
+{-0x1.0080000000000p-417, 0x1.0000000000000p-490, 0x1.001ffffffc000p-985, 0x1.0000000000000p-1039, -0x0.0000000000000p+0, -0x0.0000000000000p+0},
+{-0x1.0080000000000p-417, 0x1.0000000000000p-490, -0x1.001ffffffc000p-985, -0x1.0000000000000p-1039, 0x0.0000000000000p+0, 0x0.0000000000000p+0},
+{0x1.000001fffff80p-758, 0x1.fffffc001fffcp-813, 0x1.00001ffff8000p+939, 0x1.00007f001e000p+884, 0x1.000021fff8380p+181, 0x1.7bc05e90173aep+127},
+{0x1.000001fffff80p-758, 0x1.fffffc001fffcp-813, -0x1.00001ffff8000p+939, -0x1.00007f001e000p+884, -0x1.000021fff8380p+181, -0x1.7bc05e90173aep+127},
+{-0x1.000001fffff80p-758, -0x1.fffffc001fffcp-813, 0x1.00001ffff8000p+939, 0x1.00007f001e000p+884, -0x1.000021fff8380p+181, -0x1.7bc05e90173aep+127},
+{-0x1.000001fffff80p-758, -0x1.fffffc001fffcp-813, -0x1.00001ffff8000p+939, -0x1.00007f001e000p+884, 0x1.000021fff8380p+181, 0x1.7bc05e90173aep+127},
+{0x1.00f3ffffff000p-189, 0x1.fff8000000000p-257, 0x1.3dfffffffc000p+294, 0x1.ff000003ffe00p+233, 0x1.3f2f17fffabe3p+105, 0x1.02efbc1200d00p+45},
+{0x1.00f3ffffff000p-189, 0x1.fff8000000000p-257, -0x1.3dfffffffc000p+294, -0x1.ff000003ffe00p+233, -0x1.3f2f17fffabe3p+105, -0x1.02efbc1200d00p+45},
+{-0x1.00f3ffffff000p-189, -0x1.fff8000000000p-257, 0x1.3dfffffffc000p+294, 0x1.ff000003ffe00p+233, -0x1.3f2f17fffabe3p+105, -0x1.02efbc1200d00p+45},
+{-0x1.00f3ffffff000p-189, -0x1.fff8000000000p-257, -0x1.3dfffffffc000p+294, -0x1.ff000003ffe00p+233, 0x1.3f2f17fffabe3p+105, 0x1.02efbc1200d00p+45},
+{0x1.0000001ffff80p-98, 0x1.fffffdfffff8ep-152, 0x1.0000000000000p+1023, -0x1.0000000000000p+953, 0x1.0000001ffff80p+925, 0x1.fffefdffffd8ep+871},
+{0x1.0000001ffff80p-98, 0x1.fffffdfffff8ep-152, -0x1.0000000000000p+1023, 0x1.0000000000000p+953, -0x1.0000001ffff80p+925, -0x1.fffefdffffd8ep+871},
+{-0x1.0000001ffff80p-98, -0x1.fffffdfffff8ep-152, 0x1.0000000000000p+1023, -0x1.0000000000000p+953, -0x1.0000001ffff80p+925, -0x1.fffefdffffd8ep+871},
+{-0x1.0000001ffff80p-98, -0x1.fffffdfffff8ep-152, -0x1.0000000000000p+1023, 0x1.0000000000000p+953, 0x1.0000001ffff80p+925, 0x1.fffefdffffd8ep+871},
+{0x1.001fffffffe00p+730, 0x0.0000000000000p+0, 0x1.0000002000000p+702, -0x1.0000000000000p+602, INFINITY, 0x0.0000000000000p+0},
+{0x1.001fffffffe00p+730, 0x0.0000000000000p+0, -0x1.0000002000000p+702, 0x1.0000000000000p+602, -INFINITY, 0x0.0000000000000p+0},
+{-0x1.001fffffffe00p+730, 0x0.0000000000000p+0, 0x1.0000002000000p+702, -0x1.0000000000000p+602, -INFINITY, 0x0.0000000000000p+0},
+{-0x1.001fffffffe00p+730, 0x0.0000000000000p+0, -0x1.0000002000000p+702, 0x1.0000000000000p+602, INFINITY, 0x0.0000000000000p+0},
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+{0x1.0000000800000p+490, -0x1.0000000000000p+385, 0x1.7ffff80000000p+812, 0x1.ffffffffe0000p+756, INFINITY, 0x0.0000000000000p+0},
