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[24.228.8.148]) by smtp.gmail.com with ESMTPSA id o10sm7994149qtx.33.2022.01.16.10.06.54 (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Sun, 16 Jan 2022 10:06:54 -0800 (PST) To: gcc-patches@gcc.gnu.org Subject: [PATCH 1/6 v2] libstdc++: Directly implement hexfloat std::from_chars for binary32/64 Date: Sun, 16 Jan 2022 13:06:47 -0500 Message-Id: <20220116180652.3694791-1-ppalka@redhat.com> X-Mailer: git-send-email 2.35.0.rc1 MIME-Version: 1.0 X-Mimecast-Spam-Score: 0 X-Mimecast-Originator: redhat.com X-Spam-Status: No, score=-14.8 required=5.0 tests=BAYES_00, DKIMWL_WL_HIGH, DKIM_SIGNED, DKIM_VALID, DKIM_VALID_AU, DKIM_VALID_EF, GIT_PATCH_0, KAM_NUMSUBJECT, RCVD_IN_DNSWL_LOW, RCVD_IN_MSPIKE_H3, RCVD_IN_MSPIKE_WL, SPF_HELO_NONE, SPF_NONE, TXREP autolearn=unavailable autolearn_force=no version=3.4.4 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on server2.sourceware.org X-BeenThere: gcc-patches@gcc.gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Gcc-patches mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-Patchwork-Original-From: Patrick Palka via Gcc-patches From: Patrick Palka Reply-To: Patrick Palka Cc: libstdc++@gcc.gnu.org Errors-To: gcc-patches-bounces+patchwork=sourceware.org@gcc.gnu.org Sender: "Gcc-patches" Series tested on x86_64, i686, ppc64, ppc64le, aarch64, does it look OK for trunk? libstdc++-v3/ChangeLog: * src/c++17/floating_from_chars.cc: Include . (ascii_to_hexit, starts_with_ci): Define. (__floating_from_chars_hex): Define. (from_chars): Conditionally call __floating_from_chars_hex. (testsuite/20_util/from_chars/7.cc): New test. --- libstdc++-v3/src/c++17/floating_from_chars.cc | 376 ++++++++++++++++++ .../testsuite/20_util/from_chars/7.cc | 151 +++++++ 2 files changed, 527 insertions(+) create mode 100644 libstdc++-v3/testsuite/20_util/from_chars/7.cc diff --git a/libstdc++-v3/src/c++17/floating_from_chars.cc b/libstdc++-v3/src/c++17/floating_from_chars.cc index 479e042bb5f..b186da9a955 100644 --- a/libstdc++-v3/src/c++17/floating_from_chars.cc +++ b/libstdc++-v3/src/c++17/floating_from_chars.cc @@ -31,6 +31,7 @@ #define _GLIBCXX_USE_CXX11_ABI 1 #include +#include #include #include #include @@ -396,6 +397,371 @@ namespace } #endif +#if _GLIBCXX_FLOAT_IS_IEEE_BINARY32 && _GLIBCXX_DOUBLE_IS_IEEE_BINARY64 + // If the given ASCII character represents a hexit, return that hexit. + // Otherwise return -1. + int + ascii_to_hexit(char ch) + { + if (ch >= '0' && ch <= '9') + return ch - '0'; + if (ch >= 'a' && ch <= 'f') + return ch - 'a' + 10; + if (ch >= 'A' && ch <= 'F') + return ch - 'A' + 10; + return -1; + } + + // Return true iff [FIRST,LAST) begins with PREFIX, ignoring case. + bool + starts_with_ci(const char* first, const char* last, string_view prefix) + { + __glibcxx_requires_valid_range(first, last); + + for (char ch : prefix) + { + __glibcxx_assert(ch >= 'a' && ch <= 'z'); + if (first == last || (*first != ch && *first != ch - 32)) + return false; + ++first; + } + + return true; + } + + // An implementation of hexadecimal float parsing for binary32/64. + template + from_chars_result + __floating_from_chars_hex(const char* first, const char* last, T& value) + { + static_assert(is_same_v || is_same_v); + + using uint_t = conditional_t, uint32_t, uint64_t>; + constexpr int mantissa_width = is_same_v ? 23 : 52; + constexpr int exponent_width = is_same_v ? 8 : 11; + constexpr int exponent_bias = (1 << (exponent_width - 1)) - 1; + + __glibcxx_requires_valid_range(first, last); + if (first == last) + return {first, errc::invalid_argument}; + + // Consume the sign bit. + const char* const orig_first = first; + bool sign_bit = false; + if (*first == '-') + { + sign_bit = true; + ++first; + } + + // Handle "inf", "infinity", "NaN" and variants thereof. + if (first != last) + if (*first == 'i' || *first == 'I' || *first == 'n' || *first == 'N') [[unlikely]] + { + if (starts_with_ci(first, last, "inf"sv)) + { + first += 3; + if (starts_with_ci(first, last, "inity"sv)) + first += 5; + + uint_t result = 0; + result |= sign_bit; + result <<= exponent_width; + result |= (1ull << exponent_width) - 1; + result <<= mantissa_width; + memcpy(&value, &result, sizeof(result)); + + return {first, errc{}}; + } + else if (starts_with_ci(first, last, "nan")) + { + first += 3; + + if (first != last && *first == '(') + { + // Tentatively consume the '(' as we look for an optional + // n-char-sequence followed by a ')'. + const char* const fallback_first = first; + for (;;) + { + ++first; + if (first == last) + { + first = fallback_first; + break; + } + + char ch = *first; + if (ch == ')') + { + ++first; + break; + } + else if ((ch >= '0' && ch <= '9') + || (ch >= 'a' && ch <= 'z') + || (ch >= 'A' && ch <= 'Z') + || ch == '_') + continue; + else + { + first = fallback_first; + break; + } + } + } + + // We make the implementation-defined decision of ignoring the + // sign bit and the n-char-sequence when assembling the NaN. + uint_t result = 0; + result <<= exponent_width; + result |= (1ull << exponent_width) - 1; + result <<= mantissa_width; + result |= (1ull << (mantissa_width - 1)) | 1; + memcpy(&value, &result, sizeof(result)); + + return {first, errc{}}; + } + } + + // Consume all insignificant leading zeros in the whole part of the + // mantissa. + bool seen_digit = false; + while (first != last && *first == '0') + { + seen_digit = true; + ++first; + } + + // Now consume the rest of the written mantissa, populating MANTISSA with the + // first MANTISSA_WIDTH+k significant bits of the written mantissa, where 1 + // <= k <= 4 is the bit width of the leading significant written hexit. + // + // Examples: + // After parsing "1.2f3", MANTISSA is 0x12f30000000000 (bit_width=52+1). + // After parsing ".0000f0e", MANTISSA is 0xf0e00000000000 (bit_width=52+4). + // After parsing ".1234567890abcd8", MANTISSA is 0x1234567890abcd (bit_width=52+1) + // and MIDPOINT_BIT is true and NONZERO_TAIL is false. + uint_t mantissa = 0; + int mantissa_idx = mantissa_width; // The current bit index into MANTISSA + // into which we'll write the next hexit. + int exponent_adjustment = 0; // How much we'd have to adjust the written + // exponent in order to represent the mantissa + // in scientific form h.hhhhhhhhhhhhh. + bool midpoint_bit = false; // Whether the MANTISSA_WIDTH+k+1 significant + // bit is set in the written mantissa. + bool nonzero_tail = false; // Whether some bit thereafter is set in the + // written mantissa. + bool seen_decimal_point = false; + for (; first != last; ++first) + { + char ch = *first; + if (ch == '.' && !seen_decimal_point) + { + seen_decimal_point = true; + continue; + } + + int hexit = ascii_to_hexit(ch); + if (hexit == -1) + break; + seen_digit = true; + + if (!seen_decimal_point && mantissa != 0) + exponent_adjustment += 4; + else if (seen_decimal_point && mantissa == 0) + { + exponent_adjustment -= 4; + if (hexit == 0x0) + continue; + } + + if (mantissa_idx >= 0) + mantissa |= uint_t(hexit) << mantissa_idx; + else if (mantissa_idx >= -4) + { + if constexpr (is_same_v) + { + __glibcxx_assert(mantissa_idx == -1); + mantissa |= hexit >> 1; + midpoint_bit = (hexit & 0b0001) != 0; + } + else + { + __glibcxx_assert(mantissa_idx == -4); + midpoint_bit = (hexit & 0b1000) != 0; + nonzero_tail = (hexit & 0b0111) != 0; + } + } + else + nonzero_tail |= (hexit != 0x0); + + mantissa_idx -= 4; + } + if (mantissa != 0) + __glibcxx_assert(__bit_width(mantissa) >= mantissa_width + 1 + && __bit_width(mantissa) <= mantissa_width + 4); + else + __glibcxx_assert(!midpoint_bit && !nonzero_tail); + + if (!seen_digit) + { + // If we haven't seen any digit at this point, the parse failed. + first = orig_first; + return {first, errc::invalid_argument}; + } + + // Parse the written exponent. + int written_exponent = 0; + if (first != last && *first == 'p') + { + // Tentatively consume the the 'p' and try to parse a decimal number. + const char* const fallback_first = first; + ++first; + if (first != last && *first == '+') + ++first; + from_chars_result fcr = from_chars(first, last, written_exponent, 10); + if (fcr.ptr == first) + // The parse failed, so undo consuming the 'p' and carry on as if the + // exponent was omitted (i.e. is 0). + first = fallback_first; + else + { + first = fcr.ptr; + if (mantissa != 0 && fcr.ec == errc::result_out_of_range) + // FIXME: Punt on large exponents for now. + return {first, errc::result_out_of_range}; + } + } + int biased_exponent = written_exponent + exponent_bias; + if (exponent_adjustment != 0) + // The mantissa wasn't written in scientific form. Adjust the exponent + // so that we may assume scientific form. + // + // Examples; + // For input "a.bcp5", EXPONENT_ADJUSTMENT would be 0 since this + // written mantissa is already in scientific form. + // For input "ab.cp5", EXPONENT_ADJUSTMENT would be 4 since the + // scientific form is "a.bcp9". + // For input 0.0abcp5", EXPONENT_ADJUSTMENT would be -8 since the + // scientific form is "a.bcp-3". + biased_exponent += exponent_adjustment; + + // Shifts the mantissa to the right by AMOUNT while updating + // BIASED_EXPONENT, MIDPOINT_BIT and NONZERO_TAIL accordingly. + auto shift_mantissa = [&] (int amount) { + __glibcxx_assert(amount >= 0); + if (amount > mantissa_width + 1) + { + // Shifting the mantissa by an amount greater than its precision. + nonzero_tail |= midpoint_bit; + nonzero_tail |= mantissa != 0; + midpoint_bit = false; + mantissa = 0; + biased_exponent += amount; + } + else if (amount != 0) + { + nonzero_tail |= midpoint_bit; + nonzero_tail |= (mantissa & ((1ull << (amount - 1)) - 1)) != 0; + midpoint_bit = (mantissa & (1ull << (amount - 1))) != 0; + mantissa >>= amount; + biased_exponent += amount; + } + }; + + if (mantissa != 0) + { + // If the leading hexit is not '1', shift MANTISSA to make it so. + // This normalizes input like "4.04p0" into "1.01p2". + const int leading_hexit = mantissa >> mantissa_width; + const int leading_hexit_width = __bit_width(leading_hexit); // FIXME: optimize? + __glibcxx_assert(leading_hexit_width >= 1 && leading_hexit_width <= 4); + shift_mantissa(leading_hexit_width - 1); + // After this adjustment, we can assume the leading hexit is a '1'. + __glibcxx_assert((mantissa >> mantissa_width) == 0x1); + } + + if (biased_exponent <= 0) + { + // This number is too small to be represented as a normal number, so + // try for a subnormal number by shifting the mantissa sufficiently. + // We need to shift by 1 more than -BIASED_EXPONENT because the leading + // mantissa bit is omitted in the representation of a normal number but + // not in a subnormal number. + shift_mantissa(-biased_exponent + 1); + __glibcxx_assert(!