// Copyright 2017 The Abseil Authors. // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // https://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. // This file contains string processing functions related to // numeric values. #include "absl/strings/numbers.h" #include #include #include // for DBL_DIG and FLT_DIG #include // for HUGE_VAL #include #include #include #include #include #include #include // NOLINT(build/c++11) #include #include "absl/base/attributes.h" #include "absl/base/config.h" #include "absl/base/internal/endian.h" #include "absl/base/internal/raw_logging.h" #include "absl/base/optimization.h" #include "absl/numeric/bits.h" #include "absl/numeric/int128.h" #include "absl/strings/ascii.h" #include "absl/strings/charconv.h" #include "absl/strings/match.h" #include "absl/strings/string_view.h" namespace absl { ABSL_NAMESPACE_BEGIN bool SimpleAtof(absl::string_view str, float* out) { *out = 0.0; str = StripAsciiWhitespace(str); // std::from_chars doesn't accept an initial +, but SimpleAtof does, so if one // is present, skip it, while avoiding accepting "+-0" as valid. if (!str.empty() && str[0] == '+') { str.remove_prefix(1); if (!str.empty() && str[0] == '-') { return false; } } auto result = absl::from_chars(str.data(), str.data() + str.size(), *out); if (result.ec == std::errc::invalid_argument) { return false; } if (result.ptr != str.data() + str.size()) { // not all non-whitespace characters consumed return false; } // from_chars() with DR 3081's current wording will return max() on // overflow. SimpleAtof returns infinity instead. if (result.ec == std::errc::result_out_of_range) { if (*out > 1.0) { *out = std::numeric_limits::infinity(); } else if (*out < -1.0) { *out = -std::numeric_limits::infinity(); } } return true; } bool SimpleAtod(absl::string_view str, double* out) { *out = 0.0; str = StripAsciiWhitespace(str); // std::from_chars doesn't accept an initial +, but SimpleAtod does, so if one // is present, skip it, while avoiding accepting "+-0" as valid. if (!str.empty() && str[0] == '+') { str.remove_prefix(1); if (!str.empty() && str[0] == '-') { return false; } } auto result = absl::from_chars(str.data(), str.data() + str.size(), *out); if (result.ec == std::errc::invalid_argument) { return false; } if (result.ptr != str.data() + str.size()) { // not all non-whitespace characters consumed return false; } // from_chars() with DR 3081's current wording will return max() on // overflow. SimpleAtod returns infinity instead. if (result.ec == std::errc::result_out_of_range) { if (*out > 1.0) { *out = std::numeric_limits::infinity(); } else if (*out < -1.0) { *out = -std::numeric_limits::infinity(); } } return true; } bool SimpleAtob(absl::string_view str, bool* out) { ABSL_RAW_CHECK(out != nullptr, "Output pointer must not be nullptr."); if (EqualsIgnoreCase(str, "true") || EqualsIgnoreCase(str, "t") || EqualsIgnoreCase(str, "yes") || EqualsIgnoreCase(str, "y") || EqualsIgnoreCase(str, "1")) { *out = true; return true; } if (EqualsIgnoreCase(str, "false") || EqualsIgnoreCase(str, "f") || EqualsIgnoreCase(str, "no") || EqualsIgnoreCase(str, "n") || EqualsIgnoreCase(str, "0")) { *out = false; return true; } return false; } // ---------------------------------------------------------------------- // FastIntToBuffer() overloads // // Like the Fast*ToBuffer() functions above, these are intended for speed. // Unlike the Fast*ToBuffer() functions, however, these functions write // their output to the beginning of the buffer. The caller is responsible // for ensuring that the buffer has enough space to hold the output. // // Returns a pointer to the end of the string (i.e. the null character // terminating the string). // ---------------------------------------------------------------------- namespace { // Various routines to encode integers to strings. // We split data encodings into a group of 2 digits, 4 digits, 8 digits as // it's easier to combine powers of two into scalar arithmetic. // Previous implementation used a lookup table of 200 bytes for every 2 bytes // and it was memory bound, any L1 cache miss would result in a much slower // result. When benchmarking with a cache eviction rate of several percent, // this implementation proved to be better. // These constants represent '00', '0000' and '00000000' as ascii strings in // integers. We can add these numbers if we encode to bytes from 0 to 9. as // 'i' = '0' + i for 0 <= i <= 9. constexpr uint32_t kTwoZeroBytes = 0x0101 * '0'; constexpr uint64_t kFourZeroBytes = 0x01010101 * '0'; constexpr uint64_t kEightZeroBytes = 0x0101010101010101ull * '0'; // * 103 / 1024 is a division by 10 for values from 0 to 99. It's also a // division of a structure [k takes 2 bytes][m takes 2 bytes], then * 103 / 1024 // will be [k / 10][m / 10]. It allows parallel division. constexpr uint64_t kDivisionBy10Mul = 103u; constexpr uint64_t kDivisionBy10Div = 1 << 10; // * 10486 / 1048576 is a division by 100 for values from 0 to 9999. constexpr uint64_t kDivisionBy100Mul = 10486u; constexpr uint64_t kDivisionBy100Div = 1 << 20; // Encode functions write the ASCII output of input `n` to `out_str`. inline char* EncodeHundred(uint32_t n, char* out_str) { int num_digits = static_cast(n - 10) >> 8; uint32_t base = kTwoZeroBytes; uint32_t div10 = (n * kDivisionBy10Mul) / kDivisionBy10Div; uint32_t mod10 = n - 10u * div10; base += div10 + (mod10 << 8); base >>= num_digits & 8; little_endian::Store16(out_str, static_cast(base)); return out_str + 2 + num_digits; } inline char* EncodeTenThousand(uint32_t n, char* out_str) { // We split lower 2 digits and upper 2 digits of n into 2 byte consecutive // blocks. 123 -> [\0\1][\0\23]. We divide by 10 both blocks // (it's 1 division + zeroing upper bits), and compute modulo 10 as well "in // parallel". Then we combine both results to have both ASCII digits, // strip trailing zeros, add ASCII '0000' and return. uint32_t div100 = (n * kDivisionBy100Mul) / kDivisionBy100Div; uint32_t mod100 = n - 100ull * div100; uint32_t hundreds = (mod100 << 16) + div100; uint32_t tens = (hundreds * kDivisionBy10Mul) / kDivisionBy10Div; tens &= (0xFull << 16) | 0xFull; tens += (hundreds - 10ull * tens) << 8; ABSL_ASSUME(tens != 0); // The result can contain trailing zero bits, we need to strip them to a first // significant byte in a final representation. For example, for n = 123, we // have tens to have representation \0\1\2\3. We do `& -8` to round // to a multiple to 8 to strip zero bytes, not all zero bits. // countr_zero to help. // 0 minus 8 to make MSVC happy. uint32_t zeroes = static_cast(absl::countr_zero(tens)) & (0 - 8ull); tens += kFourZeroBytes; tens >>= zeroes; little_endian::Store32(out_str, tens); return out_str + sizeof(tens) - zeroes / 8; } // Prepare functions return an integer that should be written to out_str // (but possibly include trailing zeros). // For hi < 10000, lo < 10000 returns uint64_t as encoded in ASCII with // possibly trailing zeroes of the number hi * 10000 + lo. inline uint64_t PrepareTenThousands(uint64_t hi, uint64_t lo) { uint64_t merged = hi | (lo << 32); uint64_t div100 = ((merged * kDivisionBy100Mul) / kDivisionBy100Div) & ((0x7Full << 32) | 0x7Full); uint64_t mod100 = merged - 100ull * div100; uint64_t hundreds = (mod100 << 16) + div100; uint64_t tens = (hundreds * kDivisionBy10Mul) / kDivisionBy10Div; tens &= (0xFull << 48) | (0xFull << 32) | (0xFull << 16) | 0xFull; tens += (hundreds - 10ull * tens) << 8; return tens; } inline char* EncodeFullU32(uint32_t n, char* out_str) { if (n < 100'000'000) { uint64_t bottom = PrepareTenThousands(n / 10000, n % 10000); ABSL_ASSUME(bottom != 0); // 0 minus 8 to make MSVC happy. uint32_t zeroes = static_cast(absl::countr_zero(bottom)) & (0 - 8ull); uint64_t bottom_res = bottom + kEightZeroBytes; bottom_res >>= zeroes; little_endian::Store64(out_str, bottom_res); return out_str + sizeof(bottom) - zeroes / 8; } uint32_t top = n / 100'000'000; n %= 100'000'000; uint64_t bottom = PrepareTenThousands(n / 10000, n % 10000); uint64_t bottom_res = bottom + kEightZeroBytes; out_str = EncodeHundred(top, out_str); little_endian::Store64(out_str, bottom_res); return out_str + sizeof(bottom); } } // namespace void numbers_internal::PutTwoDigits(uint32_t i, char* buf) { assert(i < 100); uint32_t base = kTwoZeroBytes; uint32_t div10 = (i * kDivisionBy10Mul) / kDivisionBy10Div; uint32_t mod10 = i - 10u * div10; base += div10 + (mod10 << 8); little_endian::Store16(buf, static_cast(base)); } char* numbers_internal::FastIntToBuffer(uint32_t n, char* out_str) { if (n < 100) { out_str = EncodeHundred(n, out_str); goto set_last_zero; } if (n < 10000) { out_str = EncodeTenThousand(n, out_str); goto set_last_zero; } out_str = EncodeFullU32(n, out_str); set_last_zero: *out_str = '\0'; return out_str; } char* numbers_internal::FastIntToBuffer(int32_t i, char* buffer) { uint32_t u = static_cast(i); if (i < 0) { *buffer++ = '-'; // We need to do the negation in modular (i.e., "unsigned") // arithmetic; MSVC++ apparently warns for plain "-u", so // we