1 #include <stdio.h> 2 #include "DD.h" 3 4 long double __gcc_qmul(long double x, long double y); 5 6 double testAccuracy(); 7 int testEdgeCases(); 8 9 int main(int argc, char *argv[]) { 10 if (testEdgeCases()) 11 return 1; 12 13 if (testAccuracy() > 2.0) 14 return 1; 15 16 return 0; 17 } 18 19 struct testVector { 20 double xhi; double xlo; 21 double yhi; double ylo; 22 double rhi; double rlo; 23 }; 24 25 #define INFINITY __builtin_inf() 26 #define HUGE 0x1.fffffffffffffp1023 27 #define QNAN __builtin_nan("") 28 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 }, 34 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 }, 63 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 }, 100 }; 101 102 const int numEdgeCases = sizeof(edgeCases) / sizeof(struct testVector); 103 104 105 int testEdgeCases() { 106 int i; 107 DD a, b, c, r; 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; 115 116 int error; 117 118 DD c = { .ld = __gcc_qmul(a.ld, b.ld) }; 119 120 if (r.hi != r.hi) { 121 if (c.hi == c.hi) 122 error = 1; 123 else if (c.lo != 0.0) 124 error = 1; 125 else 126 error = 0; 127 } 128 129 else if (r.hi == 0.0) 130 error = memcmp(&c, &r, sizeof(DD)); 131 132 else 133 error = ((c.hi != r.hi) || (c.lo != r.lo)); 134 135 if (error) { 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); 137 return 1; 138 } 139 } 140 141 return 0; 142 } 143 144 145 /* 146 147 Code for generating the test cases, requires the mpfr package to run. 148 149 #include <stdio.h> 150 #include <stdlib.h> 151 #include <mpfr.h> 152 #include <math.h> 153 154 #ifdef __x86_64__ 155 #define randlength 2 156 #else 157 #define randlength 4 158 #endif 159 160 void printTest(mpfr_t a, mpfr_t b, mpfr_t c) { 161 static const double INFINITYD = __builtin_INFINITY(); 162 163 MPFR_DECL_INIT(tmp, 53); 164 165 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); 170 171 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); 176 177 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); 182 } 183 184 int main(int argc, char *argv[]) { 185 186 MPFR_DECL_INIT(a, 106); 187 MPFR_DECL_INIT(b, 106); 188 MPFR_DECL_INIT(c, 106); 189 190 int exponent_range = atoi(argv[1]); 191 192 int i; 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); 197 printTest(a, b, c); 198 199 mpfr_neg(b, b, GMP_RNDN); 200 mpfr_mul(c, a, b, GMP_RNDN); 201 printTest(a, b, c); 202 203 mpfr_neg(a, a, GMP_RNDN); 204 mpfr_neg(b, b, GMP_RNDN); 205 mpfr_mul(c, a, b, GMP_RNDN); 206 printTest(a, b, c); 207 208 mpfr_neg(b, b, GMP_RNDN); 209 mpfr_mul(c, a, b, GMP_RNDN); 210 printTest(a, b, c); 211 } 212 return 0; 213 } 214 215 */ 216 217 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-152, 0x1.0000000000000p+1023, -0x1.0000000000000p+953, -0x1.0000001ffff80p+925, -0x1.fffefdffffd8ep+871}, 269 {-0x1.0000001ffff80p-98, -0x1.fffffdfffff8ep-152, -0x1.0000000000000p+1023, 0x1.0000000000000p+953, 0x1.0000001ffff80p+925, 0x1.fffefdffffd8ep+871}, 270 {0x1.001fffffffe00p+730, 0x0.0000000000000p+0, 0x1.0000002000000p+702, -0x1.0000000000000p+602, INFINITY, 0x0.0000000000000p+0}, 271 {0x1.001fffffffe00p+730, 0x0.0000000000000p+0, -0x1.0000002000000p+702, 0x1.0000000000000p+602, -INFINITY, 0x0.0000000000000p+0}, 272 {-0x1.001fffffffe00p+730, 0x0.0000000000000p+0, 0x1.0000002000000p+702, -0x1.0000000000000p+602, -INFINITY, 0x0.0000000000000p+0}, 273 {-0x1.001fffffffe00p+730, 0x0.0000000000000p+0, -0x1.0000002000000p+702, 