diff --git a/README.md b/README.md index 427cced5f..f709cf29b 100644 --- a/README.md +++ b/README.md @@ -402,7 +402,7 @@ _We do not aim to provide a general-purpose JSON library._ A library like RapidJ - The input string is unmodified. (Parsers like sajson and RapidJSON use the input string as a buffer.) - We parse integers and floating-point numbers as separate types which allows us to support large signed 64-bit integers in [-9223372036854775808,9223372036854775808), like a Java `long` or a C/C++ `long long` and large unsigned integers up to the value 18446744073709551615. Among the parsers that differentiate between integers and floating-point numbers, not all support 64-bit integers. (For example, sajson rejects JSON files with integers larger than or equal to 2147483648. RapidJSON will parse a file containing an overly long integer like 18446744073709551616 as a floating-point number.) When we cannot represent exactly an integer as a signed or unsigned 64-bit value, we reject the JSON document. - We support the full range of 64-bit floating-point numbers (binary64). The values range from ` std::numeric_limits::lowest()` to `std::numeric_limits::max()`, so from -1.7976e308 all the way to 1.7975e308. Extreme values (less or equal to -1e308, greater or equal to 1e308) are rejected: we refuse to parse the input document. -- We test for accurate float parsing with a bound on the [unit of least precision (ULP)](https://en.wikipedia.org/wiki/Unit_in_the_last_place) of one. Practically speaking, this implies 15 digits of accuracy or better. +- We test for accurate float parsing with a perfect (ULP 0) accuracy. Many parsers offer only approximate floating parsing. RapidJSON also offers the option of accurate float parsing (`kParseFullPrecisionFlag`) but it comes at a significant performance penalty compared to the default settings. - We do full UTF-8 validation as part of the parsing. (Parsers like fastjson, gason and dropbox json11 do not do UTF-8 validation. The sajson parser does incomplete UTF-8 validation, accepting code point sequences like 0xb1 0x87.) - We fully validate the numbers. (Parsers like gason and ultranjson will accept `[0e+]` as valid JSON.) diff --git a/benchmark/parseandstatcompetition.cpp b/benchmark/parseandstatcompetition.cpp index af36ca79c..1173962a5 100644 --- a/benchmark/parseandstatcompetition.cpp +++ b/benchmark/parseandstatcompetition.cpp @@ -238,6 +238,32 @@ rapid_compute_stats(const simdjson::padded_string &p) { return answer; } +__attribute__((noinline)) stat_t +rapid_accurate_compute_stats(const simdjson::padded_string &p) { + stat_t answer; + char *buffer = (char *)malloc(p.size() + 1); + if(buffer == nullptr) { + return answer; + } + memcpy(buffer, p.data(), p.size()); + buffer[p.size()] = '\0'; + rapidjson::Document d; + d.ParseInsitu(buffer); + answer.valid = !d.HasParseError(); + if (!answer.valid) { + free(buffer); + return answer; + } + answer.number_count = 0; + answer.object_count = 0; + answer.array_count = 0; + answer.null_count = 0; + answer.true_count = 0; + answer.false_count = 0; + rapid_traverse(answer, d); + free(buffer); + return answer; +} int main(int argc, char *argv[]) { bool verbose = false; bool just_data = false; @@ -294,6 +320,11 @@ int main(int argc, char *argv[]) { printf("rapid: "); print_stat(s2); } + stat_t s2a = rapid_accurate_compute_stats(p); + if (verbose) { + printf("rapid full: "); + print_stat(s2); + } stat_t s3 = sasjon_compute_stats(p); if (verbose) { printf("sasjon: "); diff --git a/benchmark/parsingcompetition.cpp b/benchmark/parsingcompetition.cpp index 17d8d4ed7..ee287bf41 100644 --- a/benchmark/parsingcompetition.cpp +++ b/benchmark/parsingcompetition.cpp @@ -130,11 +130,24 @@ bool bench(const char *filename, bool verbose, bool just_data, int repeat_multip .HasParseError(), false, memcpy(buffer, p.data(), p.size()), repeat, volume, !just_data); +#ifndef ALLPARSER + if (!just_data) +#endif + BEST_TIME("RapidJSON (accurate number parsing) ", + d.Parse((const char *)buffer) + .HasParseError(), + false, memcpy(buffer, p.data(), p.size()), repeat, volume, + !just_data); BEST_TIME("RapidJSON (insitu)", d.ParseInsitu(buffer).HasParseError(), false, memcpy(buffer, p.data(), p.size()) && (buffer[p.size()] = '\0'), repeat, volume, !just_data); + BEST_TIME("RapidJSON (insitu, accurate number parsing)", + d.ParseInsitu(buffer).HasParseError(), + false, + memcpy(buffer, p.data(), p.size()) && (buffer[p.size()] = '\0'), + repeat, volume, !just_data); #ifndef ALLPARSER if (!just_data) #endif diff --git a/src/generic/numberparsing.h b/src/generic/numberparsing.h index 33aaf9924..76b9342e2 100644 --- a/src/generic/numberparsing.h +++ b/src/generic/numberparsing.h @@ -1,80 +1,205 @@ namespace numberparsing { -// Allowable floating-point values range -// std::numeric_limits::lowest() to std::numeric_limits::max(), -// so from -1.7976e308 all the way to 1.7975e308 in binary64. The lowest -// non-zero normal values is std::numeric_limits::min() or -// about 2.225074e-308. -static const double power_of_ten[] = { - 1e-308, 1e-307, 1e-306, 1e-305, 1e-304, 1e-303, 1e-302, 1e-301, 1e-300, - 1e-299, 1e-298, 1e-297, 1e-296, 1e-295, 1e-294, 1e-293, 1e-292, 1e-291, - 1e-290, 1e-289, 1e-288, 1e-287, 1e-286, 1e-285, 1e-284, 1e-283, 1e-282, - 1e-281, 1e-280, 1e-279, 1e-278, 1e-277, 1e-276, 1e-275, 1e-274, 1e-273, - 1e-272, 1e-271, 1e-270, 1e-269, 1e-268, 1e-267, 1e-266, 1e-265, 1e-264, - 1e-263, 1e-262, 1e-261, 1e-260, 1e-259, 1e-258, 1e-257, 1e-256, 1e-255, - 1e-254, 1e-253, 1e-252, 1e-251, 1e-250, 1e-249, 1e-248, 1e-247, 1e-246, - 1e-245, 1e-244, 1e-243, 1e-242, 1e-241, 1e-240, 1e-239, 1e-238, 1e-237, - 1e-236, 1e-235, 1e-234, 1e-233, 1e-232, 1e-231, 1e-230, 1e-229, 1e-228, - 1e-227, 1e-226, 1e-225, 1e-224, 1e-223, 1e-222, 1e-221, 1e-220, 1e-219, - 1e-218, 1e-217, 1e-216, 1e-215, 1e-214, 1e-213, 1e-212, 1e-211, 1e-210, - 1e-209, 1e-208, 1e-207, 1e-206, 1e-205, 1e-204, 1e-203, 1e-202, 1e-201, - 1e-200, 1e-199, 1e-198, 1e-197, 1e-196, 1e-195, 1e-194, 1e-193, 1e-192, - 1e-191, 1e-190, 1e-189, 1e-188, 1e-187, 1e-186, 1e-185, 1e-184, 1e-183, - 1e-182, 1e-181, 1e-180, 1e-179, 1e-178, 1e-177, 1e-176, 1e-175, 1e-174, - 1e-173, 1e-172, 1e-171, 1e-170, 1e-169, 1e-168, 1e-167, 1e-166, 1e-165, - 1e-164, 1e-163, 1e-162, 1e-161, 1e-160, 1e-159, 1e-158, 1e-157, 1e-156, - 1e-155, 1e-154, 1e-153, 1e-152, 1e-151, 1e-150, 1e-149, 1e-148, 1e-147, - 1e-146, 1e-145, 1e-144, 1e-143, 1e-142, 1e-141, 1e-140, 1e-139, 1e-138, - 1e-137, 1e-136, 1e-135, 1e-134, 1e-133, 1e-132, 1e-131, 1e-130, 1e-129, - 1e-128, 1e-127, 1e-126, 1e-125, 1e-124, 1e-123, 1e-122, 1e-121, 1e-120, - 1e-119, 1e-118, 1e-117, 1e-116, 1e-115, 1e-114, 1e-113, 1e-112, 1e-111, - 1e-110, 1e-109, 1e-108, 1e-107, 1e-106, 1e-105, 1e-104, 1e-103, 1e-102, - 1e-101, 1e-100, 1e-99, 1e-98, 1e-97, 1e-96, 1e-95, 1e-94, 1e-93, - 1e-92, 1e-91, 1e-90, 1e-89, 1e-88, 1e-87, 1e-86, 1e-85, 1e-84, - 1e-83, 1e-82, 1e-81, 1e-80, 1e-79, 1e-78, 1e-77, 1e-76, 1e-75, - 1e-74, 1e-73, 1e-72, 1e-71, 1e-70, 1e-69, 1e-68, 1e-67, 1e-66, - 1e-65, 1e-64, 1e-63, 1e-62, 1e-61, 1e-60, 1e-59, 1e-58, 1e-57, - 1e-56, 1e-55, 1e-54, 1e-53, 1e-52, 1e-51, 1e-50, 1e-49, 1e-48, - 1e-47, 1e-46, 1e-45, 1e-44, 1e-43, 1e-42, 1e-41, 1e-40, 1e-39, - 1e-38, 1e-37, 1e-36, 1e-35, 1e-34, 1e-33, 1e-32, 1e-31, 1e-30, - 1e-29, 1e-28, 1e-27, 1e-26, 1e-25, 1e-24, 1e-23, 1e-22, 1e-21, - 1e-20, 1e-19, 1e-18, 1e-17, 1e-16, 1e-15, 1e-14, 1e-13, 1e-12, - 1e-11, 1e-10, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, - 1e-2, 1e-1, 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, - 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, - 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22, 1e23, 1e24, - 1e25, 1e26, 1e27, 1e28, 1e29, 1e30, 1e31, 1e32, 1e33, - 1e34, 1e35, 1e36, 1e37, 1e38, 1e39, 1e40, 1e41, 1e42, - 1e43, 1e44, 1e45, 1e46, 1e47, 1e48, 1e49, 1e50, 1e51, - 1e52, 1e53, 1e54, 1e55, 1e56, 1e57, 1e58, 1e59, 1e60, - 1e61, 1e62, 1e63, 1e64, 1e65, 1e66, 1e67, 1e68, 1e69, - 1e70, 1e71, 1e72, 1e73, 1e74, 1e75, 1e76, 1e77, 1e78, - 1e79, 1e80, 1e81, 1e82, 1e83, 1e84, 1e85, 1e86, 1e87, - 1e88, 1e89, 1e90, 1e91, 1e92, 1e93, 1e94, 1e95, 1e96, - 1e97, 1e98, 1e99, 1e100, 1e101, 1e102, 1e103, 1e104, 1e105, - 1e106, 1e107, 1e108, 1e109, 1e110, 1e111, 1e112, 1e113, 1e114, - 1e115, 1e116, 1e117, 1e118, 1e119, 1e120, 1e121, 1e122, 1e123, - 1e124, 1e125, 1e126, 1e127, 1e128, 1e129, 1e130, 1e131, 1e132, - 1e133, 1e134, 1e135, 1e136, 1e137, 1e138, 1e139, 1e140, 