4 long double __gcc_qmul(long double x
, long double y
);
9 int main(int argc
, char *argv
[]) {
13 if (testAccuracy() > 2.0)
20 double xhi
; double xlo
;
21 double yhi
; double ylo
;
22 double rhi
; double rlo
;
25 #define INFINITY __builtin_inf()
26 #define HUGE 0x1.fffffffffffffp1023
27 #define QNAN __builtin_nan("")
29 const struct testVector edgeCases
[] = {
30 { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 },
31 { -0.0, 0.0, 0.0, 0.0, -0.0, 0.0 },
32 { 0.0, 0.0, -0.0, 0.0, -0.0, 0.0 },
33 { -0.0, 0.0, -0.0, 0.0, 0.0, 0.0 },
35 { INFINITY
, 0.0, 0.0, 0.0, QNAN
, 0.0 },
36 { -INFINITY
, 0.0, 0.0, 0.0, QNAN
, 0.0 },
37 { INFINITY
, 0.0, -0.0, 0.0, QNAN
, 0.0 },
38 { -INFINITY
, 0.0, -0.0, 0.0, QNAN
, 0.0 },
39 { INFINITY
, 0.0, 1.0, 0.0, INFINITY
, 0.0 },
40 { -INFINITY
, 0.0, 1.0, 0.0, -INFINITY
, 0.0 },
41 { INFINITY
, 0.0, -1.0, 0.0, -INFINITY
, 0.0 },
42 { -INFINITY
, 0.0, -1.0, 0.0, INFINITY
, 0.0 },
43 { INFINITY
, 0.0, HUGE
, 0.0, INFINITY
, 0.0 },
44 { -INFINITY
, 0.0, HUGE
, 0.0, -INFINITY
, 0.0 },
45 { INFINITY
, 0.0, -HUGE
, 0.0, -INFINITY
, 0.0 },
46 { -INFINITY
, 0.0, -HUGE
, 0.0, INFINITY
, 0.0 },
47 { INFINITY
, 0.0, INFINITY
, 0.0, INFINITY
, 0.0 },
48 { -INFINITY
, 0.0, INFINITY
, 0.0, -INFINITY
, 0.0 },
49 { INFINITY
, 0.0, -INFINITY
, 0.0, -INFINITY
, 0.0 },
50 { -INFINITY
, 0.0, -INFINITY
, 0.0, INFINITY
, 0.0 },
51 { 0.0, 0.0, INFINITY
, 0.0, QNAN
, 0.0 },
52 { 0.0, 0.0, -INFINITY
, 0.0, QNAN
, 0.0 },
53 { -0.0, 0.0, INFINITY
, 0.0, QNAN
, 0.0 },
54 { -0.0, 0.0, -INFINITY
, 0.0, QNAN
, 0.0 },
55 { 1.0, 0.0, INFINITY
, 0.0, INFINITY
, 0.0 },
56 { 1.0, 0.0, -INFINITY
, 0.0, -INFINITY
, 0.0 },
57 { -1.0, 0.0, INFINITY
, 0.0, -INFINITY
, 0.0 },
58 { -1.0, 0.0, -INFINITY
, 0.0, INFINITY
, 0.0 },
59 { HUGE
, 0.0, INFINITY
, 0.0, INFINITY
, 0.0 },
60 { HUGE
, 0.0, -INFINITY
, 0.0, -INFINITY
, 0.0 },
61 { -HUGE
, 0.0, INFINITY
, 0.0, -INFINITY
, 0.0 },
62 { -HUGE
, 0.0, -INFINITY
, 0.0, INFINITY
, 0.0 },
64 { QNAN
, 0.0, 0.0, 0.0, QNAN
, 0.0 },
65 { -QNAN
, 0.0, 0.0, 0.0, QNAN
, 0.0 },
66 { QNAN
, 0.0, -0.0, 0.0, QNAN
