1 #include <stdio.h> 2 #include "DD.h" 3 4 long double __gcc_qdiv(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() > 4.0) 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, QNAN, 0.0 }, 31 { -0.0, 0.0, 0.0, 0.0, QNAN, 0.0 }, 32 { 0.0, 0.0, -0.0, 0.0, QNAN, 0.0 }, 33 { -0.0, 0.0, -0.0, 0.0, QNAN, 0.0 }, 34 35 { INFINITY, 0.0, 0.0, 0.0, INFINITY, 0.0 }, 36 { -INFINITY, 0.0, 0.0, 0.0, -INFINITY, 0.0 }, 37 { INFINITY, 0.0, -0.0, 0.0, -INFINITY, 0.0 }, 38 { -INFINITY, 0.0, -0.0, 0.0, INFINITY, 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, QNAN, 0.0 }, 48 { -INFINITY, 0.0, INFINITY, 0.0, -QNAN, 0.0 }, 49 { INFINITY, 0.0, -INFINITY, 0.0, -QNAN, 0.0 }, 50 { -INFINITY, 0.0, -INFINITY, 0.0, QNAN, 0.0 }, 51 { 0.0, 0.0, INFINITY, 0.0, 0.0, 0.0 }, 52 { 0.0, 0.0, -INFINITY, 0.0, -0.0, 0.0 }, 53 { -0.0, 0.0, INFINITY, 0.0, -0.0, 0.0 }, 54 { -0.0, 0.0, -INFINITY, 0.0, 0.0, 0.0 }, 55 { 1.0, 0.0, INFINITY, 0.0, 0.0, 0.0 }, 56 { 1.0, 0.0, -INFINITY, 0.0, -0.0, 0.0 }, 57 { -1.0, 0.0, INFINITY, 0.0, -0.0, 0.0 }, 58 { -1.0, 0.0, -INFINITY, 0.0, 0.0, 0.0 }, 59 { HUGE, 0.0, INFINITY, 0.0, 0.0, 0.0 }, 60 { HUGE, 0.0, -INFINITY, 0.0, -0.0, 0.0 }, 61 { -HUGE, 0.0, INFINITY, 0.0, -0.0, 0.0 }, 62 { -HUGE, 0.0, -INFINITY, 0.0, 0.0, 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_qdiv(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 / %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 #include <stdio.h> 148 #include <stdlib.h> 149 #include <mpfr.h> 150 #include <math.h> 151 152 #ifdef __x86_64__ 153 #define randlength 2 154 #else 155 #define randlength 4 156 #endif 157 158 void printTest(mpfr_t a, mpfr_t b, mpfr_t c) { 159 static const double infinityD = __builtin_inf(); 160 161 MPFR_DECL_INIT(tmp, 53); 162 163 double ahi = mpfr_get_d(a, GMP_RNDN); 164 mpfr_set_d(tmp, ahi, GMP_RNDN); 165 mpfr_sub(tmp, a, tmp, GMP_RNDN); 166 double alo = mpfr_get_d(tmp, GMP_RNDN); 167 printf("{%0.13a, %0.13a, ", ahi, alo); 168 169 double bhi = mpfr_get_d(b, GMP_RNDN); 170 mpfr_set_d(tmp, bhi, GMP_RNDN); 171 mpfr_sub(tmp, b, tmp, GMP_RNDN); 172 double blo = mpfr_get_d(tmp, GMP_RNDN); 173 printf("%0.13a, %0.13a, ", bhi, blo); 174 175 double chi = mpfr_get_d(c, GMP_RNDN); 176 mpfr_set_d(tmp, chi, GMP_RNDN); 177 mpfr_sub(tmp, c, tmp, GMP_RNDN); 178 double clo = isinf(chi) ? 0.0 : mpfr_get_d(tmp, GMP_RNDN); 179 printf("%0.13a, %0.13a},\n", chi, clo); 180 } 181 182 int main(int argc, char *argv[]) { 183 184 MPFR_DECL_INIT(a, 106); 185 MPFR_DECL_INIT(b, 106); 186 MPFR_DECL_INIT(c, 106); 187 188 int exponent_range = atoi(argv[1]); 189 190 int i; 191 for (i=0; i<128; ++i) { 192 mpfr_random2(a, randlength, exponent_range); 193 mpfr_random2(b, randlength, exponent_range); 194 mpfr_div(c, a, b, GMP_RNDN); 