1e141, - 1e142, 1e143, 1e144, 1e145, 1e146, 1e147, 1e148, 1e149, 1e150, - 1e151, 1e152, 1e153, 1e154, 1e155, 1e156, 1e157, 1e158, 1e159, - 1e160, 1e161, 1e162, 1e163, 1e164, 1e165, 1e166, 1e167, 1e168, - 1e169, 1e170, 1e171, 1e172, 1e173, 1e174, 1e175, 1e176, 1e177, - 1e178, 1e179, 1e180, 1e181, 1e182, 1e183, 1e184, 1e185, 1e186, - 1e187, 1e188, 1e189, 1e190, 1e191, 1e192, 1e193, 1e194, 1e195, - 1e196, 1e197, 1e198, 1e199, 1e200, 1e201, 1e202, 1e203, 1e204, - 1e205, 1e206, 1e207, 1e208, 1e209, 1e210, 1e211, 1e212, 1e213, - 1e214, 1e215, 1e216, 1e217, 1e218, 1e219, 1e220, 1e221, 1e222, - 1e223, 1e224, 1e225, 1e226, 1e227, 1e228, 1e229, 1e230, 1e231, - 1e232, 1e233, 1e234, 1e235, 1e236, 1e237, 1e238, 1e239, 1e240, - 1e241, 1e242, 1e243, 1e244, 1e245, 1e246, 1e247, 1e248, 1e249, - 1e250, 1e251, 1e252, 1e253, 1e254, 1e255, 1e256, 1e257, 1e258, - 1e259, 1e260, 1e261, 1e262, 1e263, 1e264, 1e265, 1e266, 1e267, - 1e268, 1e269, 1e270, 1e271, 1e272, 1e273, 1e274, 1e275, 1e276, - 1e277, 1e278, 1e279, 1e280, 1e281, 1e282, 1e283, 1e284, 1e285, - 1e286, 1e287, 1e288, 1e289, 1e290, 1e291, 1e292, 1e293, 1e294, - 1e295, 1e296, 1e297, 1e298, 1e299, 1e300, 1e301, 1e302, 1e303, - 1e304, 1e305, 1e306, 1e307, 1e308}; + +// Attempts to compute i * 10^(power) exactly; and if "negative" is +// true, negate the result. +// This function will only work in some cases, when it does not work, success is +// set to false. This should work *most of the time* (like 99% of the time). +// We assume that power is in the [FASTFLOAT_SMALLEST_POWER, +// FASTFLOAT_LARGEST_POWER] interval: the caller is responsible for this check. +really_inline double compute_float_64(int64_t power, uint64_t i, bool negative, + bool *success) { + // we start with a fast path + if (-22 <= power && power <= 22 && i <= 9007199254740991) { + // convert the integer into a double. This is lossless since + // 0 <= i <= 2^53 - 1. + double d = i; + // + // The general idea is as follows. + // If 0 <= s < 2^53 and if 10^0 <= p <= 10^22 then + // 1) Both s and p can be represented exactly as 64-bit floating-point + // values + // (binary64). + // 2) Because s and p can be represented exactly as floating-point values, + // then s * p + // and s / p will produce correctly rounded values. + // + if (power < 0) { + d = d / power_of_ten[-power]; + } else { + d = d * power_of_ten[power]; + } + if (negative) { + d = -d; + } + *success = true; + return d; + } + + // When 22 < power && power < 22 + 16, we could + // hope for another, secondary fast path. If + // you need to compute i * 10^(22 + x) for x < 16, + // first compute i * 10^x, if you know that result is exact + // (e.g., when i * 10^x < 2^53), + // then you can still proceed and do (i * 10^x) * 10^22. + // Is this worth your time? + // You need 22 < power *and* power < 22 + 16 *and* (i * 10^(x-22) < 2^53) + // for this second fast path to work. + // If you you have 22 < power *and* power < 22 + 16, and then you + // optimistically compute "i * 10^(x-22)", there is still a chance that you + // have wasted your time if i * 10^(x-22) >= 2^53. It makes the use cases of + // this optimization maybe less common than we would like. Source: + // http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/ + // also used in RapidJSON: https://rapidjson.org/strtod_8h_source.html + + // The fast path has now failed, so we are failing back on the slower path. + + // In the slow path, we need to adjust i so that it is > 1<<63 which is always + // possible, except if i == 0, so we handle i == 0 separately. + if(i == 0) { + return 0.0; + } + + // We are going to need to do some 64-bit arithmetic to get a more precise product. + // We use a table lookup approach. + components c = + power_of_ten_components[power - FASTFLOAT_SMALLEST_POWER]; // safe because + // power_index + // <= 2*308 + // we recover the mantissa of the power, it has a leading 1. It is always + // rounded down. + uint64_t factor_mantissa = c.mantissa; + + // We want the most significant bit of i to be 1. Shift if needed. + int lz = leading_zeroes(i); + i <<= lz; + // We want the most significant 64 bits of the product. We know + // this will be non-zero because the most significant bit of i is + // 1. + value128 product = full_multiplication(i, factor_mantissa); + uint64_t lower = product.low; + uint64_t upper = product.high; + + // We know that upper has at most one leading zero because + // both i and factor_mantissa have a leading one. This means + // that the result is at least as large as ((1<<63)*(1<<63))/(1<<64). + + // As long as the first 9 bits of "upper" are not "1", then we + // know that we have an exact computed value for the leading + // 55 bits because any imprecision would play out as a +1, in + // the worst case. + if (unlikely((upper & 0x1FF) == 0x1FF) && (lower + i < lower)) { + uint64_t factor_mantissa_low = + mantissa_128[power - FASTFLOAT_SMALLEST_POWER]; + // next, we compute the 64-bit x 128-bit multiplication, getting a 192-bit + // result (three 64-bit values) + product = full_multiplication(i, factor_mantissa_low); + uint64_t product_low = product.low; + uint64_t product_middle2 = product.high; + uint64_t product_middle1 = lower; + uint64_t product_high = upper; + uint64_t product_middle = product_middle1 + product_middle2; + if (product_middle < product_middle1) { + product_high++; // overflow carry + } + // We want to check whether mantissa *i + i would affect our result. + // This does happen, e.g. with 7.3177701707893310e+15. + if (((product_middle + 1 == 0) && ((product_high & 0x1FF) == 0x1FF) && + (product_low + i < product_low))) { // let us be prudent and bail out. + *success = false; + return 0; + } + upper = product_high; + lower = product_middle; + } + // The final mantissa should be 53 bits with a leading 1. + // We shift it so that it occupies 54 bits with a leading 1. + /////// + uint64_t upperbit = upper >> 63; + uint64_t mantissa = upper >> (upperbit + 9); + lz += 1 ^ upperbit; + + // Here we have mantissa < (1<<54). + + // We have to round to even. The "to even" part + // is only a problem when we are right in between two floats + // which we guard against. + // If we have lots of trailing zeros, we may fall right between two + // floating-point values. + if (unlikely((lower == 0) && ((upper & 0x1FF) == 0) && + ((mantissa & 3) == 1))) { + // if mantissa & 1 == 1 we might need to round up. + // + // Scenarios: + // 1. We are not in the middle. Then we should round up. + // + // 2. We are right in the middle. Whether we round up depends + // on the last significant bit: if it is "one" then we round + // up (round to even) otherwise, we do not. + // + // So if the last significant bit is 1, we can safely round up. + // Hence we only need to bail out if (mantissa & 3) == 1. + // Otherwise we may need more accuracy or analysis to determine whether + // we are exactly between two floating-point numbers. + // It can be triggered with 1e23. + *success = false; + return 0; + } + + mantissa += mantissa & 1; + mantissa >>= 1; + + // Here we have mantissa < (1<<53), unless there was an overflow + if (mantissa >= (1ULL << 53)) { + ////////// + // This will happen when parsing values such as 7.2057594037927933e+16 + //////// + mantissa = (1ULL << 52); + lz--; // undo previous addition + } + mantissa &= ~(1ULL << 52); + uint64_t real_exponent = c.exp - lz; + // we have to check that real_exponent is in range, otherwise we bail out + if (unlikely((real_exponent < 1) || (real_exponent > 2046))) { + *success = false; + return 0; + } + mantissa |= real_exponent << 52; + mantissa |= (((uint64_t)negative) << 63); + double d; + memcpy(&d, &mantissa, sizeof(d)); + *success = true; + return d; +} + +static bool parse_float_strtod(const char *ptr, double *outDouble) { + char *endptr; + *outDouble = strtod(ptr, &endptr); + // Some libraries will set errno = ERANGE when the value is subnormal, + // yet we may want to be able to parse subnormal values. + // However, we do not want to tolerate NAN or infinite values. + // + // Values like infinity or NaN are not allowed in the JSON specification. + // If you consume a large value and you map it to "infinity", you will no + // longer be able to serialize back a standard-compliant JSON. And there is + // no realistic application where you might need values so large than they + // can't fit in binary64. The maximal value is about 1.7976931348623157 × + // 10^308 It is an unimaginable large number. There will never be any piece of + // engineering involving as many as 10^308 parts. It is estimated that there + // are about 10^80 atoms in the universe.  