, 0.0 },
67 { -QNAN
, 0.0, -0.0, 0.0, QNAN
, 0.0 },
68 { QNAN
, 0.0, 1.0, 0.0, QNAN
, 0.0 },
69 { -QNAN
, 0.0, 1.0, 0.0, QNAN
, 0.0 },
70 { QNAN
, 0.0, -1.0, 0.0, QNAN
, 0.0 },
71 { -QNAN
, 0.0, -1.0, 0.0, QNAN
, 0.0 },
72 { QNAN
, 0.0, HUGE
, 0.0, QNAN
, 0.0 },
73 { -QNAN
, 0.0, HUGE
, 0.0, QNAN
, 0.0 },
74 { QNAN
, 0.0, -HUGE
, 0.0, QNAN
, 0.0 },
75 { -QNAN
, 0.0, -HUGE
, 0.0, QNAN
, 0.0 },
76 { QNAN
, 0.0, INFINITY
, 0.0, QNAN
, 0.0 },
77 { -QNAN
, 0.0, INFINITY
, 0.0, QNAN
, 0.0 },
78 { QNAN
, 0.0, -INFINITY
, 0.0, QNAN
, 0.0 },
79 { -QNAN
, 0.0, -INFINITY
, 0.0, QNAN
, 0.0 },
80 { QNAN
, 0.0, QNAN
, 0.0, QNAN
, 0.0 },
81 { -QNAN
, 0.0, QNAN
, 0.0, QNAN
, 0.0 },
82 { QNAN
, 0.0, -QNAN
, 0.0, QNAN
, 0.0 },
83 { -QNAN
, 0.0, -QNAN
, 0.0, QNAN
, 0.0 },
84 { 0.0, 0.0, QNAN
, 0.0, QNAN
, 0.0 },
85 { 0.0, 0.0, -QNAN
, 0.0, QNAN
, 0.0 },
86 { -0.0, 0.0, QNAN
, 0.0, QNAN
, 0.0 },
87 { -0.0, 0.0, -QNAN
, 0.0, QNAN
, 0.0 },
88 { 1.0, 0.0, QNAN
, 0.0, QNAN
, 0.0 },
89 { 1.0, 0.0, -QNAN
, 0.0, QNAN
, 0.0 },
90 { -1.0, 0.0, QNAN
, 0.0, QNAN
, 0.0 },
91 { -1.0, 0.0, -QNAN
, 0.0, QNAN
, 0.0 },
92 { HUGE
, 0.0, QNAN
, 0.0, QNAN
, 0.0 },
93 { HUGE
, 0.0, -QNAN
, 0.0, QNAN
, 0.0 },
94 { -HUGE
, 0.0, QNAN
, 0.0, QNAN
, 0.0 },
95 { -HUGE
, 0.0, -QNAN
, 0.0, QNAN
, 0.0 },
96 { INFINITY
, 0.0, QNAN
, 0.0, QNAN
, 0.0 },
97 { INFINITY
, 0.0, -QNAN
, 0.0, QNAN
, 0.0 },
98 { -INFINITY
, 0.0, QNAN
, 0.0, QNAN
, 0.0 },
99 { -INFINITY
, 0.0, -QNAN
, 0.0, QNAN
, 0.0 },
102 const int numEdgeCases
= sizeof(edgeCases
) / sizeof(struct testVector
);
105 int testEdgeCases() {
108 for (i
=0; i
<numEdgeCases
; ++i
) {
109 a
.hi
= edgeCases
[i
].xhi
;
110 a
.lo
= edgeCases
[i
].xlo
;
111 b
.hi
= edgeCases
[i
].yhi
;
112 b
.lo
= edgeCases
[i
].ylo
;
113 r
.hi
= edgeCases
[i
].rhi
;
114 r
.lo
= edgeCases
[i
].rlo
;
118 DD c
= { .ld
= __gcc_qmul(a
.ld
, b
.ld
) };
123 else if (c
.lo
!= 0.0)
129 else if (r
.hi
== 0.0)
130 error
= memcmp(&c
, &r
, sizeof(DD
));
133 error
= ((c
.hi
!= r
.hi
) || (c
.lo
!= r
.lo
));
136 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
);