write the equivalent expression "0 - u" instead. u = 0 - u; } return numbers_internal::FastIntToBuffer(u, buffer); } char* numbers_internal::FastIntToBuffer(uint64_t i, char* buffer) { uint32_t u32 = static_cast(i); if (u32 == i) return numbers_internal::FastIntToBuffer(u32, buffer); // 10**9 < 2**32 <= i < 10**10, we can do 2+8 uint64_t div08 = i / 100'000'000ull; uint64_t mod08 = i % 100'000'000ull; uint64_t mod_result = PrepareTenThousands(mod08 / 10000, mod08 % 10000) + kEightZeroBytes; if (i < 10'000'000'000ull) { buffer = EncodeHundred(static_cast(div08), buffer); little_endian::Store64(buffer, mod_result); buffer += 8; goto set_last_zero; } // i < 10**16, in this case 8+8 if (i < 10'000'000'000'000'000ull) { buffer = EncodeFullU32(static_cast(div08), buffer); little_endian::Store64(buffer, mod_result); buffer += 8; goto set_last_zero; } else { // 4 + 8 + 8 uint64_t div016 = i / 10'000'000'000'000'000ull; buffer = EncodeTenThousand(static_cast(div016), buffer); uint64_t mid_result = div08 - div016 * 100'000'000ull; mid_result = PrepareTenThousands(mid_result / 10000, mid_result % 10000) + kEightZeroBytes; little_endian::Store64(buffer, mid_result); buffer += 8; little_endian::Store64(buffer, mod_result); buffer += 8; goto set_last_zero; } set_last_zero: *buffer = '\0'; return buffer; } char* numbers_internal::FastIntToBuffer(int64_t i, char* buffer) { uint64_t u = static_cast(i); if (i < 0) { *buffer++ = '-'; u = 0 - u; } return numbers_internal::FastIntToBuffer(u, buffer); } // Given a 128-bit number expressed as a pair of uint64_t, high half first, // return that number multiplied by the given 32-bit value. If the result is // too large to fit in a 128-bit number, divide it by 2 until it fits. static std::pair Mul32(std::pair num, uint32_t mul) { uint64_t bits0_31 = num.second & 0xFFFFFFFF; uint64_t bits32_63 = num.second >> 32; uint64_t bits64_95 = num.first & 0xFFFFFFFF; uint64_t bits96_127 = num.first >> 32; // The picture so far: each of these 64-bit values has only the lower 32 bits // filled in. // bits96_127: [ 00000000 xxxxxxxx ] // bits64_95: [ 00000000 xxxxxxxx ] // bits32_63: [ 00000000 xxxxxxxx ] // bits0_31: [ 00000000 xxxxxxxx ] bits0_31 *= mul; bits32_63 *= mul; bits64_95 *= mul; bits96_127 *= mul; // Now the top halves may also have value, though all 64 of their bits will // never be set at the same time, since they are a result of a 32x32 bit // multiply. This makes the carry calculation slightly easier. // bits96_127: [ mmmmmmmm | mmmmmmmm ] // bits64_95: [ | mmmmmmmm mmmmmmmm | ] // bits32_63: | [ mmmmmmmm | mmmmmmmm ] // bits0_31: | [ | mmmmmmmm mmmmmmmm ] // eventually: [ bits128_up | ...bits64_127.... | ..bits0_63... ] uint64_t bits0_63 = bits0_31 + (bits32_63 << 32); uint64_t bits64_127 = bits64_95 + (bits96_127 << 32) + (bits32_63 >> 32) + (bits0_63 < bits0_31); uint64_t bits128_up = (bits96_127 >> 32) + (bits64_127 < bits64_95); if (bits128_up == 0) return {bits64_127, bits0_63}; auto shift = static_cast(bit_width(bits128_up)); uint64_t lo = (bits0_63 >> shift) + (bits64_127 << (64 - shift)); uint64_t hi = (bits64_127 >> shift) + (bits128_up << (64 - shift)); return {hi, lo}; } // Compute num * 5 ^ expfive, and return the first 128 bits of the result, // where the first bit is always a one. So PowFive(1, 0) starts 0b100000, // PowFive(1, 1) starts 0b101000, PowFive(1, 2) starts 0b110010, etc. static std::pair PowFive(uint64_t num, int expfive) { std::pair result = {num, 0}; while (expfive >= 13) { // 5^13 is the highest power of five that will fit in a 32-bit integer. result = Mul32(result, 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5); expfive -= 13; } constexpr uint32_t powers_of_five[13] = { 1, 5, 5 * 5, 5 * 5 * 5, 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5, 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5}; result = Mul32(result, powers_of_five[expfive & 15]); int shift = countl_zero(result.first); if (shift != 0) { result.first = (result.first << shift) + (result.second >> (64 - shift)); result.second = (result.second << shift); } return result; } struct ExpDigits { int32_t exponent; char digits[6]; }; // SplitToSix converts value, a positive double-precision floating-point number, // into a base-10 exponent and 6 ASCII digits, where the first digit is never // zero. For example, SplitToSix(1) returns an exponent of zero and a digits // array of {'1', '0', '0', '0', '0', '0'}. If value is exactly halfway between // two possible representations, e.g. value = 100000.5, then "round to