The estimate for the total number + // of electrons is similar. Using a double-precision floating-point value, we + // can represent easily the number of atoms in the universe. We could also + // represent the number of ways you can pick any three individual atoms at + // random in the universe. If you ever encounter a number much larger than + // 10^308, you know that you have a bug. RapidJSON will reject a document with + // a float that does not fit in binary64. JSON for Modern C++ (nlohmann/json) + // will flat out throw an exception. + // + if ((endptr == ptr) || (!std::isfinite(*outDouble))) { + return false; + } + return true; +} really_inline bool is_integer(char c) { return (c >= '0' && c <= '9'); @@ -120,161 +245,6 @@ really_inline bool is_made_of_eight_digits_fast(const char *chars) { 0x3333333333333333); } - -// -// This function computes base * 10 ^ (- negative_exponent ). -// It is only even going to be used when negative_exponent is tiny. -really_inline double subnormal_power10(double base, int64_t negative_exponent) { - // avoid integer overflows in the pow expression, those values would - // become zero anyway. - if(negative_exponent < -1000) { - return 0; - } - - // this is probably not going to be fast - return base * 1e-308 * pow(10, negative_exponent + 308); -} - -// called by parse_number when we know that the output is a float, -// but where there might be some integer overflow. The trick here is to -// parse using floats from the start. -// Do not call this function directly as it skips some of the checks from -// parse_number -// -// This function will almost never be called!!! -// -// Note: a redesign could avoid this function entirely. -// -never_inline bool parse_float(const uint8_t *const src, document::parser &parser, bool found_minus) { - const char *p = reinterpret_cast(src); - bool negative = false; - if (found_minus) { - ++p; - negative = true; - } - long double i; - if (*p == '0') { // 0 cannot be followed by an integer - ++p; - i = 0; - } else { - unsigned char digit = *p - '0'; - i = digit; - p++; - while (is_integer(*p)) { - digit = *p - '0'; - i = 10 * i + digit; - ++p; - } - } - if ('.' == *p) { - ++p; - int fractional_weight = 308; - if (is_integer(*p)) { - unsigned char digit = *p - '0'; - ++p; - - fractional_weight--; - i = i + digit * (fractional_weight >= 0 ? power_of_ten[fractional_weight] - : 0); - } else { -#ifdef JSON_TEST_NUMBERS // for unit testing - found_invalid_number(src); -#endif - return false; - } - while (is_integer(*p)) { - unsigned char digit = *p - '0'; - ++p; - fractional_weight--; - i = i + digit * (fractional_weight >= 0 ? power_of_ten[fractional_weight] - : 0); - } - } - if (('e' == *p) || ('E' == *p)) { - ++p; - bool neg_exp = false; - if ('-' == *p) { - neg_exp = true; - ++p; - } else if ('+' == *p) { - ++p; - } - if (!is_integer(*p)) { -#ifdef JSON_TEST_NUMBERS // for unit testing - found_invalid_number(src); -#endif - return false; - } - unsigned char digit = *p - '0'; - int64_t exp_number = digit; // exponential part - p++; - if (is_integer(*p)) { - digit = *p - '0'; - exp_number = 10 * exp_number + digit; - ++p; - } - if (is_integer(*p)) { - digit = *p - '0'; - exp_number = 10 * exp_number + digit; - ++p; - } - if (is_integer(*p)) { - digit = *p - '0'; - exp_number = 10 * exp_number + digit; - ++p; - } - while (is_integer(*p)) { - if (exp_number > 0x100000000) { // we need to check for overflows -// we refuse to parse this -#ifdef JSON_TEST_NUMBERS // for unit testing - found_invalid_number(src); -#endif - return false; - } - digit = *p - '0'; - exp_number = 10 * exp_number + digit; - ++p; - } - if (unlikely(exp_number > 308)) { - // this path is unlikely - if (neg_exp) { - // We either have zero or a subnormal. - // We expect this to be uncommon so we go through a slow path. - i = subnormal_power10(i, -exp_number); - } else { -// We know for sure that we have a number that is too large, -// we refuse to parse this -#ifdef JSON_TEST_NUMBERS // for unit testing - found_invalid_number(src); -#endif - return false; - } - } else { - int exponent = (neg_exp ? -exp_number : exp_number); - // we have that exp_number is [0,308] so that - // exponent is [-308,308] so that - // 308 + exponent is in [0, 2 * 308] - i *= power_of_ten[308 + exponent]; - } - } - if (is_not_structural_or_whitespace(*p)) { - return false; - } - // check that we can go from long double to double safely. - if(i > std::numeric_limits::max()) { -#ifdef JSON_TEST_NUMBERS // for unit testing - found_invalid_number(src); -#endif - return false; - } - double d = negative ? -i : i; - parser.on_number_double(d); -#ifdef JSON_TEST_NUMBERS // for unit testing - found_float(d, src); -#endif - return is_structural_or_whitespace(*p); -} - // called by parse_number when we know that the output is an integer, // but where there might be some integer overflow. // we want to catch overflows! @@ -283,7 +253,9 @@ never_inline bool parse_float(const uint8_t *const src, document::parser &parser // // This function will almost never be called!!! // -never_inline bool parse_large_integer(const uint8_t *const src, document::parser &parser, bool found_minus) { +never_inline bool parse_large_integer(const uint8_t *const src, + document::parser &parser, + bool found_minus) { const char *p = reinterpret_cast(src); bool negative = false; @@ -320,14 +292,14 @@ never_inline bool parse_large_integer(const uint8_t *const src, document::parser } if (negative) { if (i > 0x8000000000000000) { - // overflows! + // overflows! #ifdef JSON_TEST_NUMBERS // for unit testing found_invalid_number(src); #endif return false; // overflow } else if (i == 0x8000000000000000) { // In two's complement, we cannot represent 0x8000000000000000 - // as a positive signed integer, but the negative version is + // as a positive signed integer, but the negative version is // possible. constexpr int64_t signed_answer = INT64_MIN; parser.on_number_s64(signed_answer); @@ -344,9 +316,9 @@ never_inline bool parse_large_integer(const uint8_t *const src, document::parser } } else { // we have a positive integer, the contract is that - // we try to represent it as a signed integer and only + // we try to represent it as a signed integer and only // fallback on unsigned integers if absolutely necessary. - if(i < 0x8000000000000000) { + if (i < 0x8000000000000000) { #ifdef JSON_TEST_NUMBERS // for unit testing found_integer(i, src); #endif @@ -361,6 +333,21 @@ never_inline bool parse_large_integer(const uint8_t *const src, document::parser return is_structural_or_whitespace(*p); } +bool slow_float_parsing(UNUSED const char * src, document::parser &parser) { + double d; + if (parse_float_strtod(src, &d)) { + parser.on_number_double(d); +#ifdef JSON_TEST_NUMBERS // for unit testing + found_float(d, (const uint8_t *)src); +#endif + return true; + } +#ifdef JSON_TEST_NUMBERS // for unit testing + found_invalid_number((const uint8_t *)src); +#endif + return false; +} + // parse the number at src // define JSON_TEST_NUMBERS for unit testing // @@ -369,13 +356,13 @@ never_inline bool parse_large_integer(const uint8_t *const src, document::parser // document is made of a single number), then it is necessary to copy the // content and append a space before calling this function. // -// Our objective is accurate parsing (ULP of 0 or 1) at high speed. +// Our objective is accurate parsing (ULP of 0) at high speed. really_inline bool parse_number(UNUSED const uint8_t *const src, UNUSED bool found_minus, document::parser &parser) { #ifdef SIMDJSON_SKIPNUMBERPARSING // for performance analysis, it is sometimes // useful to skip parsing - parser.on_number_s64(0); // always write zero + parser.on_number_s64(0); // always write zero return true; // always succeeds #else const char *p = reinterpret_cast(src); @@ -507,7 +494,9 @@ really_inline bool parse_number(UNUSED const uint8_t *const src, exponent += (neg_exp ? -exp_number : exp_number); } if (is_float) { - uint64_t power_index = 308 + exponent; + // If we frequently had to deal with long strings of digits, + // we could extend our code by using a 128-bit integer instead + // of a 64-bit integer. However, this is uncommon in practice. if (unlikely((digit_count >= 19))) { // this is uncommon // It is possible