147 Code for generating the test cases, requires the mpfr package to run.
160 void printTest(mpfr_t a, mpfr_t b, mpfr_t c) {
161 static const double INFINITYD = __builtin_INFINITY();
163 MPFR_DECL_INIT(tmp, 53);
165 double ahi = mpfr_get_d(a, GMP_RNDN);
166 mpfr_set_d(tmp, ahi, GMP_RNDN);
167 mpfr_sub(tmp, a, tmp, GMP_RNDN);
168 double alo = mpfr_get_d(tmp, GMP_RNDN);
169 printf("{%0.13a, %0.13a, ", ahi, alo);
171 double bhi = mpfr_get_d(b, GMP_RNDN);
172 mpfr_set_d(tmp, bhi, GMP_RNDN);
173 mpfr_sub(tmp, b, tmp, GMP_RNDN);
174 double blo = mpfr_get_d(tmp, GMP_RNDN);
175 printf("%0.13a, %0.13a, ", bhi, blo);
177 double chi = mpfr_get_d(c, GMP_RNDN);
178 mpfr_set_d(tmp, chi, GMP_RNDN);
179 mpfr_sub(tmp, c, tmp, GMP_RNDN);
180 double clo = isINFINITY(chi) ? 0.0 : mpfr_get_d(tmp, GMP_RNDN);
181 printf("%0.13a, %0.13a},\n", chi, clo);
184 int main(int argc, char *argv[]) {
186 MPFR_DECL_INIT(a, 106);
187 MPFR_DECL_INIT(b, 106);
188 MPFR_DECL_INIT(c, 106);
190 int exponent_range = atoi(argv[1]);
193 for (i=0; i<128; ++i) {
194 mpfr_random2(a, randlength, exponent_range);
195 mpfr_random2(b, randlength, exponent_range);
196 mpfr_mul(c, a, b, GMP_RNDN);
199 mpfr_neg(b, b, GMP_RNDN);
200 mpfr_mul(c, a, b, GMP_RNDN);
203 mpfr_neg(a, a, GMP_RNDN);
204 mpfr_neg(b, b, GMP_RNDN);
205 mpfr_mul(c, a, b, GMP_RNDN);
208 mpfr_neg(b, b, GMP_RNDN);
209 mpfr_mul(c, a, b, GMP_RNDN);
217 const struct testVector accuracyTests
[] = {
218 {0x1.00001ffffff00p
-784, 0x1.fffff83ff8000p
-839, 0x1.00ffc00ffff00p
-771, 0x1.fe0007fffff00p
-827, 0x0.0000000000000p
+0, 0x0.0000000000000p
+0},
219 {0x1.00001ffffff00p
-784, 0x1.fffff83ff8000p
-839, -0x1.00ffc00ffff00p
-771, -0x1.fe0007fffff00p
-827, -0x0.0000000000000p
+0, -0x0.0000000000000p
+0},
220 {-0x1.00001ffffff00p
-784, -0x1.fffff83ff8000p
-839, 0x1.00ffc00ffff00p
-771, 0x1.fe0007fffff00p
-827, -0x0.0000000000000p
+0, -0x0.0000000000000p
+0},
221 {-0x1.00001ffffff00p
-784, -0x1.fffff83ff8000p
-839, -0x1.00ffc00ffff00p
-771, -0x1.fe0007fffff00p
-827, 0x0.0000000000000p
+0, 0x0.0000000000000p
+0},
222 {0x1.00001fffff800p
-705, 0x1.fffffffe00000p
-779, 0x1.3fffffff80000p
+666, 0x1.ffffffff00000p
+593, 0x1.400027ff7f5ffp
-39, 0x1.e0001ffe80000p
-111},
223 {0x1.00001fffff800p
-705, 0x1.fffffffe00000p
-779, -0x1.3fffffff80000p
+666, -0x1.ffffffff00000p
+593, -0x1.400027ff7f5ffp
-39, -0x1.e0001ffe80000p
-111},
224 {-0x1.00001fffff800p
-705, -0x1.fffffffe00000p
-779, 0x1.3fffffff80000p
