}
return h;
}
+/*
+** The following array holds (approximate) powers-of-ten between
+** 1.0e-348 and 1.0e+347. Each value is an unsigned 64-bit integer,
+** shifted so that its most significant bit is 1.
+*/
+static const u64 sqlite3PowerOfTen[] = {
+ 0xfa8fd5a0081c0288, /* 0: 1.0e-348 << 1220 */
+ 0x9c99e58405118195, /* 1: 1.0e-347 << 1216 */
+ 0xc3c05ee50655e1fa, /* 2: 1.0e-346 << 1213 */
+ 0xf4b0769e47eb5a78, /* 3: 1.0e-345 << 1210 */
+ 0x98ee4a22ecf3188b, /* 4: 1.0e-344 << 1206 */
+ 0xbf29dcaba82fdeae, /* 5: 1.0e-343 << 1203 */
+ 0xeef453d6923bd65a, /* 6: 1.0e-342 << 1200 */
+ 0x9558b4661b6565f8, /* 7: 1.0e-341 << 1196 */
+ 0xbaaee17fa23ebf76, /* 8: 1.0e-340 << 1193 */
+ 0xe95a99df8ace6f53, /* 9: 1.0e-339 << 1190 */
+ 0x91d8a02bb6c10594, /* 10: 1.0e-338 << 1186 */
+ 0xb64ec836a47146f9, /* 11: 1.0e-337 << 1183 */
+ 0xe3e27a444d8d98b7, /* 12: 1.0e-336 << 1180 */
+ 0x8e6d8c6ab0787f72, /* 13: 1.0e-335 << 1176 */
+ 0xb208ef855c969f4f, /* 14: 1.0e-334 << 1173 */
+ 0xde8b2b66b3bc4723, /* 15: 1.0e-333 << 1170 */
+ 0x8b16fb203055ac76, /* 16: 1.0e-332 << 1166 */
+ 0xaddcb9e83c6b1793, /* 17: 1.0e-331 << 1163 */
+ 0xd953e8624b85dd78, /* 18: 1.0e-330 << 1160 */
+ 0x87d4713d6f33aa6b, /* 19: 1.0e-329 << 1156 */
+ 0xa9c98d8ccb009506, /* 20: 1.0e-328 << 1153 */
+ 0xd43bf0effdc0ba48, /* 21: 1.0e-327 << 1150 */
+ 0x84a57695fe98746d, /* 22: 1.0e-326 << 1146 */
+ 0xa5ced43b7e3e9188, /* 23: 1.0e-325 << 1143 */
+ 0xcf42894a5dce35ea, /* 24: 1.0e-324 << 1140 */
+ 0x818995ce7aa0e1b2, /* 25: 1.0e-323 << 1136 */
+ 0xa1ebfb4219491a1f, /* 26: 1.0e-322 << 1133 */
+ 0xca66fa129f9b60a6, /* 27: 1.0e-321 << 1130 */
+ 0xfd00b897478238d0, /* 28: 1.0e-320 << 1127 */
+ 0x9e20735e8cb16382, /* 29: 1.0e-319 << 1123 */
+ 0xc5a890362fddbc62, /* 30: 1.0e-318 << 1120 */
+ 0xf712b443bbd52b7b, /* 31: 1.0e-317 << 1117 */
+ 0x9a6bb0aa55653b2d, /* 32: 1.0e-316 << 1113 */
+ 0xc1069cd4eabe89f8, /* 33: 1.0e-315 << 1110 */
+ 0xf148440a256e2c76, /* 34: 1.0e-314 << 1107 */
+ 0x96cd2a865764dbca, /* 35: 1.0e-313 << 1103 */
+ 0xbc807527ed3e12bc, /* 36: 1.0e-312 << 1100 */
+ 0xeba09271e88d976b, /* 37: 1.0e-311 << 1097 */
+ 0x93445b8731587ea3, /* 38: 1.0e-310 << 1093 */
+ 0xb8157268fdae9e4c, /* 39: 1.0e-309 << 1090 */
+ 0xe61acf033d1a45df, /* 40: 1.0e-308 << 1087 */
+ 0x8fd0c16206306bab, /* 41: 1.0e-307 << 1083 */
+ 0xb3c4f1ba87bc8696, /* 42: 1.0e-306 << 1080 */
+ 0xe0b62e2929aba83c, /* 43: 1.0e-305 << 1077 */
+ 0x8c71dcd9ba0b4925, /* 44: 1.0e-304 << 1073 */
+ 0xaf8e5410288e1b6f, /* 45: 1.0e-303 << 1070 */
+ 0xdb71e91432b1a24a, /* 46: 1.0e-302 << 1067 */
+ 0x892731ac9faf056e, /* 47: 1.0e-301 << 1063 */
+ 0xab70fe17c79ac6ca, /* 48: 1.0e-300 << 1060 */
+ 0xd64d3d9db981787d, /* 49: 1.0e-299 << 1057 */
+ 0x85f0468293f0eb4e, /* 50: 1.0e-298 << 1053 */
+ 0xa76c582338ed2621, /* 51: 1.0e-297 << 1050 */
+ 0xd1476e2c07286faa, /* 52: 1.0e-296 << 1047 */
+ 0x82cca4db847945ca, /* 53: 1.0e-295 << 1043 */
+ 0xa37fce126597973c, /* 54: 1.0e-294 << 1040 */
+ 0xcc5fc196fefd7d0c, /* 55: 1.0e-293 << 1037 */
+ 0xff77b1fcbebcdc4f, /* 56: 1.0e-292 << 1034 */
+ 0x9faacf3df73609b1, /* 57: 1.0e-291 << 1030 */
+ 0xc795830d75038c1d, /* 58: 1.0e-290 << 1027 */
+ 0xf97ae3d0d2446f25, /* 59: 1.0e-289 << 1024 */
+ 0x9becce62836ac577, /* 60: 1.0e-288 << 1020 */
+ 0xc2e801fb244576d5, /* 61: 1.0e-287 << 1017 */
+ 0xf3a20279ed56d48a, /* 62: 1.0e-286 << 1014 */
+ 0x9845418c345644d6, /* 63: 1.0e-285 << 1010 */
+ 0xbe5691ef416bd60c, /* 64: 1.0e-284 << 1007 */
+ 0xedec366b11c6cb8f, /* 65: 1.0e-283 << 1004 */
+ 0x94b3a202eb1c3f39, /* 66: 1.0e-282 << 1000 */
+ 0xb9e08a83a5e34f07, /* 67: 1.0e-281 << 997 */
+ 0xe858ad248f5c22c9, /* 68: 1.0e-280 << 994 */
+ 0x91376c36d99995be, /* 69: 1.0e-279 << 990 */
+ 0xb58547448ffffb2d, /* 70: 1.0e-278 << 987 */
+ 0xe2e69915b3fff9f9, /* 71: 1.0e-277 << 984 */
+ 0x8dd01fad907ffc3b, /* 72: 1.0e-276 << 980 */
+ 0xb1442798f49ffb4a, /* 73: 1.0e-275 << 977 */
+ 0xdd95317f31c7fa1d, /* 74: 1.0e-274 << 974 */
+ 0x8a7d3eef7f1cfc52, /* 75: 1.0e-273 << 970 */
+ 0xad1c8eab5ee43b66, /* 76: 1.0e-272 << 967 */
+ 0xd863b256369d4a40, /* 77: 1.0e-271 << 964 */
+ 0x873e4f75e2224e68, /* 78: 1.0e-270 << 960 */
+ 0xa90de3535aaae202, /* 79: 1.0e-269 << 957 */
+ 0xd3515c2831559a83, /* 80: 1.0e-268 << 954 */
+ 0x8412d9991ed58091, /* 81: 1.0e-267 << 950 */
+ 0xa5178fff668ae0b6, /* 82: 1.0e-266 << 947 */
+ 0xce5d73ff402d98e3, /* 83: 1.0e-265 << 944 */
+ 0x80fa687f881c7f8e, /* 84: 1.0e-264 << 940 */
+ 0xa139029f6a239f72, /* 85: 1.0e-263 << 937 */
+ 0xc987434744ac874e, /* 86: 1.0e-262 << 934 */
+ 0xfbe9141915d7a922, /* 87: 1.0e-261 << 931 */
+ 0x9d71ac8fada6c9b5, /* 88: 1.0e-260 << 927 */
+ 0xc4ce17b399107c22, /* 89: 1.0e-259 << 924 */
+ 0xf6019da07f549b2b, /* 90: 1.0e-258 << 921 */
+ 0x99c102844f94e0fb, /* 91: 1.0e-257 << 917 */
+ 0xc0314325637a1939, /* 92: 1.0e-256 << 914 */
+ 0xf03d93eebc589f88, /* 93: 1.0e-255 << 911 */
+ 0x96267c7535b763b5, /* 94: 1.0e-254 << 907 */
+ 0xbbb01b9283253ca2, /* 95: 1.0e-253 << 904 */
+ 0xea9c227723ee8bcb, /* 96: 1.0e-252 << 901 */
+ 0x92a1958a7675175f, /* 97: 1.0e-251 << 897 */
+ 0xb749faed14125d36, /* 98: 1.0e-250 << 894 */
+ 0xe51c79a85916f484, /* 99: 1.0e-249 << 891 */
+ 0x8f31cc0937ae58d2, /* 100: 1.0e-248 << 887 */
+ 0xb2fe3f0b8599ef07, /* 101: 1.0e-247 << 884 */
+ 0xdfbdcece67006ac9, /* 102: 1.0e-246 << 881 */