that the integer had an overflow. // We have to handle the case where we have 0.0000somenumber. @@ -521,21 +510,37 @@ really_inline bool parse_number(UNUSED const uint8_t *const src, // Ok, chances are good that we had an overflow! // this is almost never going to get called!!! // we start anew, going slowly!!! - return parse_float(src, parser, found_minus); + // This will happen in the following examples: + // 10000000000000000000000000000000000000000000e+308 + // 3.1415926535897932384626433832795028841971693993751 + // + return slow_float_parsing((const char *) src, parser); } } - if (unlikely((power_index > 2 * 308))) { // this is uncommon!!! + if (unlikely(exponent < FASTFLOAT_SMALLEST_POWER) || + (exponent > FASTFLOAT_LARGEST_POWER)) { // this is uncommon!!! // this is almost never going to get called!!! // we start anew, going slowly!!! - return parse_float(src, parser, found_minus); + return slow_float_parsing((const char *) src, parser); } - double factor = power_of_ten[power_index]; - factor = negative ? -factor : factor; - double d = i * factor; - parser.on_number_double(d); + bool success = true; + double d = compute_float_64(exponent, i, negative, &success); + if (!success) { + // we are almost never going to get here. + success = parse_float_strtod((const char *)src, &d); + } + if (success) { + parser.on_number_double(d); #ifdef JSON_TEST_NUMBERS // for unit testing - found_float(d, src); + found_float(d, src); #endif + return true; + } else { +#ifdef JSON_TEST_NUMBERS // for unit testing + found_invalid_number(src); +#endif + return false; + } } else { if (unlikely(digit_count >= 18)) { // this is uncommon!!! // there is a good chance that we had an overflow, so we need diff --git a/src/jsoncharutils.h b/src/jsoncharutils.h index 35df619ea..a03df71be 100644 --- a/src/jsoncharutils.h +++ b/src/jsoncharutils.h @@ -306,6 +306,1014 @@ inline size_t codepoint_to_utf8(uint32_t cp, uint8_t *c) { // will return 0 when the code point was too large. return 0; // bad r } + + +//// +// The following code is used in number parsing. It is not +// properly "char utils" stuff, but we move it here so that +// it does not get copied multiple times in the binaries (once +// per instructin set). +/// + + +constexpr int FASTFLOAT_SMALLEST_POWER = -325; +constexpr int FASTFLOAT_LARGEST_POWER = 308; + +struct value128 { + uint64_t low; + uint64_t high; +}; + +really_inline value128 full_multiplication(uint64_t value1, uint64_t value2) { + value128 answer; +#ifdef _MSC_VER + // todo: this might fail under visual studio for ARM + answer.low = _umul128(value1, value2, &answer.high); +#else + __uint128_t r = ((__uint128_t)value1) * value2; + answer.low = r; + answer.high = r >> 64; +#endif + return answer; +} + +// Precomputed powers of ten from 10^0 to 10^22. These +// can be represented exactly using the double type. +static const double power_of_ten[] = { + 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, + 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22}; + +// the mantissas of powers of ten from -308 to 308, extended out to sixty four +// bits +// This struct will likely get padded to 16 bytes. +typedef struct { + uint64_t mantissa; + int32_t exp; +} components; + +// The array power_of_ten_components contain the powers of ten approximated +// as a 64-bit mantissa, with an exponent part. It goes from 10^ +// FASTFLOAT_SMALLEST_POWER to +// 10^FASTFLOAT_LARGEST_POWER (inclusively). The mantissa is truncated, and +// never rounded up. +// Uses about 10KB. +static const components power_of_ten_components[] = { + {0xa5ced43b7e3e9188L, 7}, {0xcf42894a5dce35eaL, 10}, + {0x818995ce7aa0e1b2L, 14}, {0xa1ebfb4219491a1fL, 17}, + {0xca66fa129f9b60a6L, 20}, {0xfd00b897478238d0L, 23}, + {0x9e20735e8cb16382L, 27}, {0xc5a890362fddbc62L, 30}, + {0xf712b443bbd52b7bL, 33}, {0x9a6bb0aa55653b2dL, 37}, + {0xc1069cd4eabe89f8L, 40}, {0xf148440a256e2c76L, 43}, + {0x96cd2a865764dbcaL, 47}, {0xbc807527ed3e12bcL, 50}, + {0xeba09271e88d976bL, 53}, {0x93445b8731587ea3L, 57}, + {0xb8157268fdae9e4cL, 60}, {0xe61acf033d1a45dfL, 63}, + {0x8fd0c16206306babL, 67}, {0xb3c4f1ba87bc8696L, 70}, + {0xe0b62e2929aba83cL, 73}, {0x8c71dcd9ba0b4925L, 77}, + {0xaf8e5410288e1b6fL, 80}, {0xdb71e91432b1a24aL, 83}, + {0x892731ac9faf056eL, 87}, {0xab70fe17c79ac6caL, 90}, + {0xd64d3d9db981787dL, 93}, {0x85f0468293f0eb4eL, 97}, + {0xa76c582338ed2621L, 100}, {0xd1476e2c07286faaL, 103}, + {0x82cca4db847945caL, 107}, {0xa37fce126597973cL, 110}, + {0xcc5fc196fefd7d0cL, 113}, {0xff77b1fcbebcdc4fL, 116}, + {0x9faacf3df73609b1L, 120}, {0xc795830d75038c1dL, 123}, + {0xf97ae3d0d2446f25L, 126}, {0x9becce62836ac577L, 130}, + {0xc2e801fb244576d5L, 133}, {0xf3a20279ed56d48aL, 136}, + {0x9845418c345644d6L, 140}, {0xbe5691ef416bd60cL, 143}, + {0xedec366b11c6cb8fL, 146}, {0x94b3a202eb1c3f39L, 150}, + {0xb9e08a83a5e34f07L, 153}, {0xe858ad248f5c22c9L, 156}, + {0x91376c36d99995beL, 160}, {0xb58547448ffffb2dL, 163}, + {0xe2e69915b3fff9f9L, 166}, {0x8dd01fad907ffc3bL, 170}, + {0xb1442798f49ffb4aL, 173}, {0xdd95317f31c7fa1dL, 176}, + {0x8a7d3eef7f1cfc52L, 180}, {0xad1c8eab5ee43b66L, 183}, + {0xd863b256369d4a40L, 186}, {0x873e4f75e2224e68L, 190}, + {0xa90de3535aaae202L, 193}, {0xd3515c2831559a83L, 196}, + {0x8412d9991ed58091L, 200}, {0xa5178fff668ae0b6L, 203}, + {0xce5d73ff402d98e3L, 206}, {0x80fa687f881c7f8eL, 210}, + {0xa139029f6a239f72L, 213}, {0xc987434744ac874eL, 216}, + {0xfbe9141915d7a922L, 219}, {0x9d71ac8fada6c9b5L, 223}, + {0xc4ce17b399107c22L, 226}, {0xf6019da07f549b2bL, 229}, + {0x99c102844f94e0fbL, 233}, {0xc0314325637a1939L, 236}, + {0xf03d93eebc589f88L, 239}, {0x96267c7535b763b5L, 243}, + {0xbbb01b9283253ca2L, 246}, {0xea9c227723ee8bcbL, 249}, + {0x92a1958a7675175fL, 253}, {0xb749faed14125d36L, 256}, + {0xe51c79a85916f484L, 259}, {0x8f31cc0937ae58d2L, 263}, + {0xb2fe3f0b8599ef07L, 266}, {0xdfbdcece67006ac9L, 269}, + {0x8bd6a141006042bdL, 273}, {0xaecc49914078536dL, 276}, + {0xda7f5bf590966848L, 279}, {0x888f99797a5e012dL, 283}, + {0xaab37fd7d8f58178L, 286}, {0xd5605fcdcf32e1d6L, 289}, + {0x855c3be0a17fcd26L, 293}, {0xa6b34ad8c9dfc06fL, 296}, + {0xd0601d8efc57b08bL, 299}, {0x823c12795db6ce57L, 303}, + {0xa2cb1717b52481edL, 306}, {0xcb7ddcdda26da268L, 309}, + {0xfe5d54150b090b02L, 312}, {0x9efa548d26e5a6e1L, 316}, + {0xc6b8e9b0709f109aL, 319}, {0xf867241c8cc6d4c0L, 322}, + {0x9b407691d7fc44f8L, 326}, {0xc21094364dfb5636L, 329}, + {0xf294b943e17a2bc4L, 332}, {0x979cf3ca6cec5b5aL, 336}, + {0xbd8430bd08277231L, 339}, {0xece53cec4a314ebdL, 342}, + {0x940f4613ae5ed136L, 346}, {0xb913179899f68584L, 349}, + {0xe757dd7ec07426e5L, 352}, {0x9096ea6f3848984fL, 356}, + {0xb4bca50b065abe63L, 359}, {0xe1ebce4dc7f16dfbL, 362}, + {0x8d3360f09cf6e4bdL, 366}, {0xb080392cc4349decL, 369}, + {0xdca04777f541c567L, 372}, {0x89e42caaf9491b60L, 376}, + {0xac5d37d5b79b6239L, 379}, {0xd77485cb25823ac7L, 382}, + {0x86a8d39ef77164bcL, 386}, {0xa8530886b54dbdebL, 389}, + {0xd267caa862a12d66L, 392}, {0x8380dea93da4bc60L, 396}, + {0xa46116538d0deb78L, 399}, {0xcd795be870516656L, 402}, + {0x806bd9714632dff6L, 406}, {0xa086cfcd97bf97f3L, 409}, + {0xc8a883c0fdaf7df0L, 412}, {0xfad2a4b13d1b5d6cL, 415}, + {0x9cc3a6eec6311a63L, 419}, {0xc3f490aa77bd60fcL, 422}, + {0xf4f1b4d515acb93bL, 425}, {0x991711052d8bf3c5L, 429}, + {0xbf5cd54678eef0b6L, 432}, {0xef340a98172aace4L, 435}, + {0x9580869f0e7aac0eL, 439}, {0xbae0a846d2195712L, 442}, + {0xe998d258869facd7L, 445}, {0x91ff83775423cc06L, 449}, + {0xb67f6455292cbf08L, 452}, {0xe41f3d6a7377eecaL, 455}, + {0x8e938662882af53eL, 459}, {0xb23867fb2a35b28dL, 462}, + {0xdec681f9f4c31f31L, 465}, {0x8b3c113c38f9f37eL, 469}, + {0xae0b158b4738705eL, 472}, {0xd98ddaee19068c76L, 475}, + {0x87f8a8d4cfa417c9L, 479}, {0xa9f6d30a038d1dbcL, 482}, + {0xd47487cc8470652bL, 485}, {0x84c8d4dfd2c63f3bL, 489}, + {0xa5fb0a17c777cf09L, 492}, {0xcf79cc9db955c2ccL, 495}, + {0x81ac1fe293d599bfL, 499}, {0xa21727db38cb002fL, 502}, + {0xca9cf1d206fdc03bL, 505}, {0xfd442e4688bd304aL, 508}, + {0x9e4a9cec15763e2eL, 512}, {0xc5dd44271ad3cdbaL, 515}, + {0xf7549530e188c128L, 518}, {0x9a94dd3e8cf578b9L, 522}, + {0xc13a148e3032d6e7L, 525}, {0xf18899b1bc3f8ca1L, 528}, + {0x96f5600f15a7b7e5L, 532}, {0xbcb2b812db11a5deL, 535}, + {0xebdf661791d60f56L, 538}, {0x936b9fcebb25c995L, 542}, + {0xb84687c269ef3bfbL, 545}, {0xe65829b3046b0afaL, 548}, + {0x8ff71a0fe2c2e6dcL, 552}, {0xb3f4e093db73a093L, 555}, + {0xe0f218b8d25088b8L, 558}, {0x8c974f7383725573L, 562}, + {0xafbd2350644eeacfL, 