(mantissa & (1ull << mantissa_width))); + __glibcxx_assert(biased_exponent == 1); + biased_exponent = 0; + } + + // Perform round-to-nearest, tie-to-even rounding. + if (midpoint_bit && (nonzero_tail || (mantissa % 2) != 0)) + { + // Rounding away from zero. + ++mantissa; + midpoint_bit = false; + nonzero_tail = false; + + // Deal with a couple of corner cases after rounding. + if (mantissa == (1ull << mantissa_width)) + { + // We rounded the subnormal number 1.fffffffffffff...p-1023 + // up to the normal number 1p-1022. + __glibcxx_assert(biased_exponent == 0); + ++biased_exponent; + } + else if (mantissa & (1ull << (mantissa_width + 1))) + { + // We rounded the normal number 1.fffffffffffff8pN (with maximal + // mantissa) up to to 1p(N+1). + mantissa >>= 1; + ++biased_exponent; + } + } + else + { + // Rounding towards zero. + + if (mantissa == 0 && (midpoint_bit || nonzero_tail)) + { + // A nonzero number that rounds to zero is unrepresentable. + __glibcxx_assert(biased_exponent == 0); + return {first, errc::result_out_of_range}; + } + + midpoint_bit = false; + nonzero_tail = false; + } + + if (mantissa != 0 && biased_exponent >= (1 << exponent_width) - 1) + // The exponent of this number is too large to be representable. + return {first, errc::result_out_of_range}; + + uint_t result = 0; + if (mantissa == 0) + { + // Assemble a (possibly signed) zero. + if (sign_bit) + result |= 1ull << (exponent_width + mantissa_width); + } + else + { + // Assemble a nonzero normal or subnormal value. + result |= sign_bit; + result <<= exponent_width; + result |= biased_exponent; + result <<= mantissa_width; + result |= mantissa & ((1ull << mantissa_width) - 1); + // The implicit leading mantissa bit is set iff the number is normal. + __glibcxx_assert(((mantissa & (1ull << mantissa_width)) != 0) + == (biased_exponent != 0)); + } + memcpy(&value, &result, sizeof(result)); + + return {first, errc{}}; + } +#endif + } // namespace // FIXME: This should be reimplemented so it doesn't use strtod and newlocale. @@ -406,6 +772,11 @@ from_chars_result from_chars(const char* first, const char* last, float& value, chars_format fmt) noexcept { +#if _GLIBCXX_FLOAT_IS_IEEE_BINARY32 && _GLIBCXX_DOUBLE_IS_IEEE_BINARY64 + if (fmt == chars_format::hex) + return __floating_from_chars_hex(first, last, value); +#endif + errc ec = errc::invalid_argument; #if _GLIBCXX_USE_CXX11_ABI buffer_resource mr; @@ -432,6 +803,11 @@ from_chars_result from_chars(const char* first, const char* last, double& value, chars_format fmt) noexcept { +#if _GLIBCXX_FLOAT_IS_IEEE_BINARY32 && _GLIBCXX_DOUBLE_IS_IEEE_BINARY64 + if (fmt == chars_format::hex) + return __floating_from_chars_hex(first, last, value); +#endif + errc ec = errc::invalid_argument; #if _GLIBCXX_USE_CXX11_ABI buffer_resource mr; diff --git a/libstdc++-v3/testsuite/20_util/from_chars/7.cc b/libstdc++-v3/testsuite/20_util/from_chars/7.cc new file mode 100644 index 00000000000..090ad7a87bb --- /dev/null +++ b/libstdc++-v3/testsuite/20_util/from_chars/7.cc @@ -0,0 +1,151 @@ +// Various testcases for binary64 hexfloat std::from_chars. +// { dg-do run { target c++17 } } +// { dg-require-effective-target ieee_floats } + +#include + +#include +#include +#include +#include +#include +#include + +struct testcase { + const char* input; + size_t correct_idx; + std::errc correct_ec; + double correct_value; +}; + +constexpr testcase testcases[] = { + { "1.fffffffffffff8p0", 18, {}, 0x1.fffffffffffff8p0 }, + { "0.fffffffffffff8p-1022", 22, std::errc{}, 0x0.fffffffffffffep-1022 }, + { "inf", 3, {}, std::numeric_limits::infinity() }, + { "inff", 3, {}, std::numeric_limits::infinity() }, + { "-inf", 4, {}, -std::numeric_limits::infinity() }, + { "-inff", 4, {}, -std::numeric_limits::infinity() }, + { "NAN", 3, {}, std::numeric_limits::quiet_NaN() }, + { "-NAN", 4, {}, std::numeric_limits::quiet_NaN() }, + { "NAN()", 5, {}, std::numeric_limits::quiet_NaN() }, + { "-NAN()", 6, {}, std::numeric_limits::quiet_NaN() }, + { "-NAN(test)", 10, {}, std::numeric_limits::quiet_NaN() }, + { "-NAN(test", 4, {}, std::numeric_limits::quiet_NaN() }, + { "-NAN(", 4, {}, std::numeric_limits::quiet_NaN() }, + { "0.000000000000001p-100000000000000000", 37, std::errc::result_out_of_range, 0 }, + { "-lol", 0, std::errc::invalid_argument, 1 }, + { " 0", 0, std::errc::invalid_argument, 1 }, + { "", 0, std::errc::invalid_argument, 0 }, + { "1", 1, {}, 1 }, + { "2", 1, {}, 2 }, + { "3", 1, {}, 3 }, + { "4", 1, {}, 4 }, + { "5", 1, {}, 5 }, + { "6", 1, {}, 6 }, + { "7", 1, {}, 7 }, + { "8", 1, {}, 8 }, + { "9", 1, {}, 9 }, + { "a", 1, {}, 0xa }, + { "b", 1, {}, 0xb }, + { "c", 1, {}, 0xc }, + { "d", 1, {}, 0xd }, + { "e", 1, {}, 0xe }, + { "f", 1, {}, 0xf }, + { "0.000000000000000000000000000000000000000000001p-1022", 53, + std::errc::result_out_of_range, 0 }, + { "0.00000000000000p-1022", 22, {}, 0 }, + { "0.00000000000009", 16, {}, 0x0.00000000000009p0 }, + { "0.0", 3, {}, 0 }, + { "1p10000000000000000000000", 25, std::errc::result_out_of_range, 0 }, + { "-0.0", 4, {}, -0.0 }, + { "0.00000000000000", 16, {}, 0 }, + { "0.0000000000000p-1022", 21, {}, 0 }, + { ".", 0, std::errc::invalid_argument, 0 }, + { "-.", 0, std::errc::invalid_argument, 0 }, + { "0", 1, {}, 0 }, + { "00", 2, {}, 0 }, + { "00.", 3, {}, 0 }, + { "0.", 2, {}, 0 }, + { "1.ffffFFFFFFFFFF", 16, {}, 0x2 }, + { "1.ffffffffffffff", 16, {}, 0x2 }, + { "1.00000000000029", 16, {}, 0x1.0000000000003p0 }, + { "0.00000000000008p-1022", 22, std::errc::result_out_of_range, 0 }, + { "1.fffffffffffffp-1023", 21, {}, 0x1p-1022 }, + { "1.fffffffffffff8p+1023", 22, std::errc::result_out_of_range, 0 }, + { "0.ffffffffffffe8p-1022", 22, {}, 0x0.ffffffffffffep-1022 }, + { "2.11111111111111", 16, {}, 0x1.0888888888889p+1 }, + { "1.1111111111111", 15, {}, 0x1.1111111111111p0 }, + { "1.11111111111111", 16, {}, 0x1.1111111111111p0 }, + { "1.11111111111118", 16, {}, 0x1.1111111111112p0 }, + { "1.11111111111128", 16, {}, 0x1.1111111111112p0 }, + { "1.1111111111112801", 18, {}, 0x1.1111111111113p0 }, + { "1.08888888888888", 16, {}, 0x1.0888888888888p0 }, + { "1.088888888888888", 17, {}, 0x1.0888888888889p0 }, + { "2.00000000000029", 16, {}, 0x2.0000000000002p0 }, + { "0.ffffffffffffep-1022", 21, {}, 0x0.ffffffffffffep-1022 }, + { "3.ffffffffffffep-1024", 21, {}, 0x1p-1022 }, + { "1.00000000000008p+0", 19, {}, 1 }, + { "1p-1023", 7, {}, 0x0.8p-1022 }, + { "1p-1022", 7, {}, 0x1p-1022 }, + { "1.1p-1033", 9, {}, 0x1.1p-1033 }, // 0.0022p-1022 + { "22p-1038", 8, {}, 0x1.1p-1033 }, + { "5", 1, {}, 0x5 }, + { "a", 1, {}, 0xa }, + { "1", 1, {}, 1.0 }, + { "1p1", 3, {}, 0x1p1 }, + { "1p-1", 4, {}, 0x1p-1 }, + { "0", 1, {}, 0.0 }, + { "A", 1, {}, 0xA }, + { "-1", 2, {}, -1.0 }, + { "-0", 2, {}, -0.0 }, + { "42", 2, {}, 0x42p0 }, + { "-42", 3, {}, -0x42p0 }, + { ".1", 2, {}, 0x0.1p0 }, + { "22p-1000", 8, {}, 0x22p-1000 }, + { ".0000008", 8, {}, 0x.0000008p0 }, + { ".0000008p-1022", 14, {}, 0x.0000008p-1022 }, + { "1p-1074", 7, {}, 0x.0000000000001p-1022 }, + { "9999999999999", 13, {}, 0x9999999999999p0 }, + { "1.000000000000a000", 18, {}, 0x1.000000000000ap0 }, + { "1.000000000000a001", 18, {}, 0x1.000000000000ap0 }, + { "1.000000000000a800", 18, {}, 0x1.000000000000ap0 }, + { "1.000000000000a801", 18, {}, 0x1.000000000000bp0 }, + { "1.000000000000b800", 18, {}, 0x1.000000000000cp0 }, + { "000000", 6, {}, 0x0 }, + { "1p", 1, {}, 0x1 }, + { "0p99999999999999999999", 22, {}, 0 }, + { "1p99999999999999999999", 22, std::errc::result_out_of_range, 0 }, + { "0p-99999999999999999999", 23, {}, 0 }, + { "1p-99999999999999999999", 23, std::errc::result_out_of_range, 0 }, + { "99999999999999999999999", 23, {}, 0x99999999999999999999999p0 }, + { "-1.fffffffffffffp-1023", 22, {}, -0x1p-1022 }, + { "1.337", 5, {}, 0x1.337p0 }, +}; + +void +test01() +{ + for (auto [input,correct_idx,correct_ec,correct_value] : testcases) + { + double value; + auto [ptr,ec] = std::from_chars(input, input+strlen(input), + value, std::chars_format::hex); + VERIFY( ptr == input + correct_idx ); + VERIFY( ec == correct_ec ); + if (ec == std::errc{}) + { + if (std::isnan(value) && std::isnan(value)) + ; + else + { + VERIFY( value == correct_value ); + VERIFY( !memcmp(&value, &correct_value, sizeof(value)) ); + } + } + } +} + +int main() +{ + test01(); +} From patchwork Sun Jan 16 18:06:48 2022 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 8bit X-Patchwork-Submitter: Patrick Palka X-Patchwork-Id: 50086 Return-Path: X-Original-To: patchwork@sourceware.org Delivered-To: patchwork@sourceware.org Received: from server2.sourceware.org (localhost [IPv6:::1]) by sourceware.org (Postfix) with ESMTP id 97DCA3858430 for ; Sun, 16 Jan 2022 18:15:56 +0000 (GMT) DKIM-Filter: OpenDKIM Filter v2.11.0 sourceware.org 97DCA3858430 DKIM-Signature: v=1; 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[24.228.8.148]) by smtp.gmail.com with ESMTPSA id o10sm7994149qtx.33.2022.01.16.10.06.55 (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Sun, 16 Jan 2022 10:06:56 -0800 (PST) To: gcc-patches@gcc.gnu.org Subject: [PATCH 2/6] libstdc++: Import the fast_float library Date: Sun, 16 Jan 2022 13:06:48 -0500 Message-Id: <20220116180652.3694791-2-ppalka@redhat.com> X-Mailer: git-send-email 2.35.0.rc1 In-Reply-To: <20220116180652.3694791-1-ppalka@redhat.com> References: <20220116180652.3694791-1-ppalka@redhat.com> MIME-Version: 1.0 X-Mimecast-Spam-Score: 0 X-Mimecast-Originator: redhat.com X-Spam-Status: No, score=-14.3 required=5.0 tests=BAYES_00, DKIMWL_WL_HIGH, DKIM_SIGNED, DKIM_VALID, DKIM_VALID_AU, DKIM_VALID_EF, GIT_PATCH_0, KAM_INFOUSMEBIZ, KAM_SHORT, RCVD_IN_DNSWL_LOW, RCVD_IN_MSPIKE_H3, RCVD_IN_MSPIKE_WL, SPF_HELO_NONE, SPF_NONE, TXREP autolearn=unavailable autolearn_force=no version=3.4.4 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on server2.sourceware.org X-BeenThere: gcc-patches@gcc.gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Gcc-patches mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-Patchwork-Original-From: Patrick Palka via Gcc-patches From: Patrick Palka Reply-To: Patrick Palka Cc: libstdc++@gcc.gnu.org Errors-To: gcc-patches-bounces+patchwork=sourceware.org@gcc.gnu.org Sender: "Gcc-patches" We're going to use the fast_float library in our (compiled-in) floating-point std::from_chars implementation for faster and more portable parsing of binary32/64 decimal strings. The single file fast_float.h is an amalgamation of the entire library, which can be (re)generated with the command python3 ./script/amalgamate.py --license=MIT \ > $GCC_SRC/libstdc++-v3/c++17/fast_float/fast_float.h [1]: https://github.com/fastfloat/fast_float libstdc++-v3/ChangeLog: * src/c++17/fast_float/LOCAL_PATCHES: New file. * src/c++17/fast_float/MERGE: New file. * src/c++17/fast_float/README.fd: New file, copied from the fast_float library sources. * src/c++17/fast_float/fast_float.h: New file, an amalgamation of the fast_float library. Signed-off-by: Patrick Palka --- .../src/c++17/fast_float/LOCAL_PATCHES | 0 libstdc++-v3/src/c++17/fast_float/MERGE | 4 + libstdc++-v3/src/c++17/fast_float/README.md | 218 ++ .../src/c++17/fast_float/fast_float.h | 2944 +++++++++++++++++ 4 files changed, 3166 insertions(+) create mode 100644 libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES create mode 100644 libstdc++-v3/src/c++17/fast_float/MERGE create mode 100644 libstdc++-v3/src/c++17/fast_float/README.md create mode 100644 libstdc++-v3/src/c++17/fast_float/fast_float.h diff --git a/libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES b/libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES new file mode 100644 index 00000000000..e69de29bb2d diff --git a/libstdc++-v3/src/c++17/fast_float/MERGE b/libstdc++-v3/src/c++17/fast_float/MERGE new file mode 100644 index 00000000000..43bdc3981c8 --- /dev/null +++ b/libstdc++-v3/src/c++17/fast_float/MERGE @@ -0,0 +1,4 @@ +d35368cae610b4edeec61cd41e4d2367a4d33f58 + +The first line of this file holds the git revision number of the +last merge done from the master library sources. diff --git a/libstdc++-v3/src/c++17/fast_float/README.md b/libstdc++-v3/src/c++17/fast_float/README.md new file mode 100644 index 00000000000..1e1c06d0a3e --- /dev/null +++ b/libstdc++-v3/src/c++17/fast_float/README.md @@ -0,0 +1,218 @@ +## fast_float number parsing library: 4x faster than strtod + +![Ubuntu 20.04 CI (GCC 9)](https://github.com/lemire/fast_float/workflows/Ubuntu%2020.04%20CI%20(GCC%209)/badge.svg) +![Ubuntu 18.04 CI (GCC 7)](https://github.com/lemire/fast_float/workflows/Ubuntu%2018.04%20CI%20(GCC%207)/badge.svg) +![Alpine Linux](https://github.com/lemire/fast_float/workflows/Alpine%20Linux/badge.svg) +![MSYS2-CI](https://github.com/lemire/fast_float/workflows/MSYS2-CI/badge.svg) +![VS16-CLANG-CI](https://github.com/lemire/fast_float/workflows/VS16-CLANG-CI/badge.svg) +[![VS16-CI](https://github.com/fastfloat/fast_float/actions/workflows/vs16-ci.yml/badge.svg)](https://github.com/fastfloat/fast_float/actions/workflows/vs16-ci.yml) + +The fast_float library provides fast header-only implementations for the C++ from_chars +functions for `float` and `double` types. These functions convert ASCII strings representing +decimal values (e.g., `1.3e10`) into binary types. We provide exact rounding (including +round to even). In our experience, these `fast_float` functions many times faster than comparable number-parsing functions from existing C++ standard libraries. + +Specifically, `fast_float` provides the following two functions with a C++17-like syntax (the library itself only requires C++11): + +```C++ +from_chars_result from_chars(const char* first, const char* last, float& value, ...); +from_chars_result from_chars(const char* first, const char* last, double& value, ...); +``` + +The return type (`from_chars_result`) is defined as the struct: +```C++ +struct from_chars_result { + const char* ptr; + std::errc ec; +}; +``` + +It parses the character sequence [first,last) for a number. It parses floating-point numbers expecting +a locale-independent format equivalent to the C++17 from_chars function. +The resulting floating-point value is the closest floating-point values (using either float or double), +using the "round to even" convention for values that would otherwise fall right in-between two values. +That is, we provide exact parsing according to the IEEE standard. + + +Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the +parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned +`ec` contains a representative error, otherwise the default (`std::errc()`) value is stored. + +The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`). + +It will parse infinity and nan values. + +Example: + +``` C++ +#include "fast_float/fast_float.h" +#include + +int main() { + const std::string input = "3.1416 xyz "; + double result; + auto answer = fast_float::from_chars(input.data(), input.data()+input.size(), result); + if(answer.ec != std::errc()) { std::cerr << "parsing failure\n"; return EXIT_FAILURE; } + std::cout << "parsed the number " << result << std::endl; + return EXIT_SUCCESS; +} +``` + + +Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of +the type `fast_float::chars_format`. It is a bitset value: we check whether +`fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set +to determine whether we allow the fixed point and scientific notation respectively. +The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`. + +The library seeks to follow the C++17 (see [20.19.3](http://eel.is/c++draft/charconv.from.chars).(7.1)) specification. +* The `from_chars` function does not skip leading white-space characters. +* [A leading `+` sign](https://en.cppreference.com/w/cpp/utility/from_chars) is forbidden. +* It is generally impossible to represent a decimal value exactly as binary floating-point number (`float` and `double` types). We seek the nearest value. We round to an even mantissa when we are in-between two binary floating-point numbers. + +Furthermore, we have the following restrictions: +* We only support `float` and `double` types at this time. +* We only support the decimal format: we do not support hexadecimal strings. +* For values that are either very large or very small (e.g., `1e9999`), we represent it using the infinity or negative infinity value. + +We support Visual Studio, macOS, Linux, freeBSD. We support big and little endian. We support 32-bit and 64-bit systems. + + + +## Using commas as decimal separator + + +The C++ standard stipulate that `from_chars` has to be locale-independent. In +particular, the decimal separator has to be the period (`.`). However, +some users still want to use the `fast_float` library with in a locale-dependent +manner. Using a separate function called `from_chars_advanced`, we allow the users +to pass a `parse_options` instance which contains a custom decimal separator (e.g., +the comma). You may use it as follows. + +```C++ +#include "fast_float/fast_float.h" +#include + +int main() { + const std::string input = "3,1416 xyz "; + double result; + fast_float::parse_options options{fast_float::chars_format::general, ','}; + auto answer = fast_float::from_chars_advanced(input.data(), input.data()+input.size(), result, options); + if((answer.ec != std::errc()) || ((result != 3.1416))) { std::cerr << "parsing failure\n"; return EXIT_FAILURE; } + std::cout << "parsed the number " << result << std::endl; + return EXIT_SUCCESS; +} +``` + + +## Reference + +- Daniel Lemire, [Number Parsing at a Gigabyte per Second](https://arxiv.org/abs/2101.11408), Software: Pratice and Experience 51 (8), 2021. + +## Other programming languages + +- [There is an R binding](https://github.com/eddelbuettel/rcppfastfloat) called `rcppfastfloat`. +- [There is a Rust port of the fast_float library](https://github.com/aldanor/fast-float-rust/) called `fast-float-rust`. +- [There is a Java port of the fast_float library](https://github.com/wrandelshofer/FastDoubleParser) called `FastDoubleParser`. +- [There is a C# port of the fast_float library](https://github.com/CarlVerret/csFastFloat) called `csFastFloat`. + + +## Relation With Other Work + +The fastfloat algorithm is part of the [LLVM standard libraries](https://github.com/llvm/llvm-project/commit/87c016078ad72c46505461e4ff8bfa04819fe7ba). + +The fast_float library provides a performance similar to that of the [fast_double_parser](https://github.com/lemire/fast_double_parser) library but using an updated algorithm reworked from the ground up, and while offering an API more in line with the expectations of C++ programmers. The fast_double_parser library is part of the [Microsoft LightGBM machine-learning framework](https://github.com/microsoft/LightGBM). + +## Users + +The fast_float library is used by [Apache Arrow](https://github.com/apache/arrow/pull/8494) where it multiplied the number parsing speed by two or three times. It is also used by [Yandex ClickHouse](https://github.com/ClickHouse/ClickHouse) and by [Google Jsonnet](https://github.com/google/jsonnet). + + +## How fast is it? + +It can parse random floating-point numbers at a speed of 1 GB/s on some systems. We find that it is often twice as fast as the best available competitor, and many times faster than many standard-library implementations. + + + +``` +$ ./build/benchmarks/benchmark +# parsing random integers in the range [0,1) +volume = 2.09808 MB +netlib : 271.18 MB/s (+/- 1.2 %) 12.93 Mfloat/s +doubleconversion : 225.35 MB/s (+/- 1.2 %) 10.74 Mfloat/s +strtod : 190.94 MB/s (+/- 1.6 %) 9.10 Mfloat/s +abseil : 430.45 MB/s (+/- 2.2 %) 20.52 Mfloat/s +fastfloat : 1042.38 MB/s (+/- 9.9 %) 49.68 Mfloat/s +``` + +See https://github.com/lemire/simple_fastfloat_benchmark for our benchmarking code. + + +## Video + +[![Go Systems 2020](http://img.youtube.com/vi/AVXgvlMeIm4/0.jpg)](http://www.youtube.com/watch?v=AVXgvlMeIm4)
+ +## Using as a CMake dependency + +This library is header-only by design. The CMake file provides the `fast_float` target +which is merely a pointer to the `include` directory. + +If you drop the `fast_float` repository in your CMake project, you should be able to use +it in this manner: + +```cmake +add_subdirectory(fast_float) +target_link_libraries(myprogram PUBLIC fast_float) +``` + +Or you may want to retrieve the dependency automatically if you have a sufficiently recent version of CMake (3.11 or better at least): + +```cmake +FetchContent_Declare( + fast_float + GIT_REPOSITORY https://github.com/lemire/fast_float.git + GIT_TAG tags/v1.1.2 + GIT_SHALLOW TRUE) + +FetchContent_MakeAvailable(fast_float) +target_link_libraries(myprogram PUBLIC fast_float) + +``` + +You should change the `GIT_TAG` line so that you recover the version you wish to use. + +## Using as single header + +The script `script/amalgamate.py` may be used to generate a single header +version of the library if so desired. +Just run the script from the root directory of this repository. +You can customize the license type and output file if desired as described in +the command line help. + +You may directly download automatically generated single-header files: + +https://github.com/fastfloat/fast_float/releases/download/v1.1.2/fast_float.h + +## Credit + +Though this work is inspired by many different people, this work benefited especially from exchanges with +Michael Eisel, who motivated the original research with his key insights, and with Nigel Tao who provided +invaluable feedback. Rémy Oudompheng first implemented a fast path we use in the case of long digits. + +The library includes code adapted from Google Wuffs (written by Nigel Tao) which was originally published +under the Apache 2.0 license. + +## License + + +Licensed under either of Apache License, Version +2.0 or MIT license at your option. + + +