+{0x1.0000000800000p+490, -0x1.0000000000000p+385, -0x1.7ffff80000000p+812, -0x1.ffffffffe0000p+756, -INFINITY, 0x0.0000000000000p+0},
+{-0x1.0000000800000p+490, 0x1.0000000000000p+385, 0x1.7ffff80000000p+812, 0x1.ffffffffe0000p+756, -INFINITY, 0x0.0000000000000p+0},
+{-0x1.0000000800000p+490, 0x1.0000000000000p+385, -0x1.7ffff80000000p+812, -0x1.ffffffffe0000p+756, INFINITY, 0x0.0000000000000p+0},
+{0x1.00fffffff8000p-776, 0x1.fffe000000000p-850, 0x1.0000100000000p+556, -0x1.fffffffffc100p+501, 0x1.0100100ff8000p-220, -0x1.20ffe00014060p-274},
+{0x1.00fffffff8000p-776, 0x1.fffe000000000p-850, -0x1.0000100000000p+556, 0x1.fffffffffc100p+501, -0x1.0100100ff8000p-220, 0x1.20ffe00014060p-274},
+{-0x1.00fffffff8000p-776, -0x1.fffe000000000p-850, 0x1.0000100000000p+556, -0x1.fffffffffc100p+501, -0x1.0100100ff8000p-220, 0x1.20ffe00014060p-274},
+{-0x1.00fffffff8000p-776, -0x1.fffe000000000p-850, -0x1.0000100000000p+556, 0x1.fffffffffc100p+501, 0x1.0100100ff8000p-220, -0x1.20ffe00014060p-274},
+{0x1.0007ffffffff0p+441, 0x1.fffffc0000000p+358, 0x1.0003800000080p+407, -0x1.0000000000000p+302, 0x1.000b801c00070p+848, 0x1.e40001ffc6f80p+789},
+{0x1.0007ffffffff0p+441, 0x1.fffffc0000000p+358, -0x1.0003800000080p+407, 0x1.0000000000000p+302, -0x1.000b801c00070p+848, -0x1.e40001ffc6f80p+789},
+{-0x1.0007ffffffff0p+441, -0x1.fffffc0000000p+358, 0x1.0003800000080p+407, -0x1.0000000000000p+302, -0x1.000b801c00070p+848, -0x1.e40001ffc6f80p+789},
+{-0x1.0007ffffffff0p+441, -0x1.fffffc0000000p+358, -0x1.0003800000080p+407, 0x1.0000000000000p+302, 0x1.000b801c00070p+848, 0x1.e40001ffc6f80p+789},
+{0x1.000001fffff80p-397, 0x1.ff00000000000p-481, 0x1.0000020000000p+10, -0x1.8002000000000p-66, 0x1.000003fffffc0p-387, -0x1.017e030300000p-455},
+{0x1.000001fffff80p-397, 0x1.ff00000000000p-481, -0x1.0000020000000p+10, 0x1.8002000000000p-66, -0x1.000003fffffc0p-387, 0x1.017e030300000p-455},
+{-0x1.000001fffff80p-397, -0x1.ff00000000000p-481, 0x1.0000020000000p+10, -0x1.8002000000000p-66, -0x1.000003fffffc0p-387, 0x1.017e030300000p-455},
+{-0x1.000001fffff80p-397, -0x1.ff00000000000p-481, -0x1.0000020000000p+10, 0x1.8002000000000p-66, 0x1.000003fffffc0p-387, -0x1.017e030300000p-455},
+{0x1.0003fffff0000p+165, 0x1.ffff800007f80p+105, 0x1.000007ffffe00p+981, -0x1.fe0c000004000p+923, INFINITY, 0x0.0000000000000p+0},
+{0x1.0003fffff0000p+165, 0x1.ffff800007f80p+105, -0x1.000007ffffe00p+981, 0x1.fe0c000004000p+923, -INFINITY, 0x0.0000000000000p+0},
+{-0x1.0003fffff0000p+165, -0x1.ffff800007f80p+105, 0x1.000007ffffe00p+981, -0x1.fe0c000004000p+923, -INFINITY, 0x0.0000000000000p+0},
+{-0x1.0003fffff0000p+165, -0x1.ffff800007f80p+105, -0x1.000007ffffe00p+981, 0x1.fe0c000004000p+923, INFINITY, 0x0.0000000000000p+0},
+{0x1.00000003f0000p+687, 0x1.ffffffe000000p+609, 0x1.0100000000000p-215, -0x1.fffffff000080p-275, 0x1.01000003f3f00p+472, -0x1.ffff7f77e0100p+412},