+ 0x8bd6a141006042bd, /* 103: 1.0e-245 << 877 */
+ 0xaecc49914078536d, /* 104: 1.0e-244 << 874 */
+ 0xda7f5bf590966848, /* 105: 1.0e-243 << 871 */
+ 0x888f99797a5e012d, /* 106: 1.0e-242 << 867 */
+ 0xaab37fd7d8f58178, /* 107: 1.0e-241 << 864 */
+ 0xd5605fcdcf32e1d6, /* 108: 1.0e-240 << 861 */
+ 0x855c3be0a17fcd26, /* 109: 1.0e-239 << 857 */
+ 0xa6b34ad8c9dfc06f, /* 110: 1.0e-238 << 854 */
+ 0xd0601d8efc57b08b, /* 111: 1.0e-237 << 851 */
+ 0x823c12795db6ce57, /* 112: 1.0e-236 << 847 */
+ 0xa2cb1717b52481ed, /* 113: 1.0e-235 << 844 */
+ 0xcb7ddcdda26da268, /* 114: 1.0e-234 << 841 */
+ 0xfe5d54150b090b02, /* 115: 1.0e-233 << 838 */
+ 0x9efa548d26e5a6e1, /* 116: 1.0e-232 << 834 */
+ 0xc6b8e9b0709f109a, /* 117: 1.0e-231 << 831 */
+ 0xf867241c8cc6d4c0, /* 118: 1.0e-230 << 828 */
+ 0x9b407691d7fc44f8, /* 119: 1.0e-229 << 824 */
+ 0xc21094364dfb5636, /* 120: 1.0e-228 << 821 */
+ 0xf294b943e17a2bc4, /* 121: 1.0e-227 << 818 */
+ 0x979cf3ca6cec5b5a, /* 122: 1.0e-226 << 814 */
+ 0xbd8430bd08277231, /* 123: 1.0e-225 << 811 */
+ 0xece53cec4a314ebd, /* 124: 1.0e-224 << 808 */
+ 0x940f4613ae5ed136, /* 125: 1.0e-223 << 804 */
+ 0xb913179899f68584, /* 126: 1.0e-222 << 801 */
+ 0xe757dd7ec07426e5, /* 127: 1.0e-221 << 798 */
+ 0x9096ea6f3848984f, /* 128: 1.0e-220 << 794 */
+ 0xb4bca50b065abe63, /* 129: 1.0e-219 << 791 */
+ 0xe1ebce4dc7f16dfb, /* 130: 1.0e-218 << 788 */
+ 0x8d3360f09cf6e4bd, /* 131: 1.0e-217 << 784 */
+ 0xb080392cc4349dec, /* 132: 1.0e-216 << 781 */
+ 0xdca04777f541c567, /* 133: 1.0e-215 << 778 */
+ 0x89e42caaf9491b60, /* 134: 1.0e-214 << 774 */
+ 0xac5d37d5b79b6239, /* 135: 1.0e-213 << 771 */
+ 0xd77485cb25823ac7, /* 136: 1.0e-212 << 768 */
+ 0x86a8d39ef77164bc, /* 137: 1.0e-211 << 764 */
+ 0xa8530886b54dbdeb, /* 138: 1.0e-210 << 761 */
+ 0xd267caa862a12d66, /* 139: 1.0e-209 << 758 */
+ 0x8380dea93da4bc60, /* 140: 1.0e-208 << 754 */
+ 0xa46116538d0deb78, /* 141: 1.0e-207 << 751 */
+ 0xcd795be870516656, /* 142: 1.0e-206 << 748 */
+ 0x806bd9714632dff6, /* 143: 1.0e-205 << 744 */
+ 0xa086cfcd97bf97f3, /* 144: 1.0e-204 << 741 */
+ 0xc8a883c0fdaf7df0, /* 145: 1.0e-203 << 738 */
+ 0xfad2a4b13d1b5d6c, /* 146: 1.0e-202 << 735 */
+ 0x9cc3a6eec6311a63, /* 147: 1.0e-201 << 731 */
+ 0xc3f490aa77bd60fc, /* 148: 1.0e-200 << 728 */
+ 0xf4f1b4d515acb93b, /* 149: 1.0e-199 << 725 */
+ 0x991711052d8bf3c5, /* 150: 1.0e-198 << 721 */
+ 0xbf5cd54678eef0b6, /* 151: 1.0e-197 << 718 */
+ 0xef340a98172aace4, /* 152: 1.0e-196 << 715 */
+ 0x9580869f0e7aac0e, /* 153: 1.0e-195 << 711 */
+ 0xbae0a846d2195712, /* 154: 1.0e-194 << 708 */
+ 0xe998d258869facd7, /* 155: 1.0e-193 << 705 */
+ 0x91ff83775423cc06, /* 156: 1.0e-192 << 701 */
+ 0xb67f6455292cbf08, /* 157: 1.0e-191 << 698 */
+ 0xe41f3d6a7377eeca, /* 158: 1.0e-190 << 695 */
+ 0x8e938662882af53e, /* 159: 1.0e-189 << 691 */
+ 0xb23867fb2a35b28d, /* 160: 1.0e-188 << 688 */
+ 0xdec681f9f4c31f31, /* 161: 1.0e-187 << 685 */
+ 0x8b3c113c38f9f37e, /* 162: 1.0e-186 << 681 */
+ 0xae0b158b4738705e, /* 163: 1.0e-185 << 678 */
+ 0xd98ddaee19068c76, /* 164: 1.0e-184 << 675 */
+ 0x87f8a8d4cfa417c9, /* 165: 1.0e-183 << 671 */
+ 0xa9f6d30a038d1dbc, /* 166: 1.0e-182 << 668 */
+ 0xd47487cc8470652b, /* 167: 1.0e-181 << 665 */
+ 0x84c8d4dfd2c63f3b, /* 168: 1.0e-180 << 661 */
+ 0xa5fb0a17c777cf09, /* 169: 1.0e-179 << 658 */
+ 0xcf79cc9db955c2cc, /* 170: 1.0e-178 << 655 */
+ 0x81ac1fe293d599bf, /* 171: 1.0e-177 << 651 */
+ 0xa21727db38cb002f, /* 172: 1.0e-176 << 648 */
+ 0xca9cf1d206fdc03b, /* 173: 1.0e-175 << 645 */
+ 0xfd442e4688bd304a, /* 174: 1.0e-174 << 642 */
+ 0x9e4a9cec15763e2e, /* 175: 1.0e-173 << 638 */
+ 0xc5dd44271ad3cdba, /* 176: 1.0e-172 << 635 */
+ 0xf7549530e188c128, /* 177: 1.0e-171 << 632 */
+ 0x9a94dd3e8cf578b9, /* 178: 1.0e-170 << 628 */
+ 0xc13a148e3032d6e7, /* 179: 1.0e-169 << 625 */
+ 0xf18899b1bc3f8ca1, /* 180: 1.0e-168 << 622 */
+ 0x96f5600f15a7b7e5, /* 181: 1.0e-167 << 618 */
+ 0xbcb2b812db11a5de, /* 182: 1.0e-166 << 615 */
+ 0xebdf661791d60f56, /* 183: 1.0e-165 << 612 */
+ 0x936b9fcebb25c995, /* 184: 1.0e-164 << 608 */
+ 0xb84687c269ef3bfb, /* 185: 1.0e-163 << 605 */
+ 0xe65829b3046b0afa, /* 186: 1.0e-162 << 602 */
+ 0x8ff71a0fe2c2e6dc, /* 187: 1.0e-161 << 598 */
+ 0xb3f4e093db73a093, /* 188: 1.0e-160 << 595 */
+ 0xe0f218b8d25088b8, /* 189: 1.0e-159 << 592 */
+ 0x8c974f7383725573, /* 190: 1.0e-158 << 588 */
+ 0xafbd2350644eeacf, /* 191: 1.0e-157 << 585 */
+ 0xdbac6c247d62a583, /* 192: 1.0e-156 << 582 */
+ 0x894bc396ce5da772, /* 193: 1.0e-155 << 578 */
+ 0xab9eb47c81f5114f, /* 194: 1.0e-154 << 575 */
+ 0xd686619ba27255a2, /* 195: 1.0e-153 << 572 */
+ 0x8613fd0145877585, /* 196: 1.0e-152 << 568 */
+ 0xa798fc4196e952e7, /* 197: 1.0e-151 << 565 */
+ 0xd17f3b51fca3a7a0, /* 198: 1.0e-150 << 562 */
+ 0x82ef85133de648c4, /* 199: 1.0e-149 << 558 */
+ 0xa3ab66580d5fdaf5, /* 200: 1.0e-148 << 555 */
+ 0xcc963fee10b7d1b3, /* 201: 1.0e-147 << 552 */
+ 0xffbbcfe994e5c61f, /* 202: 1.0e-146 << 549 */
+ 0x9fd561f1fd0f9bd3, /* 203: 1.0e-145 << 545 */
+ 0xc7caba6e7c5382c8, /* 204: 1.0e-144 << 542 */
+ 0xf9bd690a1b68637b, /* 205: 1.0e-143 << 539 */
+ 0x9c1661a651213e2d, /* 206: 1.0e-142 << 535 */
+ 0xc31bfa0fe5698db8, /* 207: 1.0e-141 << 532 */
+ 0xf3e2f893dec3f126, /* 208: 1.0e-140 << 529 */
+ 0x986ddb5c6b3a76b7, /* 209: 1.0e-139 << 525 */