565}, {0xdbac6c247d62a583L, 568}, + {0x894bc396ce5da772L, 572}, {0xab9eb47c81f5114fL, 575}, + {0xd686619ba27255a2L, 578}, {0x8613fd0145877585L, 582}, + {0xa798fc4196e952e7L, 585}, {0xd17f3b51fca3a7a0L, 588}, + {0x82ef85133de648c4L, 592}, {0xa3ab66580d5fdaf5L, 595}, + {0xcc963fee10b7d1b3L, 598}, {0xffbbcfe994e5c61fL, 601}, + {0x9fd561f1fd0f9bd3L, 605}, {0xc7caba6e7c5382c8L, 608}, + {0xf9bd690a1b68637bL, 611}, {0x9c1661a651213e2dL, 615}, + {0xc31bfa0fe5698db8L, 618}, {0xf3e2f893dec3f126L, 621}, + {0x986ddb5c6b3a76b7L, 625}, {0xbe89523386091465L, 628}, + {0xee2ba6c0678b597fL, 631}, {0x94db483840b717efL, 635}, + {0xba121a4650e4ddebL, 638}, {0xe896a0d7e51e1566L, 641}, + {0x915e2486ef32cd60L, 645}, {0xb5b5ada8aaff80b8L, 648}, + {0xe3231912d5bf60e6L, 651}, {0x8df5efabc5979c8fL, 655}, + {0xb1736b96b6fd83b3L, 658}, {0xddd0467c64bce4a0L, 661}, + {0x8aa22c0dbef60ee4L, 665}, {0xad4ab7112eb3929dL, 668}, + {0xd89d64d57a607744L, 671}, {0x87625f056c7c4a8bL, 675}, + {0xa93af6c6c79b5d2dL, 678}, {0xd389b47879823479L, 681}, + {0x843610cb4bf160cbL, 685}, {0xa54394fe1eedb8feL, 688}, + {0xce947a3da6a9273eL, 691}, {0x811ccc668829b887L, 695}, + {0xa163ff802a3426a8L, 698}, {0xc9bcff6034c13052L, 701}, + {0xfc2c3f3841f17c67L, 704}, {0x9d9ba7832936edc0L, 708}, + {0xc5029163f384a931L, 711}, {0xf64335bcf065d37dL, 714}, + {0x99ea0196163fa42eL, 718}, {0xc06481fb9bcf8d39L, 721}, + {0xf07da27a82c37088L, 724}, {0x964e858c91ba2655L, 728}, + {0xbbe226efb628afeaL, 731}, {0xeadab0aba3b2dbe5L, 734}, + {0x92c8ae6b464fc96fL, 738}, {0xb77ada0617e3bbcbL, 741}, + {0xe55990879ddcaabdL, 744}, {0x8f57fa54c2a9eab6L, 748}, + {0xb32df8e9f3546564L, 751}, {0xdff9772470297ebdL, 754}, + {0x8bfbea76c619ef36L, 758}, {0xaefae51477a06b03L, 761}, + {0xdab99e59958885c4L, 764}, {0x88b402f7fd75539bL, 768}, + {0xaae103b5fcd2a881L, 771}, {0xd59944a37c0752a2L, 774}, + {0x857fcae62d8493a5L, 778}, {0xa6dfbd9fb8e5b88eL, 781}, + {0xd097ad07a71f26b2L, 784}, {0x825ecc24c873782fL, 788}, + {0xa2f67f2dfa90563bL, 791}, {0xcbb41ef979346bcaL, 794}, + {0xfea126b7d78186bcL, 797}, {0x9f24b832e6b0f436L, 801}, + {0xc6ede63fa05d3143L, 804}, {0xf8a95fcf88747d94L, 807}, + {0x9b69dbe1b548ce7cL, 811}, {0xc24452da229b021bL, 814}, + {0xf2d56790ab41c2a2L, 817}, {0x97c560ba6b0919a5L, 821}, + {0xbdb6b8e905cb600fL, 824}, {0xed246723473e3813L, 827}, + {0x9436c0760c86e30bL, 831}, {0xb94470938fa89bceL, 834}, + {0xe7958cb87392c2c2L, 837}, {0x90bd77f3483bb9b9L, 841}, + {0xb4ecd5f01a4aa828L, 844}, {0xe2280b6c20dd5232L, 847}, + {0x8d590723948a535fL, 851}, {0xb0af48ec79ace837L, 854}, + {0xdcdb1b2798182244L, 857}, {0x8a08f0f8bf0f156bL, 861}, + {0xac8b2d36eed2dac5L, 864}, {0xd7adf884aa879177L, 867}, + {0x86ccbb52ea94baeaL, 871}, {0xa87fea27a539e9a5L, 874}, + {0xd29fe4b18e88640eL, 877}, {0x83a3eeeef9153e89L, 881}, + {0xa48ceaaab75a8e2bL, 884}, {0xcdb02555653131b6L, 887}, + {0x808e17555f3ebf11L, 891}, {0xa0b19d2ab70e6ed6L, 894}, + {0xc8de047564d20a8bL, 897}, {0xfb158592be068d2eL, 900}, + {0x9ced737bb6c4183dL, 904}, {0xc428d05aa4751e4cL, 907}, + {0xf53304714d9265dfL, 910}, {0x993fe2c6d07b7fabL, 914}, + {0xbf8fdb78849a5f96L, 917}, {0xef73d256a5c0f77cL, 920}, + {0x95a8637627989aadL, 924}, {0xbb127c53b17ec159L, 927}, + {0xe9d71b689dde71afL, 930}, {0x9226712162ab070dL, 934}, + {0xb6b00d69bb55c8d1L, 937}, {0xe45c10c42a2b3b05L, 940}, + {0x8eb98a7a9a5b04e3L, 944}, {0xb267ed1940f1c61cL, 947}, + {0xdf01e85f912e37a3L, 950}, {0x8b61313bbabce2c6L, 954}, + {0xae397d8aa96c1b77L, 957}, {0xd9c7dced53c72255L, 960}, + {0x881cea14545c7575L, 964}, {0xaa242499697392d2L, 967}, + {0xd4ad2dbfc3d07787L, 970}, {0x84ec3c97da624ab4L, 974}, + {0xa6274bbdd0fadd61L, 977}, {0xcfb11ead453994baL, 980}, + {0x81ceb32c4b43fcf4L, 984}, {0xa2425ff75e14fc31L, 987}, + {0xcad2f7f5359a3b3eL, 990}, {0xfd87b5f28300ca0dL, 993}, + {0x9e74d1b791e07e48L, 997}, {0xc612062576589ddaL, 1000}, + {0xf79687aed3eec551L, 1003}, {0x9abe14cd44753b52L, 1007}, + {0xc16d9a0095928a27L, 1010}, {0xf1c90080baf72cb1L, 1013}, + {0x971da05074da7beeL, 1017}, {0xbce5086492111aeaL, 1020}, + {0xec1e4a7db69561a5L, 1023}, {0x9392ee8e921d5d07L, 1027}, + {0xb877aa3236a4b449L, 1030}, {0xe69594bec44de15bL, 1033}, + {0x901d7cf73ab0acd9L, 1037}, {0xb424dc35095cd80fL, 1040}, + {0xe12e13424bb40e13L, 1043}, {0x8cbccc096f5088cbL, 1047}, + {0xafebff0bcb24aafeL, 1050}, {0xdbe6fecebdedd5beL, 1053}, + {0x89705f4136b4a597L, 1057}, {0xabcc77118461cefcL, 1060}, + {0xd6bf94d5e57a42bcL, 1063}, {0x8637bd05af6c69b5L, 1067}, + {0xa7c5ac471b478423L, 1070}, {0xd1b71758e219652bL, 1073}, + {0x83126e978d4fdf3bL, 1077}, {0xa3d70a3d70a3d70aL, 1080}, + {0xccccccccccccccccL, 1083}, {0x8000000000000000L, 1087}, + {0xa000000000000000L, 1090}, {0xc800000000000000L, 1093}, + {0xfa00000000000000L, 1096}, {0x9c40000000000000L, 1100}, + {0xc350000000000000L, 1103}, {0xf424000000000000L, 1106}, + {0x9896800000000000L, 1110}, {0xbebc200000000000L, 1113}, + {0xee6b280000000000L, 1116}, {0x9502f90000000000L, 1120}, + {0xba43b74000000000L, 1123}, {0xe8d4a51000000000L, 1126}, + {0x9184e72a00000000L, 1130}, {0xb5e620f480000000L, 1133}, + {0xe35fa931a0000000L, 1136}, {0x8e1bc9bf04000000L, 1140}, + {0xb1a2bc2ec5000000L, 1143}, {0xde0b6b3a76400000L, 1146}, + {0x8ac7230489e80000L, 1150}, {0xad78ebc5ac620000L, 1153}, + {0xd8d726b7177a8000L, 1156}, {0x878678326eac9000L, 1160}, + {0xa968163f0a57b400L, 1163}, {0xd3c21bcecceda100L, 1166}, + {0x84595161401484a0L, 1170}, {0xa56fa5b99019a5c8L, 1173}, + {0xcecb8f27f4200f3aL, 1176}, {0x813f3978f8940984L, 1180}, + {0xa18f07d736b90be5L, 1183}, {0xc9f2c9cd04674edeL, 1186}, + {0xfc6f7c4045812296L, 1189}, {0x9dc5ada82b70b59dL, 1193}, + {0xc5371912364ce305L, 1196}, {0xf684df56c3e01bc6L, 1199}, + {0x9a130b963a6c115cL, 1203}, {0xc097ce7bc90715b3L, 1206}, + {0xf0bdc21abb48db20L, 1209}, {0x96769950b50d88f4L, 1213}, + {0xbc143fa4e250eb31L, 1216}, {0xeb194f8e1ae525fdL, 1219}, + {0x92efd1b8d0cf37beL, 1223}, {0xb7abc627050305adL, 1226}, + {0xe596b7b0c643c719L, 1229}, {0x8f7e32ce7bea5c6fL, 1233}, + {0xb35dbf821ae4f38bL, 1236}, {0xe0352f62a19e306eL, 1239}, + {0x8c213d9da502de45L, 1243}, {0xaf298d050e4395d6L, 1246}, + {0xdaf3f04651d47b4cL, 1249}, {0x88d8762bf324cd0fL, 1253}, + {0xab0e93b6efee0053L, 1256}, {0xd5d238a4abe98068L, 1259}, + {0x85a36366eb71f041L, 1263}, {0xa70c3c40a64e6c51L, 1266}, + {0xd0cf4b50cfe20765L, 1269}, {0x82818f1281ed449fL, 1273}, + {0xa321f2d7226895c7L, 1276}, {0xcbea6f8ceb02bb39L, 1279}, + {0xfee50b7025c36a08L, 1282}, {0x9f4f2726179a2245L, 1286}, + {0xc722f0ef9d80aad6L, 1289}, {0xf8ebad2b84e0d58bL, 1292}, + {0x9b934c3b330c8577L, 1296}, {0xc2781f49ffcfa6d5L, 1299}, + {0xf316271c7fc3908aL, 1302}, {0x97edd871cfda3a56L, 1306}, + {0xbde94e8e43d0c8ecL, 1309}, {0xed63a231d4c4fb27L, 1312}, + {0x945e455f24fb1cf8L, 1316}, {0xb975d6b6ee39e436L, 1319}, + {0xe7d34c64a9c85d44L, 1322}, {0x90e40fbeea1d3a4aL, 1326}, + {0xb51d13aea4a488ddL, 1329}, {0xe264589a4dcdab14L, 1332}, + {0x8d7eb76070a08aecL, 1336}, {0xb0de65388cc8ada8L, 1339}, + {0xdd15fe86affad912L, 1342}, {0x8a2dbf142dfcc7abL, 1346}, + {0xacb92ed9397bf996L, 1349}, {0xd7e77a8f87daf7fbL, 1352}, + {0x86f0ac99b4e8dafdL, 1356}, {0xa8acd7c0222311bcL, 1359}, + {0xd2d80db02aabd62bL, 1362}, {0x83c7088e1aab65dbL, 1366}, + {0xa4b8cab1a1563f52L, 1369}, {0xcde6fd5e09abcf26L, 1372}, + {0x80b05e5ac60b6178L, 1376}, {0xa0dc75f1778e39d6L, 1379}, + {0xc913936dd571c84cL, 1382}, {0xfb5878494ace3a5fL, 1385}, + {0x9d174b2dcec0e47bL, 1389}, {0xc45d1df942711d9aL, 1392}, + {0xf5746577930d6500L, 1395}, {0x9968bf6abbe85f20L, 1399}, + {0xbfc2ef456ae276e8L, 1402}, {0xefb3ab16c59b14a2L, 1405}, + {0x95d04aee3b80ece5L, 1409}, {0xbb445da9ca61281fL, 1412}, + {0xea1575143cf97226L, 1415}, {0x924d692ca61be758L, 1419}, + {0xb6e0c377cfa2e12eL, 1422}, {0xe498f455c38b997aL, 1425}, + {0x8edf98b59a373fecL, 1429}, {0xb2977ee300c50fe7L, 1432}, + {0xdf3d5e9bc0f653e1L, 1435}, {0x8b865b215899f46cL, 1439}, + {0xae67f1e9aec07187L, 1442}, {0xda01ee641a708de9L, 1445}, + {0x884134fe908658b2L, 1449}, {0xaa51823e34a7eedeL, 1452}, + {0xd4e5e2cdc1d1ea96L, 1455}, {0x850fadc09923329eL, 1459}, + {0xa6539930bf6bff45L, 1462}, {0xcfe87f7cef46ff16L, 1465}, + {0x81f14fae158c5f6eL, 1469}, {0xa26da3999aef7749L, 1472}, + {0xcb090c8001ab551cL, 1475}, {0xfdcb4fa002162a63L, 1478}, + {0x9e9f11c4014dda7eL, 1482}, {0xc646d63501a1511dL, 1485}, + {0xf7d88bc24209a565L, 1488}, {0x9ae757596946075fL, 1492}, + {0xc1a12d2fc3978937L, 1495}, {0xf209787bb47d6b84L, 1498}, + {0x9745eb4d50ce6332L, 1502}, {0xbd176620a501fbffL, 1505}, + {0xec5d3fa8ce427affL, 1508}, {0x93ba47c980e98cdfL, 1512}, + {0xb8a8d9bbe123f017L, 