0x1.0000000000000p+602, INFINITY, 0x0.0000000000000p+0}, 274 {0x1.01ffffffe0000p+902, 0x1.c000000200000p+841, 0x1.0001fff800ffep-251, 0x1.c000000000000p-354, 0x1.020203f7d101ap+651, -0x1.88001fe2ff740p+592}, 275 {0x1.01ffffffe0000p+902, 0x1.c000000200000p+841, -0x1.0001fff800ffep-251, -0x1.c000000000000p-354, -0x1.020203f7d101ap+651, 0x1.88001fe2ff740p+592}, 276 {-0x1.01ffffffe0000p+902, -0x1.c000000200000p+841, 0x1.0001fff800ffep-251, 0x1.c000000000000p-354, -0x1.020203f7d101ap+651, 0x1.88001fe2ff740p+592}, 277 {-0x1.01ffffffe0000p+902, -0x1.c000000200000p+841, -0x1.0001fff800ffep-251, -0x1.c000000000000p-354, 0x1.020203f7d101ap+651, -0x1.88001fe2ff740p+592}, 278 {0x1.00000007ff800p-179, 0x1.ffff800000000p-267, 0x1.00003fe0c4000p+973, -0x1.fffc032000000p+910, 0x1.00003fe8c3820p+794, -0x1.1dd05a045ffe0p+738}, 279 {0x1.00000007ff800p-179, 0x1.ffff800000000p-267, -0x1.00003fe0c4000p+973, 0x1.fffc032000000p+910, -0x1.00003fe8c3820p+794, 0x1.1dd05a045ffe0p+738}, 280 {-0x1.00000007ff800p-179, -0x1.ffff800000000p-267, 0x1.00003fe0c4000p+973, -0x1.fffc032000000p+910, -0x1.00003fe8c3820p+794, 0x1.1dd05a045ffe0p+738}, 281 {-0x1.00000007ff800p-179, -0x1.ffff800000000p-267, -0x1.00003fe0c4000p+973, 0x1.fffc032000000p+910, 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0x1.008401fffbfdfp-245, -0x1.bf5ffdf221f10p-302}, 707 {0x1.007ffffffc000p-157, 0x1.ffffff8000000p-224, -0x1.0003fffffffe0p-88, -0x1.fffffff000780p-148, -0x1.008401fffbfdfp-245, 0x1.bf5ffdf221f10p-302}, 708 {-0x1.007ffffffc000p-157, -0x1.ffffff8000000p-224, 0x1.0003fffffffe0p-88, 0x1.fffffff000780p-148, -0x1.008401fffbfdfp-245, 0x1.bf5ffdf221f10p-302}, 709 {-0x1.007ffffffc000p-157, -0x1.ffffff8000000p-224, -0x1.0003fffffffe0p-88, -0x1.fffffff000780p-148, 0x1.008401fffbfdfp-245, -0x1.bf5ffdf221f10p-302}, 710 {0x1.07fffffe0003cp-432, 0x1.ffe000007f000p-497, 0x1.1ffff00800000p+307, -0x1.0000000000000p+210, 0x1.28ffef8600045p-125, 0x1.fc3902fc0230cp-179}, 711 {0x1.07fffffe0003cp-432, 0x1.ffe000007f000p-497, -0x1.1ffff00800000p+307, 0x1.0000000000000p+210, -0x1.28ffef8600045p-125, -0x1.fc3902fc0230cp-179}, 712 {-0x1.07fffffe0003cp-432, -0x1.ffe000007f000p-497, 0x1.1ffff00800000p+307, -0x1.0000000000000p+210, -0x1.28ffef8600045p-125, -0x1.fc3902fc0230cp-179}, 713 {-0x1.07fffffe0003cp-432, -0x1.ffe000007f000p-497, -0x1.1ffff00800000p+307, 0x1.0000000000000p+210, 0x1.28ffef8600045p-125, 0x1.fc3902fc0230cp-179}, 714 {0x1.000003fff8000p+711, 0x1.ffff00000003cp+656, 0x1.000001ffff020p+18, -0x1.fff0000200000p-52, 0x1.000005fff70a0p+729, 0x1.f5ff0817ec048p+674}, 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}, 726 }; 727 728 const int numAccuracyTests = sizeof(accuracyTests) / sizeof(struct testVector); 729 730 #include <math.h> 731 732 double testAccuracy() { 733 int i; 734 DD a, b, c, r; 735 736 double worstUlps = 0.5; 737 738 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; 745 746 DD c = { .ld = __gcc_qmul(a.ld, b.ld) }; 747 748 double error = __builtin_fabs(((r.hi - c.hi) + r.lo) - c.lo); 749 750 if (error != 0.0) { 751 752 int exponent = ilogb(r.hi); 753 exponent = (exponent < -1022 ? -1022 : exponent); 754 double ulpError = scalbn(error, 106 - exponent); 755 756 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); 762 #endif 763 worstUlps = ulpError; 764 } 765 } 766 } 767 768 return worstUlps; 769 } 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794