+{0x1.00000003f0000p+687, 0x1.ffffffe000000p+609, -0x1.0100000000000p-215, 0x1.fffffff000080p-275, -0x1.01000003f3f00p+472, 0x1.ffff7f77e0100p+412},
+{-0x1.00000003f0000p+687, -0x1.ffffffe000000p+609, 0x1.0100000000000p-215, -0x1.fffffff000080p-275, -0x1.01000003f3f00p+472, 0x1.ffff7f77e0100p+412},
+{-0x1.00000003f0000p+687, -0x1.ffffffe000000p+609, -0x1.0100000000000p-215, 0x1.fffffff000080p-275, 0x1.01000003f3f00p+472, -0x1.ffff7f77e0100p+412},
+{0x1.007fffffffc00p-448, 0x1.fffffe0000000p-530, 0x1.0000003fffff8p-643, 0x1.fffff80000000p-714, 0x0.0000000000000p+0, 0x0.0000000000000p+0},
+{0x1.007fffffffc00p-448, 0x1.fffffe0000000p-530, -0x1.0000003fffff8p-643, -0x1.fffff80000000p-714, -0x0.0000000000000p+0, -0x0.0000000000000p+0},
+{-0x1.007fffffffc00p-448, -0x1.fffffe0000000p-530, 0x1.0000003fffff8p-643, 0x1.fffff80000000p-714, -0x0.0000000000000p+0, -0x0.0000000000000p+0},
+{-0x1.007fffffffc00p-448, -0x1.fffffe0000000p-530, -0x1.0000003fffff8p-643, -0x1.fffff80000000p-714, 0x0.0000000000000p+0, 0x0.0000000000000p+0},
+{0x1.00000003ff000p-711, 0x1.ffffff0000000p-773, 0x1.0000ffff80000p+16, 0x1.e0000000fffc0p-43, 0x1.000100037f040p-695, -0x1.7bfef005e8810p-752},
+{0x1.00000003ff000p-711, 0x1.ffffff0000000p-773, -0x1.0000ffff80000p+16, -0x1.e0000000fffc0p-43, -0x1.000100037f040p-695, 0x1.7bfef005e8810p-752},
+{-0x1.00000003ff000p-711, -0x1.ffffff0000000p-773, 0x1.0000ffff80000p+16, 0x1.e0000000fffc0p-43, -0x1.000100037f040p-695, 0x1.7bfef005e8810p-752},
+{-0x1.00000003ff000p-711, -0x1.ffffff0000000p-773, -0x1.0000ffff80000p+16, -0x1.e0000000fffc0p-43, 0x1.000100037f040p-695, -0x1.7bfef005e8810p-752},
+{0x1.007ffffffc000p-157, 0x1.ffffff8000000p-224, 0x1.0003fffffffe0p-88, 0x1.fffffff000780p-148, 0x1.008401fffbfdfp-245, -0x1.bf5ffdf221f10p-302},
+{0x1.007ffffffc000p-157, 0x1.ffffff8000000p-224, -0x1.0003fffffffe0p-88, -0x1.fffffff000780p-148, -0x1.008401fffbfdfp-245, 0x1.bf5ffdf221f10p-302},
+{-0x1.007ffffffc000p-157, -0x1.ffffff8000000p-224, 0x1.0003fffffffe0p-88, 0x1.fffffff000780p-148, -0x1.008401fffbfdfp-245, 0x1.bf5ffdf221f10p-302},
+{-0x1.007ffffffc000p-157, -0x1.ffffff8000000p-224, -0x1.0003fffffffe0p-88, -0x1.fffffff000780p-148, 0x1.008401fffbfdfp-245, -0x1.bf5ffdf221f10p-302},
+{0x1.07fffffe0003cp-432, 0x1.ffe000007f000p-497, 0x1.1ffff00800000p+307, -0x1.0000000000000p+210, 0x1.28ffef8600045p-125, 0x1.fc3902fc0230cp-179},
+{0x1.07fffffe0003cp-432, 0x1.ffe000007f000p-497, -0x1.1ffff00800000p+307, 0x1.0000000000000p+210, -0x1.28ffef8600045p-125, -0x1.fc3902fc0230cp-179},
+{-0x1.07fffffe0003cp-432, -0x1.ffe000007f000p-497, 0x1.1ffff00800000p+307, -0x1.0000000000000p+210, -0x1.28ffef8600045p-125, -0x1.fc3902fc0230cp-179},
+{-0x1.07fffffe0003cp-432, -0x1.ffe000007f000p-497, -0x1.1ffff00800000p+307, 0x1.0000000000000p+210, 0x1.28ffef8600045p-125, 0x1.fc3902fc0230cp-179},