1515}, {0xe6d3102ad96cec1dL, 1518}, + {0x9043ea1ac7e41392L, 1522}, {0xb454e4a179dd1877L, 1525}, + {0xe16a1dc9d8545e94L, 1528}, {0x8ce2529e2734bb1dL, 1532}, + {0xb01ae745b101e9e4L, 1535}, {0xdc21a1171d42645dL, 1538}, + {0x899504ae72497ebaL, 1542}, {0xabfa45da0edbde69L, 1545}, + {0xd6f8d7509292d603L, 1548}, {0x865b86925b9bc5c2L, 1552}, + {0xa7f26836f282b732L, 1555}, {0xd1ef0244af2364ffL, 1558}, + {0x8335616aed761f1fL, 1562}, {0xa402b9c5a8d3a6e7L, 1565}, + {0xcd036837130890a1L, 1568}, {0x802221226be55a64L, 1572}, + {0xa02aa96b06deb0fdL, 1575}, {0xc83553c5c8965d3dL, 1578}, + {0xfa42a8b73abbf48cL, 1581}, {0x9c69a97284b578d7L, 1585}, + {0xc38413cf25e2d70dL, 1588}, {0xf46518c2ef5b8cd1L, 1591}, + {0x98bf2f79d5993802L, 1595}, {0xbeeefb584aff8603L, 1598}, + {0xeeaaba2e5dbf6784L, 1601}, {0x952ab45cfa97a0b2L, 1605}, + {0xba756174393d88dfL, 1608}, {0xe912b9d1478ceb17L, 1611}, + {0x91abb422ccb812eeL, 1615}, {0xb616a12b7fe617aaL, 1618}, + {0xe39c49765fdf9d94L, 1621}, {0x8e41ade9fbebc27dL, 1625}, + {0xb1d219647ae6b31cL, 1628}, {0xde469fbd99a05fe3L, 1631}, + {0x8aec23d680043beeL, 1635}, {0xada72ccc20054ae9L, 1638}, + {0xd910f7ff28069da4L, 1641}, {0x87aa9aff79042286L, 1645}, + {0xa99541bf57452b28L, 1648}, {0xd3fa922f2d1675f2L, 1651}, + {0x847c9b5d7c2e09b7L, 1655}, {0xa59bc234db398c25L, 1658}, + {0xcf02b2c21207ef2eL, 1661}, {0x8161afb94b44f57dL, 1665}, + {0xa1ba1ba79e1632dcL, 1668}, {0xca28a291859bbf93L, 1671}, + {0xfcb2cb35e702af78L, 1674}, {0x9defbf01b061adabL, 1678}, + {0xc56baec21c7a1916L, 1681}, {0xf6c69a72a3989f5bL, 1684}, + {0x9a3c2087a63f6399L, 1688}, {0xc0cb28a98fcf3c7fL, 1691}, + {0xf0fdf2d3f3c30b9fL, 1694}, {0x969eb7c47859e743L, 1698}, + {0xbc4665b596706114L, 1701}, {0xeb57ff22fc0c7959L, 1704}, + {0x9316ff75dd87cbd8L, 1708}, {0xb7dcbf5354e9beceL, 1711}, + {0xe5d3ef282a242e81L, 1714}, {0x8fa475791a569d10L, 1718}, + {0xb38d92d760ec4455L, 1721}, {0xe070f78d3927556aL, 1724}, + {0x8c469ab843b89562L, 1728}, {0xaf58416654a6babbL, 1731}, + {0xdb2e51bfe9d0696aL, 1734}, {0x88fcf317f22241e2L, 1738}, + {0xab3c2fddeeaad25aL, 1741}, {0xd60b3bd56a5586f1L, 1744}, + {0x85c7056562757456L, 1748}, {0xa738c6bebb12d16cL, 1751}, + {0xd106f86e69d785c7L, 1754}, {0x82a45b450226b39cL, 1758}, + {0xa34d721642b06084L, 1761}, {0xcc20ce9bd35c78a5L, 1764}, + {0xff290242c83396ceL, 1767}, {0x9f79a169bd203e41L, 1771}, + {0xc75809c42c684dd1L, 1774}, {0xf92e0c3537826145L, 1777}, + {0x9bbcc7a142b17ccbL, 1781}, {0xc2abf989935ddbfeL, 1784}, + {0xf356f7ebf83552feL, 1787}, {0x98165af37b2153deL, 1791}, + {0xbe1bf1b059e9a8d6L, 1794}, {0xeda2ee1c7064130cL, 1797}, + {0x9485d4d1c63e8be7L, 1801}, {0xb9a74a0637ce2ee1L, 1804}, + {0xe8111c87c5c1ba99L, 1807}, {0x910ab1d4db9914a0L, 1811}, + {0xb54d5e4a127f59c8L, 1814}, {0xe2a0b5dc971f303aL, 1817}, + {0x8da471a9de737e24L, 1821}, {0xb10d8e1456105dadL, 1824}, + {0xdd50f1996b947518L, 1827}, {0x8a5296ffe33cc92fL, 1831}, + {0xace73cbfdc0bfb7bL, 1834}, {0xd8210befd30efa5aL, 1837}, + {0x8714a775e3e95c78L, 1841}, {0xa8d9d1535ce3b396L, 1844}, + {0xd31045a8341ca07cL, 1847}, {0x83ea2b892091e44dL, 1851}, + {0xa4e4b66b68b65d60L, 1854}, {0xce1de40642e3f4b9L, 1857}, + {0x80d2ae83e9ce78f3L, 1861}, {0xa1075a24e4421730L, 1864}, + {0xc94930ae1d529cfcL, 1867}, {0xfb9b7cd9a4a7443cL, 1870}, + {0x9d412e0806e88aa5L, 1874}, {0xc491798a08a2ad4eL, 1877}, + {0xf5b5d7ec8acb58a2L, 1880}, {0x9991a6f3d6bf1765L, 1884}, + {0xbff610b0cc6edd3fL, 1887}, {0xeff394dcff8a948eL, 1890}, + {0x95f83d0a1fb69cd9L, 1894}, {0xbb764c4ca7a4440fL, 1897}, + {0xea53df5fd18d5513L, 1900}, {0x92746b9be2f8552cL, 1904}, + {0xb7118682dbb66a77L, 1907}, {0xe4d5e82392a40515L, 1910}, + {0x8f05b1163ba6832dL, 1914}, {0xb2c71d5bca9023f8L, 1917}, + {0xdf78e4b2bd342cf6L, 1920}, {0x8bab8eefb6409c1aL, 1924}, + {0xae9672aba3d0c320L, 1927}, {0xda3c0f568cc4f3e8L, 1930}, + {0x8865899617fb1871L, 1934}, {0xaa7eebfb9df9de8dL, 1937}, + {0xd51ea6fa85785631L, 1940}, {0x8533285c936b35deL, 1944}, + {0xa67ff273b8460356L, 1947}, {0xd01fef10a657842cL, 1950}, + {0x8213f56a67f6b29bL, 1954}, {0xa298f2c501f45f42L, 1957}, + {0xcb3f2f7642717713L, 1960}, {0xfe0efb53d30dd4d7L, 1963}, + {0x9ec95d1463e8a506L, 1967}, {0xc67bb4597ce2ce48L, 1970}, + {0xf81aa16fdc1b81daL, 1973}, {0x9b10a4e5e9913128L, 1977}, + {0xc1d4ce1f63f57d72L, 1980}, {0xf24a01a73cf2dccfL, 1983}, + {0x976e41088617ca01L, 1987}, {0xbd49d14aa79dbc82L, 1990}, + {0xec9c459d51852ba2L, 1993}, {0x93e1ab8252f33b45L, 1997}, + {0xb8da1662e7b00a17L, 2000}, {0xe7109bfba19c0c9dL, 2003}, + {0x906a617d450187e2L, 2007}, {0xb484f9dc9641e9daL, 2010}, + {0xe1a63853bbd26451L, 2013}, {0x8d07e33455637eb2L, 2017}, + {0xb049dc016abc5e5fL, 2020}, {0xdc5c5301c56b75f7L, 2023}, + {0x89b9b3e11b6329baL, 2027}, {0xac2820d9623bf429L, 2030}, + {0xd732290fbacaf133L, 2033}, {0x867f59a9d4bed6c0L, 2037}, + {0xa81f301449ee8c70L, 2040}, {0xd226fc195c6a2f8cL, 2043}, + {0x83585d8fd9c25db7L, 2047}, {0xa42e74f3d032f525L, 2050}, + {0xcd3a1230c43fb26fL, 2053}, {0x80444b5e7aa7cf85L, 2057}, + {0xa0555e361951c366L, 2060}, {0xc86ab5c39fa63440L, 2063}, + {0xfa856334878fc150L, 2066}, {0x9c935e00d4b9d8d2L, 2070}, + {0xc3b8358109e84f07L, 2073}, {0xf4a642e14c6262c8L, 2076}, + {0x98e7e9cccfbd7dbdL, 2080}, {0xbf21e44003acdd2cL, 2083}, + {0xeeea5d5004981478L, 2086}, {0x95527a5202df0ccbL, 2090}, + {0xbaa718e68396cffdL, 2093}, {0xe950df20247c83fdL, 2096}, + {0x91d28b7416cdd27eL, 2100}, {0xb6472e511c81471dL, 2103}, + {0xe3d8f9e563a198e5L, 2106}, {0x8e679c2f5e44ff8fL, 2110}}; + +// A complement from power_of_ten_components +// complete to a 128-bit mantissa. +const uint64_t mantissa_128[] = {0x419ea3bd35385e2d, + 0x52064cac828675b9, + 0x7343efebd1940993, + 0x1014ebe6c5f90bf8, + 0xd41a26e077774ef6, + 0x8920b098955522b4, + 0x55b46e5f5d5535b0, + 0xeb2189f734aa831d, + 0xa5e9ec7501d523e4, + 0x47b233c92125366e, + 0x999ec0bb696e840a, + 0xc00670ea43ca250d, + 0x380406926a5e5728, + 0xc605083704f5ecf2, + 0xf7864a44c633682e, + 0x7ab3ee6afbe0211d, + 0x5960ea05bad82964, + 0x6fb92487298e33bd, + 0xa5d3b6d479f8e056, + 0x8f48a4899877186c, + 0x331acdabfe94de87, + 0x9ff0c08b7f1d0b14, + 0x7ecf0ae5ee44dd9, + 0xc9e82cd9f69d6150, + 0xbe311c083a225cd2, + 0x6dbd630a48aaf406, + 0x92cbbccdad5b108, + 0x25bbf56008c58ea5, + 0xaf2af2b80af6f24e, + 0x1af5af660db4aee1, + 0x50d98d9fc890ed4d, + 0xe50ff107bab528a0, + 0x1e53ed49a96272c8, + 0x25e8e89c13bb0f7a, + 0x77b191618c54e9ac, + 0xd59df5b9ef6a2417, + 0x4b0573286b44ad1d, + 0x4ee367f9430aec32, + 0x229c41f793cda73f, + 0x6b43527578c1110f, + 0x830a13896b78aaa9, + 0x23cc986bc656d553, + 0x2cbfbe86b7ec8aa8, + 0x7bf7d71432f3d6a9, + 0xdaf5ccd93fb0cc53, + 0xd1b3400f8f9cff68, + 0x23100809b9c21fa1, + 0xabd40a0c2832a78a, + 0x16c90c8f323f516c, + 0xae3da7d97f6792e3, + 0x99cd11cfdf41779c, + 0x40405643d711d583, + 0x482835ea666b2572, + 0xda3243650005eecf, + 0x90bed43e40076a82, + 0x5a7744a6e804a291, + 0x711515d0a205cb36, + 0xd5a5b44ca873e03, + 0xe858790afe9486c2, + 0x626e974dbe39a872, + 0xfb0a3d212dc8128f, + 0x7ce66634bc9d0b99, + 0x1c1fffc1ebc44e80, + 0xa327ffb266b56220, + 0x4bf1ff9f0062baa8, + 0x6f773fc3603db4a9, + 0xcb550fb4384d21d3, + 0x7e2a53a146606a48, + 0x2eda7444cbfc426d, + 0xfa911155fefb5308, + 0x793555ab7eba27ca, + 0x4bc1558b2f3458de, + 0x9eb1aaedfb016f16, + 0x465e15a979c1cadc, + 0xbfacd89ec191ec9, + 0xcef980ec671f667b, + 0x82b7e12780e7401a, + 0xd1b2ecb8b0908810, + 0x861fa7e6dcb4aa15, + 0x67a791e093e1d49a, + 0xe0c8bb2c5c6d24e0, + 0x58fae9f773886e18, + 0xaf39a475506a899e, + 0x6d8406c952429603, + 0xc8e5087ba6d33b83, + 0xfb1e4a9a90880a64, + 0x5cf2eea09a55067f, + 0xf42faa48c0ea481e, + 0xf13b94daf124da26, + 0x76c53d08d6b70858, + 0x54768c4b0c64ca6e, + 0xa9942f5dcf7dfd09, + 0xd3f93b35435d7c4c, + 0xc47bc5014a1a6daf, + 0x359ab6419ca1091b, + 0xc30163d203c94b62, + 0x79e0de63425dcf1d, + 0x985915fc12f542e4, + 0x3e6f5b7b17b2939d, + 0xa705992ceecf9c42, + 0x50c6ff782a838353, + 0xa4f8bf5635246428, + 0x871b7795e136be99, + 0x28e2557b59846e3f, + 0x331aeada2fe589cf, + 0x3ff0d2c85def7621, + 0xfed077a756b53a9, + 0xd3e8495912c62894, + 0x64712dd7abbbd95c, + 0xbd8d794d96aacfb3, + 0xecf0d7a0fc5583a0, + 0xf41686c49db57244, + 0x311c2875c522ced5, + 0x7d633293366b828b, + 0xae5dff9c02033197, + 0xd9f57f830283fdfc, + 0xd072df63c324fd7b, + 0x4247cb9e59f71e6d, + 0x52d9be85f074e608, + 0x67902e276c921f8b, + 0xba1cd8a3db53b6, + 0x80e8a40eccd228a4, + 0x6122cd128006b2cd, + 0x796b805720085f81, + 0xcbe3303674053bb0, + 0xbedbfc4411068a9c, + 0xee92fb5515482d44, + 0x751bdd152d4d1c4a, + 0xd262d45a78a0635d, + 0x86fb897116c87c34, + 0xd45d35e6ae3d4da0, + 0x8974836059cca109, + 0x2bd1a438703fc94b, + 0x7b6306a34627ddcf, + 