+ + +Unless you explicitly state otherwise, any contribution intentionally submitted +for inclusion in this repository by you, as defined in the Apache-2.0 license, +shall be dual licensed as above, without any additional terms or conditions. + diff --git a/libstdc++-v3/src/c++17/fast_float/fast_float.h b/libstdc++-v3/src/c++17/fast_float/fast_float.h new file mode 100644 index 00000000000..8a45ebca8a8 --- /dev/null +++ b/libstdc++-v3/src/c++17/fast_float/fast_float.h @@ -0,0 +1,2944 @@ +// fast_float by Daniel Lemire +// fast_float by João Paulo Magalhaes +// +// with contributions from Eugene Golushkov +// with contributions from Maksim Kita +// with contributions from Marcin Wojdyr +// with contributions from Neal Richardson +// with contributions from Tim Paine +// with contributions from Fabio Pellacini +// +// MIT License Notice +// +// MIT License +// +// Copyright (c) 2021 The fast_float authors +// +// Permission is hereby granted, free of charge, to any +// person obtaining a copy of this software and associated +// documentation files (the "Software"), to deal in the +// Software without restriction, including without +// limitation the rights to use, copy, modify, merge, +// publish, distribute, sublicense, and/or sell copies of +// the Software, and to permit persons to whom the Software +// is furnished to do so, subject to the following +// conditions: +// +// The above copyright notice and this permission notice +// shall be included in all copies or substantial portions +// of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF +// ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED +// TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A +// PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT +// SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY +// CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION +// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR +// IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +// DEALINGS IN THE SOFTWARE. +// + +#ifndef FASTFLOAT_FAST_FLOAT_H +#define FASTFLOAT_FAST_FLOAT_H + +#include + +namespace fast_float { +enum chars_format { + scientific = 1<<0, + fixed = 1<<2, + hex = 1<<3, + general = fixed | scientific +}; + + +struct from_chars_result { + const char *ptr; + std::errc ec; +}; + +struct parse_options { + constexpr explicit parse_options(chars_format fmt = chars_format::general, + char dot = '.') + : format(fmt), decimal_point(dot) {} + + /** Which number formats are accepted */ + chars_format format; + /** The character used as decimal point */ + char decimal_point; +}; + +/** + * This function parses the character sequence [first,last) for a number. It parses floating-point numbers expecting + * a locale-indepent format equivalent to what is used by std::strtod in the default ("C") locale. + * The resulting floating-point value is the closest floating-point values (using either float or double), + * using the "round to even" convention for values that would otherwise fall right in-between two values. + * That is, we provide exact parsing according to the IEEE standard. + * + * Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the + * parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned + * `ec` contains a representative error, otherwise the default (`std::errc()`) value is stored. + * + * The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`). + * + * Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of + * the type `fast_float::chars_format`. It is a bitset value: we check whether + * `fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set + * to determine whether we allowe the fixed point and scientific notation respectively. + * The default is `fast_float::chars_format::general` which allows both `fixed` and `scientific`. + */ +template +from_chars_result from_chars(const char *first, const char *last, + T &value, chars_format fmt = chars_format::general) noexcept; + +/** + * Like from_chars, but accepts an `options` argument to govern number parsing. + */ +template +from_chars_result from_chars_advanced(const char *first, const char *last, + T &value, parse_options options) noexcept; + +} +#endif // FASTFLOAT_FAST_FLOAT_H + +#ifndef FASTFLOAT_FLOAT_COMMON_H +#define FASTFLOAT_FLOAT_COMMON_H + +#include +#include +#include +#include + +#if (defined(__x86_64) || defined(__x86_64__) || defined(_M_X64) \ + || defined(__amd64) || defined(__aarch64__) || defined(_M_ARM64) \ + || defined(__MINGW64__) \ + || defined(__s390x__) \ + || (defined(__ppc64__) || defined(__PPC64__) || defined(__ppc64le__) || defined(__PPC64LE__)) \ + || defined(__EMSCRIPTEN__)) +#define FASTFLOAT_64BIT +#elif (defined(__i386) || defined(__i386__) || defined(_M_IX86) \ + || defined(__arm__) || defined(_M_ARM) \ + || defined(__MINGW32__)) +#define FASTFLOAT_32BIT +#else + // Need to check incrementally, since SIZE_MAX is a size_t, avoid overflow. + // We can never tell the register width, but the SIZE_MAX is a good approximation. + // UINTPTR_MAX and INTPTR_MAX are optional, so avoid them for max portability. + #if SIZE_MAX == 0xffff + #error Unknown platform (16-bit, unsupported) + #elif SIZE_MAX == 0xffffffff + #define FASTFLOAT_32BIT + #elif SIZE_MAX == 0xffffffffffffffff + #define FASTFLOAT_64BIT + #else + #error Unknown platform (not 32-bit, not 64-bit?) + #endif +#endif + +#if ((defined(_WIN32) || defined(_WIN64)) && !defined(__clang__)) +#include +#endif + +#if defined(_MSC_VER) && !defined(__clang__) +#define FASTFLOAT_VISUAL_STUDIO 1 +#endif + +#ifdef _WIN32 +#define FASTFLOAT_IS_BIG_ENDIAN 0 +#else +#if defined(__APPLE__) || defined(__FreeBSD__) +#include +#elif defined(sun) || defined(__sun) +#include +#else +#include +#endif +# +#ifndef __BYTE_ORDER__ +// safe choice +#define FASTFLOAT_IS_BIG_ENDIAN 0 +#endif +# +#ifndef __ORDER_LITTLE_ENDIAN__ +// safe choice +#define FASTFLOAT_IS_BIG_ENDIAN 0 +#endif +# +#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ +#define FASTFLOAT_IS_BIG_ENDIAN 0 +#else +#define FASTFLOAT_IS_BIG_ENDIAN 1 +#endif +#endif + +#ifdef FASTFLOAT_VISUAL_STUDIO +#define fastfloat_really_inline __forceinline +#else +#define fastfloat_really_inline inline __attribute__((always_inline)) +#endif + +#ifndef FASTFLOAT_ASSERT +#define FASTFLOAT_ASSERT(x) { if (!(x)) abort(); } +#endif + +#ifndef FASTFLOAT_DEBUG_ASSERT +#include +#define FASTFLOAT_DEBUG_ASSERT(x) assert(x) +#endif + +// rust style `try!()` macro, or `?` operator +#define FASTFLOAT_TRY(x) { if (!(x)) return false; } + +namespace fast_float { + +// Compares two ASCII strings in a case insensitive manner. +inline bool fastfloat_strncasecmp(const char *input1, const char *input2, + size_t length) { + char running_diff{0}; + for (size_t i = 0; i < length; i++) { + running_diff |= (input1[i] ^ input2[i]); + } + return (running_diff == 0) || (running_diff == 32); +} + +#ifndef FLT_EVAL_METHOD +#error "FLT_EVAL_METHOD should be defined, please include cfloat." +#endif + +// a pointer and a length to a contiguous block of memory +template +struct span { + const T* ptr; + size_t length; + span(const T* _ptr, size_t _length) : ptr(_ptr), length(_length) {} + span() : ptr(nullptr), length(0) {} + + constexpr size_t len() const noexcept { + return length; + } + + const T& operator[](size_t index) const noexcept { + FASTFLOAT_DEBUG_ASSERT(index < length); + return ptr[index]; + } +}; + +struct value128 { + uint64_t low; + uint64_t high; + value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {} + value128() : low(0), high(0) {} +}; + +/* result might be undefined when input_num is zero */ +fastfloat_really_inline int leading_zeroes(uint64_t input_num) { + assert(input_num > 0); +#ifdef FASTFLOAT_VISUAL_STUDIO + #if defined(_M_X64) || defined(_M_ARM64) + unsigned long leading_zero = 0; + // Search the mask data from most significant bit (MSB) + // to least significant bit (LSB) for a set bit (1). + _BitScanReverse64(&leading_zero, input_num); + return (int)(63 - leading_zero); + #else + int last_bit = 0; + if(input_num & uint64_t(0xffffffff00000000)) input_num >>= 32, last_bit |= 32; + if(input_num & uint64_t( 0xffff0000)) input_num >>= 16, last_bit |= 16; + if(input_num & uint64_t( 0xff00)) input_num >>= 8, last_bit |= 8; + if(input_num & uint64_t( 0xf0)) input_num >>= 4, last_bit |= 4; + if(input_num & uint64_t( 0xc)) input_num >>= 2, last_bit |= 2; + if(input_num & uint64_t( 0x2)) input_num >>= 1, last_bit |= 1; + return 63 - last_bit; + #endif +#else + return __builtin_clzll(input_num); +#endif +} + +#ifdef FASTFLOAT_32BIT + +// slow emulation routine for 32-bit +fastfloat_really_inline uint64_t emulu(uint32_t x, uint32_t y) { + return x * (uint64_t)y; +} + +// slow emulation routine for 32-bit +#if !defined(__MINGW64__) +fastfloat_really_inline uint64_t _umul128(uint64_t ab, uint64_t cd, + uint64_t *hi) { + uint64_t ad = emulu((uint32_t)(ab >> 32), (uint32_t)cd); + uint64_t bd = emulu((uint32_t)ab, (uint32_t)cd); + uint64_t adbc = ad + emulu((uint32_t)ab, (uint32_t)(cd >> 32)); + uint64_t adbc_carry = !!(adbc < ad); + uint64_t lo = bd + (adbc << 32); + *hi = emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) + + (adbc_carry << 32) + !!(lo < bd); + return lo; +} +#endif // !__MINGW64__ + +#endif // FASTFLOAT_32BIT + + +// compute 64-bit a*b +fastfloat_really_inline value128 full_multiplication(uint64_t a, + uint64_t b) { + value128 answer; +#ifdef _M_ARM64 + // ARM64 has native support for 64-bit multiplications, no need to emulate + answer.high = __umulh(a, b); + answer.low = a * b; +#elif defined(FASTFLOAT_32BIT) || (defined(_WIN64) && !defined(__clang__)) + answer.low = _umul128(a, b, &answer.high); // _umul128 not available on ARM64 +#elif defined(FASTFLOAT_64BIT) + __uint128_t r = ((__uint128_t)a) * b; + answer.low = uint64_t(r); + answer.high = uint64_t(r >> 64); +#else + #error Not implemented +#endif + return answer; +} + +struct adjusted_mantissa { + uint64_t mantissa{0}; + int32_t power2{0}; // a negative value indicates an invalid result + adjusted_mantissa() = default; + bool operator==(const adjusted_mantissa &o) const { + return mantissa == o.mantissa && power2 == o.power2; + } + bool operator!