+{0x1.000003fff8000p+711, 0x1.ffff00000003cp+656, 0x1.000001ffff020p+18, -0x1.fff0000200000p-52, 0x1.000005fff70a0p+729, 0x1.f5ff0817ec048p+674},
+{0x1.000003fff8000p+711, 0x1.ffff00000003cp+656, -0x1.000001ffff020p+18, 0x1.fff0000200000p-52, -0x1.000005fff70a0p+729, -0x1.f5ff0817ec048p+674},
+{-0x1.000003fff8000p+711, -0x1.ffff00000003cp+656, 0x1.000001ffff020p+18, -0x1.fff0000200000p-52, -0x1.000005fff70a0p+729, -0x1.f5ff0817ec048p+674},
+{-0x1.000003fff8000p+711, -0x1.ffff00000003cp+656, -0x1.000001ffff020p+18, 0x1.fff0000200000p-52, 0x1.000005fff70a0p+729, 0x1.f5ff0817ec048p+674},
+{0x1.00ffe00000000p-302, 0x1.fe00000000000p-362, 0x1.0000100000000p+87, -0x1.ffff800010000p+18, 0x1.00fff00ffe000p-215, 0x1.fcff20403ff00p-275},
+{0x1.00ffe00000000p-302, 0x1.fe00000000000p-362, -0x1.0000100000000p+87, 0x1.ffff800010000p+18, -0x1.00fff00ffe000p-215, -0x1.fcff20403ff00p-275},
+{-0x1.00ffe00000000p-302, -0x1.fe00000000000p-362, 0x1.0000100000000p+87, -0x1.ffff800010000p+18, -0x1.00fff00ffe000p-215, -0x1.fcff20403ff00p-275},
+{-0x1.00ffe00000000p-302, -0x1.fe00000000000p-362, -0x1.0000100000000p+87, 0x1.ffff800010000p+18, 0x1.00fff00ffe000p-215, 0x1.fcff20403ff00p-275},
+{0x1.fffffff000008p+565, -0x1.ffffff1000000p+488, 0x1.0001fffffff80p-162, 0x1.fffe000000000p-247, 0x1.0001fff7ffe84p+404, 0x1.00701fdbe7000p+339},
+{0x1.fffffff000008p+565, -0x1.ffffff1000000p+488, -0x1.0001fffffff80p-162, -0x1.fffe000000000p-247, -0x1.0001fff7ffe84p+404, -0x1.00701fdbe7000p+339},
+{-0x1.fffffff000008p+565, 0x1.ffffff1000000p+488, 0x1.0001fffffff80p-162, 0x1.fffe000000000p-247, -0x1.0001fff7ffe84p+404, -0x1.00701fdbe7000p+339},
+{-0x1.fffffff000008p+565, 0x1.ffffff1000000p+488, -0x1.0001fffffff80p-162, -0x1.fffe000000000p-247, 0x1.0001fff7ffe84p+404, 0x1.00701fdbe7000p+339},
+};
+
+const int numAccuracyTests = sizeof(accuracyTests) / sizeof(struct testVector);
+
+#include <math.h>
+
+double testAccuracy() {
+ int i;
+ DD a, b, c, r;
+
+ double worstUlps = 0.5;
+
+ for (i=0; i<numAccuracyTests; ++i) {
+ a.hi = accuracyTests[i].xhi;
+ a.lo = accuracyTests[i].xlo;
+ b.hi = accuracyTests[i].yhi;
+ b.lo = accuracyTests[i].ylo;
+ r.hi = accuracyTests[i].rhi;
+ r.lo = accuracyTests[i].rlo;
+
+ DD c = { .ld = __gcc_qmul(a.ld, b.ld) };
+
+ double error = __builtin_fabs(((r.hi - c.hi) + r.lo) - c.lo);
+
+ if (error != 0.0) {
+
+ int exponent = ilogb(r.hi);
+ exponent = (exponent < -1022 ? -1022 : exponent);
+ double ulpError = scalbn(error, 106 - exponent);
+
+ if (ulpError > worstUlps) {
+#ifdef PRINT_ACCURACY_INFORMATION
+ printf("New worst rounding error for (%a,%a) x (%a,%a):\n", a.hi, a.lo, b.hi, b.lo);
+ printf("\tExpected: (%a,%a)\n", r.hi, r.lo);
+ printf("\tComputed: (%a,%a)\n", c.hi, c.lo);
+ printf("\tError: %f ulps\n", ulpError);
+#endif
+ worstUlps = ulpError;
+ }
+ }
+ }
+
+ return worstUlps;
+}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+