0x1a3bc84c17b1d542, + 0x20caba5f1d9e4a93, + 0x547eb47b7282ee9c, + 0xe99e619a4f23aa43, + 0x6405fa00e2ec94d4, + 0xde83bc408dd3dd04, + 0x9624ab50b148d445, + 0x3badd624dd9b0957, + 0xe54ca5d70a80e5d6, + 0x5e9fcf4ccd211f4c, + 0x7647c3200069671f, + 0x29ecd9f40041e073, + 0xf468107100525890, + 0x7182148d4066eeb4, + 0xc6f14cd848405530, + 0xb8ada00e5a506a7c, + 0xa6d90811f0e4851c, + 0x908f4a166d1da663, + 0x9a598e4e043287fe, + 0x40eff1e1853f29fd, + 0xd12bee59e68ef47c, + 0x82bb74f8301958ce, + 0xe36a52363c1faf01, + 0xdc44e6c3cb279ac1, + 0x29ab103a5ef8c0b9, + 0x7415d448f6b6f0e7, + 0x111b495b3464ad21, + 0xcab10dd900beec34, + 0x3d5d514f40eea742, + 0xcb4a5a3112a5112, + 0x47f0e785eaba72ab, + 0x59ed216765690f56, + 0x306869c13ec3532c, + 0x1e414218c73a13fb, + 0xe5d1929ef90898fa, + 0xdf45f746b74abf39, + 0x6b8bba8c328eb783, + 0x66ea92f3f326564, + 0xc80a537b0efefebd, + 0xbd06742ce95f5f36, + 0x2c48113823b73704, + 0xf75a15862ca504c5, + 0x9a984d73dbe722fb, + 0xc13e60d0d2e0ebba, + 0x318df905079926a8, + 0xfdf17746497f7052, + 0xfeb6ea8bedefa633, + 0xfe64a52ee96b8fc0, + 0x3dfdce7aa3c673b0, + 0x6bea10ca65c084e, + 0x486e494fcff30a62, + 0x5a89dba3c3efccfa, + 0xf89629465a75e01c, + 0xf6bbb397f1135823, + 0x746aa07ded582e2c, + 0xa8c2a44eb4571cdc, + 0x92f34d62616ce413, + 0x77b020baf9c81d17, + 0xace1474dc1d122e, + 0xd819992132456ba, + 0x10e1fff697ed6c69, + 0xca8d3ffa1ef463c1, + 0xbd308ff8a6b17cb2, + 0xac7cb3f6d05ddbde, + 0x6bcdf07a423aa96b, + 0x86c16c98d2c953c6, + 0xe871c7bf077ba8b7, + 0x11471cd764ad4972, + 0xd598e40d3dd89bcf, + 0x4aff1d108d4ec2c3, + 0xcedf722a585139ba, + 0xc2974eb4ee658828, + 0x733d226229feea32, + 0x806357d5a3f525f, + 0xca07c2dcb0cf26f7, + 0xfc89b393dd02f0b5, + 0xbbac2078d443ace2, + 0xd54b944b84aa4c0d, + 0xa9e795e65d4df11, + 0x4d4617b5ff4a16d5, + 0x504bced1bf8e4e45, + 0xe45ec2862f71e1d6, + 0x5d767327bb4e5a4c, + 0x3a6a07f8d510f86f, + 0x890489f70a55368b, + 0x2b45ac74ccea842e, + 0x3b0b8bc90012929d, + 0x9ce6ebb40173744, + 0xcc420a6a101d0515, + 0x9fa946824a12232d, + 0x47939822dc96abf9, + 0x59787e2b93bc56f7, + 0x57eb4edb3c55b65a, + 0xede622920b6b23f1, + 0xe95fab368e45eced, + 0x11dbcb0218ebb414, + 0xd652bdc29f26a119, + 0x4be76d3346f0495f, + 0x6f70a4400c562ddb, + 0xcb4ccd500f6bb952, + 0x7e2000a41346a7a7, + 0x8ed400668c0c28c8, + 0x728900802f0f32fa, + 0x4f2b40a03ad2ffb9, + 0xe2f610c84987bfa8, + 0xdd9ca7d2df4d7c9, + 0x91503d1c79720dbb, + 0x75a44c6397ce912a, + 0xc986afbe3ee11aba, + 0xfbe85badce996168, + 0xfae27299423fb9c3, + 0xdccd879fc967d41a, + 0x5400e987bbc1c920, + 0x290123e9aab23b68, + 0xf9a0b6720aaf6521, + 0xf808e40e8d5b3e69, + 0xb60b1d1230b20e04, + 0xb1c6f22b5e6f48c2, + 0x1e38aeb6360b1af3, + 0x25c6da63c38de1b0, + 0x579c487e5a38ad0e, + 0x2d835a9df0c6d851, + 0xf8e431456cf88e65, + 0x1b8e9ecb641b58ff, + 0xe272467e3d222f3f, + 0x5b0ed81dcc6abb0f, + 0x98e947129fc2b4e9, + 0x3f2398d747b36224, + 0x8eec7f0d19a03aad, + 0x1953cf68300424ac, + 0x5fa8c3423c052dd7, + 0x3792f412cb06794d, + 0xe2bbd88bbee40bd0, + 0x5b6aceaeae9d0ec4, + 0xf245825a5a445275, + 0xeed6e2f0f0d56712, + 0x55464dd69685606b, + 0xaa97e14c3c26b886, + 0xd53dd99f4b3066a8, + 0xe546a8038efe4029, + 0xde98520472bdd033, + 0x963e66858f6d4440, + 0xdde7001379a44aa8, + 0x5560c018580d5d52, + 0xaab8f01e6e10b4a6, + 0xcab3961304ca70e8, + 0x3d607b97c5fd0d22, + 0x8cb89a7db77c506a, + 0x77f3608e92adb242, + 0x55f038b237591ed3, + 0x6b6c46dec52f6688, + 0x2323ac4b3b3da015, + 0xabec975e0a0d081a, + 0x96e7bd358c904a21, + 0x7e50d64177da2e54, + 0xdde50bd1d5d0b9e9, + 0x955e4ec64b44e864, + 0xbd5af13bef0b113e, + 0xecb1ad8aeacdd58e, + 0x67de18eda5814af2, + 0x80eacf948770ced7, + 0xa1258379a94d028d, + 0x96ee45813a04330, + 0x8bca9d6e188853fc, + 0x775ea264cf55347d, + 0x95364afe032a819d, + 0x3a83ddbd83f52204, + 0xc4926a9672793542, + 0x75b7053c0f178293, + 0x5324c68b12dd6338, + 0xd3f6fc16ebca5e03, + 0x88f4bb1ca6bcf584, + 0x2b31e9e3d06c32e5, + 0x3aff322e62439fcf, + 0x9befeb9fad487c2, + 0x4c2ebe687989a9b3, + 0xf9d37014bf60a10, + 0x538484c19ef38c94, + 0x2865a5f206b06fb9, + 0xf93f87b7442e45d3, + 0xf78f69a51539d748, + 0xb573440e5a884d1b, + 0x31680a88f8953030, + 0xfdc20d2b36ba7c3d, + 0x3d32907604691b4c, + 0xa63f9a49c2c1b10f, + 0xfcf80dc33721d53, + 0xd3c36113404ea4a8, + 0x645a1cac083126e9, + 0x3d70a3d70a3d70a3, + 0xcccccccccccccccc, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x0, + 0x4000000000000000, + 0x5000000000000000, + 0xa400000000000000, + 0x4d00000000000000, + 0xf020000000000000, + 0x6c28000000000000, + 0xc732000000000000, + 0x3c7f400000000000, + 0x4b9f100000000000, + 0x1e86d40000000000, + 0x1314448000000000, + 0x17d955a000000000, + 0x5dcfab0800000000, + 0x5aa1cae500000000, + 0xf14a3d9e40000000, + 0x6d9ccd05d0000000, + 0xe4820023a2000000, + 0xdda2802c8a800000, + 0xd50b2037ad200000, + 0x4526f422cc340000, + 0x9670b12b7f410000, + 0x3c0cdd765f114000, + 0xa5880a69fb6ac800, + 0x8eea0d047a457a00, + 0x72a4904598d6d880, + 0x47a6da2b7f864750, + 0x999090b65f67d924, + 0xfff4b4e3f741cf6d, + 0xbff8f10e7a8921a4, + 0xaff72d52192b6a0d, + 0x9bf4f8a69f764490, + 0x2f236d04753d5b4, + 0x1d762422c946590, + 0x424d3ad2b7b97ef5, + 0xd2e0898765a7deb2, + 0x63cc55f49f88eb2f, + 0x3cbf6b71c76b25fb, + 0x8bef464e3945ef7a, + 0x97758bf0e3cbb5ac, + 0x3d52eeed1cbea317, + 0x4ca7aaa863ee4bdd, + 0x8fe8caa93e74ef6a, + 0xb3e2fd538e122b44, + 0x60dbbca87196b616, + 0xbc8955e946fe31cd, + 0x6babab6398bdbe41, + 0xc696963c7eed2dd1, + 0xfc1e1de5cf543ca2, + 0x3b25a55f43294bcb, + 0x49ef0eb713f39ebe, + 0x6e3569326c784337, + 0x49c2c37f07965404, + 0xdc33745ec97be906, + 0x69a028bb3ded71a3, + 0xc40832ea0d68ce0c, + 0xf50a3fa490c30190, + 0x792667c6da79e0fa, + 0x577001b891185938, + 0xed4c0226b55e6f86, + 0x544f8158315b05b4, + 0x696361ae3db1c721, + 0x3bc3a19cd1e38e9, + 0x4ab48a04065c723, + 0x62eb0d64283f9c76, + 0x3ba5d0bd324f8394, + 0xca8f44ec7ee36479, + 0x7e998b13cf4e1ecb, + 0x9e3fedd8c321a67e, + 0xc5cfe94ef3ea101e, + 0xbba1f1d158724a12, + 0x2a8a6e45ae8edc97, + 0xf52d09d71a3293bd, + 0x593c2626705f9c56, + 0x6f8b2fb00c77836c, + 0xb6dfb9c0f956447, + 0x4724bd4189bd5eac, + 0x58edec91ec2cb657, + 0x2f2967b66737e3ed, + 0xbd79e0d20082ee74, + 0xecd8590680a3aa11, + 0xe80e6f4820cc9495, + 0x3109058d147fdcdd, + 0xbd4b46f0599fd415, + 0x6c9e18ac7007c91a, + 0x3e2cf6bc604ddb0, + 0x84db8346b786151c, + 0xe612641865679a63, + 0x4fcb7e8f3f60c07e, + 0xe3be5e330f38f09d, + 0x5cadf5bfd3072cc5, + 0x73d9732fc7c8f7f6, + 0x2867e7fddcdd9afa, + 0xb281e1fd541501b8, + 0x1f225a7ca91a4226, + 0x3375788de9b06958, + 0x52d6b1641c83ae, + 0xc0678c5dbd23a49a, + 0xf840b7ba963646e0, + 0xb650e5a93bc3d898, + 0xa3e51f138ab4cebe, + 0xc66f336c36b10137, + 0xb80b0047445d4184, + 0xa60dc059157491e5, + 0x87c89837ad68db2f, + 0x29babe4598c311fb, + 0xf4296dd6fef3d67a, + 0x1899e4a65f58660c, + 0x5ec05dcff72e7f8f, + 0x76707543f4fa1f73, + 0x6a06494a791c53a8, + 0x487db9d17636892, + 0x45a9d2845d3c42b6, + 0xb8a2392ba45a9b2, + 0x8e6cac7768d7141e, + 0x3207d795430cd926, + 0x7f44e6bd49e807b8, + 0x5f16206c9c6209a6, + 0x36dba887c37a8c0f, + 0xc2494954da2c9789, + 0xf2db9baa10b7bd6c, + 0x6f92829494e5acc7, + 0xcb772339ba1f17f9, + 0xff2a760414536efb, + 0xfef5138519684aba, + 0x7eb258665fc25d69, + 0xef2f773ffbd97a61, + 0xaafb550ffacfd8fa, + 0x95ba2a53f983cf38, + 0xdd945a747bf26183, + 0x94f971119aeef9e4, + 0x7a37cd5601aab85d, + 0xac62e055c10ab33a, + 0x577b986b314d6009, + 0xed5a7e85fda0b80b, + 0x14588f13be847307, + 0x596eb2d8ae258fc8, + 0x6fca5f8ed9aef3bb, + 0x25de7bb9480d5854, + 0xaf561aa79a10ae6a, + 0x1b2ba1518094da04, + 0x90fb44d2f05d0842, + 0x353a1607ac744a53, + 0x42889b8997915ce8, + 0x69956135febada11, + 0x43fab9837e699095, + 0x94f967e45e03f4bb, + 0x1d1be0eebac278f5, + 0x6462d92a69731732, + 0x7d7b8f7503cfdcfe, + 0x5cda735244c3d43e, + 0x3a0888136afa64a7, + 0x88aaa1845b8fdd0, + 0x8aad549e57273d45, + 0x36ac54e2f678864b, + 0x84576a1bb416a7dd, + 0x656d44a2a11c51d5, + 0x9f644ae5a4b1b325, + 0x873d5d9f0dde1fee, + 0xa90cb506d155a7ea, + 0x9a7f12442d588f2, + 0xc11ed6d538aeb2f, + 0x8f1668c8a86da5fa, + 0xf96e017d694487bc, + 0x37c981dcc395a9ac, + 0x85bbe253f47b1417, + 0x93956d7478ccec8e, + 0x387ac8d1970027b2, + 0x6997b05fcc0319e, + 0x441fece3bdf81f03, + 0xd527e81cad7626c3, + 0x8a71e223d8d3b074, + 0xf6872d5667844e49, + 0xb428f8ac016561db, + 0xe13336d701beba52, + 0xecc0024661173473, + 0x27f002d7f95d0190, + 0x31ec038df7b441f4, + 0x7e67047175a15271, + 0xf0062c6e984d386, + 0x52c07b78a3e60868, + 0xa7709a56ccdf8a82, + 0x88a66076400bb691, + 0x6acff893d00ea435, + 0x583f6b8c4124d43, + 0xc3727a337a8b704a, + 0x744f18c0592e4c5c, + 0x1162def06f79df73, + 0x8addcb5645ac2ba8, + 0x6d953e2bd7173692, + 0xc8fa8db6ccdd0437, + 0x1d9c9892400a22a2, + 