=(const adjusted_mantissa &o) const { + return mantissa != o.mantissa || power2 != o.power2; + } +}; + +// Bias so we can get the real exponent with an invalid adjusted_mantissa. +constexpr static int32_t invalid_am_bias = -0x8000; + +constexpr static double powers_of_ten_double[] = { + 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, + 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22}; +constexpr static float powers_of_ten_float[] = {1e0, 1e1, 1e2, 1e3, 1e4, 1e5, + 1e6, 1e7, 1e8, 1e9, 1e10}; + +template struct binary_format { + static inline constexpr int mantissa_explicit_bits(); + static inline constexpr int minimum_exponent(); + static inline constexpr int infinite_power(); + static inline constexpr int sign_index(); + static inline constexpr int min_exponent_fast_path(); + static inline constexpr int max_exponent_fast_path(); + static inline constexpr int max_exponent_round_to_even(); + static inline constexpr int min_exponent_round_to_even(); + static inline constexpr uint64_t max_mantissa_fast_path(); + static inline constexpr int largest_power_of_ten(); + static inline constexpr int smallest_power_of_ten(); + static inline constexpr T exact_power_of_ten(int64_t power); + static inline constexpr size_t max_digits(); +}; + +template <> inline constexpr int binary_format::mantissa_explicit_bits() { + return 52; +} +template <> inline constexpr int binary_format::mantissa_explicit_bits() { + return 23; +} + +template <> inline constexpr int binary_format::max_exponent_round_to_even() { + return 23; +} + +template <> inline constexpr int binary_format::max_exponent_round_to_even() { + return 10; +} + +template <> inline constexpr int binary_format::min_exponent_round_to_even() { + return -4; +} + +template <> inline constexpr int binary_format::min_exponent_round_to_even() { + return -17; +} + +template <> inline constexpr int binary_format::minimum_exponent() { + return -1023; +} +template <> inline constexpr int binary_format::minimum_exponent() { + return -127; +} + +template <> inline constexpr int binary_format::infinite_power() { + return 0x7FF; +} +template <> inline constexpr int binary_format::infinite_power() { + return 0xFF; +} + +template <> inline constexpr int binary_format::sign_index() { return 63; } +template <> inline constexpr int binary_format::sign_index() { return 31; } + +template <> inline constexpr int binary_format::min_exponent_fast_path() { +#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0) + return 0; +#else + return -22; +#endif +} +template <> inline constexpr int binary_format::min_exponent_fast_path() { +#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0) + return 0; +#else + return -10; +#endif +} + +template <> inline constexpr int binary_format::max_exponent_fast_path() { + return 22; +} +template <> inline constexpr int binary_format::max_exponent_fast_path() { + return 10; +} + +template <> inline constexpr uint64_t binary_format::max_mantissa_fast_path() { + return uint64_t(2) << mantissa_explicit_bits(); +} +template <> inline constexpr uint64_t binary_format::max_mantissa_fast_path() { + return uint64_t(2) << mantissa_explicit_bits(); +} + +template <> +inline constexpr double binary_format::exact_power_of_ten(int64_t power) { + return powers_of_ten_double[power]; +} +template <> +inline constexpr float binary_format::exact_power_of_ten(int64_t power) { + + return powers_of_ten_float[power]; +} + + +template <> +inline constexpr int binary_format::largest_power_of_ten() { + return 308; +} +template <> +inline constexpr int binary_format::largest_power_of_ten() { + return 38; +} + +template <> +inline constexpr int binary_format::smallest_power_of_ten() { + return -342; +} +template <> +inline constexpr int binary_format::smallest_power_of_ten() { + return -65; +} + +template <> inline constexpr size_t binary_format::max_digits() { + return 769; +} +template <> inline constexpr size_t binary_format::max_digits() { + return 114; +} + +template +fastfloat_really_inline void to_float(bool negative, adjusted_mantissa am, T &value) { + uint64_t word = am.mantissa; + word |= uint64_t(am.power2) << binary_format::mantissa_explicit_bits(); + word = negative + ? word | (uint64_t(1) << binary_format::sign_index()) : word; +#if FASTFLOAT_IS_BIG_ENDIAN == 1 + if (std::is_same::value) { + ::memcpy(&value, (char *)&word + 4, sizeof(T)); // extract value at offset 4-7 if float on big-endian + } else { + ::memcpy(&value, &word, sizeof(T)); + } +#else + // For little-endian systems: + ::memcpy(&value, &word, sizeof(T)); +#endif +} + +} // namespace fast_float + +#endif + +#ifndef FASTFLOAT_ASCII_NUMBER_H +#define FASTFLOAT_ASCII_NUMBER_H + +#include +#include +#include +#include + + +namespace fast_float { + +// Next function can be micro-optimized, but compilers are entirely +// able to optimize it well. +fastfloat_really_inline bool is_integer(char c) noexcept { return c >= '0' && c <= '9'; } + +fastfloat_really_inline uint64_t byteswap(uint64_t val) { + return (val & 0xFF00000000000000) >> 56 + | (val & 0x00FF000000000000) >> 40 + | (val & 0x0000FF0000000000) >> 24 + | (val & 0x000000FF00000000) >> 8 + | (val & 0x00000000FF000000) << 8 + | (val & 0x0000000000FF0000) << 24 + | (val & 0x000000000000FF00) << 40 + | (val & 0x00000000000000FF) << 56; +} + +fastfloat_really_inline uint64_t read_u64(const char *chars) { + uint64_t val; + ::memcpy(&val, chars, sizeof(uint64_t)); +#if FASTFLOAT_IS_BIG_ENDIAN == 1 + // Need to read as-if the number was in little-endian order. + val = byteswap(val); +#endif + return val; +} + +fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) { +#if FASTFLOAT_IS_BIG_ENDIAN == 1 + // Need to read as-if the number was in little-endian order. + val = byteswap(val); +#endif + ::memcpy(chars, &val, sizeof(uint64_t)); +} + +// credit @aqrit +fastfloat_really_inline uint32_t parse_eight_digits_unrolled(uint64_t val) { + const uint64_t mask = 0x000000FF000000FF; + const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32) + const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32) + val -= 0x3030303030303030; + val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8; + val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32; + return uint32_t(val); +} + +fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) noexcept { + return parse_eight_digits_unrolled(read_u64(chars)); +} + +// credit @aqrit +fastfloat_really_inline bool is_made_of_eight_digits_fast(uint64_t val) noexcept { + return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) & + 0x8080808080808080)); +} + +fastfloat_really_inline bool is_made_of_eight_digits_fast(const char *chars) noexcept { + return is_made_of_eight_digits_fast(read_u64(chars)); +} + +typedef span byte_span; + +struct parsed_number_string { + int64_t exponent{0}; + uint64_t mantissa{0}; + const char *lastmatch{nullptr}; + bool negative{false}; + bool valid{false}; + bool too_many_digits{false}; + // contains the range of the significant digits + byte_span integer{}; // non-nullable + byte_span fraction{}; // nullable +}; + +// Assuming that you use no more than 19 digits, this will +// parse an ASCII string. +fastfloat_really_inline +parsed_number_string parse_number_string(const char *p, const char *pend, parse_options options) noexcept { + const chars_format fmt = options.format; + const char decimal_point = options.decimal_point; + + parsed_number_string answer; + answer.valid = false; + answer.too_many_digits = false; + answer.negative = (*p == '-'); + if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here + ++p; + if (p == pend) { + return answer; + } + if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot + return answer; + } + } + const char *const start_digits = p; + + uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad) + + while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) { + i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok + p += 8; + } + while ((p != pend) && is_integer(*p)) { + // a multiplication by 10 is cheaper than an arbitrary integer + // multiplication + i = 10 * i + + uint64_t(*p - '0'); // might overflow, we will handle the overflow later + ++p; + } + const char *const end_of_integer_part = p; + int64_t digit_count = int64_t(end_of_integer_part - start_digits); + answer.integer = byte_span(start_digits, size_t(digit_count)); + int64_t exponent = 0; + if ((p != pend) && (*p == decimal_point)) { + ++p; + const char* before = p; + // can occur at most twice without overflowing, but let it occur more, since + // for integers with many digits, digit parsing is the primary bottleneck. + while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) { + i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok + p += 8; + } + while ((p != pend) && is_integer(*p)) { + uint8_t digit = uint8_t(*p - '0'); + ++p; + i = i * 10 + digit; // in rare cases, this will overflow, but that's ok + } + exponent = before - p; + answer.fraction = byte_span(before, size_t(p - before)); + digit_count -= exponent; + } + // we must have encountered at least one integer! + if (digit_count == 0) { + return answer; + } + int64_t exp_number = 0; // explicit exponential part + if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) { + const char * location_of_e = p; + ++p; + bool neg_exp = false; + if ((p != pend) && ('-' == *p)) { + neg_exp = true; + ++p; + } else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1) + ++p; + } + if ((p == pend) || !is_integer(*p)) { + if(!