even" is // performed. static ExpDigits SplitToSix(const double value) { ExpDigits exp_dig; int exp = 5; double d = value; // First step: calculate a close approximation of the output, where the // value d will be between 100,000 and 999,999, representing the digits // in the output ASCII array, and exp is the base-10 exponent. It would be // faster to use a table here, and to look up the base-2 exponent of value, // however value is an IEEE-754 64-bit number, so the table would have 2,000 // entries, which is not cache-friendly. if (d >= 999999.5) { if (d >= 1e+261) exp += 256, d *= 1e-256; if (d >= 1e+133) exp += 128, d *= 1e-128; if (d >= 1e+69) exp += 64, d *= 1e-64; if (d >= 1e+37) exp += 32, d *= 1e-32; if (d >= 1e+21) exp += 16, d *= 1e-16; if (d >= 1e+13) exp += 8, d *= 1e-8; if (d >= 1e+9) exp += 4, d *= 1e-4; if (d >= 1e+7) exp += 2, d *= 1e-2; if (d >= 1e+6) exp += 1, d *= 1e-1; } else { if (d < 1e-250) exp -= 256, d *= 1e256; if (d < 1e-122) exp -= 128, d *= 1e128; if (d < 1e-58) exp -= 64, d *= 1e64; if (d < 1e-26) exp -= 32, d *= 1e32; if (d < 1e-10) exp -= 16, d *= 1e16; if (d < 1e-2) exp -= 8, d *= 1e8; if (d < 1e+2) exp -= 4, d *= 1e4; if (d < 1e+4) exp -= 2, d *= 1e2; if (d < 1e+5) exp -= 1, d *= 1e1; } // At this point, d is in the range [99999.5..999999.5) and exp is in the // range [-324..308]. Since we need to round d up, we want to add a half // and truncate. // However, the technique above may have lost some precision, due to its // repeated multiplication by constants that each may be off by half a bit // of precision. This only matters if we're close to the edge though. // Since we'd like to know if the fractional part of d is close to a half, // we multiply it by 65536 and see if the fractional part is close to 32768. // (The number doesn't have to be a power of two,but powers of two are faster) uint64_t d64k = d * 65536; uint32_t dddddd; // A 6-digit decimal integer. if ((d64k % 65536) == 32767 || (d64k % 65536) == 32768) { // OK, it's fairly likely that precision was lost above, which is // not a surprise given only 52 mantissa bits are available. Therefore // redo the calculation using 128-bit numbers. (64 bits are not enough). // Start out with digits rounded down; maybe add one below. dddddd = static_cast(d64k / 65536); // mantissa is a 64-bit integer representing M.mmm... * 2^63. The actual // value we're representing, of course, is M.mmm... * 2^exp2. int exp2; double m = std::frexp(value, &exp2); uint64_t mantissa = m * (32768.0 * 65536.0 * 65536.0 * 65536.0); // std::frexp returns an m value in the range [0.5, 1.0), however we // can't multiply it by 2^64 and convert to an integer because some FPUs // throw an exception when converting an number higher than 2^63 into an // integer - even an unsigned 64-bit integer! Fortunately it doesn't matter // since m only has 52 significant bits anyway. mantissa <<= 1; exp2 -= 64; // not needed, but nice for debugging // OK, we are here to compare: // (dddddd + 0.5) * 10^(exp-5) vs. mantissa * 2^exp2 // so we can round up dddddd if appropriate. Those values span the full // range of 600 orders of magnitude of IEE 64-bit floating-point. // Fortunately, we already know they are very close, so we don't need to // track the base-2 exponent of both sides. This greatly simplifies the // the math since the 2^exp2 calculation is unnecessary and the power-of-10 // calculation can become a power-of-5 instead. std::pair edge, val; if (exp >= 6) { // Compare (dddddd + 0.5) * 5 ^ (exp - 5) to mantissa // Since we're tossing powers of two, 2 * dddddd + 1 is the // same as dddddd + 0.5 edge = PowFive(2 * dddddd + 1, exp - 5); val.first = mantissa; val.second = 0; } else { // We can't compare (dddddd + 0.5) * 5 ^ (exp - 5) to mantissa as we did // above because (exp - 5) is negative. So we compare (dddddd + 0.5) to // mantissa * 5 ^ (5 - exp) edge = PowFive(2 * dddddd + 1, 0); val = PowFive(mantissa, 5 - exp); } // printf("exp=%d %016lx %016lx vs %016lx %016lx\n", exp, val.first, // val.second, edge.first, edge.second); if (val > edge) { dddddd++; } else if (val == edge) { dddddd += (dddddd & 1); } } else { // Here, we are not close to the edge. dddddd = static_cast((d64k + 32768) / 65536); } if (dddddd == 1000000) { dddddd = 100000; exp += 1; } exp_dig.exponent = exp; uint32_t two_digits = dddddd / 10000; dddddd -= two_digits * 10000; numbers_internal::PutTwoDigits(two_digits, &exp_dig.digits[0]); two_digits = dddddd / 100; dddddd -= two_digits * 