195 printTest(a, b, c); 196 197 mpfr_neg(b, b, GMP_RNDN); 198 mpfr_div(c, a, b, GMP_RNDN); 199 printTest(a, b, c); 200 201 mpfr_neg(a, a, GMP_RNDN); 202 mpfr_neg(b, b, GMP_RNDN); 203 mpfr_div(c, a, b, GMP_RNDN); 204 printTest(a, b, c); 205 206 mpfr_neg(b, b, GMP_RNDN); 207 mpfr_div(c, a, b, GMP_RNDN); 208 printTest(a, b, c); 209 } 210 return 0; 211 } 212 213 */ 214 215 const struct testVector accuracyTests[] = { 216 {0x1.00001ffffff00p+419, 0x1.fffff83ff8000p+364, 0x1.00ffc00ffff00p-598, 0x1.fe0007fffff00p-654, 0x1.fe02bca42ad25p+1016, 0x1.29aa5d717c42cp+961}, 217 {0x1.00001ffffff00p+419, 0x1.fffff83ff8000p+364, -0x1.00ffc00ffff00p-598, -0x1.fe0007fffff00p-654, -0x1.fe02bca42ad25p+1016, -0x1.29aa5d717c42cp+961}, 218 {-0x1.00001ffffff00p+419, -0x1.fffff83ff8000p+364, 0x1.00ffc00ffff00p-598, 0x1.fe0007fffff00p-654, -0x1.fe02bca42ad25p+1016, -0x1.29aa5d717c42cp+961}, 219 {-0x1.00001ffffff00p+419, -0x1.fffff83ff8000p+364, -0x1.00ffc00ffff00p-598, -0x1.fe0007fffff00p-654, 0x1.fe02bca42ad25p+1016, 0x1.29aa5d717c42cp+961}, 220 {0x1.00001fffff800p-575, 0x1.fffffffe00000p-649, 0x1.3fffffff80000p-17, 0x1.ffffffff00000p-90, 0x1.9999cccd6fd72p-559, -0x1.476d58085a038p-615}, 221 {0x1.00001fffff800p-575, 0x1.fffffffe00000p-649, -0x1.3fffffff80000p-17, -0x1.ffffffff00000p-90, -0x1.9999cccd6fd72p-559, 0x1.476d58085a038p-615}, 222 {-0x1.00001fffff800p-575, -0x1.fffffffe00000p-649, 0x1.3fffffff80000p-17, 0x1.ffffffff00000p-90, -0x1.9999cccd6fd72p-559, 0x1.476d58085a038p-615}, 223 {-0x1.00001fffff800p-575, -0x1.fffffffe00000p-649, -0x1.3fffffff80000p-17, -0x1.ffffffff00000p-90, 0x1.9999cccd6fd72p-559, -0x1.476d58085a038p-615}, 224 {0x1.0000000800000p-557, -0x1.0000000000000p-629, 0x1.000003fffc002p+323, -0x1.0000000000000p+218, 0x1.fffff810081f8p-881, -0x1.00fb820825b80p-939}, 225 {0x1.0000000800000p-557, -0x1.0000000000000p-629, -0x1.000003fffc002p+323, 0x1.0000000000000p+218, -0x1.fffff810081f8p-881, 0x1.00fb820825b80p-939}, 226 {-0x1.0000000800000p-557, 0x1.0000000000000p-629, 0x1.000003fffc002p+323, -0x1.0000000000000p+218, -0x1.fffff810081f8p-881, 0x1.00fb820825b80p-939}, 227 {-0x1.0000000800000p-557, 0x1.0000000000000p-629, -0x1.000003fffc002p+323, 0x1.0000000000000p+218, 0x1.fffff810081f8p-881, -0x1.00fb820825b80p-939}, 228 {0x1.000003ffffffep+356, -0x1.ffe0080000000p+272, 0x1.0800000000000p-150, -0x1.0000000000000p-246, 0x1.f07c26c9b26c6p+505, -0x1.745d1764d6558p+450}, 229 {0x1.000003ffffffep+356, -0x1.ffe0080000000p+272, -0x1.0800000000000p-150, 0x1.0000000000000p-246, -0x1.f07c26c9b26c6p+505, 0x1.745d1764d6558p+450}, 230 {-0x1.000003ffffffep+356, 0x1.ffe0080000000p+272, 0x1.0800000000000p-150, -0x1.0000000000000p-246, -0x1.f07c26c9b26c6p+505, 0x1.745d1764d6558p+450}, 