(fmt & chars_format::fixed)) { + // We are in error. + return answer; + } + // Otherwise, we will be ignoring the 'e'. + p = location_of_e; + } else { + while ((p != pend) && is_integer(*p)) { + uint8_t digit = uint8_t(*p - '0'); + if (exp_number < 0x10000000) { + exp_number = 10 * exp_number + digit; + } + ++p; + } + if(neg_exp) { exp_number = - exp_number; } + exponent += exp_number; + } + } else { + // If it scientific and not fixed, we have to bail out. + if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; } + } + answer.lastmatch = p; + answer.valid = true; + + // 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. + // + // We can deal with up to 19 digits. + if (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. + // We need to be mindful of the case where we only have zeroes... + // E.g., 0.000000000...000. + const char *start = start_digits; + while ((start != pend) && (*start == '0' || *start == decimal_point)) { + if(*start == '0') { digit_count --; } + start++; + } + if (digit_count > 19) { + answer.too_many_digits = true; + // Let us start again, this time, avoiding overflows. + // We don't need to check if is_integer, since we use the + // pre-tokenized spans from above. + i = 0; + p = answer.integer.ptr; + const char* int_end = p + answer.integer.len(); + const uint64_t minimal_nineteen_digit_integer{1000000000000000000}; + while((i < minimal_nineteen_digit_integer) && (p != int_end)) { + i = i * 10 + uint64_t(*p - '0'); + ++p; + } + if (i >= minimal_nineteen_digit_integer) { // We have a big integers + exponent = end_of_integer_part - p + exp_number; + } else { // We have a value with a fractional component. + p = answer.fraction.ptr; + const char* frac_end = p + answer.fraction.len(); + while((i < minimal_nineteen_digit_integer) && (p != frac_end)) { + i = i * 10 + uint64_t(*p - '0'); + ++p; + } + exponent = answer.fraction.ptr - p + exp_number; + } + // We have now corrected both exponent and i, to a truncated value + } + } + answer.exponent = exponent; + answer.mantissa = i; + return answer; +} + +} // namespace fast_float + +#endif + +#ifndef FASTFLOAT_FAST_TABLE_H +#define FASTFLOAT_FAST_TABLE_H + +#include + +namespace fast_float { + +/** + * When mapping numbers from decimal to binary, + * we go from w * 10^q to m * 2^p but we have + * 10^q = 5^q * 2^q, so effectively + * we are trying to match + * w * 2^q * 5^q to m * 2^p. Thus the powers of two + * are not a concern since they can be represented + * exactly using the binary notation, only the powers of five + * affect the binary significand. + */ + +/** + * The smallest non-zero float (binary64) is 2^−1074. + * We take as input numbers of the form w x 10^q where w < 2^64. + * We have that w * 10^-343 < 2^(64-344) 5^-343 < 2^-1076. + * However, we have that + * (2^64-1) * 10^-342 = (2^64-1) * 2^-342 * 5^-342 > 2^−1074. + * Thus it is possible for a number of the form w * 10^-342 where + * w is a 64-bit value to be a non-zero floating-point number. + ********* + * Any number of form w * 10^309 where w>= 1 is going to be + * infinite in binary64 so we never need to worry about powers + * of 5 greater than 308. + */ +template +struct powers_template { + +constexpr static int smallest_power_of_five = binary_format::smallest_power_of_ten(); +constexpr static int largest_power_of_five = binary_format::largest_power_of_ten(); +constexpr static int number_of_entries = 2 * (largest_power_of_five - smallest_power_of_five + 1); +// Powers of five from 5^-342 all the way to 5^308 rounded toward one. +static const uint64_t power_of_five_128[number_of_entries]; +}; + +template +const uint64_t powers_template::power_of_five_128[number_of_entries] = { + 0xeef453d6923bd65a,0x113faa2906a13b3f, + 0x9558b4661b6565f8,0x4ac7ca59a424c507, + 0xbaaee17fa23ebf76,0x5d79bcf00d2df649, + 0xe95a99df8ace6f53,0xf4d82c2c107973dc, + 0x91d8a02bb6c10594,0x79071b9b8a4be869, + 0xb64ec836a47146f9,0x9748e2826cdee284, + 0xe3e27a444d8d98b7,0xfd1b1b2308169b25, + 0x8e6d8c6ab0787f72,0xfe30f0f5e50e20f7, + 0xb208ef855c969f4f,0xbdbd2d335e51a935, + 0xde8b2b66b3bc4723,0xad2c788035e61382, + 0x8b16fb203055ac76,0x4c3bcb5021afcc31, + 0xaddcb9e83c6b1793,0xdf4abe242a1bbf3d, + 0xd953e8624b85dd78,0xd71d6dad34a2af0d, + 0x87d4713d6f33aa6b,0x8672648c40e5ad68, + 0xa9c98d8ccb009506,0x680efdaf511f18c2, + 0xd43bf0effdc0ba48,0x212bd1b2566def2, + 0x84a57695fe98746d,0x14bb630f7604b57, + 0xa5ced43b7e3e9188,0x419ea3bd35385e2d, + 0xcf42894a5dce35ea,0x52064cac828675b9, + 0x818995ce7aa0e1b2,0x7343efebd1940993, + 0xa1ebfb4219491a1f,0x1014ebe6c5f90bf8, + 0xca66fa129f9b60a6,0xd41a26e077774ef6, + 0xfd00b897478238d0,0x8920b098955522b4, + 0x9e20735e8cb16382,0x55b46e5f5d5535b0, + 0xc5a890362fddbc62,0xeb2189f734aa831d, + 0xf712b443bbd52b7b,0xa5e9ec7501d523e4, + 0x9a6bb0aa55653b2d,0x47b233c92125366e, + 0xc1069cd4eabe89f8,0x999ec0bb696e840a, + 0xf148440a256e2c76,0xc00670ea43ca250d, + 0x96cd2a865764dbca,0x380406926a5e5728, + 0xbc807527ed3e12bc,0xc605083704f5ecf2, + 0xeba09271e88d976b,0xf7864a44c633682e, + 0x93445b8731587ea3,0x7ab3ee6afbe0211d, + 0xb8157268fdae9e4c,0x5960ea05bad82964, + 0xe61acf033d1a45df,0x6fb92487298e33bd, + 0x8fd0c16206306bab,0xa5d3b6d479f8e056, + 0xb3c4f1ba87bc8696,0x8f48a4899877186c, + 0xe0b62e2929aba83c,0x331acdabfe94de87, + 0x8c71dcd9ba0b4925,0x9ff0c08b7f1d0b14, + 0xaf8e5410288e1b6f,0x7ecf0ae5ee44dd9, + 0xdb71e91432b1a24a,0xc9e82cd9f69d6150, + 0x892731ac9faf056e,0xbe311c083a225cd2, + 0xab70fe17c79ac6ca,0x6dbd630a48aaf406, + 0xd64d3d9db981787d,0x92cbbccdad5b108, + 0x85f0468293f0eb4e,0x25bbf56008c58ea5, + 0xa76c582338ed2621,0xaf2af2b80af6f24e, + 0xd1476e2c07286faa,0x1af5af660db4aee1, + 0x82cca4db847945ca,0x50d98d9fc890ed4d, + 0xa37fce126597973c,0xe50ff107bab528a0, + 0xcc5fc196fefd7d0c,0x1e53ed49a96272c8, + 0xff77b1fcbebcdc4f,0x25e8e89c13bb0f7a, + 0x9faacf3df73609b1,0x77b191618c54e9ac, + 0xc795830d75038c1d,0xd59df5b9ef6a2417, + 0xf97ae3d0d2446f25,0x4b0573286b44ad1d, + 0x9becce62836ac577,0x4ee367f9430aec32, + 0xc2e801fb244576d5,0x229c41f793cda73f, + 0xf3a20279ed56d48a,0x6b43527578c1110f, + 0x9845418c345644d6,0x830a13896b78aaa9, + 0xbe5691ef416bd60c,0x23cc986bc656d553, + 0xedec366b11c6cb8f,0x2cbfbe86b7ec8aa8, + 0x94b3a202eb1c3f39,0x7bf7d71432f3d6a9, + 0xb9e08a83a5e34f07,0xdaf5ccd93fb0cc53, + 0xe858ad248f5c22c9,0xd1b3400f8f9cff68, + 0x91376c36d99995be,0x23100809b9c21fa1, + 0xb58547448ffffb2d,0xabd40a0c2832a78a, + 0xe2e69915b3fff9f9,0x16c90c8f323f516c, + 0x8dd01fad907ffc3b,0xae3da7d97f6792e3, + 0xb1442798f49ffb4a,0x99cd11cfdf41779c, + 0xdd95317f31c7fa1d,0x40405643d711d583, + 0x8a7d3eef7f1cfc52,0x482835ea666b2572, + 0xad1c8eab5ee43b66,0xda3243650005eecf, + 0xd863b256369d4a40,0x90bed43e40076a82, + 0x873e4f75e2224e68,0x5a7744a6e804a291, + 0xa90de3535aaae202,0x711515d0a205cb36, + 0xd3515c2831559a83,0xd5a5b44ca873e03, + 0x8412d9991ed58091,0xe858790afe9486c2, + 0xa5178fff668ae0b6,0x626e974dbe39a872, + 0xce5d73ff402d98e3,0xfb0a3d212dc8128f, + 0x80fa687f881c7f8e,0x7ce66634bc9d0b99, + 0xa139029f6a239f72,0x1c1fffc1ebc44e80, + 0xc987434744ac874e,0xa327ffb266b56220, + 0xfbe9141915d7a922,0x4bf1ff9f0062baa8, + 0x9d71ac8fada6c9b5,0x6f773fc3603db4a9, + 0xc4ce17b399107c22,0xcb550fb4384d21d3, + 0xf6019da07f549b2b,0x7e2a53a146606a48, + 0x99c102844f94e0fb,0x2eda7444cbfc426d, + 0xc0314325637a1939,0xfa911155fefb5308, + 0xf03d93eebc589f88,0x793555ab7eba27ca, + 0x96267c7535b763b5,0x4bc1558b2f3458de, + 0xbbb01b9283253ca2,0x9eb1aaedfb016f16, + 0xea9c227723ee8bcb,0x465e15a979c1cadc, + 0x92a1958a7675175f,0xbfacd89ec191ec9, + 0xb749faed14125d36,0xcef980ec671f667b, + 0xe51c79a85916f484,0x82b7e12780e7401a, + 0x8f31cc0937ae58d2,0xd1b2ecb8b0908810, + 0xb2fe3f0b8599ef07,0x861fa7e6dcb4aa15, + 0xdfbdcece67006ac9,0x67a791e093e1d49a, + 0x8bd6a141006042bd,0xe0c8bb2c5c6d24e0, + 0xaecc49914078536d,0x58fae9f773886e18, + 0xda7f5bf590966848,0xaf39a475506a899e, + 0x888f99797a5e012d,0x6d8406c952429603, + 0xaab37fd7d8f58178,0xc8e5087ba6d33b83, + 0xd5605fcdcf32e1d6,0xfb1e4a9a90880a64, + 0x855c3be0a17fcd26,0x5cf2eea09a55067f, + 0xa6b34ad8c9dfc06f,0xf42faa48c0ea481e, + 0xd0601d8efc57b08b,0xf13b94daf124da26, + 0x823c12795db6ce57,0x76c53d08d6b70858, + 0xa2cb1717b52481ed,0x54768c4b0c64ca6e, + 0xcb7ddcdda26da268,0xa9942f5dcf7dfd09, + 0xfe5d54150b090b02,0xd3f93b35435d7c4c, + 0x9efa548d26e5a6e1,0xc47bc5014a1a6daf, + 0xc6b8e9b0709f109a,0x359ab6419ca1091b, + 0xf867241c8cc6d4c0,0xc30163d203c94b62, + 0x9b407691d7fc44f8,0x79e0de63425dcf1d, + 0xc21094364dfb5636,0x985915fc12f542e4, + 0xf294b943e17a2bc4,0x3e6f5b7b17b2939d, + 0x979cf3ca6cec5b5a,0xa705992ceecf9c42, + 0xbd8430bd08277231,0x50c6ff782a838353, + 0xece53cec4a314ebd,0xa4f8bf5635246428, + 0x940f4613ae5ed136,0x871b7795e136be99, + 0xb913179899f68584,0x28e2557b59846e3f, + 0xe757dd7ec07426e5,0x331aeada2fe589cf, + 0x9096ea6f3848984f,0x3ff0d2c85def7621, + 0xb4bca50b065abe63,0xfed077a756b53a9, + 0xe1ebce4dc7f16dfb,0xd3e8495912c62894, + 0x8d3360f09cf6e4bd,0x64712dd7abbbd95c, + 0xb080392cc4349dec,0xbd8d794d96aacfb3, + 0xdca04777f541c567,0xecf0d7a0fc5583a0, + 0x89e42caaf9491b60,0xf41686c49db57244, + 0xac5d37d5b79b6239,0x311c2875c522ced5, + 0xd77485cb25823ac7,0x7d633293366b828b, + 0x86a8d39ef77164bc,0xae5dff9c02033197, + 0xa8530886b54dbdeb,0xd9f57f830283fdfc, + 0xd267caa862a12d66,0xd072df63c324fd7b, + 0x8380dea93da4bc60,0x4247cb9e59f71e6d, + 0xa46116538d0deb78,0x52d9be85f074e608, + 0xcd795be870516656,0x67902e276c921f8b, + 0x806bd9714632dff6,0xba1cd8a3db53b6, + 0xa086cfcd97bf97f3,0x80e8a40eccd228a4, + 0xc8a883c0fdaf7df0,0x6122cd128006b2cd, + 0xfad2a4b13d1b5d6c,0x796b805720085f81, + 0x9cc3a6eec6311a63,0xcbe3303674053bb0, + 0xc3f490aa77bd60fc,0xbedbfc4411068a9c, + 0xf4f1b4d515acb93b,0xee92fb5515482d44, + 0x991711052d8bf3c5,0x751bdd152d4d1c4a, + 0xbf5cd54678eef0b6,0xd262d45a78a0635d, + 0xef340a98172aace4,0x86fb897116c87c34, + 0x9580869f0e7aac0e,0xd45d35e6ae3d4da0, + 0xbae0a846d2195712,0x8974836059cca109, + 0xe998d258869facd7,0x2bd1a438703fc94b, + 0x91ff83775423cc06,0x7b6306a34627ddcf, + 0xb67f6455292cbf08,0x1a3bc84c17b1d542, + 0xe41f3d6a7377eeca,0x20caba5f1d9e4a93, + 0x8e938662882af53e,0x547eb47b7282ee9c, + 0xb23867fb2a35b28d,0xe99e619a4f23aa43, + 0xdec681f9f4c31f31,0x6405fa00e2ec94d4, + 0x8b3c113c38f9f37e,0xde83bc408dd3dd04, + 0xae0b158b4738705e,0x9624ab50b148d445, + 0xd98ddaee19068c76,0x3badd624dd9b0957, + 0x87f8a8d4cfa417c9,0xe54ca5d70a80e5d6, + 0xa9f6d30a038d1dbc,0x5e9fcf4ccd211f4c, + 0xd47487cc8470652b,0x7647c3200069671f, + 0x84c8d4dfd2c63f3b,0x29ecd9f40041e073, + 0xa5fb0a17c777cf09,0xf468107100525890, + 0xcf79cc9db955c2cc,0x7182148d4066eeb4, + 0x81ac1fe293d599bf,0xc6f14cd848405530, + 0xa21727db38cb002f,0xb8ada00e5a506a7c, + 0xca9cf1d206fdc03b,0xa6d90811f0e4851c, + 0xfd442e4688bd304a,0x908f4a166d1da663, + 0x9e4a9cec15763e2e,0x9a598e4e043287fe, + 0xc5dd44271ad3cdba,0x40eff1e1853f29fd, + 0xf7549530e188c128,0xd12bee59e68ef47c, + 0x9a94dd3e8cf578b9,0x82bb74f8301958ce, + 0xc13a148e3032d6e7,0xe36a52363c1faf01, + 0xf18899b1bc3f8ca1,0xdc44e6c3cb279ac1, + 0x96f5600f15a7b7e5,0x29ab103a5ef8c0b9, + 0xbcb2b812db11a5de,0x7415d448f6b6f0e7, + 0xebdf661791d60f56,0x111b495b3464ad21, + 0x936b9fcebb25c995,0xcab10dd900beec34, + 0xb84687c269ef3bfb,0x3d5d514f40eea742, + 0xe65829b3046b0afa,0xcb4a5a3112a5112, + 0x8ff71a0fe2c2e6dc,0x47f0e785eaba72ab, + 0xb3f4e093db73a093,0x59ed216765690f56, + 0xe0f218b8d25088b8,0x306869c13ec3532c, + 0x8c974f7383725573,0x1e414218c73a13fb, + 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0xada72ccc20054ae9,0xaf561aa79a10ae6a, + 0xd910f7ff28069da4,0x1b2ba1518094da04, + 0x87aa9aff79042286,0x90fb44d2f05d0842, + 0xa99541bf57452b28,0x353a1607ac744a53, + 0xd3fa922f2d1675f2,0x42889b8997915ce8, + 0x847c9b5d7c2e09b7,0x69956135febada11, + 0xa59bc234db398c25,0x43fab9837e699095, + 0xcf02b2c21207ef2e,0x94f967e45e03f4bb, + 0x8161afb94b44f57d,0x1d1be0eebac278f5, + 0xa1ba1ba79e1632dc,0x6462d92a69731732, + 0xca28a291859bbf93,0x7d7b8f7503cfdcfe, + 0xfcb2cb35e702af78,0x5cda735244c3d43e, + 0x9defbf01b061adab,0x3a0888136afa64a7, + 0xc56baec21c7a1916,0x88aaa1845b8fdd0, + 0xf6c69a72a3989f5b,0x8aad549e57273d45, + 0x9a3c2087a63f6399,0x36ac54e2f678864b, + 