+ 0xbe89523386091465, /* 210: 1.0e-138 << 522 */
+ 0xee2ba6c0678b597f, /* 211: 1.0e-137 << 519 */
+ 0x94db483840b717ef, /* 212: 1.0e-136 << 515 */
+ 0xba121a4650e4ddeb, /* 213: 1.0e-135 << 512 */
+ 0xe896a0d7e51e1566, /* 214: 1.0e-134 << 509 */
+ 0x915e2486ef32cd60, /* 215: 1.0e-133 << 505 */
+ 0xb5b5ada8aaff80b8, /* 216: 1.0e-132 << 502 */
+ 0xe3231912d5bf60e6, /* 217: 1.0e-131 << 499 */
+ 0x8df5efabc5979c8f, /* 218: 1.0e-130 << 495 */
+ 0xb1736b96b6fd83b3, /* 219: 1.0e-129 << 492 */
+ 0xddd0467c64bce4a0, /* 220: 1.0e-128 << 489 */
+ 0x8aa22c0dbef60ee4, /* 221: 1.0e-127 << 485 */
+ 0xad4ab7112eb3929d, /* 222: 1.0e-126 << 482 */
+ 0xd89d64d57a607744, /* 223: 1.0e-125 << 479 */
+ 0x87625f056c7c4a8b, /* 224: 1.0e-124 << 475 */
+ 0xa93af6c6c79b5d2d, /* 225: 1.0e-123 << 472 */
+ 0xd389b47879823479, /* 226: 1.0e-122 << 469 */
+ 0x843610cb4bf160cb, /* 227: 1.0e-121 << 465 */
+ 0xa54394fe1eedb8fe, /* 228: 1.0e-120 << 462 */
+ 0xce947a3da6a9273e, /* 229: 1.0e-119 << 459 */
+ 0x811ccc668829b887, /* 230: 1.0e-118 << 455 */
+ 0xa163ff802a3426a8, /* 231: 1.0e-117 << 452 */
+ 0xc9bcff6034c13052, /* 232: 1.0e-116 << 449 */
+ 0xfc2c3f3841f17c67, /* 233: 1.0e-115 << 446 */
+ 0x9d9ba7832936edc0, /* 234: 1.0e-114 << 442 */
+ 0xc5029163f384a931, /* 235: 1.0e-113 << 439 */
+ 0xf64335bcf065d37d, /* 236: 1.0e-112 << 436 */
+ 0x99ea0196163fa42e, /* 237: 1.0e-111 << 432 */
+ 0xc06481fb9bcf8d39, /* 238: 1.0e-110 << 429 */
+ 0xf07da27a82c37088, /* 239: 1.0e-109 << 426 */
+ 0x964e858c91ba2655, /* 240: 1.0e-108 << 422 */
+ 0xbbe226efb628afea, /* 241: 1.0e-107 << 419 */
+ 0xeadab0aba3b2dbe5, /* 242: 1.0e-106 << 416 */
+ 0x92c8ae6b464fc96f, /* 243: 1.0e-105 << 412 */
+ 0xb77ada0617e3bbcb, /* 244: 1.0e-104 << 409 */
+ 0xe55990879ddcaabd, /* 245: 1.0e-103 << 406 */
+ 0x8f57fa54c2a9eab6, /* 246: 1.0e-102 << 402 */
+ 0xb32df8e9f3546564, /* 247: 1.0e-101 << 399 */
+ 0xdff9772470297ebd, /* 248: 1.0e-100 << 396 */
+ 0x8bfbea76c619ef36, /* 249: 1.0e-99 << 392 */
+ 0xaefae51477a06b03, /* 250: 1.0e-98 << 389 */
+ 0xdab99e59958885c4, /* 251: 1.0e-97 << 386 */
+ 0x88b402f7fd75539b, /* 252: 1.0e-96 << 382 */
+ 0xaae103b5fcd2a881, /* 253: 1.0e-95 << 379 */
+ 0xd59944a37c0752a2, /* 254: 1.0e-94 << 376 */
+ 0x857fcae62d8493a5, /* 255: 1.0e-93 << 372 */
+ 0xa6dfbd9fb8e5b88e, /* 256: 1.0e-92 << 369 */
+ 0xd097ad07a71f26b2, /* 257: 1.0e-91 << 366 */
+ 0x825ecc24c873782f, /* 258: 1.0e-90 << 362 */
+ 0xa2f67f2dfa90563b, /* 259: 1.0e-89 << 359 */
+ 0xcbb41ef979346bca, /* 260: 1.0e-88 << 356 */
+ 0xfea126b7d78186bc, /* 261: 1.0e-87 << 353 */
+ 0x9f24b832e6b0f436, /* 262: 1.0e-86 << 349 */
+ 0xc6ede63fa05d3143, /* 263: 1.0e-85 << 346 */
+ 0xf8a95fcf88747d94, /* 264: 1.0e-84 << 343 */
+ 0x9b69dbe1b548ce7c, /* 265: 1.0e-83 << 339 */
+ 0xc24452da229b021b, /* 266: 1.0e-82 << 336 */
+ 0xf2d56790ab41c2a2, /* 267: 1.0e-81 << 333 */
+ 0x97c560ba6b0919a5, /* 268: 1.0e-80 << 329 */
+ 0xbdb6b8e905cb600f, /* 269: 1.0e-79 << 326 */
+ 0xed246723473e3813, /* 270: 1.0e-78 << 323 */
+ 0x9436c0760c86e30b, /* 271: 1.0e-77 << 319 */
+ 0xb94470938fa89bce, /* 272: 1.0e-76 << 316 */
+ 0xe7958cb87392c2c2, /* 273: 1.0e-75 << 313 */
+ 0x90bd77f3483bb9b9, /* 274: 1.0e-74 << 309 */
+ 0xb4ecd5f01a4aa828, /* 275: 1.0e-73 << 306 */
+ 0xe2280b6c20dd5232, /* 276: 1.0e-72 << 303 */
+ 0x8d590723948a535f, /* 277: 1.0e-71 << 299 */
+ 0xb0af48ec79ace837, /* 278: 1.0e-70 << 296 */
+ 0xdcdb1b2798182244, /* 279: 1.0e-69 << 293 */
+ 0x8a08f0f8bf0f156b, /* 280: 1.0e-68 << 289 */
+ 0xac8b2d36eed2dac5, /* 281: 1.0e-67 << 286 */
+ 0xd7adf884aa879177, /* 282: 1.0e-66 << 283 */
+ 0x86ccbb52ea94baea, /* 283: 1.0e-65 << 279 */
+ 0xa87fea27a539e9a5, /* 284: 1.0e-64 << 276 */
+ 0xd29fe4b18e88640e, /* 285: 1.0e-63 << 273 */
+ 0x83a3eeeef9153e89, /* 286: 1.0e-62 << 269 */
+ 0xa48ceaaab75a8e2b, /* 287: 1.0e-61 << 266 */
+ 0xcdb02555653131b6, /* 288: 1.0e-60 << 263 */
+ 0x808e17555f3ebf11, /* 289: 1.0e-59 << 259 */
+ 0xa0b19d2ab70e6ed6, /* 290: 1.0e-58 << 256 */
+ 0xc8de047564d20a8b, /* 291: 1.0e-57 << 253 */
+ 0xfb158592be068d2e, /* 292: 1.0e-56 << 250 */
+ 0x9ced737bb6c4183d, /* 293: 1.0e-55 << 246 */
+ 0xc428d05aa4751e4c, /* 294: 1.0e-54 << 243 */
+ 0xf53304714d9265df, /* 295: 1.0e-53 << 240 */
+ 0x993fe2c6d07b7fab, /* 296: 1.0e-52 << 236 */
+ 0xbf8fdb78849a5f96, /* 297: 1.0e-51 << 233 */
+ 0xef73d256a5c0f77c, /* 298: 1.0e-50 << 230 */
+ 0x95a8637627989aad, /* 299: 1.0e-49 << 226 */
+ 0xbb127c53b17ec159, /* 300: 1.0e-48 << 223 */
+ 0xe9d71b689dde71af, /* 301: 1.0e-47 << 220 */
+ 0x9226712162ab070d, /* 302: 1.0e-46 << 216 */
+ 0xb6b00d69bb55c8d1, /* 303: 1.0e-45 << 213 */
+ 0xe45c10c42a2b3b05, /* 304: 1.0e-44 << 210 */
+ 0x8eb98a7a9a5b04e3, /* 305: 1.0e-43 << 206 */
+ 0xb267ed1940f1c61c, /* 306: 1.0e-42 << 203 */
+ 0xdf01e85f912e37a3, /* 307: 1.0e-41 << 200 */
+ 0x8b61313bbabce2c6, /* 308: 1.0e-40 << 196 */
+ 0xae397d8aa96c1b77, /* 309: 1.0e-39 << 193 */
+ 0xd9c7dced53c72255, /* 310: 1.0e-38 << 190 */
+ 0x881cea14545c7575, /* 311: 1.0e-37 << 186 */
+ 0xaa242499697392d2, /* 312: 1.0e-36 << 183 */
+ 0xd4ad2dbfc3d07787, /* 313: 1.0e-35 << 180 */
+ 0x84ec3c97da624ab4, /* 314: 1.0e-34 << 176 */
+ 0xa6274bbdd0fadd61, /* 315: 1.0e-33 << 173 */
+ 0xcfb11ead453994ba, /* 316: 1.0e-32 << 170 */
+ 0x81ceb32c4b43fcf4, /* 317: 1.0e-31 << 166 */
+ 0xa2425ff75e14fc31, /* 318: 1.0e-30 << 163 */