+666, 0x1.ffffffff00000p
+593, -0x1.400027ff7f5ffp
-39, -0x1.e0001ffe80000p
-111},
225 {-0x1.00001fffff800p
-705, -0x1.fffffffe00000p
-779, -0x1.3fffffff80000p
+666, -0x1.ffffffff00000p
+593, 0x1.400027ff7f5ffp
-39, 0x1.e0001ffe80000p
-111},
226 {0x1.0000000800000p
-800, -0x1.0000000000000p
-872, 0x1.000003fffc002p
-916, -0x1.0000000000000p
-1021, 0x0.0000000000000p
+0, 0x0.0000000000000p
+0},
227 {0x1.0000000800000p
-800, -0x1.0000000000000p
-872, -0x1.000003fffc002p
-916, 0x1.0000000000000p
-1021, -0x0.0000000000000p
+0, -0x0.0000000000000p
+0},
228 {-0x1.0000000800000p
-800, 0x1.0000000000000p
-872, 0x1.000003fffc002p
-916, -0x1.0000000000000p
-1021, -0x0.0000000000000p
+0, -0x0.0000000000000p
+0},
229 {-0x1.0000000800000p
-800, 0x1.0000000000000p
-872, -0x1.000003fffc002p
-916, 0x1.0000000000000p
-1021, 0x0.0000000000000p
+0, 0x0.0000000000000p
+0},
230 {0x1.000003ffffffep
-19, -0x1.ffe0080000000p
-103, 0x1.0800000000000p
-211, -0x1.0000000000000p
-307, 0x1.0800041fffffep
-230, -0x1.00000020fef08p
-286},
231 {0x1.000003ffffffep
-19, -0x1.ffe0080000000p
-103, -0x1.0800000000000p
-211, 0x1.0000000000000p
-307, -0x1.0800041fffffep
-230, 0x1.00000020fef08p
-286},
232 {-0x1.000003ffffffep
-19, 0x1.ffe0080000000p
-103, 0x1.0800000000000p
-211, -0x1.0000000000000p
-307, -0x1.0800041fffffep
-230, 0x1.00000020fef08p
-286},
233 {-0x1.000003ffffffep
-19, 0x1.ffe0080000000p
-103, -0x1.0800000000000p
-211, 0x1.0000000000000p
-307, 0x1.0800041fffffep
-230, -0x1.00000020fef08p
-286},
234 {0x1.0000007fffc00p
-464, 0x1.efe0000000000p
-558, 0x1.007fffffe0000p
+756, 0x0.0000000000000p
+0, 0x1.008000801fbfep
+292, -0x1.fffeffff07900p
+231},
235 {0x1.0000007fffc00p
-464, 0x1.efe0000000000p
-558, -0x1.007fffffe0000p
+756, 0x0.0000000000000p
+0, -0x1.008000801fbfep
+292, 0x1.fffeffff07900p
+231},
236 {-0x1.0000007fffc00p
-464, -0x1.efe0000000000p
-558, 0x1.007fffffe0000p
+756, 0x0.0000000000000p
+0, -0x1.008000801fbfep
+292, 0x1.fffeffff07900p
+231},
237 {-0x1.0000007fffc00p
-464, -0x1.efe0000000000p
-558, -0x1.007fffffe0000p
+756, 0x0.0000000000000p
+0, 0x1.008000801fbfep
+292, -0x1.fffeffff07900p
+231},
238 {0x1.3fe0000100000p
-20, -0x1.0000000000000p
-93, 0x1.3fffffffffe00p
-397, 0x1.fe00040000000p
-472, 0x1.8fd800013fd80p
-417, 0x1.ffffc7d404500p
-472},
239 {0x1.3fe0000100000p
-20, -0x1.0000000000000p
-93, -0x1.3fffffffffe00p
-397, -0x1.fe00040000000p
-472, -0x1.8fd800013fd80p