0xc0cb28a98fcf3c7f,0x84576a1bb416a7dd, + 0xf0fdf2d3f3c30b9f,0x656d44a2a11c51d5, + 0x969eb7c47859e743,0x9f644ae5a4b1b325, + 0xbc4665b596706114,0x873d5d9f0dde1fee, + 0xeb57ff22fc0c7959,0xa90cb506d155a7ea, + 0x9316ff75dd87cbd8,0x9a7f12442d588f2, + 0xb7dcbf5354e9bece,0xc11ed6d538aeb2f, + 0xe5d3ef282a242e81,0x8f1668c8a86da5fa, + 0x8fa475791a569d10,0xf96e017d694487bc, + 0xb38d92d760ec4455,0x37c981dcc395a9ac, + 0xe070f78d3927556a,0x85bbe253f47b1417, + 0x8c469ab843b89562,0x93956d7478ccec8e, + 0xaf58416654a6babb,0x387ac8d1970027b2, + 0xdb2e51bfe9d0696a,0x6997b05fcc0319e, + 0x88fcf317f22241e2,0x441fece3bdf81f03, + 0xab3c2fddeeaad25a,0xd527e81cad7626c3, + 0xd60b3bd56a5586f1,0x8a71e223d8d3b074, + 0x85c7056562757456,0xf6872d5667844e49, + 0xa738c6bebb12d16c,0xb428f8ac016561db, + 0xd106f86e69d785c7,0xe13336d701beba52, + 0x82a45b450226b39c,0xecc0024661173473, + 0xa34d721642b06084,0x27f002d7f95d0190, + 0xcc20ce9bd35c78a5,0x31ec038df7b441f4, + 0xff290242c83396ce,0x7e67047175a15271, + 0x9f79a169bd203e41,0xf0062c6e984d386, + 0xc75809c42c684dd1,0x52c07b78a3e60868, + 0xf92e0c3537826145,0xa7709a56ccdf8a82, + 0x9bbcc7a142b17ccb,0x88a66076400bb691, + 0xc2abf989935ddbfe,0x6acff893d00ea435, + 0xf356f7ebf83552fe,0x583f6b8c4124d43, + 0x98165af37b2153de,0xc3727a337a8b704a, + 0xbe1bf1b059e9a8d6,0x744f18c0592e4c5c, + 0xeda2ee1c7064130c,0x1162def06f79df73, + 0x9485d4d1c63e8be7,0x8addcb5645ac2ba8, + 0xb9a74a0637ce2ee1,0x6d953e2bd7173692, + 0xe8111c87c5c1ba99,0xc8fa8db6ccdd0437, + 0x910ab1d4db9914a0,0x1d9c9892400a22a2, + 0xb54d5e4a127f59c8,0x2503beb6d00cab4b, + 0xe2a0b5dc971f303a,0x2e44ae64840fd61d, + 0x8da471a9de737e24,0x5ceaecfed289e5d2, + 0xb10d8e1456105dad,0x7425a83e872c5f47, + 0xdd50f1996b947518,0xd12f124e28f77719, + 0x8a5296ffe33cc92f,0x82bd6b70d99aaa6f, + 0xace73cbfdc0bfb7b,0x636cc64d1001550b, + 0xd8210befd30efa5a,0x3c47f7e05401aa4e, + 0x8714a775e3e95c78,0x65acfaec34810a71, + 0xa8d9d1535ce3b396,0x7f1839a741a14d0d, + 0xd31045a8341ca07c,0x1ede48111209a050, + 0x83ea2b892091e44d,0x934aed0aab460432, + 0xa4e4b66b68b65d60,0xf81da84d5617853f, + 0xce1de40642e3f4b9,0x36251260ab9d668e, + 0x80d2ae83e9ce78f3,0xc1d72b7c6b426019, + 0xa1075a24e4421730,0xb24cf65b8612f81f, + 0xc94930ae1d529cfc,0xdee033f26797b627, + 0xfb9b7cd9a4a7443c,0x169840ef017da3b1, + 0x9d412e0806e88aa5,0x8e1f289560ee864e, + 0xc491798a08a2ad4e,0xf1a6f2bab92a27e2, + 0xf5b5d7ec8acb58a2,0xae10af696774b1db, + 0x9991a6f3d6bf1765,0xacca6da1e0a8ef29, + 0xbff610b0cc6edd3f,0x17fd090a58d32af3, + 0xeff394dcff8a948e,0xddfc4b4cef07f5b0, + 0x95f83d0a1fb69cd9,0x4abdaf101564f98e, + 0xbb764c4ca7a4440f,0x9d6d1ad41abe37f1, + 0xea53df5fd18d5513,0x84c86189216dc5ed, + 0x92746b9be2f8552c,0x32fd3cf5b4e49bb4, + 0xb7118682dbb66a77,0x3fbc8c33221dc2a1, + 0xe4d5e82392a40515,0xfabaf3feaa5334a, + 0x8f05b1163ba6832d,0x29cb4d87f2a7400e, + 0xb2c71d5bca9023f8,0x743e20e9ef511012, + 0xdf78e4b2bd342cf6,0x914da9246b255416, + 0x8bab8eefb6409c1a,0x1ad089b6c2f7548e, + 0xae9672aba3d0c320,0xa184ac2473b529b1, + 0xda3c0f568cc4f3e8,0xc9e5d72d90a2741e, + 0x8865899617fb1871,0x7e2fa67c7a658892, + 0xaa7eebfb9df9de8d,0xddbb901b98feeab7, + 0xd51ea6fa85785631,0x552a74227f3ea565, + 0x8533285c936b35de,0xd53a88958f87275f, + 0xa67ff273b8460356,0x8a892abaf368f137, + 0xd01fef10a657842c,0x2d2b7569b0432d85, + 0x8213f56a67f6b29b,0x9c3b29620e29fc73, + 0xa298f2c501f45f42,0x8349f3ba91b47b8f, + 0xcb3f2f7642717713,0x241c70a936219a73, + 0xfe0efb53d30dd4d7,0xed238cd383aa0110, + 0x9ec95d1463e8a506,0xf4363804324a40aa, + 0xc67bb4597ce2ce48,0xb143c6053edcd0d5, + 0xf81aa16fdc1b81da,0xdd94b7868e94050a, + 0x9b10a4e5e9913128,0xca7cf2b4191c8326, + 0xc1d4ce1f63f57d72,0xfd1c2f611f63a3f0, + 0xf24a01a73cf2dccf,0xbc633b39673c8cec, + 0x976e41088617ca01,0xd5be0503e085d813, + 0xbd49d14aa79dbc82,0x4b2d8644d8a74e18, + 0xec9c459d51852ba2,0xddf8e7d60ed1219e, + 0x93e1ab8252f33b45,0xcabb90e5c942b503, + 0xb8da1662e7b00a17,0x3d6a751f3b936243, + 0xe7109bfba19c0c9d,0xcc512670a783ad4, + 0x906a617d450187e2,0x27fb2b80668b24c5, + 0xb484f9dc9641e9da,0xb1f9f660802dedf6, + 0xe1a63853bbd26451,0x5e7873f8a0396973, + 0x8d07e33455637eb2,0xdb0b487b6423e1e8, + 0xb049dc016abc5e5f,0x91ce1a9a3d2cda62, + 0xdc5c5301c56b75f7,0x7641a140cc7810fb, + 0x89b9b3e11b6329ba,0xa9e904c87fcb0a9d, + 0xac2820d9623bf429,0x546345fa9fbdcd44, + 0xd732290fbacaf133,0xa97c177947ad4095, + 0x867f59a9d4bed6c0,0x49ed8eabcccc485d, + 0xa81f301449ee8c70,0x5c68f256bfff5a74, + 0xd226fc195c6a2f8c,0x73832eec6fff3111, + 0x83585d8fd9c25db7,0xc831fd53c5ff7eab, + 0xa42e74f3d032f525,0xba3e7ca8b77f5e55, + 0xcd3a1230c43fb26f,0x28ce1bd2e55f35eb, + 0x80444b5e7aa7cf85,0x7980d163cf5b81b3, + 0xa0555e361951c366,0xd7e105bcc332621f, + 0xc86ab5c39fa63440,0x8dd9472bf3fefaa7, + 0xfa856334878fc150,0xb14f98f6f0feb951, + 0x9c935e00d4b9d8d2,0x6ed1bf9a569f33d3, + 0xc3b8358109e84f07,0xa862f80ec4700c8, + 0xf4a642e14c6262c8,0xcd27bb612758c0fa, + 0x98e7e9cccfbd7dbd,0x8038d51cb897789c, + 0xbf21e44003acdd2c,0xe0470a63e6bd56c3, + 0xeeea5d5004981478,0x1858ccfce06cac74, + 0x95527a5202df0ccb,0xf37801e0c43ebc8, + 0xbaa718e68396cffd,0xd30560258f54e6ba, + 0xe950df20247c83fd,0x47c6b82ef32a2069, + 0x91d28b7416cdd27e,0x4cdc331d57fa5441, + 0xb6472e511c81471d,0xe0133fe4adf8e952, + 0xe3d8f9e563a198e5,0x58180fddd97723a6, + 0x8e679c2f5e44ff8f,0x570f09eaa7ea7648,}; +using powers = powers_template<>; + +} + +#endif + +#ifndef FASTFLOAT_DECIMAL_TO_BINARY_H +#define FASTFLOAT_DECIMAL_TO_BINARY_H + +#include +#include +#include +#include +#include +#include + +namespace fast_float { + +// This will compute or rather approximate w * 5**q and return a pair of 64-bit words approximating +// the result, with the "high" part corresponding to the most significant bits and the +// low part corresponding to the least significant bits. +// +template +fastfloat_really_inline +value128 compute_product_approximation(int64_t q, uint64_t w) { + const int index = 2 * int(q - powers::smallest_power_of_five); + // For small values of q, e.g., q in [0,27], the answer is always exact because + // The line value128 firstproduct = full_multiplication(w, power_of_five_128[index]); + // gives the exact answer. + value128 firstproduct = full_multiplication(w, powers::power_of_five_128[index]); + static_assert((bit_precision >= 0) && (bit_precision <= 64), " precision should be in (0,64]"); + constexpr uint64_t precision_mask = (bit_precision < 64) ? + (uint64_t(0xFFFFFFFFFFFFFFFF) >> bit_precision) + : uint64_t(0xFFFFFFFFFFFFFFFF); + if((firstproduct.high & precision_mask) == precision_mask) { // could further guard with (lower + w < lower) + // regarding the second product, we only need secondproduct.high, but our expectation is that the compiler will optimize this extra work away if needed. + value128 secondproduct = full_multiplication(w, powers::power_of_five_128[index + 1]); + firstproduct.low += secondproduct.high; + if(secondproduct.high > firstproduct.low) { + firstproduct.high++; + } + } + return firstproduct; +} + +namespace detail { +/** + * For q in (0,350), we have that + * f = (((152170 + 65536) * q ) >> 16); + * is equal to + * floor(p) + q + * where + * p = log(5**q)/log(2) = q * log(5)/log(2) + * + * For negative values of q in (-400,0), we have that + * f = (((152170 + 65536) * q ) >> 16); + * is equal to + * -ceil(p) + q + * where + * p = log(5**-q)/log(2) = -q * log(5)/log(2) + */ + constexpr fastfloat_really_inline int32_t power(int32_t q) noexcept { + return (((152170 + 65536) * q) >> 16) + 63; + } +} // namespace detail + +// create an adjusted mantissa, biased by the invalid power2 +// for significant digits already multiplied by 10 ** q. +template +fastfloat_really_inline +adjusted_mantissa compute_error_scaled(int64_t q, uint64_t w, int lz) noexcept { + int hilz = int(w >> 63) ^ 1; + adjusted_mantissa answer; + answer.mantissa = w << hilz; + int bias = binary::mantissa_explicit_bits() - binary::minimum_exponent(); + answer.power2 = int32_t(detail::power(int32_t(q)) + bias - hilz - lz - 62 + invalid_am_bias); + return answer; +} + +// w * 10 ** q, without rounding the representation up. +// the power2 in the exponent will be adjusted by invalid_am_bias. +template +fastfloat_really_inline +adjusted_mantissa compute_error(int64_t q, uint64_t w) noexcept { + int lz = leading_zeroes(w); + w <<= lz; + value128 product = compute_product_approximation(q, w); + return compute_error_scaled(q, product.high, lz); +} + +// w * 10 ** q +// The returned value should be a valid ieee64 number that simply need to be packed. +// However, in some very rare cases, the computation will fail. In such cases, we +// return an adjusted_mantissa with a negative power of 2: the caller should recompute +// in such cases. +template +fastfloat_really_inline +adjusted_mantissa compute_float(int64_t q, uint64_t w) noexcept { + adjusted_mantissa answer; + if ((w == 0) || (q < binary::smallest_power_of_ten())) { + answer.power2 = 0; + answer.mantissa = 0; + // result should be zero + return answer; + } + if (q > binary::largest_power_of_ten()) { + // we want to get infinity: + answer.power2 = binary::infinite_power(); + answer.mantissa = 0; + return answer; + } + // At this point in time q is in [powers::smallest_power_of_five, powers::largest_power_of_five]. + + // We want the most significant bit of i to be 1. Shift if needed. + int lz = leading_zeroes(w); + w <<= lz; + + // The required precision is binary::mantissa_explicit_bits() + 3 because + // 1. We need the implicit bit + // 2. We need an extra bit for rounding purposes + // 3. We might lose a bit due to the "upperbit" routine (result too small, requiring a shift) + + value128 product = compute_product_approximation(q, w); + if(product.low == 0xFFFFFFFFFFFFFFFF) { // could guard it further + // In some very rare cases, this could happen, in which case we might need a more accurate + // computation that what we can provide cheaply. This is very, very unlikely. + // + const bool inside_safe_exponent = (q >= -27) && (q <= 55); // always good because 5**q <2**128 when q>=0, + // and otherwise, for q<0, we have 5**-q<2**64 and the 128-bit reciprocal allows for exact computation. + if(!inside_safe_exponent) { + return compute_error_scaled(q, product.high, lz); + } + } + // The "compute_product_approximation" function can be slightly slower than a branchless approach: + // value128 product = compute_product(q, w); + // but in practice, we can win big with the compute_product_approximation if its additional branch + // is easily predicted. Which is best is data specific. + int upperbit = int(product.high >> 63); + + answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3); + + answer.power2 = int32_t(detail::power(int32_t(q)) + upperbit - lz - binary::minimum_exponent()); + if (answer.power2 <= 0) { // we have a subnormal? + // Here have that answer.power2 <= 0 so -answer.power2 >= 0 + if(-answer.power2 + 1 >= 64) { // if we have more than 64 bits below the minimum exponent, you have a zero for sure. + answer.power2 = 0; + answer.mantissa = 0; + // result should be zero + return answer; + } + // next line is safe because -answer.power2 + 1 < 64 + answer.mantissa >>= -answer.power2 + 1; + // Thankfully, we can't have both "round-to-even" and subnormals because + // "round-to-even" only occurs for powers close to 0. + answer.mantissa += (answer.mantissa & 1); // round up + answer.mantissa >>= 1; + // There is a weird scenario where we don't have a subnormal but just. + // Suppose we start with 2.2250738585072013e-308, we end up + // with 0x3fffffffffffff x 2^-1023-53 which is technically subnormal + // whereas 0x40000000000000 x 2^-1023-53 is normal. Now, we need to round + // up 0x3fffffffffffff x 2^-1023-53 and once we do, we are no longer + // subnormal, but we can only know this after rounding. + // So we only declare a subnormal if we are smaller than the threshold. + answer.power2 = (answer.mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) ? 