+ 0xcad2f7f5359a3b3e, /* 319: 1.0e-29 << 160 */
+ 0xfd87b5f28300ca0d, /* 320: 1.0e-28 << 157 */
+ 0x9e74d1b791e07e48, /* 321: 1.0e-27 << 153 */
+ 0xc612062576589dda, /* 322: 1.0e-26 << 150 */
+ 0xf79687aed3eec551, /* 323: 1.0e-25 << 147 */
+ 0x9abe14cd44753b52, /* 324: 1.0e-24 << 143 */
+ 0xc16d9a0095928a27, /* 325: 1.0e-23 << 140 */
+ 0xf1c90080baf72cb1, /* 326: 1.0e-22 << 137 */
+ 0x971da05074da7bee, /* 327: 1.0e-21 << 133 */
+ 0xbce5086492111aea, /* 328: 1.0e-20 << 130 */
+ 0xec1e4a7db69561a5, /* 329: 1.0e-19 << 127 */
+ 0x9392ee8e921d5d07, /* 330: 1.0e-18 << 123 */
+ 0xb877aa3236a4b449, /* 331: 1.0e-17 << 120 */
+ 0xe69594bec44de15b, /* 332: 1.0e-16 << 117 */
+ 0x901d7cf73ab0acd9, /* 333: 1.0e-15 << 113 */
+ 0xb424dc35095cd80f, /* 334: 1.0e-14 << 110 */
+ 0xe12e13424bb40e13, /* 335: 1.0e-13 << 107 */
+ 0x8cbccc096f5088cb, /* 336: 1.0e-12 << 103 */
+ 0xafebff0bcb24aafe, /* 337: 1.0e-11 << 100 */
+ 0xdbe6fecebdedd5be, /* 338: 1.0e-10 << 97 */
+ 0x89705f4136b4a597, /* 339: 1.0e-9 << 93 */
+ 0xabcc77118461cefc, /* 340: 1.0e-8 << 90 */
+ 0xd6bf94d5e57a42bc, /* 341: 1.0e-7 << 87 */
+ 0x8637bd05af6c69b5, /* 342: 1.0e-6 << 83 */
+ 0xa7c5ac471b478423, /* 343: 1.0e-5 << 80 */
+ 0xd1b71758e219652b, /* 344: 1.0e-4 << 77 */
+ 0x83126e978d4fdf3b, /* 345: 1.0e-3 << 73 */
+ 0xa3d70a3d70a3d70a, /* 346: 1.0e-2 << 70 */
+ 0xcccccccccccccccc, /* 347: 1.0e-1 << 67 */
+ 0x8000000000000000, /* 348: 1.0e+0 << 63 */
+ 0xa000000000000000, /* 349: 1.0e+1 << 60 */
+ 0xc800000000000000, /* 350: 1.0e+2 << 57 */
+ 0xfa00000000000000, /* 351: 1.0e+3 << 54 */
+ 0x9c40000000000000, /* 352: 1.0e+4 << 50 */
+ 0xc350000000000000, /* 353: 1.0e+5 << 47 */
+ 0xf424000000000000, /* 354: 1.0e+6 << 44 */
+ 0x9896800000000000, /* 355: 1.0e+7 << 40 */
+ 0xbebc200000000000, /* 356: 1.0e+8 << 37 */
+ 0xee6b280000000000, /* 357: 1.0e+9 << 34 */
+ 0x9502f90000000000, /* 358: 1.0e+10 << 30 */
+ 0xba43b74000000000, /* 359: 1.0e+11 << 27 */
+ 0xe8d4a51000000000, /* 360: 1.0e+12 << 24 */
+ 0x9184e72a00000000, /* 361: 1.0e+13 << 20 */
+ 0xb5e620f480000000, /* 362: 1.0e+14 << 17 */
+ 0xe35fa931a0000000, /* 363: 1.0e+15 << 14 */
+ 0x8e1bc9bf04000000, /* 364: 1.0e+16 << 10 */
+ 0xb1a2bc2ec5000000, /* 365: 1.0e+17 << 7 */
+ 0xde0b6b3a76400000, /* 366: 1.0e+18 << 4 */
+ 0x8ac7230489e80000, /* 367: 1.0e+19 >> 0 */
+ 0xad78ebc5ac620000, /* 368: 1.0e+20 >> 3 */
+ 0xd8d726b7177a8000, /* 369: 1.0e+21 >> 6 */
+ 0x878678326eac9000, /* 370: 1.0e+22 >> 10 */
+ 0xa968163f0a57b400, /* 371: 1.0e+23 >> 13 */
+ 0xd3c21bcecceda100, /* 372: 1.0e+24 >> 16 */
+ 0x84595161401484a0, /* 373: 1.0e+25 >> 20 */
+ 0xa56fa5b99019a5c8, /* 374: 1.0e+26 >> 23 */
+ 0xcecb8f27f4200f3a, /* 375: 1.0e+27 >> 26 */
+ 0x813f3978f8940984, /* 376: 1.0e+28 >> 30 */
+ 0xa18f07d736b90be5, /* 377: 1.0e+29 >> 33 */
+ 0xc9f2c9cd04674ede, /* 378: 1.0e+30 >> 36 */
+ 0xfc6f7c4045812296, /* 379: 1.0e+31 >> 39 */
+ 0x9dc5ada82b70b59d, /* 380: 1.0e+32 >> 43 */
+ 0xc5371912364ce305, /* 381: 1.0e+33 >> 46 */
+ 0xf684df56c3e01bc6, /* 382: 1.0e+34 >> 49 */
+ 0x9a130b963a6c115c, /* 383: 1.0e+35 >> 53 */
+ 0xc097ce7bc90715b3, /* 384: 1.0e+36 >> 56 */
+ 0xf0bdc21abb48db20, /* 385: 1.0e+37 >> 59 */
+ 0x96769950b50d88f4, /* 386: 1.0e+38 >> 63 */
+ 0xbc143fa4e250eb31, /* 387: 1.0e+39 >> 66 */
+ 0xeb194f8e1ae525fd, /* 388: 1.0e+40 >> 69 */
+ 0x92efd1b8d0cf37be, /* 389: 1.0e+41 >> 73 */
+ 0xb7abc627050305ad, /* 390: 1.0e+42 >> 76 */
+ 0xe596b7b0c643c719, /* 391: 1.0e+43 >> 79 */
+ 0x8f7e32ce7bea5c6f, /* 392: 1.0e+44 >> 83 */
+ 0xb35dbf821ae4f38b, /* 393: 1.0e+45 >> 86 */
+ 0xe0352f62a19e306e, /* 394: 1.0e+46 >> 89 */
+ 0x8c213d9da502de45, /* 395: 1.0e+47 >> 93 */
+ 0xaf298d050e4395d6, /* 396: 1.0e+48 >> 96 */
+ 0xdaf3f04651d47b4c, /* 397: 1.0e+49 >> 99 */
+ 0x88d8762bf324cd0f, /* 398: 1.0e+50 >> 103 */
+ 0xab0e93b6efee0053, /* 399: 1.0e+51 >> 106 */
+ 0xd5d238a4abe98068, /* 400: 1.0e+52 >> 109 */
+ 0x85a36366eb71f041, /* 401: 1.0e+53 >> 113 */
+ 0xa70c3c40a64e6c51, /* 402: 1.0e+54 >> 116 */
+ 0xd0cf4b50cfe20765, /* 403: 1.0e+55 >> 119 */
+ 0x82818f1281ed449f, /* 404: 1.0e+56 >> 123 */
+ 0xa321f2d7226895c7, /* 405: 1.0e+57 >> 126 */
+ 0xcbea6f8ceb02bb39, /* 406: 1.0e+58 >> 129 */
+ 0xfee50b7025c36a08, /* 407: 1.0e+59 >> 132 */
+ 0x9f4f2726179a2245, /* 408: 1.0e+60 >> 136 */
+ 0xc722f0ef9d80aad6, /* 409: 1.0e+61 >> 139 */
+ 0xf8ebad2b84e0d58b, /* 410: 1.0e+62 >> 142 */
+ 0x9b934c3b330c8577, /* 411: 1.0e+63 >> 146 */
+ 0xc2781f49ffcfa6d5, /* 412: 1.0e+64 >> 149 */
+ 0xf316271c7fc3908a, /* 413: 1.0e+65 >> 152 */
+ 0x97edd871cfda3a56, /* 414: 1.0e+66 >> 156 */
+ 0xbde94e8e43d0c8ec, /* 415: 1.0e+67 >> 159 */
+ 0xed63a231d4c4fb27, /* 416: 1.0e+68 >> 162 */
+ 0x945e455f24fb1cf8, /* 417: 1.0e+69 >> 166 */
+ 0xb975d6b6ee39e436, /* 418: 1.0e+70 >> 169 */
+ 0xe7d34c64a9c85d44, /* 419: 1.0e+71 >> 172 */
+ 0x90e40fbeea1d3a4a, /* 420: 1.0e+72 >> 176 */
+ 0xb51d13aea4a488dd, /* 421: 1.0e+73 >> 179 */
+ 0xe264589a4dcdab14, /* 422: 1.0e+74 >> 182 */
+ 0x8d7eb76070a08aec, /* 423: 1.0e+75 >> 186 */
+ 0xb0de65388cc8ada8, /* 424: 1.0e+76 >> 189 */
+ 0xdd15fe86affad912, /* 425: 1.0e+77 >> 192 */
+ 0x8a2dbf142dfcc7ab, /* 426: 1.0e+78 >> 196 */
+ 0xacb92ed9397bf996, /* 427: 1.0e+79 >> 199 */
+ 0xd7e77a8f87daf7fb, /* 428: 1.0e+80 >> 202 */
+ 0x86f0ac99b4e8dafd, /* 429: 1.0e+81 >> 206 */