231 {-0x1.000003ffffffep+356, 0x1.ffe0080000000p+272, -0x1.0800000000000p-150, 0x1.0000000000000p-246, 0x1.f07c26c9b26c6p+505, -0x1.745d1764d6558p+450}, 232 {0x1.0000007fffc00p-14, 0x1.efe0000000000p-108, 0x1.007fffffe0000p-312, 0x0.0000000000000p+0, 0x1.ff0080bfdf705p+297, 0x1.fb017ac5608fap+243}, 233 {0x1.0000007fffc00p-14, 0x1.efe0000000000p-108, -0x1.007fffffe0000p-312, 0x0.0000000000000p+0, -0x1.ff0080bfdf705p+297, -0x1.fb017ac5608fap+243}, 234 {-0x1.0000007fffc00p-14, -0x1.efe0000000000p-108, 0x1.007fffffe0000p-312, 0x0.0000000000000p+0, -0x1.ff0080bfdf705p+297, -0x1.fb017ac5608fap+243}, 235 {-0x1.0000007fffc00p-14, -0x1.efe0000000000p-108, -0x1.007fffffe0000p-312, 0x0.0000000000000p+0, 0x1.ff0080bfdf705p+297, 0x1.fb017ac5608fap+243}, 236 {0x1.3fe0000100000p-744, -0x1.0000000000000p-817, 0x1.3fffffffffe00p+293, 0x1.fe00040000000p+218, 0x1.ffccccce60000p-1038, 0x0.0000000000000p+0}, 237 {0x1.3fe0000100000p-744, -0x1.0000000000000p-817, -0x1.3fffffffffe00p+293, -0x1.fe00040000000p+218, -0x1.ffccccce60000p-1038, -0x0.0000000000000p+0}, 238 {-0x1.3fe0000100000p-744, 0x1.0000000000000p-817, 0x1.3fffffffffe00p+293, 0x1.fe00040000000p+218, -0x1.ffccccce60000p-1038, -0x0.0000000000000p+0}, 239 {-0x1.3fe0000100000p-744, 0x1.0000000000000p-817, -0x1.3fffffffffe00p+293, -0x1.fe00040000000p+218, 0x1.ffccccce60000p-1038, 0x0.0000000000000p+0}, 240 {0x1.0001fff800000p+0, 0x1.ffffff0000ffep-54, 0x1.00ff000000800p+11, -0x1.0000000800000p-55, 0x1.fe07f601f30ffp-12, -0x1.b3714144d2a90p-69}, 241 {0x1.0001fff800000p+0, 0x1.ffffff0000ffep-54, -0x1.00ff000000800p+11, 0x1.0000000800000p-55, -0x1.fe07f601f30ffp-12, 0x1.b3714144d2a90p-69}, 242 {-0x1.0001fff800000p+0, -0x1.ffffff0000ffep-54, 0x1.00ff000000800p+11, -0x1.0000000800000p-55, -0x1.fe07f601f30ffp-12, 0x1.b3714144d2a90p-69}, 243 {-0x1.0001fff800000p+0, -0x1.ffffff0000ffep-54, -0x1.00ff000000800p+11, 0x1.0000000800000p-55, 0x1.fe07f601f30ffp-12, -0x1.b3714144d2a90p-69}, 244 {0x1.0000800000000p-381, -0x1.ffffffe400000p-444, 0x1.000001ffffffap+606, -0x1.ffe1f80400000p+531, 0x1.00007dffff046p-987, -0x1.d940000000000p-1051}, 245 {0x1.0000800000000p-381, -0x1.ffffffe400000p-444, -0x1.000001ffffffap+606, 0x1.ffe1f80400000p+531, -0x1.00007dffff046p-987, 0x1.d940000000000p-1051}, 246 {-0x1.0000800000000p-381, 0x1.ffffffe400000p-444, 0x1.000001ffffffap+606, -0x1.ffe1f80400000p+531, -0x1.00007dffff046p-987, 0x1.d940000000000p-1051}, 247 {-0x1.0000800000000p-381, 0x1.ffffffe400000p-444, -0x1.000001ffffffap+606, 0x1.ffe1f80400000p+531, 0x1.00007dffff046p-987, -0x1.d940000000000p-1051}, 248 {0x1.0000010000000p+772, -0x1.0000000000000p+667, 0x1.007fffffffc00p+750, 0x1.fffffc0000000p+679, 0x1.ff0081bf20ef5p+21, -0x1.e0f5922874ff2p-33}, 249 {0x1.0000010000000p+772, -0x1.0000000000000p+667, -0x1.007fffffffc00p+750, -0x1.fffffc0000000p+679, -0x1.ff0081bf20ef5p+21, 0x1.e0f5922874ff2p-33}, 250 {-0x1.0000010000000p+772, 0x1.0000000000000p+667, 0x1.007fffffffc00p+750, 0x1.fffffc0000000p+679, -0x1.ff0081bf20ef5p+21, 0x1.e0f5922874ff2p-33}, 251 {-0x1.0000010000000p+772, 0x1.0000000000000p+667, -0x1.007fffffffc00p+750, -0x1.fffffc0000000p+679, 0x1.ff0081bf20ef5p+21, -0x1.e0f5922874ff2p-33}, 252 {0x1.0080000000000p-547, -0x1.0000000000000p-620, 0x1.001ffffffc000p+963, 0x1.fffffffff001cp+908, 0x0.0000000000000p+0, 0x0.0000000000000p+0}, 253 {0x1.0080000000000p-547, -0x1.0000000000000p-620, -0x1.001ffffffc000p+963, -0x1.fffffffff001cp+908, -0x0.0000000000000p+0, -0x0.0000000000000p+0}, 254 {-0x1.0080000000000p-547, 0x1.0000000000000p-620, 0x1.001ffffffc000p+963, 0x1.fffffffff001cp+908, -0x0.0000000000000p+0, -0x0.0000000000000p+0}, 255 {-0x1.0080000000000p-547, 0x1.0000000000000p-620, -0x1.001ffffffc000p+963, -0x1.fffffffff001cp+908, 0x0.0000000000000p+0, 0x0.0000000000000p+0}, 256 {0x1.000001fffff80p-138, 0x1.fffffc001fffcp-193, 0x1.00001ffff8000p-554, 0x1.00007f001e000p-609, 0x1.ffffc40017700p+415, -0x1.9c017d7fb3e20p+358}, 257 {0x1.000001fffff80p-138, 0x1.fffffc001fffcp-193, -0x1.00001ffff8000p-554, -0x1.00007f001e000p-609, -0x1.ffffc40017700p+415, 0x1.9c017d7fb3e20p+358}, 258 {-0x1.000001fffff80p-138, -0x1.fffffc001fffcp-193, 0x1.00001ffff8000p-554, 0x1.00007f001e000p-609, -0x1.ffffc40017700p+415, 0x1.9c017d7fb3e20p+358}, 259 {-0x1.000001fffff80p-138, -0x1.fffffc001fffcp-193, -0x1.00001ffff8000p-554, -0x1.00007f001e000p-609, 0x1.ffffc40017700p+415, -0x1.9c017d7fb3e20p+358}, 260 {0x1.00f3ffffff000p-238, 0x1.fff8000000000p-306, 0x1.3dfffffffc000p-529, 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{-0x1.0000001ffff80p-69, -0x1.fffffdfffff8ep-123, -0x1.0000000000000p-311, 0x1.0000000000000p-381, 0x1.0000001ffff81p+242, -0x1.ffff01ffffe72p+188}, 268 {0x1.001fffffffe00p-160, 0x0.0000000000000p+0, 0x1.0000002000000p+499, -0x1.0000000000000p+399, 0x1.001fffdffbe00p-659, 0x1.0020ffdffbe40p-713}, 269 {0x1.001fffffffe00p-160, 0x0.0000000000000p+0, -0x1.0000002000000p+499, 0x1.0000000000000p+399, -0x1.001fffdffbe00p-659, -0x1.0020ffdffbe40p-713}, 270 {-0x1.001fffffffe00p-160, 0x0.0000000000000p+0, 0x1.0000002000000p+499, -0x1.0000000000000p+399, -0x1.001fffdffbe00p-659, -0x1.0020ffdffbe40p-713}, 271 {-0x1.001fffffffe00p-160, 0x0.0000000000000p+0, -0x1.0000002000000p+499, 0x1.0000000000000p+399, 0x1.001fffdffbe00p-659, 0x1.0020ffdffbe40p-713}, 272 {0x1.01ffffffe0000p+182, 0x1.c000000200000p+121, 0x1.0001fff800ffep-8, 0x1.c000000000000p-111, 0x1.01fdfc0bf6d61p+190, 0x1.41500c3427868p+136}, 273 {0x1.01ffffffe0000p+182, 