-417, -0x1.ffffc7d404500p
-472},
240 {-0x1.3fe0000100000p
-20, 0x1.0000000000000p
-93, 0x1.3fffffffffe00p
-397, 0x1.fe00040000000p
-472, -0x1.8fd800013fd80p
-417, -0x1.ffffc7d404500p
-472},
241 {-0x1.3fe0000100000p
-20, 0x1.0000000000000p
-93, -0x1.3fffffffffe00p
-397, -0x1.fe00040000000p
-472, 0x1.8fd800013fd80p
-417, 0x1.ffffc7d404500p
-472},
242 {0x1.0001fff800000p
-371, 0x1.ffffff0000ffep
-425, 0x1.00ff000000800p
-806, -0x1.0000000800000p
-872, 0x0.0000000000000p
+0, 0x0.0000000000000p
+0},
243 {0x1.0001fff800000p
-371, 0x1.ffffff0000ffep
-425, -0x1.00ff000000800p
-806, 0x1.0000000800000p
-872, -0x0.0000000000000p
+0, -0x0.0000000000000p
+0},
244 {-0x1.0001fff800000p
-371, -0x1.ffffff0000ffep
-425, 0x1.00ff000000800p
-806, -0x1.0000000800000p
-872, -0x0.0000000000000p
+0, -0x0.0000000000000p
+0},
245 {-0x1.0001fff800000p
-371, -0x1.ffffff0000ffep
-425, -0x1.00ff000000800p
-806, 0x1.0000000800000p
-872, 0x0.0000000000000p
+0, 0x0.0000000000000p
+0},
246 {0x1.0000800000000p
-723, -0x1.ffffffe400000p
-786, 0x1.000001ffffffap
-94, -0x1.ffe1f80400000p
-169, 0x1.0000820000ffap
-817, -0x1.0c100109bfa00p
-879},
247 {0x1.0000800000000p
-723, -0x1.ffffffe400000p
-786, -0x1.000001ffffffap
-94, 0x1.ffe1f80400000p
-169, -0x1.0000820000ffap
-817, 0x1.0c100109bfa00p
-879},
248 {-0x1.0000800000000p
-723, 0x1.ffffffe400000p
-786, 0x1.000001ffffffap
-94, -0x1.ffe1f80400000p
-169, -0x1.0000820000ffap
-817, 0x1.0c100109bfa00p
-879},
249 {-0x1.0000800000000p
-723, 0x1.ffffffe400000p
-786, -0x1.000001ffffffap
-94, 0x1.ffe1f80400000p
-169, 0x1.0000820000ffap
-817, -0x1.0c100109bfa00p
-879},
250 {0x1.0000010000000p
-343, -0x1.0000000000000p
-448, 0x1.007fffffffc00p
-425, 0x1.fffffc0000000p
-496, 0x1.008001007fc00p
-768, -0x1.e000002004000p
-835},
251 {0x1.0000010000000p
-343, -0x1.0000000000000p
-448, -0x1.007fffffffc00p
-425, -0x1.fffffc0000000p
-496, -0x1.008001007fc00p
-768, 0x1.e000002004000p
-835},
252 {-0x1.0000010000000p
-343, 0x1.0000000000000p
-448, 0x1.007fffffffc00p
-425, 0x1.fffffc0000000p
-496, -0x1.008001007fc00p
-768, 0x1.e000002004000p
-835},
253 {-0x1.0000010000000p
-343, 0x1.0000000000000p
-448, -0x1.007fffffffc00p
-425, -0x1.fffffc0000000p
-496, 0x1.008001007fc00p
-768, -0x1.e000002004000p
-835},
254 {0x1.0080000000000p
-417, -0x1.0000000000000p
-490, 0x1.001ffffffc000p
-985, 0x1.0000000000000p
-1039, 0x0.0000000000000p
+0, 0x0.0000000000000p
+0},
255 {0x1.0080000000000p
-417, -0x1.0000000000000p