+ 0xa8acd7c0222311bc, /* 430: 1.0e+82 >> 209 */
+ 0xd2d80db02aabd62b, /* 431: 1.0e+83 >> 212 */
+ 0x83c7088e1aab65db, /* 432: 1.0e+84 >> 216 */
+ 0xa4b8cab1a1563f52, /* 433: 1.0e+85 >> 219 */
+ 0xcde6fd5e09abcf26, /* 434: 1.0e+86 >> 222 */
+ 0x80b05e5ac60b6178, /* 435: 1.0e+87 >> 226 */
+ 0xa0dc75f1778e39d6, /* 436: 1.0e+88 >> 229 */
+ 0xc913936dd571c84c, /* 437: 1.0e+89 >> 232 */
+ 0xfb5878494ace3a5f, /* 438: 1.0e+90 >> 235 */
+ 0x9d174b2dcec0e47b, /* 439: 1.0e+91 >> 239 */
+ 0xc45d1df942711d9a, /* 440: 1.0e+92 >> 242 */
+ 0xf5746577930d6500, /* 441: 1.0e+93 >> 245 */
+ 0x9968bf6abbe85f20, /* 442: 1.0e+94 >> 249 */
+ 0xbfc2ef456ae276e8, /* 443: 1.0e+95 >> 252 */
+ 0xefb3ab16c59b14a2, /* 444: 1.0e+96 >> 255 */
+ 0x95d04aee3b80ece5, /* 445: 1.0e+97 >> 259 */
+ 0xbb445da9ca61281f, /* 446: 1.0e+98 >> 262 */
+ 0xea1575143cf97226, /* 447: 1.0e+99 >> 265 */
+ 0x924d692ca61be758, /* 448: 1.0e+100 >> 269 */
+ 0xb6e0c377cfa2e12e, /* 449: 1.0e+101 >> 272 */
+ 0xe498f455c38b997a, /* 450: 1.0e+102 >> 275 */
+ 0x8edf98b59a373fec, /* 451: 1.0e+103 >> 279 */
+ 0xb2977ee300c50fe7, /* 452: 1.0e+104 >> 282 */
+ 0xdf3d5e9bc0f653e1, /* 453: 1.0e+105 >> 285 */
+ 0x8b865b215899f46c, /* 454: 1.0e+106 >> 289 */
+ 0xae67f1e9aec07187, /* 455: 1.0e+107 >> 292 */
+ 0xda01ee641a708de9, /* 456: 1.0e+108 >> 295 */
+ 0x884134fe908658b2, /* 457: 1.0e+109 >> 299 */
+ 0xaa51823e34a7eede, /* 458: 1.0e+110 >> 302 */
+ 0xd4e5e2cdc1d1ea96, /* 459: 1.0e+111 >> 305 */
+ 0x850fadc09923329e, /* 460: 1.0e+112 >> 309 */
+ 0xa6539930bf6bff45, /* 461: 1.0e+113 >> 312 */
+ 0xcfe87f7cef46ff16, /* 462: 1.0e+114 >> 315 */
+ 0x81f14fae158c5f6e, /* 463: 1.0e+115 >> 319 */
+ 0xa26da3999aef7749, /* 464: 1.0e+116 >> 322 */
+ 0xcb090c8001ab551c, /* 465: 1.0e+117 >> 325 */
+ 0xfdcb4fa002162a63, /* 466: 1.0e+118 >> 328 */
+ 0x9e9f11c4014dda7e, /* 467: 1.0e+119 >> 332 */
+ 0xc646d63501a1511d, /* 468: 1.0e+120 >> 335 */
+ 0xf7d88bc24209a565, /* 469: 1.0e+121 >> 338 */
+ 0x9ae757596946075f, /* 470: 1.0e+122 >> 342 */
+ 0xc1a12d2fc3978937, /* 471: 1.0e+123 >> 345 */
+ 0xf209787bb47d6b84, /* 472: 1.0e+124 >> 348 */
+ 0x9745eb4d50ce6332, /* 473: 1.0e+125 >> 352 */
+ 0xbd176620a501fbff, /* 474: 1.0e+126 >> 355 */
+ 0xec5d3fa8ce427aff, /* 475: 1.0e+127 >> 358 */
+ 0x93ba47c980e98cdf, /* 476: 1.0e+128 >> 362 */
+ 0xb8a8d9bbe123f017, /* 477: 1.0e+129 >> 365 */
+ 0xe6d3102ad96cec1d, /* 478: 1.0e+130 >> 368 */
+ 0x9043ea1ac7e41392, /* 479: 1.0e+131 >> 372 */
+ 0xb454e4a179dd1877, /* 480: 1.0e+132 >> 375 */
+ 0xe16a1dc9d8545e94, /* 481: 1.0e+133 >> 378 */
+ 0x8ce2529e2734bb1d, /* 482: 1.0e+134 >> 382 */
+ 0xb01ae745b101e9e4, /* 483: 1.0e+135 >> 385 */
+ 0xdc21a1171d42645d, /* 484: 1.0e+136 >> 388 */
+ 0x899504ae72497eba, /* 485: 1.0e+137 >> 392 */
+ 0xabfa45da0edbde69, /* 486: 1.0e+138 >> 395 */
+ 0xd6f8d7509292d603, /* 487: 1.0e+139 >> 398 */
+ 0x865b86925b9bc5c2, /* 488: 1.0e+140 >> 402 */
+ 0xa7f26836f282b732, /* 489: 1.0e+141 >> 405 */
+ 0xd1ef0244af2364ff, /* 490: 1.0e+142 >> 408 */
+ 0x8335616aed761f1f, /* 491: 1.0e+143 >> 412 */
+ 0xa402b9c5a8d3a6e7, /* 492: 1.0e+144 >> 415 */
+ 0xcd036837130890a1, /* 493: 1.0e+145 >> 418 */
+ 0x802221226be55a64, /* 494: 1.0e+146 >> 422 */
+ 0xa02aa96b06deb0fd, /* 495: 1.0e+147 >> 425 */
+ 0xc83553c5c8965d3d, /* 496: 1.0e+148 >> 428 */
+ 0xfa42a8b73abbf48c, /* 497: 1.0e+149 >> 431 */
+ 0x9c69a97284b578d7, /* 498: 1.0e+150 >> 435 */
+ 0xc38413cf25e2d70d, /* 499: 1.0e+151 >> 438 */
+ 0xf46518c2ef5b8cd1, /* 500: 1.0e+152 >> 441 */
+ 0x98bf2f79d5993802, /* 501: 1.0e+153 >> 445 */
+ 0xbeeefb584aff8603, /* 502: 1.0e+154 >> 448 */
+ 0xeeaaba2e5dbf6784, /* 503: 1.0e+155 >> 451 */
+ 0x952ab45cfa97a0b2, /* 504: 1.0e+156 >> 455 */
+ 0xba756174393d88df, /* 505: 1.0e+157 >> 458 */
+ 0xe912b9d1478ceb17, /* 506: 1.0e+158 >> 461 */
+ 0x91abb422ccb812ee, /* 507: 1.0e+159 >> 465 */
+ 0xb616a12b7fe617aa, /* 508: 1.0e+160 >> 468 */
+ 0xe39c49765fdf9d94, /* 509: 1.0e+161 >> 471 */
+ 0x8e41ade9fbebc27d, /* 510: 1.0e+162 >> 475 */
+ 0xb1d219647ae6b31c, /* 511: 1.0e+163 >> 478 */
+ 0xde469fbd99a05fe3, /* 512: 1.0e+164 >> 481 */
+ 0x8aec23d680043bee, /* 513: 1.0e+165 >> 485 */
+ 0xada72ccc20054ae9, /* 514: 1.0e+166 >> 488 */
+ 0xd910f7ff28069da4, /* 515: 1.0e+167 >> 491 */
+ 0x87aa9aff79042286, /* 516: 1.0e+168 >> 495 */
+ 0xa99541bf57452b28, /* 517: 1.0e+169 >> 498 */
+ 0xd3fa922f2d1675f2, /* 518: 1.0e+170 >> 501 */
+ 0x847c9b5d7c2e09b7, /* 519: 1.0e+171 >> 505 */
+ 0xa59bc234db398c25, /* 520: 1.0e+172 >> 508 */
+ 0xcf02b2c21207ef2e, /* 521: 1.0e+173 >> 511 */
+ 0x8161afb94b44f57d, /* 522: 1.0e+174 >> 515 */
+ 0xa1ba1ba79e1632dc, /* 523: 1.0e+175 >> 518 */
+ 0xca28a291859bbf93, /* 524: 1.0e+176 >> 521 */
+ 0xfcb2cb35e702af78, /* 525: 1.0e+177 >> 524 */
+ 0x9defbf01b061adab, /* 526: 1.0e+178 >> 528 */
+ 0xc56baec21c7a1916, /* 527: 1.0e+179 >> 531 */
+ 0xf6c69a72a3989f5b, /* 528: 1.0e+180 >> 534 */
+ 0x9a3c2087a63f6399, /* 529: 1.0e+181 >> 538 */
+ 0xc0cb28a98fcf3c7f, /* 530: 1.0e+182 >> 541 */
+ 0xf0fdf2d3f3c30b9f, /* 531: 1.0e+183 >> 544 */
+ 0x969eb7c47859e743, /* 532: 1.0e+184 >> 548 */
+ 0xbc4665b596706114, /* 533: 1.0e+185 >> 551 */
+ 0xeb57ff22fc0c7959, /* 534: 1.0e+186 >> 554 */
+ 0x9316ff75dd87cbd8, /* 535: 1.0e+187 >> 558 */
+ 0xb7dcbf5354e9bece, /* 536: 1.0e+188 >> 561 */
+ 0xe5d3ef282a242e81, /* 537: 1.0e+189 >> 564 */