100; numbers_internal::PutTwoDigits(two_digits, &exp_dig.digits[2]); numbers_internal::PutTwoDigits(dddddd, &exp_dig.digits[4]); return exp_dig; } // Helper function for fast formatting of floating-point. // The result is the same as "%g", a.k.a. "%.6g". size_t numbers_internal::SixDigitsToBuffer(double d, char* const buffer) { static_assert(std::numeric_limits::is_iec559, "IEEE-754/IEC-559 support only"); char* out = buffer; // we write data to out, incrementing as we go, but // FloatToBuffer always returns the address of the buffer // passed in. if (std::isnan(d)) { strcpy(out, "nan"); // NOLINT(runtime/printf) return 3; } if (d == 0) { // +0 and -0 are handled here if (std::signbit(d)) *out++ = '-'; *out++ = '0'; *out = 0; return static_cast(out - buffer); } if (d < 0) { *out++ = '-'; d = -d; } if (d > std::numeric_limits::max()) { strcpy(out, "inf"); // NOLINT(runtime/printf) return static_cast(out + 3 - buffer); } auto exp_dig = SplitToSix(d); int exp = exp_dig.exponent; const char* digits = exp_dig.digits; out[0] = '0'; out[1] = '.'; switch (exp) { case 5: memcpy(out, &digits[0], 6), out += 6; *out = 0; return static_cast(out - buffer); case 4: memcpy(out, &digits[0], 5), out += 5; if (digits[5] != '0') { *out++ = '.'; *out++ = digits[5]; } *out = 0; return static_cast(out - buffer); case 3: memcpy(out, &digits[0], 4), out += 4; if ((digits[5] | digits[4]) != '0') { *out++ = '.'; *out++ = digits[4]; if (digits[5] != '0') *out++ = digits[5]; } *out = 0; return static_cast(out - buffer); case 2: memcpy(out, &digits[0], 3), out += 3; *out++ = '.'; memcpy(out, &digits[3], 3); out += 3; while (out[-1] == '0') --out; if (out[-1] == '.') --out; *out = 0; return static_cast(out - buffer); case 1: memcpy(out, &digits[0], 2), out += 2; *out++ = '.'; memcpy(out, &digits[2], 4); out += 4; while (out[-1] == '0') --out; if (out[-1] == '.') --out; *out = 0; return static_cast(out - buffer); case 0: memcpy(out, &digits[0], 1), out += 1; *out++ = '.'; memcpy(out, &digits[1], 5); out += 5; while (out[-1] == '0') --out; if (out[-1] == '.') --out; *out = 0; return static_cast(out - buffer); case -4: out[2] = '0'; ++out; ABSL_FALLTHROUGH_INTENDED; case -3: out[2] = '0'; ++out; ABSL_FALLTHROUGH_INTENDED; case -2: out[2] = '0'; ++out; ABSL_FALLTHROUGH_INTENDED; case -1: out += 2; memcpy(out, &digits[0], 6); out += 6; while (out[-1] == '0') --out; *out = 0; return static_cast(out - buffer); } assert(exp < -4 || exp >= 6); out[0] = digits[0]; assert(out[1] == '.'); out += 2; memcpy(out, &digits[1], 5), out += 5; while (out[-1] == '0') --out; if (out[-1] == '.') --out; *out++ = 'e'; if (exp > 0) { *out++ = '+'; } else { *out++ = '-'; exp = -exp; } if (exp > 99) { int dig1 = exp / 100; exp -= dig1 * 100; *out++ = '0' + static_cast(dig1); } PutTwoDigits(static_cast(exp), out); out += 2; *out = 0; return static_cast(out - buffer); } namespace { // Represents integer values of digits. // Uses 36 to indicate an invalid character since we support // bases up to 36. static const int8_t kAsciiToInt[256] = { 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, // 16 36s. 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 36, 36, 36, 36, 36, 36, 36, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 36, 36, 36, 36, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36}; // Parse the sign and optional hex or oct prefix in text. inline bool safe_parse_sign_and_base(absl::string_view* text /*inout*/, int* base_ptr /*inout*/, bool* negative_ptr /*output*/) { if (text->data() == nullptr) { return false; } const char* start = text->data(); const char* end = start + text->size(); int base = *base_ptr; // Consume whitespace. while (start < end && absl::ascii_isspace(static_cast(start[0]))) { ++start; } while (start < end && absl::ascii_isspace(static_cast(end[-1]))) { --end; } if (start >= end) { return false; } // Consume sign. *negative_ptr = (start[0] == '-'); if (*negative_ptr || start[0] == '+') { ++start; if (start >= end) { return false; } } // Consume base-dependent prefix. // base 0: "0x" -> base 16, "0" -> base 8, default -> base 10 // base 16: "0x" -> base 16 // Also validate the base. if (base == 0) { if (end - start >= 2 && start[0] == '0' && (start[1] == 'x' || start[1] == 'X')) { base = 16; start += 2; if (start >= end) { // "0x" with no digits after is invalid. return false; } } else if (end - start >= 1 && start[0] == '0') { base = 8; start += 1; } else { base = 10; } } else if (base == 16) { if (end - start >= 2 && start[0] == '0' && (start[1] == 'x' || start[1] == 'X')) { start += 2; if (start >= end) { // "0x" with no digits after is invalid. return false; } } } else if (base >= 2 && base <= 36) { // okay } else { return false; } *text = absl::string_view(start, static_cast(end - start)); *base_ptr = base; return true; } // Consume digits. // // The classic loop: // // for each digit // value = value * base + digit // value *= sign // // The classic loop needs overflow checking. It also fails on the most // negative integer, -2147483648 in 32-bit two's complement representation. // // My improved loop: // // if (!negative) // for each digit // value = value * base // value = value + digit // else // for each digit // value = value * base // value = value - digit // // Overflow checking becomes simple. // Lookup tables per IntType: // vmax/base and vmin/base are precomputed because division costs at least 8ns. // TODO(junyer): Doing this per base instead (i.e. an array of structs, not a // struct of arrays) would probably be better in terms of d-cache for the most // commonly used bases. template struct LookupTables { ABSL_CONST_INIT static const IntType kVmaxOverBase[]; ABSL_CONST_INIT static const IntType kVminOverBase[]; }; // An array initializer macro for X/base where base in [0, 36]. // However, note that lookups for base in [0, 1] should never happen because // base has been validated to be in [2, 36] by safe_parse_sign_and_base(). #define X_OVER_BASE_INITIALIZER(X) \ { \ 0, 0, X / 2, X / 3, X / 4, X / 5, X / 6, X / 7, X / 8, X / 9, X / 10, \ X / 11, X / 12, X / 13, X / 14, X / 15, X / 16, X / 17, X / 18, \ X / 19, X / 20, X / 21, X / 22, X / 23, X / 24, X / 25, X / 26, \ X / 27, X / 28, X / 29, X / 30, X / 31, X / 32, X / 33, X / 34, \ X / 35, X / 36, \ } // This kVmaxOverBase is generated with // for (int base = 2; base < 37; ++base) { // absl::uint128 max = std::numeric_limits::max(); // auto result = max / base; // std::cout << " MakeUint128(" << absl::Uint128High64(result) << "u, " // << absl::Uint128Low64(result) << "u),\n"; // } // See https://godbolt.org/z/aneYsb // // uint128& operator/=(uint128) is not constexpr, so hardcode the resulting // array to avoid a static initializer. template <> ABSL_CONST_INIT const uint128 LookupTables::kVmaxOverBase[] = { 0, 0, MakeUint128(9223372036854775807u, 18446744073709551615u), MakeUint128(6148914691236517205u, 6148914691236517205u), MakeUint128(4611686018427387903u, 18446744073709551615u), MakeUint128(3689348814741910323u, 3689348814741910323u), MakeUint128(3074457345618258602u, 12297829382473034410u), MakeUint128(2635249153387078802u, 5270498306774157604u), MakeUint128(2305843009213693951u, 18446744073709551615u), MakeUint128(2049638230412172401u, 14347467612885206812u), MakeUint128(1844674407370955161u, 11068046444225730969u), MakeUint128(1676976733973595601u, 8384883669867978007u), MakeUint128(1537228672809129301u, 6148914691236517205u), MakeUint128(1418980313362273201u, 4256940940086819603u), MakeUint128(1317624576693539401u, 2635249153387078802u), MakeUint128(1229782938247303441u, 1229782938247303441u), MakeUint128(1152921504606846975u, 18446744073709551615u), MakeUint128(1085102592571150095u, 1085102592571150095u), MakeUint128(1024819115206086200u, 16397105843297379214u), MakeUint128(970881267037344821u, 16504981539634861972u), MakeUint128(922337203685477580u, 14757395258967641292u), MakeUint128(878416384462359600u, 14054662151397753612u), MakeUint128(838488366986797800u, 13415813871788764811u), MakeUint128(802032351030850070u, 4812194106185100421u), MakeUint128(768614336404564650u, 12297829382473034410u), MakeUint128(737869762948382064u, 11805916207174113034u), MakeUint128(709490156681136600u, 11351842506898185609u), MakeUint128(683212743470724133u, 17080318586768103348u), MakeUint128(658812288346769700u, 10540996613548315209u), MakeUint128(636094623231363848u, 15266270957552732371u), MakeUint128(614891469123651720u, 9838263505978427528u), MakeUint128(595056260442243600u, 9520900167075897608u), MakeUint128(576460752303423487u, 18446744073709551615u), MakeUint128(558992244657865200u, 8943875914525843207u), MakeUint128(542551296285575047u, 9765923333140350855u), MakeUint128(527049830677415760u, 8432797290838652167u), MakeUint128(512409557603043100u, 8198552921648689607u), }; // This kVmaxOverBase generated with // for (int base = 2; base < 37; ++base) { // absl::int128 max = std::numeric_limits::max(); // auto result = max / base; // std::cout << "\tMakeInt128(" << absl::Int128High64(result) << ", " // << absl::Int128Low64(result) << "u),\n"; // } // See https://godbolt.org/z/7djYWz // // int128& operator/=(int128) is not constexpr, so hardcode the resulting array // to avoid a static initializer. template <> ABSL_CONST_INIT const int128 LookupTables::kVmaxOverBase[] = { 0, 0, MakeInt128(4611686018427387903, 18446744073709551615u), MakeInt128(3074457345618258602, 12297829382473034410u), MakeInt128(2305843009213693951, 18446744073709551615u), MakeInt128(1844674407370955161, 11068046444225730969u), MakeInt128(1537228672809129301, 6148914691236517205u), MakeInt128(1317624576693539401, 2635249153387078802u), MakeInt128(1152921504606846975, 18446744073709551615u), MakeInt128(1024819115206086200, 16397105843297379214u), MakeInt128(922337203685477580, 14757395258967641292u), MakeInt128(838488366986797800, 13415813871788764811u), MakeInt128(768614336404564650, 12297829382473034410u), MakeInt128(709490156681136600, 11351842506898185609u), MakeInt128(658812288346769700, 10540996613548315209u), MakeInt128(614891469123651720, 9838263505978427528u), MakeInt128(576460752303423487, 18446744073709551615u), MakeInt128(542551296285575047, 9765923333140350855u), MakeInt128(512409557603043100, 8198552921648689607u), MakeInt128(485440633518672410, 17475862806672206794u), MakeInt128(461168601842738790, 7378697629483820646u), MakeInt128(439208192231179800, 7027331075698876806u), MakeInt128(419244183493398900, 6707906935894382405u), MakeInt128(401016175515425035, 2406097053092550210u), MakeInt128(384307168202282325, 6148914691236517205u), MakeInt128(368934881474191032, 5902958103587056517u), MakeInt128(354745078340568300, 5675921253449092804u), MakeInt128(341606371735362066, 17763531330238827482u), MakeInt128(329406144173384850, 5270498306774157604u), MakeInt128(318047311615681924, 7633135478776366185u), MakeInt128(307445734561825860, 4919131752989213764u), MakeInt128(297528130221121800, 4760450083537948804u), MakeInt128(288230376151711743, 18446744073709551615u), MakeInt128(279496122328932600, 4471937957262921603u), MakeInt128(271275648142787523, 14106333703424951235u), MakeInt128(263524915338707880, 4216398645419326083u), MakeInt128(256204778801521550, 4099276460824344803u), }; // This kVminOverBase generated with // for (int base = 2; base < 37; ++base) { // absl::int128 min = std::numeric_limits::min(); // auto result = min / base; // std::cout << "\tMakeInt128(" << absl::Int128High64(result) << ", " // << absl::Int128Low64(result) << "u),\n"; // } // // See https://godbolt.org/z/7djYWz // // int128& operator/=(int128) is not constexpr, so hardcode the resulting array // to avoid a static initializer. template <> ABSL_CONST_INIT const int128 LookupTables::kVminOverBase[] = { 0, 0, MakeInt128(-4611686018427387904, 0u), MakeInt128(-3074457345618258603, 6148914691236517206u), MakeInt128(-2305843009213693952, 0u), MakeInt128(-1844674407370955162, 7378697629483820647u), MakeInt128(-1537228672809129302, 12297829382473034411u), MakeInt128(-1317624576693539402, 15811494920322472814u), MakeInt128(-1152921504606846976, 0u), MakeInt128(-1024819115206086201, 2049638230412172402u), MakeInt128(-922337203685477581, 3689348814741910324u), MakeInt128(-838488366986797801, 5030930201920786805u), MakeInt128(-768614336404564651, 6148914691236517206u), MakeInt128(-709490156681136601, 7094901566811366007u), MakeInt128(-658812288346769701, 7905747460161236407u), MakeInt128(-614891469123651721, 8608480567731124088u), MakeInt128(-576460752303423488, 0u), MakeInt128(-542551296285575048, 8680820740569200761u), MakeInt128(-512409557603043101, 10248191152060862009u), MakeInt128(-485440633518672411, 970881267037344822u), MakeInt128(-461168601842738791, 11068046444225730970u), MakeInt128(-439208192231179801, 11419412998010674810u), MakeInt128(-419244183493398901, 11738837137815169211u), MakeInt128(-401016175515425036, 16040647020617001406u), MakeInt128(-384307168202282326, 12297829382473034411u), MakeInt128(-368934881474191033, 12543785970122495099u), MakeInt128(-354745078340568301, 12770822820260458812u), MakeInt128(-341606371735362067, 683212743470724134u), MakeInt128(-329406144173384851, 13176245766935394012u), MakeInt128(-318047311615681925, 10813608594933185431u), MakeInt128(-307445734561825861, 13527612320720337852u), MakeInt128(-297528130221121801, 13686293990171602812u), MakeInt128(-288230376151711744, 0u), MakeInt128(-279496122328932601, 13974806116446630013u), MakeInt128(-271275648142787524, 4340410370284600381u), MakeInt128(-263524915338707881, 14230345428290225533u), MakeInt128(-256204778801521551, 14347467612885206813u), }; template ABSL_CONST_INIT const