0x1.c000000200000p+121, -0x1.0001fff800ffep-8, -0x1.c000000000000p-111, 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{0x1.007fffffffc00p+472, 0x1.fffffe0000000p+390, -0x1.0000003fffff8p-373, -0x1.fffff80000000p-444, -0x1.007fffbfdfc09p+845, -0x1.202ee977b9860p+787}, 702 {-0x1.007fffffffc00p+472, -0x1.fffffe0000000p+390, 0x1.0000003fffff8p-373, 0x1.fffff80000000p-444, -0x1.007fffbfdfc09p+845, -0x1.202ee977b9860p+787}, 703 {-0x1.007fffffffc00p+472, -0x1.fffffe0000000p+390, -0x1.0000003fffff8p-373, -0x1.fffff80000000p-444, 0x1.007fffbfdfc09p+845, 0x1.202ee977b9860p+787}, 704 {0x1.00000003ff000p+517, 0x1.ffffff0000000p+455, 0x1.0000ffff80000p+482, 0x1.e0000000fffc0p+423, 0x1.fffe000afdf40p+34, 0x1.a97dc87838c28p-22}, 705 {0x1.00000003ff000p+517, 0x1.ffffff0000000p+455, -0x1.0000ffff80000p+482, -0x1.e0000000fffc0p+423, -0x1.fffe000afdf40p+34, -0x1.a97dc87838c28p-22}, 706 {-0x1.00000003ff000p+517, -0x1.ffffff0000000p+455, 0x1.0000ffff80000p+482, 0x1.e0000000fffc0p+423, -0x1.fffe000afdf40p+34, -0x1.a97dc87838c28p-22}, 707 {-0x1.00000003ff000p+517, -0x1.ffffff0000000p+455, -0x1.0000ffff80000p+482, -0x1.e0000000fffc0p+423, 0x1.fffe000afdf40p+34, 0x1.a97dc87838c28p-22}, 708 {0x1.007ffffffc000p-870, 0x1.ffffff8000000p-937, 0x1.0003fffffffe0p-380, 0x1.fffffff000780p-440, 0x1.007bfe1003c1fp-490, 0x1.d0655eb0f91c0p-546}, 709 {0x1.007ffffffc000p-870, 0x1.ffffff8000000p-937, -0x1.0003fffffffe0p-380, -0x1.fffffff000780p-440, -0x1.007bfe1003c1fp-490, -0x1.d0655eb0f91c0p-546}, 710 {-0x1.007ffffffc000p-870, -0x1.ffffff8000000p-937, 0x1.0003fffffffe0p-380, 0x1.fffffff000780p-440, -0x1.007bfe1003c1fp-490, -0x1.d0655eb0f91c0p-546}, 711 {-0x1.007ffffffc000p-870, -0x1.ffffff8000000p-937, -0x1.0003fffffffe0p-380, -0x1.fffffff000780p-440, 0x1.007bfe1003c1fp-490, 0x1.d0655eb0f91c0p-546}, 712 {0x1.07fffffe0003cp+175, 0x1.ffe000007f000p+110, 0x1.1ffff00800000p-290, -0x1.0000000000000p-387, 0x1.d5556f57b59dcp+464, 0x1.ea436d67e8132p+410}, 713 {0x1.07fffffe0003cp+175, 0x1.ffe000007f000p+110, -0x1.1ffff00800000p-290, 0x1.0000000000000p-387, -0x1.d5556f57b59dcp+464, -0x1.ea436d67e8132p+410}, 714 {-0x1.07fffffe0003cp+175, -0x1.ffe000007f000p+110, 0x1.1ffff00800000p-290, -0x1.0000000000000p-387, -0x1.d5556f57b59dcp+464, -0x1.ea436d67e8132p+410}, 715 {-0x1.07fffffe0003cp+175, -0x1.ffe000007f000p+110, -0x1.1ffff00800000p-290, 0x1.0000000000000p-387, 0x1.d5556f57b59dcp+464, 0x1.ea436d67e8132p+410}, 716 {0x1.000003fff8000p+401, 0x1.ffff00000003cp+346, 0x1.000001ffff020p+721, -0x1.fff0000200000p+651, 0x1.000001fff8fa0p-320, 0x1.04037c2a010d6p-374}, 717 {0x1.000003fff8000p+401, 0x1.ffff00000003cp+346, -0x1.000001ffff020p+721, 0x1.fff0000200000p+651, -0x1.000001fff8fa0p-320, -0x1.04037c2a010d6p-374}, 718 {-0x1.000003fff8000p+401, -0x1.ffff00000003cp+346, 0x1.000001ffff020p+721, -0x1.fff0000200000p+651, -0x1.000001fff8fa0p-320, -0x1.04037c2a010d6p-374}, 719 {-0x1.000003fff8000p+401, -0x1.ffff00000003cp+346, -0x1.000001ffff020p+721, 0x1.fff0000200000p+651, 0x1.000001fff8fa0p-320, 0x1.04037c2a010d6p-374}, 720 {0x1.00ffe00000000p-249, 0x1.fe00000000000p-309, 0x1.0000100000000p+516, -0x1.ffff800010000p+447, 0x1.00ffcff003010p-765, -0x1.01fef05060e00p-825}, 721 {0x1.00ffe00000000p-249, 0x1.fe00000000000p-309, -0x1.0000100000000p+516, 0x1.ffff800010000p+447, -0x1.00ffcff003010p-765, 0x1.01fef05060e00p-825}, 722 {-0x1.00ffe00000000p-249, -0x1.fe00000000000p-309, 0x1.0000100000000p+516, -0x1.ffff800010000p+447, -0x1.00ffcff003010p-765, 0x1.01fef05060e00p-825}, 723 {-0x1.00ffe00000000p-249, -0x1.fe00000000000p-309, -0x1.0000100000000p+516, 0x1.ffff800010000p+447, 0x1.00ffcff003010p-765, -0x1.01fef05060e00p-825}, 724 {0x1.fffffff000008p-375, -0x1.ffffff1000000p-452, 0x1.0001fffffff80p-412, 0x1.fffe000000000p-497, 0x1.fffbfff800208p+37, -0x1.83fe387f7d700p-21}, 725 {0x1.fffffff000008p-375, -0x1.ffffff1000000p-452, -0x1.0001fffffff80p-412, -0x1.fffe000000000p-497, -0x1.fffbfff800208p+37, 0x1.83fe387f7d700p-21}, 726 {-0x1.fffffff000008p-375, 0x1.ffffff1000000p-452, 0x1.0001fffffff80p-412, 0x1.fffe000000000p-497, -0x1.fffbfff800208p+37, 0x1.83fe387f7d700p-21}, 727 {-0x1.fffffff000008p-375, 0x1.ffffff1000000p-452, -0x1.0001fffffff80p-412, -0x1.fffe000000000p-497, 0x1.fffbfff800208p+37, -0x1.83fe387f7d700p-21}, 728 }; 729 730 const int numAccuracyTests = sizeof(accuracyTests) / sizeof(struct testVector); 731 732 #include <math.h> 733 734 double testAccuracy() { 735 int i; 736 DD a, b, c, r; 737 738 double worstUlps = 0.5; 739 740 for (i=0; i<numAccuracyTests; ++i) { 741 a.hi = accuracyTests[i].xhi; 742 a.lo = accuracyTests[i].xlo; 743 b.hi = accuracyTests[i].yhi; 744 b.lo = accuracyTests[i].ylo; 745 r.hi = accuracyTests[i].rhi; 746 r.lo = accuracyTests[i].rlo; 747 748 DD c = { .ld = __gcc_qdiv(a.ld, b.ld) }; 749 750 double error = __builtin_fabs(((r.hi - c.hi) + r.lo) - c.lo); 751 752 if (error != 0.0) { 753 754 int exponent = ilogb(r.hi); 755 exponent = (exponent < -1022 ? -1022 : exponent); 756 double ulpError = scalbn(error, 106 - exponent); 757 758 if (ulpError > worstUlps) { 759 #ifdef PRINT_ACCURACY_INFORMATION 760 printf("New worst rounding error for (%a,%a) / (%a,%a):\n", a.hi, a.lo, b.hi, b.lo); 761 printf("\tExpected: (%a,%a)\n", r.hi, r.lo); 762 printf("\tComputed: (%a,%a)\n", c.hi, c.lo); 763 printf("\tError: %f ulps\n", ulpError); 764 #endif 765 worstUlps = ulpError; 766 } 767 } 768 } 769 770 return worstUlps; 771 } 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796