+ 0x8fa475791a569d10, /* 538: 1.0e+190 >> 568 */
+ 0xb38d92d760ec4455, /* 539: 1.0e+191 >> 571 */
+ 0xe070f78d3927556a, /* 540: 1.0e+192 >> 574 */
+ 0x8c469ab843b89562, /* 541: 1.0e+193 >> 578 */
+ 0xaf58416654a6babb, /* 542: 1.0e+194 >> 581 */
+ 0xdb2e51bfe9d0696a, /* 543: 1.0e+195 >> 584 */
+ 0x88fcf317f22241e2, /* 544: 1.0e+196 >> 588 */
+ 0xab3c2fddeeaad25a, /* 545: 1.0e+197 >> 591 */
+ 0xd60b3bd56a5586f1, /* 546: 1.0e+198 >> 594 */
+ 0x85c7056562757456, /* 547: 1.0e+199 >> 598 */
+ 0xa738c6bebb12d16c, /* 548: 1.0e+200 >> 601 */
+ 0xd106f86e69d785c7, /* 549: 1.0e+201 >> 604 */
+ 0x82a45b450226b39c, /* 550: 1.0e+202 >> 608 */
+ 0xa34d721642b06084, /* 551: 1.0e+203 >> 611 */
+ 0xcc20ce9bd35c78a5, /* 552: 1.0e+204 >> 614 */
+ 0xff290242c83396ce, /* 553: 1.0e+205 >> 617 */
+ 0x9f79a169bd203e41, /* 554: 1.0e+206 >> 621 */
+ 0xc75809c42c684dd1, /* 555: 1.0e+207 >> 624 */
+ 0xf92e0c3537826145, /* 556: 1.0e+208 >> 627 */
+ 0x9bbcc7a142b17ccb, /* 557: 1.0e+209 >> 631 */
+ 0xc2abf989935ddbfe, /* 558: 1.0e+210 >> 634 */
+ 0xf356f7ebf83552fe, /* 559: 1.0e+211 >> 637 */
+ 0x98165af37b2153de, /* 560: 1.0e+212 >> 641 */
+ 0xbe1bf1b059e9a8d6, /* 561: 1.0e+213 >> 644 */
+ 0xeda2ee1c7064130c, /* 562: 1.0e+214 >> 647 */
+ 0x9485d4d1c63e8be7, /* 563: 1.0e+215 >> 651 */
+ 0xb9a74a0637ce2ee1, /* 564: 1.0e+216 >> 654 */
+ 0xe8111c87c5c1ba99, /* 565: 1.0e+217 >> 657 */
+ 0x910ab1d4db9914a0, /* 566: 1.0e+218 >> 661 */
+ 0xb54d5e4a127f59c8, /* 567: 1.0e+219 >> 664 */
+ 0xe2a0b5dc971f303a, /* 568: 1.0e+220 >> 667 */
+ 0x8da471a9de737e24, /* 569: 1.0e+221 >> 671 */
+ 0xb10d8e1456105dad, /* 570: 1.0e+222 >> 674 */
+ 0xdd50f1996b947518, /* 571: 1.0e+223 >> 677 */
+ 0x8a5296ffe33cc92f, /* 572: 1.0e+224 >> 681 */
+ 0xace73cbfdc0bfb7b, /* 573: 1.0e+225 >> 684 */
+ 0xd8210befd30efa5a, /* 574: 1.0e+226 >> 687 */
+ 0x8714a775e3e95c78, /* 575: 1.0e+227 >> 691 */
+ 0xa8d9d1535ce3b396, /* 576: 1.0e+228 >> 694 */
+ 0xd31045a8341ca07c, /* 577: 1.0e+229 >> 697 */
+ 0x83ea2b892091e44d, /* 578: 1.0e+230 >> 701 */
+ 0xa4e4b66b68b65d60, /* 579: 1.0e+231 >> 704 */
+ 0xce1de40642e3f4b9, /* 580: 1.0e+232 >> 707 */
+ 0x80d2ae83e9ce78f3, /* 581: 1.0e+233 >> 711 */
+ 0xa1075a24e4421730, /* 582: 1.0e+234 >> 714 */
+ 0xc94930ae1d529cfc, /* 583: 1.0e+235 >> 717 */
+ 0xfb9b7cd9a4a7443c, /* 584: 1.0e+236 >> 720 */
+ 0x9d412e0806e88aa5, /* 585: 1.0e+237 >> 724 */
+ 0xc491798a08a2ad4e, /* 586: 1.0e+238 >> 727 */
+ 0xf5b5d7ec8acb58a2, /* 587: 1.0e+239 >> 730 */
+ 0x9991a6f3d6bf1765, /* 588: 1.0e+240 >> 734 */
+ 0xbff610b0cc6edd3f, /* 589: 1.0e+241 >> 737 */
+ 0xeff394dcff8a948e, /* 590: 1.0e+242 >> 740 */
+ 0x95f83d0a1fb69cd9, /* 591: 1.0e+243 >> 744 */
+ 0xbb764c4ca7a4440f, /* 592: 1.0e+244 >> 747 */
+ 0xea53df5fd18d5513, /* 593: 1.0e+245 >> 750 */
+ 0x92746b9be2f8552c, /* 594: 1.0e+246 >> 754 */
+ 0xb7118682dbb66a77, /* 595: 1.0e+247 >> 757 */
+ 0xe4d5e82392a40515, /* 596: 1.0e+248 >> 760 */
+ 0x8f05b1163ba6832d, /* 597: 1.0e+249 >> 764 */
+ 0xb2c71d5bca9023f8, /* 598: 1.0e+250 >> 767 */
+ 0xdf78e4b2bd342cf6, /* 599: 1.0e+251 >> 770 */
+ 0x8bab8eefb6409c1a, /* 600: 1.0e+252 >> 774 */
+ 0xae9672aba3d0c320, /* 601: 1.0e+253 >> 777 */
+ 0xda3c0f568cc4f3e8, /* 602: 1.0e+254 >> 780 */
+ 0x8865899617fb1871, /* 603: 1.0e+255 >> 784 */
+ 0xaa7eebfb9df9de8d, /* 604: 1.0e+256 >> 787 */
+ 0xd51ea6fa85785631, /* 605: 1.0e+257 >> 790 */
+ 0x8533285c936b35de, /* 606: 1.0e+258 >> 794 */
+ 0xa67ff273b8460356, /* 607: 1.0e+259 >> 797 */
+ 0xd01fef10a657842c, /* 608: 1.0e+260 >> 800 */
+ 0x8213f56a67f6b29b, /* 609: 1.0e+261 >> 804 */
+ 0xa298f2c501f45f42, /* 610: 1.0e+262 >> 807 */
+ 0xcb3f2f7642717713, /* 611: 1.0e+263 >> 810 */
+ 0xfe0efb53d30dd4d7, /* 612: 1.0e+264 >> 813 */
+ 0x9ec95d1463e8a506, /* 613: 1.0e+265 >> 817 */
+ 0xc67bb4597ce2ce48, /* 614: 1.0e+266 >> 820 */
+ 0xf81aa16fdc1b81da, /* 615: 1.0e+267 >> 823 */
+ 0x9b10a4e5e9913128, /* 616: 1.0e+268 >> 827 */
+ 0xc1d4ce1f63f57d72, /* 617: 1.0e+269 >> 830 */
+ 0xf24a01a73cf2dccf, /* 618: 1.0e+270 >> 833 */
+ 0x976e41088617ca01, /* 619: 1.0e+271 >> 837 */
+ 0xbd49d14aa79dbc82, /* 620: 1.0e+272 >> 840 */
+ 0xec9c459d51852ba2, /* 621: 1.0e+273 >> 843 */
+ 0x93e1ab8252f33b45, /* 622: 1.0e+274 >> 847 */
+ 0xb8da1662e7b00a17, /* 623: 1.0e+275 >> 850 */
+ 0xe7109bfba19c0c9d, /* 624: 1.0e+276 >> 853 */
+ 0x906a617d450187e2, /* 625: 1.0e+277 >> 857 */
+ 0xb484f9dc9641e9da, /* 626: 1.0e+278 >> 860 */
+ 0xe1a63853bbd26451, /* 627: 1.0e+279 >> 863 */
+ 0x8d07e33455637eb2, /* 628: 1.0e+280 >> 867 */
+ 0xb049dc016abc5e5f, /* 629: 1.0e+281 >> 870 */
+ 0xdc5c5301c56b75f7, /* 630: 1.0e+282 >> 873 */
+ 0x89b9b3e11b6329ba, /* 631: 1.0e+283 >> 877 */
+ 0xac2820d9623bf429, /* 632: 1.0e+284 >> 880 */
+ 0xd732290fbacaf133, /* 633: 1.0e+285 >> 883 */
+ 0x867f59a9d4bed6c0, /* 634: 1.0e+286 >> 887 */
+ 0xa81f301449ee8c70, /* 635: 1.0e+287 >> 890 */
+ 0xd226fc195c6a2f8c, /* 636: 1.0e+288 >> 893 */
+ 0x83585d8fd9c25db7, /* 637: 1.0e+289 >> 897 */
+ 0xa42e74f3d032f525, /* 638: 1.0e+290 >> 900 */
+ 0xcd3a1230c43fb26f, /* 639: 1.0e+291 >> 903 */
+ 0x80444b5e7aa7cf85, /* 640: 1.0e+292 >> 907 */
+ 0xa0555e361951c366, /* 641: 1.0e+293 >> 910 */
+ 0xc86ab5c39fa63440, /* 642: 1.0e+294 >> 913 */
+ 0xfa856334878fc150, /* 643: 1.0e+295 >> 916 */
+ 0x9c935e00d4b9d8d2, /* 644: 1.0e+296 >> 920 */