-490, -0x1.001ffffffc000p
-985, -0x1.0000000000000p
-1039, -0x0.0000000000000p
+0, -0x0.0000000000000p
+0},
256 {-0x1.0080000000000p
-417, 0x1.0000000000000p
-490, 0x1.001ffffffc000p
-985, 0x1.0000000000000p
-1039, -0x0.0000000000000p
+0, -0x0.0000000000000p
+0},
257 {-0x1.0080000000000p
-417, 0x1.0000000000000p
-490, -0x1.001ffffffc000p
-985, -0x1.0000000000000p
-1039, 0x0.0000000000000p
+0, 0x0.0000000000000p
+0},
258 {0x1.000001fffff80p
-758, 0x1.fffffc001fffcp
-813, 0x1.00001ffff8000p
+939, 0x1.00007f001e000p
+884, 0x1.000021fff8380p
+181, 0x1.7bc05e90173aep
+127},
259 {0x1.000001fffff80p
-758, 0x1.fffffc001fffcp
-813, -0x1.00001ffff8000p
+939, -0x1.00007f001e000p
+884, -0x1.000021fff8380p
+181, -0x1.7bc05e90173aep
+127},
260 {-0x1.000001fffff80p
-758, -0x1.fffffc001fffcp
-813, 0x1.00001ffff8000p
+939, 0x1.00007f001e000p
+884, -0x1.000021fff8380p
+181, -0x1.7bc05e90173aep
+127},
261 {-0x1.000001fffff80p
-758, -0x1.fffffc001fffcp
-813, -0x1.00001ffff8000p
+939, -0x1.00007f001e000p
+884, 0x1.000021fff8380p
+181, 0x1.7bc05e90173aep
+127},
262 {0x1.00f3ffffff000p
-189, 0x1.fff8000000000p
-257, 0x1.3dfffffffc000p
+294, 0x1.ff000003ffe00p
+233, 0x1.3f2f17fffabe3p
+105, 0x1.02efbc1200d00p
+45},
263 {0x1.00f3ffffff000p
-189, 0x1.fff8000000000p
-257, -0x1.3dfffffffc000p
+294, -0x1.ff000003ffe00p
+233, -0x1.3f2f17fffabe3p
+105, -0x1.02efbc1200d00p
+45},
264 {-0x1.00f3ffffff000p
-189, -0x1.fff8000000000p
-257, 0x1.3dfffffffc000p
+294, 0x1.ff000003ffe00p
+233, -0x1.3f2f17fffabe3p
+105, -0x1.02efbc1200d00p
+45},
265 {-0x1.00f3ffffff000p
-189, -0x1.fff8000000000p
-257, -0x1.3dfffffffc000p
+294, -0x1.ff000003ffe00p
+233, 0x1.3f2f17fffabe3p
+105, 0x1.02efbc1200d00p
+45},
266 {0x1.0000001ffff80p
-98, 0x1.fffffdfffff8ep
-152, 0x1.0000000000000p
+1023, -0x1.0000000000000p
+953, 0x1.0000001ffff80p
+925, 0x1.fffefdffffd8ep
+871},
267 {0x1.0000001ffff80p
-98, 0x1.fffffdfffff8ep
-152, -0x1.0000000000000p
+1023, 0x1.0000000000000p
+953, -0x1.0000001ffff80p
+925, -0x1.fffefdffffd8ep
+871},
268 {-0x1.0000001ffff80p
-98, -0x1.fffffdfffff8ep
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715 {0x1.000003fff8000p
+711, 0x1.ffff00000003cp
+656, -0x1.000001ffff020p
+18, 0x1.fff0000200000p
-52, -0x1.000005fff70a0p
+729, -0x1.f5ff0817ec048p
+674},
716 {-0x1.000003fff8000p
+711, -0x1.ffff00000003cp
+656, 0x1.000001ffff020p
+18, -0x1.fff0000200000p
-52, -0x1.000005fff70a0p
+729, -0x1.f5ff0817ec048p
+674},