0x2503beb6d00cab4b, + 0x2e44ae64840fd61d, + 0x5ceaecfed289e5d2, + 0x7425a83e872c5f47, + 0xd12f124e28f77719, + 0x82bd6b70d99aaa6f, + 0x636cc64d1001550b, + 0x3c47f7e05401aa4e, + 0x65acfaec34810a71, + 0x7f1839a741a14d0d, + 0x1ede48111209a050, + 0x934aed0aab460432, + 0xf81da84d5617853f, + 0x36251260ab9d668e, + 0xc1d72b7c6b426019, + 0xb24cf65b8612f81f, + 0xdee033f26797b627, + 0x169840ef017da3b1, + 0x8e1f289560ee864e, + 0xf1a6f2bab92a27e2, + 0xae10af696774b1db, + 0xacca6da1e0a8ef29, + 0x17fd090a58d32af3, + 0xddfc4b4cef07f5b0, + 0x4abdaf101564f98e, + 0x9d6d1ad41abe37f1, + 0x84c86189216dc5ed, + 0x32fd3cf5b4e49bb4, + 0x3fbc8c33221dc2a1, + 0xfabaf3feaa5334a, + 0x29cb4d87f2a7400e, + 0x743e20e9ef511012, + 0x914da9246b255416, + 0x1ad089b6c2f7548e, + 0xa184ac2473b529b1, + 0xc9e5d72d90a2741e, + 0x7e2fa67c7a658892, + 0xddbb901b98feeab7, + 0x552a74227f3ea565, + 0xd53a88958f87275f, + 0x8a892abaf368f137, + 0x2d2b7569b0432d85, + 0x9c3b29620e29fc73, + 0x8349f3ba91b47b8f, + 0x241c70a936219a73, + 0xed238cd383aa0110, + 0xf4363804324a40aa, + 0xb143c6053edcd0d5, + 0xdd94b7868e94050a, + 0xca7cf2b4191c8326, + 0xfd1c2f611f63a3f0, + 0xbc633b39673c8cec, + 0xd5be0503e085d813, + 0x4b2d8644d8a74e18, + 0xddf8e7d60ed1219e, + 0xcabb90e5c942b503, + 0x3d6a751f3b936243, + 0xcc512670a783ad4, + 0x27fb2b80668b24c5, + 0xb1f9f660802dedf6, + 0x5e7873f8a0396973, + 0xdb0b487b6423e1e8, + 0x91ce1a9a3d2cda62, + 0x7641a140cc7810fb, + 0xa9e904c87fcb0a9d, + 0x546345fa9fbdcd44, + 0xa97c177947ad4095, + 0x49ed8eabcccc485d, + 0x5c68f256bfff5a74, + 0x73832eec6fff3111, + 0xc831fd53c5ff7eab, + 0xba3e7ca8b77f5e55, + 0x28ce1bd2e55f35eb, + 0x7980d163cf5b81b3, + 0xd7e105bcc332621f, + 0x8dd9472bf3fefaa7, + 0xb14f98f6f0feb951, + 0x6ed1bf9a569f33d3, + 0xa862f80ec4700c8, + 0xcd27bb612758c0fa, + 0x8038d51cb897789c, + 0xe0470a63e6bd56c3, + 0x1858ccfce06cac74, + 0xf37801e0c43ebc8, + 0xd30560258f54e6ba, + 0x47c6b82ef32a2069, + 0x4cdc331d57fa5441, + 0xe0133fe4adf8e952, + 0x58180fddd97723a6, + 0x570f09eaa7ea7648}; + + } // namespace simdjson #endif diff --git a/tests/basictests.cpp b/tests/basictests.cpp index ccee417f3..7e935d1f4 100644 --- a/tests/basictests.cpp +++ b/tests/basictests.cpp @@ -117,7 +117,7 @@ bool number_test_powers_of_two() { double x = iter.get_double(); int ulp = f64_ulp_dist(x,expected); if(ulp > maxulp) maxulp = ulp; - if(ulp > 3) { + if(ulp > 0) { printf("failed to parse %s. ULP = %d i = %d \n", buf, ulp, i); return false; } @@ -127,6 +127,79 @@ bool number_test_powers_of_two() { return true; } +static const double testing_power_of_ten[] = { + 1e-307, 1e-306, 1e-305, 1e-304, 1e-303, 1e-302, 1e-301, 1e-300, 1e-299, + 1e-298, 1e-297, 1e-296, 1e-295, 1e-294, 1e-293, 1e-292, 1e-291, 1e-290, + 1e-289, 1e-288, 1e-287, 1e-286, 1e-285, 1e-284, 1e-283, 1e-282, 1e-281, + 1e-280, 1e-279, 1e-278, 1e-277, 1e-276, 1e-275, 1e-274, 1e-273, 1e-272, + 1e-271, 1e-270, 1e-269, 1e-268, 1e-267, 1e-266, 1e-265, 1e-264, 1e-263, + 1e-262, 1e-261, 1e-260, 1e-259, 1e-258, 1e-257, 1e-256, 1e-255, 1e-254, + 1e-253, 1e-252, 1e-251, 1e-250, 1e-249, 1e-248, 1e-247, 1e-246, 1e-245, + 1e-244, 1e-243, 1e-242, 1e-241, 1e-240, 1e-239, 1e-238, 1e-237, 1e-236, + 1e-235, 1e-234, 1e-233, 1e-232, 1e-231, 1e-230, 1e-229, 1e-228, 1e-227, + 1e-226, 1e-225, 1e-224, 1e-223, 1e-222, 1e-221, 1e-220, 1e-219, 1e-218, + 1e-217, 1e-216, 1e-215, 1e-214, 1e-213, 1e-212, 1e-211, 1e-210, 1e-209, + 1e-208, 1e-207, 1e-206, 1e-205, 1e-204, 1e-203, 1e-202, 1e-201, 1e-200, + 1e-199, 1e-198, 1e-197, 1e-196, 1e-195, 1e-194, 1e-193, 1e-192, 1e-191, + 1e-190, 1e-189, 1e-188, 1e-187, 1e-186, 1e-185, 1e-184, 1e-183, 1e-182, + 1e-181, 1e-180, 1e-179, 1e-178, 1e-177, 1e-176, 1e-175, 1e-174, 1e-173, + 1e-172, 1e-171, 1e-170, 1e-169, 1e-168, 1e-167, 1e-166, 1e-165, 1e-164, + 1e-163, 1e-162, 1e-161, 1e-160, 1e-159, 1e-158, 1e-157, 1e-156, 1e-155, + 1e-154, 1e-153, 1e-152, 1e-151, 1e-150, 1e-149, 1e-148, 1e-147, 1e-146, + 1e-145, 1e-144, 1e-143, 1e-142, 1e-141, 1e-140, 1e-139, 1e-138, 1e-137, + 1e-136, 1e-135, 1e-134, 1e-133, 1e-132, 1e-131, 1e-130, 1e-129, 1e-128, + 1e-127, 1e-126, 1e-125, 1e-124, 1e-123, 1e-122, 1e-121, 1e-120, 1e-119, + 1e-118, 1e-117, 1e-116, 1e-115, 1e-114, 1e-113, 1e-112, 1e-111, 1e-110, + 1e-109, 1e-108, 1e-107, 1e-106, 1e-105, 1e-104, 1e-103, 1e-102, 1e-101, + 1e-100, 1e-99, 1e-98, 1e-97, 1e-96, 1e-95, 1e-94, 1e-93, 1e-92, + 1e-91, 1e-90, 1e-89, 1e-88, 1e-87, 1e-86, 1e-85, 1e-84, 1e-83, + 1e-82, 1e-81, 1e-80, 1e-79, 1e-78, 1e-77, 1e-76, 1e-75, 1e-74, + 1e-73, 1e-72, 1e-71, 1e-70, 1e-69, 1e-68, 1e-67, 1e-66, 1e-65, + 1e-64, 1e-63, 1e-62, 1e-61, 1e-60, 1e-59, 1e-58, 1e-57, 1e-56, + 1e-55, 1e-54, 1e-53, 1e-52, 1e-51, 1e-50, 1e-49, 1e-48, 1e-47, + 1e-46, 1e-45, 1e-44, 1e-43, 1e-42, 1e-41, 1e-40, 1e-39, 1e-38, + 1e-37, 1e-36, 1e-35, 1e-34, 1e-33, 1e-32, 1e-31, 1e-30, 1e-29, + 1e-28, 1e-27, 1e-26, 1e-25, 1e-24, 1e-23, 1e-22, 1e-21, 1e-20, + 1e-19, 1e-18, 1e-17, 1e-16, 1e-15, 1e-14, 1e-13, 1e-12, 1e-11, + 1e-10, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, + 1e-1, 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, + 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, + 1e17, 1e18, 1e19, 1e20, 1e21, 1e22, 1e23, 1e24, 1e25, + 1e26, 1e27, 1e28, 1e29, 1e30, 1e31, 1e32, 1e33, 1e34, + 1e35, 1e36, 1e37, 1e38, 1e39, 1e40, 1e41, 1e42, 1e43, + 1e44, 1e45, 1e46, 1e47, 1e48, 1e49, 1e50, 1e51, 1e52, + 1e53, 1e54, 1e55, 1e56, 1e57, 1e58, 1e59, 1e60, 1e61, + 1e62, 1e63, 1e64, 1e65, 1e66, 1e67, 1e68, 1e69, 1e70, + 1e71, 1e72, 1e73, 1e74, 1e75, 1e76, 1e77, 1e78, 1e79, + 1e80, 1e81, 1e82, 1e83, 1e84, 1e85, 1e86, 1e87, 1e88, + 1e89, 1e90, 1e91, 1e92, 1e93, 1e94, 1e95, 1e96, 1e97, + 1e98, 1e99, 1e100, 1e101, 1e102, 1e103, 1e104, 1e105, 1e106, + 1e107, 1e108, 1e109, 1e110, 1e111, 1e112, 1e113, 1e114, 1e115, + 1e116, 1e117, 1e118, 1e119, 1e120, 1e121, 1e122, 1e123, 1e124, + 1e125, 1e126, 1e127, 1e128, 1e129, 1e130, 1e131, 1e132, 1e133, + 1e134, 1e135, 1e136, 1e137, 1e138, 1e139, 1e140, 1e141, 1e142, + 1e143, 1e144, 1e145, 1e146, 1e147, 1e148, 1e149, 1e150, 1e151, + 1e152, 1e153, 1e154, 1e155, 1e156, 1e157, 1e158, 1e159, 1e160, + 1e161, 1e162, 1e163, 1e164, 1e165, 1e166, 1e167, 1e168, 1e169, + 1e170, 1e171, 1e172, 1e173, 1e174, 1e175, 1e176, 1e177, 1e178, + 1e179, 1e180, 1e181, 1e182, 1e183, 1e184, 1e185, 1e186, 1e187, + 1e188, 1e189, 1e190, 1e191, 1e192, 1e193, 1e194, 1e195, 1e196, + 1e197, 1e198, 1e199, 1e200, 1e201, 1e202, 1e203, 1e204, 1e205, + 1e206, 1e207, 1e208, 1e209, 1e210, 1e211, 1e212, 1e213, 1e214, + 1e215, 1e216, 1e217, 1e218, 1e219, 1e220, 1e221, 1e222, 1e223, + 1e224, 1e225, 1e226, 1e227, 1e228, 1e229, 1e230, 1e231, 1e232, + 1e233, 1e234, 1e235, 1e236, 1e237, 1e238, 1e239, 1e240, 1e241, + 1e242, 1e243, 1e244, 1e245, 1e246, 1e247, 1e248, 1e249, 1e250, + 1e251, 1e252, 1e253, 1e254, 1e255, 1e256, 1e257, 1e258, 1e259, + 1e260, 1e261, 1e262, 1e263, 1e264, 1e265, 1e266, 1e267, 1e268, + 1e269, 1e270, 1e271, 1e272, 1e273, 1e274, 1e275, 1e276, 1e277, + 1e278, 1e279, 1e280, 1e281, 1e282, 1e283, 1e284, 1e285, 1e286, + 1e287, 1e288, 1e289, 1e290, 1e291, 1e292, 1e293, 1e294, 1e295, + 1e296, 1e297, 1e298, 1e299, 1e300, 1e301, 1e302, 1e303, 1e304, + 1e305, 1e306, 1e307, 1e308}; + + + bool number_test_powers_of_ten() { char buf[1024]; simdjson::document::parser parser; @@ -176,9 +249,9 @@ bool number_test_powers_of_ten() { } } else { double x = iter.get_double(); - double expected = std::pow(10, i); + double expected = ((i >= -307) ? testing_power_of_ten[i + 307]: std::pow(10, i)); int ulp = (int) f64_ulp_dist(x, expected); - if(ulp > 1) { + if(ulp > 0) { printf("failed to parse %s. \n", buf); printf("actual: %.20g expected: %.20g \n", x, expected); printf("ULP: %d \n", ulp); diff --git a/tests/numberparsingcheck.cpp b/tests/numberparsingcheck.cpp index 8270ae0a6..6dc206afd 100644 --- a/tests/numberparsingcheck.cpp +++ b/tests/numberparsingcheck.cpp @@ -119,14 +119,12 @@ void found_float(double result, const uint8_t *buf) { parse_error |= PARSE_ERROR; return; } - // we want to get some reasonable relative accuracy - uint64_t ULP = f64_ulp_dist(expected, result); - if (f64_ulp_dist(expected, result) > 1) { + if (expected != result) { fprintf(stderr, "parsed %.128e from \n", result); fprintf(stderr, " %.32s whereas strtod gives\n", buf); fprintf(stderr, " %.128e,", expected); fprintf(stderr, " while parsing %s \n", fullpath); - fprintf(stderr, " =========== ULP: %u,", (unsigned int)ULP); + fprintf(stderr, " =========== ULP: %u,", (unsigned int)f64_ulp_dist(expected, result)); parse_error |= PARSE_ERROR; } }