+ 0xc3b8358109e84f07, /* 645: 1.0e+297 >> 923 */
+ 0xf4a642e14c6262c8, /* 646: 1.0e+298 >> 926 */
+ 0x98e7e9cccfbd7dbd, /* 647: 1.0e+299 >> 930 */
+ 0xbf21e44003acdd2c, /* 648: 1.0e+300 >> 933 */
+ 0xeeea5d5004981478, /* 649: 1.0e+301 >> 936 */
+ 0x95527a5202df0ccb, /* 650: 1.0e+302 >> 940 */
+ 0xbaa718e68396cffd, /* 651: 1.0e+303 >> 943 */
+ 0xe950df20247c83fd, /* 652: 1.0e+304 >> 946 */
+ 0x91d28b7416cdd27e, /* 653: 1.0e+305 >> 950 */
+ 0xb6472e511c81471d, /* 654: 1.0e+306 >> 953 */
+ 0xe3d8f9e563a198e5, /* 655: 1.0e+307 >> 956 */
+ 0x8e679c2f5e44ff8f, /* 656: 1.0e+308 >> 960 */
+ 0xb201833b35d63f73, /* 657: 1.0e+309 >> 963 */
+ 0xde81e40a034bcf4f, /* 658: 1.0e+310 >> 966 */
+ 0x8b112e86420f6191, /* 659: 1.0e+311 >> 970 */
+ 0xadd57a27d29339f6, /* 660: 1.0e+312 >> 973 */
+ 0xd94ad8b1c7380874, /* 661: 1.0e+313 >> 976 */
+ 0x87cec76f1c830548, /* 662: 1.0e+314 >> 980 */
+ 0xa9c2794ae3a3c69a, /* 663: 1.0e+315 >> 983 */
+ 0xd433179d9c8cb841, /* 664: 1.0e+316 >> 986 */
+ 0x849feec281d7f328, /* 665: 1.0e+317 >> 990 */
+ 0xa5c7ea73224deff3, /* 666: 1.0e+318 >> 993 */
+ 0xcf39e50feae16bef, /* 667: 1.0e+319 >> 996 */
+ 0x81842f29f2cce375, /* 668: 1.0e+320 >> 1000 */
+ 0xa1e53af46f801c53, /* 669: 1.0e+321 >> 1003 */
+ 0xca5e89b18b602368, /* 670: 1.0e+322 >> 1006 */
+ 0xfcf62c1dee382c42, /* 671: 1.0e+323 >> 1009 */
+ 0x9e19db92b4e31ba9, /* 672: 1.0e+324 >> 1013 */
+ 0xc5a05277621be293, /* 673: 1.0e+325 >> 1016 */
+ 0xf70867153aa2db38, /* 674: 1.0e+326 >> 1019 */
+ 0x9a65406d44a5c903, /* 675: 1.0e+327 >> 1023 */
+ 0xc0fe908895cf3b44, /* 676: 1.0e+328 >> 1026 */
+ 0xf13e34aabb430a15, /* 677: 1.0e+329 >> 1029 */
+ 0x96c6e0eab509e64d, /* 678: 1.0e+330 >> 1033 */
+ 0xbc789925624c5fe0, /* 679: 1.0e+331 >> 1036 */
+ 0xeb96bf6ebadf77d8, /* 680: 1.0e+332 >> 1039 */
+ 0x933e37a534cbaae7, /* 681: 1.0e+333 >> 1043 */
+ 0xb80dc58e81fe95a1, /* 682: 1.0e+334 >> 1046 */
+ 0xe61136f2227e3b09, /* 683: 1.0e+335 >> 1049 */
+ 0x8fcac257558ee4e6, /* 684: 1.0e+336 >> 1053 */
+ 0xb3bd72ed2af29e1f, /* 685: 1.0e+337 >> 1056 */
+ 0xe0accfa875af45a7, /* 686: 1.0e+338 >> 1059 */
+ 0x8c6c01c9498d8b88, /* 687: 1.0e+339 >> 1063 */
+ 0xaf87023b9bf0ee6a, /* 688: 1.0e+340 >> 1066 */
+ 0xdb68c2ca82ed2a05, /* 689: 1.0e+341 >> 1069 */
+ 0x892179be91d43a43, /* 690: 1.0e+342 >> 1073 */
+ 0xab69d82e364948d4, /* 691: 1.0e+343 >> 1076 */
+ 0xd6444e39c3db9b09, /* 692: 1.0e+344 >> 1079 */
+ 0x85eab0e41a6940e5, /* 693: 1.0e+345 >> 1083 */
+ 0xa7655d1d2103911f, /* 694: 1.0e+346 >> 1086 */
+ 0xd13eb46469447567, /* 695: 1.0e+347 >> 1089 */
+};
+#define POWERSOF10_FIRST (-348)
+#define POWERSOF10_LAST (+347)
+#define POWERSOF10_COUNT (696)
+
+/*
+** Two inputs are multiplied to get a 128-bit result. Return
+** the high-order 64 bits of that result.
+*/
+static u64 sqlite3Multiply128(u64 a, u64 b){
+#if (defined(__GNUC__) || defined(__clang__)) \
+ && (defined(__x86_64__) || defined(__aarch64__) || defined(__riscv))
+ return ((__uint128_t)a * b) >> 64;
+#elif defined(_MSC_VER) && defined(_M_X64)
+ return __umulh(a, b);
+#else
+ u32 a1 = (u32)a;
+ u32 a2 = a >> 32;
+ u32 b1 = (u32)b;
+ u32 b2 = b >> 32;
+ u32 p0 = a1 * b1;
+ u32 p1 = a1 * b2;
+ u32 p2 = a2 * b1;
+ u32 p3 = a2 * b2;
+ u32 mid = p1 + (p0 >> 32);
+ mid += p2;
+ u32 carry = (mid < p2) ? 1 : 0;
+ return p3 + (mid >> 32) + carry;
+#endif
+}
-/* Double-Double multiplication. (x[0],x[1]) *= (y,yy)
+/*
+** pow10to2(x) computes floor(log2(pow(10,x))).
+** pow2to10(y) computes floor(log10(pow(2,y))).
+**
+** Conceptually, pow10to2(p) converts a base-10 exponent p into
+** a corresponding base-2 exponent, and pow2to10(e) converts a base-2
+** exponent into a base-10 exponent.
+**
+** The conversions are based on the observation that:
**
-** Reference:
-** T. J. Dekker, "A Floating-Point Technique for Extending the
-** Available Precision". 1971-07-26.
+** ln(10.0)/ln(2.0) == 108853/32768 (approximately)
+** ln(2.0)/ln(10.0) == 78913/262144 (approximately)
+**
+** These ratios are approximate, but they are accurate to 5 digits,
+** which is close enough for the usage here. Right-shift is used
+** for division so that rounding of negative numbers happens in the
+** right direction.
*/
-static void dekkerMul2(volatile double *x, double y, double yy){
- /*
- ** The "volatile" keywords on parameter x[] and on local variables
- ** below are needed force intermediate results to be truncated to
- ** binary64 rather than be carried around in an extended-precision
- ** format. The truncation is necessary for the Dekker algorithm to
- ** work. Intel x86 floating point might omit the truncation without
- ** the use of volatile.
- */
- volatile double tx, ty, p, q, c, cc;
- double hx, hy;
- u64 m;
- memcpy(&m, (void*)&x[0], 8);
- m &= 0xfffffffffc000000LL;
- memcpy(&hx, &m, 8);
- tx = x[0] - hx;
- memcpy(&m, &y, 8);
- m &= 0xfffffffffc000000LL;
- memcpy(&hy, &m, 8);
- ty = y - hy;
- p = hx*hy;
- q = hx*ty + tx*hy;
- c = p+q;
- cc = p - c + q + tx*ty;
- cc = x[0]*yy + x[1]*y + cc;
- x[0] = c + cc;
- x[1] = c - x[0];
- x[1] += cc;
+static int pwr10to2(int p){ return (p*108853) >> 15; }
+static int pwr2to10(int p){ return (p*78913) >> 18; }
+
+/*
+** Return a u64 with the N-th bit set.
+*/
+#define U64_BIT(N) (((u64)1)<<(N))
+
+/*
+** Count leading zeros for a 64-bit unsigned integer.