717 {-0x1.000003fff8000p
+711, -0x1.ffff00000003cp
+656, -0x1.000001ffff020p
+18, 0x1.fff0000200000p
-52, 0x1.000005fff70a0p
+729, 0x1.f5ff0817ec048p
+674},
718 {0x1.00ffe00000000p
-302, 0x1.fe00000000000p
-362, 0x1.0000100000000p
+87, -0x1.ffff800010000p
+18, 0x1.00fff00ffe000p
-215, 0x1.fcff20403ff00p
-275},
719 {0x1.00ffe00000000p
-302, 0x1.fe00000000000p
-362, -0x1.0000100000000p
+87, 0x1.ffff800010000p
+18, -0x1.00fff00ffe000p
-215, -0x1.fcff20403ff00p
-275},
720 {-0x1.00ffe00000000p
-302, -0x1.fe00000000000p
-362, 0x1.0000100000000p
+87, -0x1.ffff800010000p
+18, -0x1.00fff00ffe000p
-215, -0x1.fcff20403ff00p
-275},
721 {-0x1.00ffe00000000p
-302, -0x1.fe00000000000p
-362, -0x1.0000100000000p
+87, 0x1.ffff800010000p
+18, 0x1.00fff00ffe000p
-215, 0x1.fcff20403ff00p
-275},
722 {0x1.fffffff000008p
+565, -0x1.ffffff1000000p
+488, 0x1.0001fffffff80p
-162, 0x1.fffe000000000p
-247, 0x1.0001fff7ffe84p
+404, 0x1.00701fdbe7000p
+339},
723 {0x1.fffffff000008p
+565, -0x1.ffffff1000000p
+488, -0x1.0001fffffff80p
-162, -0x1.fffe000000000p
-247, -0x1.0001fff7ffe84p
+404, -0x1.00701fdbe7000p
+339},
724 {-0x1.fffffff000008p
+565, 0x1.ffffff1000000p
+488, 0x1.0001fffffff80p
-162, 0x1.fffe000000000p
-247, -0x1.0001fff7ffe84p
+404, -0x1.00701fdbe7000p
+339},
725 {-0x1.fffffff000008p
+565, 0x1.ffffff1000000p
+488, -0x1.0001fffffff80p
-162, -0x1.fffe000000000p
-247, 0x1.0001fff7ffe84p
+404, 0x1.00701fdbe7000p
+339},
728 const int numAccuracyTests
= sizeof(accuracyTests
) / sizeof(struct testVector
);
732 double testAccuracy() {
736 double worstUlps
= 0.5;
738 for (i
=0; i
<numAccuracyTests
; ++i
) {
739 a
.hi
= accuracyTests
[i
].xhi
;
740 a
.lo
= accuracyTests
[i
].xlo
;
741 b
.hi
= accuracyTests
[i
].yhi
;
742 b
.lo
= accuracyTests
[i
].ylo
;
743 r
.hi
= accuracyTests
[i
].rhi
;
744 r
.lo
= accuracyTests
[i
].rlo
;
746 DD c
= { .ld
= __gcc_qmul(a
.ld
, b
.ld
) };
748 double error
= __builtin_fabs(((r
.hi
- c
.hi
) + r
.lo
) - c
.lo
);
752 int exponent
= ilogb(r
.hi
);
753 exponent
= (exponent
< -1022 ? -1022 : exponent
);
754 double ulpError
= scalbn(error
, 106 - exponent
);
756 if (ulpError
> worstUlps
) {
757 #ifdef PRINT_ACCURACY_INFORMATION
758 printf("New worst rounding error for (%a,%a) x (%a,%a):\n", a
.hi
, a
.lo
, b
.hi
, b
.lo
);
759 printf("\tExpected: (%a,%a)\n", r
.hi
, r
.lo
);
760 printf("\tComputed: (%a,%a)\n", c
.hi
, c
.lo
);
761 printf("\tError: %f ulps\n", ulpError
);
763 worstUlps
= ulpError
;