IntType LookupTables::kVmaxOverBase[] = X_OVER_BASE_INITIALIZER(std::numeric_limits::max()); template ABSL_CONST_INIT const IntType LookupTables::kVminOverBase[] = X_OVER_BASE_INITIALIZER(std::numeric_limits::min()); #undef X_OVER_BASE_INITIALIZER template inline bool safe_parse_positive_int(absl::string_view text, int base, IntType* value_p) { IntType value = 0; const IntType vmax = std::numeric_limits::max(); assert(vmax > 0); assert(base >= 0); const IntType base_inttype = static_cast(base); assert(vmax >= base_inttype); const IntType vmax_over_base = LookupTables::kVmaxOverBase[base]; assert(base < 2 || std::numeric_limits::max() / base_inttype == vmax_over_base); const char* start = text.data(); const char* end = start + text.size(); // loop over digits for (; start < end; ++start) { unsigned char c = static_cast(start[0]); IntType digit = static_cast(kAsciiToInt[c]); if (digit >= base_inttype) { *value_p = value; return false; } if (value > vmax_over_base) { *value_p = vmax; return false; } value *= base_inttype; if (value > vmax - digit) { *value_p = vmax; return false; } value += digit; } *value_p = value; return true; } template inline bool safe_parse_negative_int(absl::string_view text, int base, IntType* value_p) { IntType value = 0; const IntType vmin = std::numeric_limits::min(); assert(vmin < 0); assert(vmin <= 0 - base); IntType vmin_over_base = LookupTables::kVminOverBase[base]; assert(base < 2 || std::numeric_limits::min() / base == vmin_over_base); // 2003 c++ standard [expr.mul] // "... the sign of the remainder is implementation-defined." // Although (vmin/base)*base + vmin%base is always vmin. // 2011 c++ standard tightens the spec but we cannot rely on it. // TODO(junyer): Handle this in the lookup table generation. if (vmin % base > 0) { vmin_over_base += 1; } const char* start = text.data(); const char* end = start + text.size(); // loop over digits for (; start < end; ++start) { unsigned char c = static_cast(start[0]); int digit = kAsciiToInt[c]; if (digit >= base) { *value_p = value; return false; } if (value < vmin_over_base) { *value_p = vmin; return false; } value *= base; if (value < vmin + digit) { *value_p = vmin; return false; } value -= digit; } *value_p = value; return true; } // Input format based on POSIX.1-2008 strtol // http://pubs.opengroup.org/onlinepubs/9699919799/functions/strtol.html template inline bool safe_int_internal(absl::string_view text, IntType* value_p, int base) { *value_p = 0; bool negative; if (!safe_parse_sign_and_base(&text, &base, &negative)) { return false; } if (!negative) { return safe_parse_positive_int(text, base, value_p); } else { return safe_parse_negative_int(text, base, value_p); } } template inline bool safe_uint_internal(absl::string_view text, IntType* value_p, int base) { *value_p = 0; bool negative; if (!safe_parse_sign_and_base(&text, &base, &negative) || negative) { return false; } return safe_parse_positive_int(text, base, value_p); } } // anonymous namespace namespace numbers_internal { // Digit conversion. ABSL_CONST_INIT ABSL_DLL const char kHexChar[] = "0123456789abcdef"; ABSL_CONST_INIT ABSL_DLL const char kHexTable[513] = "000102030405060708090a0b0c0d0e0f" "101112131415161718191a1b1c1d1e1f" "202122232425262728292a2b2c2d2e2f" "303132333435363738393a3b3c3d3e3f" "404142434445464748494a4b4c4d4e4f" "505152535455565758595a5b5c5d5e5f" "606162636465666768696a6b6c6d6e6f" "707172737475767778797a7b7c7d7e7f" "808182838485868788898a8b8c8d8e8f" "909192939495969798999a9b9c9d9e9f" "a0a1a2a3a4a5a6a7a8a9aaabacadaeaf" "b0b1b2b3b4b5b6b7b8b9babbbcbdbebf" "c0c1c2c3c4c5c6c7c8c9cacbcccdcecf" "d0d1d2d3d4d5d6d7d8d9dadbdcdddedf" "e0e1e2e3e4e5e6e7e8e9eaebecedeeef" "f0f1f2f3f4f5f6f7f8f9fafbfcfdfeff"; bool safe_strto32_base(absl::string_view text, int32_t* value, int base) { return safe_int_internal(text, value, base); } bool safe_strto64_base(absl::string_view text, int64_t* value, int base) { return safe_int_internal(text, value, base); } bool safe_strto128_base(absl::string_view text, int128* value, int base) { return safe_int_internal(text, value, base); } bool safe_strtou32_base(absl::string_view text, uint32_t* value, int base) { return safe_uint_internal(text, value, base); } bool safe_strtou64_base(absl::string_view text, uint64_t* value, int base) { return safe_uint_internal(text, value, base); } bool safe_strtou128_base(absl::string_view text, uint128* value, int base) { return safe_uint_internal(text, value, base); } } // namespace numbers_internal ABSL_NAMESPACE_END } // namespace absl