+*/
+static int countLeadingZeros(u64 m){
+#if defined(__GNUC__) || defined(__clang__)
+ return __builtin_clzll(m);
+#else
+ int n = 0;
+ if( m <= 0x00000000ffffffffULL) { n += 32; m <<= 32; }
+ if( m <= 0x0000ffffffffffffULL) { n += 16; m <<= 16; }
+ if( m <= 0x00ffffffffffffffULL) { n += 8; m <<= 8; }
+ if( m <= 0x0fffffffffffffffULL) { n += 4; m <<= 4; }
+ if( m <= 0x3fffffffffffffffULL) { n += 2; m <<= 2; }
+ if( m <= 0x7fffffffffffffffULL) { n += 1; }
+ return n;
+#endif
+}
+
+/*
+** Given m and e, which represent a quantity r == m*pow(2,e),
+** return values *pD and *pP such that r == (*pD)*pow(10,*pP),
+** approximately. *pD should contain at least n significant digits.
+**
+** The input m is required to have its highest bit set. In other words,
+** m should be left-shifted, and e decremented, to maximize the value of m.
+*/
+static void sqlite3Fp2Convert10(u64 m, int e, int n, u64 *pD, int *pP){
+ int p, idx;
+ u64 h, out;
+ p = n - 1 - pwr2to10(e+63);
+ idx = p - POWERSOF10_FIRST;
+ h = sqlite3Multiply128(m, sqlite3PowerOfTen[idx]);
+ assert( -(e + pwr10to2(p) + 3) >=0 );
+ assert( -(e + pwr10to2(p) + 3) <64 );
+ out = h >> -(e + pwr10to2(p) + 3);
+ *pD = (out + 2 + ((out>>2)&1)) >> 2;
+ *pP = -p;
+}
+
+/*
+** Return an IEEE754 floating point value that approximates d*pow(10,p).
+**
+** The "d" value must not have its most significant bit set.
+*/
+static double sqlite3Fp10Convert2(u64 d, int p){
+ u64 out;
+ int b;
+ int e1;
+ int e2;
+ int lp;
+ int idx;
+ u64 h;
+ double r;
+ if( p<POWERSOF10_FIRST || d==0 ){
+ return 0.0;
+ }
+ if( p>POWERSOF10_LAST ){
+ return INFINITY;
+ }
+ b = 64 - countLeadingZeros(d);
+ lp = pwr10to2(p);
+ e1 = 53 - b - lp;
+ if( e1>1074 ){
+ if( -(b + lp) >= 1077 ) return 0.0;
+ e1 = 1074;
+ }
+ e2 = e1 - (64-b);
+ idx = p - POWERSOF10_FIRST;
+ h = sqlite3Multiply128(d<<(64-b), sqlite3PowerOfTen[idx]);
+ assert( -(e2 + lp + 3) >=0 );
+ assert( -(e2 + lp + 3) <64 );
+ out = (h >> -(e2 + lp + 3)) | 1;
+ if( out >= U64_BIT(55)-2 ){
+ out = (out>>1) | (out&1);
+ e1--;
+ }
+ if( e1<=(-972) ){
+ return INFINITY;
+ }
+ out = (out + 1 + ((out>>2)&1)) >> 2;
+ if( (out & U64_BIT(52))!=0 ){
+ out = (out & ~U64_BIT(52)) | ((u64)(1075-e1)<<52);
+ }
+ memcpy(&r, &out, 8);
+ return r;
}
/*
int eValid = 1; /* True exponent is either not used or is well-formed */
int nDigit = 0; /* Number of digits processed */
int eType = 1; /* 1: pure integer, 2+: fractional -1 or less: bad UTF16 */
- u64 s2; /* round-tripped significand */
- double rr[2];
assert( enc==SQLITE_UTF8 || enc==SQLITE_UTF16LE || enc==SQLITE_UTF16BE );
*pResult = 0.0; /* Default return value, in case of an error */
while( z<zEnd && sqlite3Isdigit(*z) ){
s = s*10 + (*z - '0');
z+=incr; nDigit++;
- if( s>=((LARGEST_UINT64-9)/10) ){
+ if( s>=((LARGEST_INT64-9)/10) ){
/* skip non-significant significand digits
** (increase exponent by d to shift decimal left) */
while( z<zEnd && sqlite3Isdigit(*z) ){ z+=incr; d++; }
/* copy digits from after decimal to significand
** (decrease exponent by d to shift decimal right) */
while( z<zEnd && sqlite3Isdigit(*z) ){
- if( s<((LARGEST_UINT64-9)/10) ){
+ if( s<((LARGEST_INT64-9)/10) ){
s = s*10 + (*z - '0');
d--;
nDigit++;
/* adjust exponent by d, and update sign */
e = (e*esign) + d;
- /* Try to adjust the exponent to make it smaller */
- while( e>0 && s<((LARGEST_UINT64-0x7ff)/10) ){
- s *= 10;
- e--;
- }
- while( e<0 && (s%10)==0 ){
- s /= 10;
- e++;
- }
-
- rr[0] = (double)s;
- assert( sizeof(s2)==sizeof(rr[0]) );
-#ifdef SQLITE_DEBUG
- rr[1] = 18446744073709549568.0;
- memcpy(&s2, &rr[1], sizeof(s2));
- assert( s2==0x43efffffffffffffLL );
-#endif
- /* Largest double that can be safely converted to u64
- ** vvvvvvvvvvvvvvvvvvvvvv */
- if( rr[0]<=18446744073709549568.0 ){
- s2 = (u64)rr[0];
- rr[1] = s>=s2 ? (double)(s - s2) : -(double)(s2 - s);
- }else{
- rr[1] = 0.0;
- }
- assert( rr[1]<=1.0e-10*rr[0] ); /* Equal only when rr[0]==0.0 */
-
- if( e>0 ){
- while( e>=100 ){
- e -= 100;
- dekkerMul2(rr, 1.0e+100, -1.5902891109759918046e+83);
- }
- while( e>=10 ){
- e -= 10;
- dekkerMul2(rr, 1.0e+10, 0.0);
- }
- while( e>=1 ){
- e -= 1;
- dekkerMul2(rr, 1.0e+01, 0.0);
- }
- }else{
- while( e<=-100 ){
- e += 100;
- dekkerMul2(rr, 1.0e-100, -1.99918998026028836196e-117);
- }
- while( e<=-10 ){
- e += 10;
- dekkerMul2(rr, 1.0e-10, -3.6432197315497741579e-27);
- }
- while( e<=-1 ){
- e += 1;
- dekkerMul2(rr, 1.0e-01, -5.5511151231257827021e-18);
- }
- }
- *pResult = rr[0]+rr[1];
- if( sqlite3IsNaN(*pResult) ) *pResult = 1e300*1e300;
+ *pResult = sqlite3Fp10Convert2(s,e);
if( sign<0 ) *pResult = -*pResult;
assert( !sqlite3IsNaN(*pResult) );
int i;
u64 v;
int e, exp = 0;
- double rr[2];
p->isSpecial = 0;
p->z = p->zBuf;
p->sign = '+';
}
memcpy(&v,&r,8);
- e = v>>52;
- if( (e&0x7ff)==0x7ff ){
+ e = (v>>52)&0x7ff;
+ if( e==0x7ff ){
p->isSpecial = 1 + (v!=0x7ff0000000000000LL);
p->n = 0;
p->iDP = 0;
return;
}
-
- /* Multiply r by powers of ten until it lands somewhere in between
- ** 1.0e+19 and 1.0e+17.
- **
- ** Use Dekker-style double-double computation to increase the
- ** precision.
- **
- ** The error terms on constants like 1.0e+100 computed using the
- ** decimal extension, for example as follows:
- **
- ** SELECT decimal_exp(decimal_sub('1.0e+100',decimal(1.0e+100)));
- */
- rr[0] = r;
- rr[1] = 0.0;
- if( rr[0]>9.223372036854774784e+18 ){
- while( rr[0]>9.223372036854774784e+118 ){
- exp += 100;
- dekkerMul2(rr, 1.0e-100, -1.99918998026028836196e-117);
- }
- while( rr[0]>9.223372036854774784e+28 ){
- exp += 10;
- dekkerMul2(rr, 1.0e-10, -3.6432197315497741579e-27);
- }
- while( rr[0]>9.223372036854774784e+18 ){
- exp += 1;
- dekkerMul2(rr, 1.0e-01, -5.5511151231257827021e-18);
- }
+ v &= 0x000fffffffffffffULL;
+ if( e==0 ){
+ int n = countLeadingZeros(v);
+ v <<= n;
+ e = -1074 - n;
}else{
- while( rr[0]<9.223372036854774784e-83 ){
- exp -= 100;
- dekkerMul2(rr, 1.0e+100, -1.5902891109759918046e+83);
- }
- while( rr[0]<9.223372036854774784e+07 ){
- exp -= 10;
- dekkerMul2(rr, 1.0e+10, 0.0);
- }
- while( rr[0]<9.22337203685477478e+17 ){
- exp -= 1;
- dekkerMul2(rr, 1.0e+01, 0.0);
- }
+ v = (v<<11) | U64_BIT(63);
+ e -= 1086;
}
- v = rr[1]<0.0 ? (u64)rr[0]-(u64)(-rr[1]) : (u64)rr[0]+(u64)rr[1];
+ sqlite3Fp2Convert10(v, e, 17, &v, &exp);
/* Extract significant digits. */
i = sizeof(p->zBuf)-1;
projects / thirdparty / sqlite.git / commitdiff