0 : 1; + return answer; + } + + // usually, we round *up*, but if we fall right in between and and we have an + // even basis, we need to round down + // We are only concerned with the cases where 5**q fits in single 64-bit word. + if ((product.low <= 1) && (q >= binary::min_exponent_round_to_even()) && (q <= binary::max_exponent_round_to_even()) && + ((answer.mantissa & 3) == 1) ) { // we may fall between two floats! + // To be in-between two floats we need that in doing + // answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3); + // ... we dropped out only zeroes. But if this happened, then we can go back!!! + if((answer.mantissa << (upperbit + 64 - binary::mantissa_explicit_bits() - 3)) == product.high) { + answer.mantissa &= ~uint64_t(1); // flip it so that we do not round up + } + } + + answer.mantissa += (answer.mantissa & 1); // round up + answer.mantissa >>= 1; + if (answer.mantissa >= (uint64_t(2) << binary::mantissa_explicit_bits())) { + answer.mantissa = (uint64_t(1) << binary::mantissa_explicit_bits()); + answer.power2++; // undo previous addition + } + + answer.mantissa &= ~(uint64_t(1) << binary::mantissa_explicit_bits()); + if (answer.power2 >= binary::infinite_power()) { // infinity + answer.power2 = binary::infinite_power(); + answer.mantissa = 0; + } + return answer; +} + +} // namespace fast_float + +#endif + +#ifndef FASTFLOAT_BIGINT_H +#define FASTFLOAT_BIGINT_H + +#include +#include +#include +#include + + +namespace fast_float { + +// the limb width: we want efficient multiplication of double the bits in +// limb, or for 64-bit limbs, at least 64-bit multiplication where we can +// extract the high and low parts efficiently. this is every 64-bit +// architecture except for sparc, which emulates 128-bit multiplication. +// we might have platforms where `CHAR_BIT` is not 8, so let's avoid +// doing `8 * sizeof(limb)`. +#if defined(FASTFLOAT_64BIT) && !defined(__sparc) +#define FASTFLOAT_64BIT_LIMB +typedef uint64_t limb; +constexpr size_t limb_bits = 64; +#else +#define FASTFLOAT_32BIT_LIMB +typedef uint32_t limb; +constexpr size_t limb_bits = 32; +#endif + +typedef span limb_span; + +// number of bits in a bigint. this needs to be at least the number +// of bits required to store the largest bigint, which is +// `log2(10**(digits + max_exp))`, or `log2(10**(767 + 342))`, or +// ~3600 bits, so we round to 4000. +constexpr size_t bigint_bits = 4000; +constexpr size_t bigint_limbs = bigint_bits / limb_bits; + +// vector-like type that is allocated on the stack. the entire +// buffer is pre-allocated, and only the length changes. +template +struct stackvec { + limb data[size]; + // we never need more than 150 limbs + uint16_t length{0}; + + stackvec() = default; + stackvec(const stackvec &) = delete; + stackvec &operator=(const stackvec &) = delete; + stackvec(stackvec &&) = delete; + stackvec &operator=(stackvec &&other) = delete; + + // create stack vector from existing limb span. + stackvec(limb_span s) { + FASTFLOAT_ASSERT(try_extend(s)); + } + + limb& operator[](size_t index) noexcept { + FASTFLOAT_DEBUG_ASSERT(index < length); + return data[index]; + } + const limb& operator[](size_t index) const noexcept { + FASTFLOAT_DEBUG_ASSERT(index < length); + return data[index]; + } + // index from the end of the container + const limb& rindex(size_t index) const noexcept { + FASTFLOAT_DEBUG_ASSERT(index < length); + size_t rindex = length - index - 1; + return data[rindex]; + } + + // set the length, without bounds checking. + void set_len(size_t len) noexcept { + length = uint16_t(len); + } + constexpr size_t len() const noexcept { + return length; + } + constexpr bool is_empty() const noexcept { + return length == 0; + } + constexpr size_t capacity() const noexcept { + return size; + } + // append item to vector, without bounds checking + void push_unchecked(limb value) noexcept { + data[length] = value; + length++; + } + // append item to vector, returning if item was added + bool try_push(limb value) noexcept { + if (len() < capacity()) { + push_unchecked(value); + return true; + } else { + return false; + } + } + // add items to the vector, from a span, without bounds checking + void extend_unchecked(limb_span s) noexcept { + limb* ptr = data + length; + ::memcpy((void*)ptr, (const void*)s.ptr, sizeof(limb) * s.len()); + set_len(len() + s.len()); + } + // try to add items to the vector, returning if items were added + bool try_extend(limb_span s) noexcept { + if (len() + s.len() <= capacity()) { + extend_unchecked(s); + return true; + } else { + return false; + } + } + // resize the vector, without bounds checking + // if the new size is longer than the vector, assign value to each + // appended item. + void resize_unchecked(size_t new_len, limb value) noexcept { + if (new_len > len()) { + size_t count = new_len - len(); + limb* first = data + len(); + limb* last = first + count; + ::std::fill(first, last, value); + set_len(new_len); + } else { + set_len(new_len); + } + } + // try to resize the vector, returning if the vector was resized. + bool try_resize(size_t new_len, limb value) noexcept { + if (new_len > capacity()) { + return false; + } else { + resize_unchecked(new_len, value); + return true; + } + } + // check if any limbs are non-zero after the given index. + // this needs to be done in reverse order, since the index + // is relative to the most significant limbs. + bool nonzero(size_t index) const noexcept { + while (index < len()) { + if (rindex(index) != 0) { + return true; + } + index++; + } + return false; + } + // normalize the big integer, so most-significant zero limbs are removed. + void normalize() noexcept { + while (len() > 0 && rindex(0) == 0) { + length--; + } + } +}; + +fastfloat_really_inline +uint64_t empty_hi64(bool& truncated) noexcept { + truncated = false; + return 0; +} + +fastfloat_really_inline +uint64_t uint64_hi64(uint64_t r0, bool& truncated) noexcept { + truncated = false; + int shl = leading_zeroes(r0); + return r0 << shl; +} + +fastfloat_really_inline +uint64_t uint64_hi64(uint64_t r0, uint64_t r1, bool& truncated) noexcept { + int shl = leading_zeroes(r0); + if (shl == 0) { + truncated = r1 != 0; + return r0; + } else { + int shr = 64 - shl; + truncated = (r1 << shl) != 0; + return (r0 << shl) | (r1 >> shr); + } +} + +fastfloat_really_inline +uint64_t uint32_hi64(uint32_t r0, bool& truncated) noexcept { + return uint64_hi64(r0, truncated); +} + +fastfloat_really_inline +uint64_t uint32_hi64(uint32_t r0, uint32_t r1, bool& truncated) noexcept { + uint64_t x0 = r0; + uint64_t x1 = r1; + return uint64_hi64((x0 << 32) | x1, truncated); +} + +fastfloat_really_inline +uint64_t uint32_hi64(uint32_t r0, uint32_t r1, uint32_t r2, bool& truncated) noexcept { + uint64_t x0 = r0; + uint64_t x1 = r1; + uint64_t x2 = r2; + return uint64_hi64(x0, (x1 << 32) | x2, truncated); +} + +// add two small integers, checking for overflow. +// we want an efficient operation. for msvc, where +// we don't have built-in intrinsics, this is still +// pretty fast. +fastfloat_really_inline +limb scalar_add(limb x, limb y, bool& overflow) noexcept { + limb z; + +// gcc and clang +#if defined(__has_builtin) + #if __has_builtin(__builtin_add_overflow) + overflow = __builtin_add_overflow(x, y, &z); + return z; + #endif +#endif + + // generic, this still optimizes correctly on MSVC. + z = x + y; + overflow = z < x; + return z; +} + +// multiply two small integers, getting both the high and low bits. +fastfloat_really_inline +limb scalar_mul(limb x, limb y, limb& carry) noexcept { +#ifdef FASTFLOAT_64BIT_LIMB + #if defined(__SIZEOF_INT128__) + // GCC and clang both define it as an extension. + __uint128_t z = __uint128_t(x) * __uint128_t(y) + __uint128_t(carry); + carry = limb(z >> limb_bits); + return limb(z); + #else + // fallback, no native 128-bit integer multiplication with carry. + // on msvc, this optimizes identically, somehow. + value128 z = full_multiplication(x, y); + bool overflow; + z.low = scalar_add(z.low, carry, overflow); + z.high += uint64_t(overflow); // cannot overflow + carry = z.high; + return z.low; + #endif +#else + uint64_t z = uint64_t(x) * uint64_t(y) + uint64_t(carry); + carry = limb(z >> limb_bits); + return limb(z); +#endif +} + +// add scalar value to bigint starting from offset. +// used in grade school multiplication +template +inline bool small_add_from(stackvec& vec, limb y, size_t start) noexcept { + size_t index = start; + limb carry = y; + bool overflow; + while (carry != 0 && index < vec.len()) { + vec[index] = scalar_add(vec[index], carry, overflow); + carry = limb(overflow); + index += 1; + } + if (carry != 0) { + FASTFLOAT_TRY(vec.try_push(carry)); + } + return true; +} + +// add scalar value to bigint. +template +fastfloat_really_inline bool small_add(stackvec& vec, limb y) noexcept { + return small_add_from(vec, y, 0); +} + +// multiply bigint by scalar value. +template +inline bool small_mul(stackvec& vec, limb y) noexcept { + limb carry = 0; + for (size_t index = 0; index < vec.len(); index++) { + vec[index] = scalar_mul(vec[index], y, carry); + } + if (carry != 0) { + FASTFLOAT_TRY(vec.try_push(carry)); + } + return true; +} + +// add bigint to bigint starting from index. +// used in grade school multiplication +template +bool large_add_from(stackvec& x, limb_span y, size_t start) noexcept { + // the effective x buffer is from `xstart..x.len()`, so exit early + // if we can't get that current range. + if (x.len() < start || y.len() > x.len() - start) { + FASTFLOAT_TRY(x.try_resize(y.len() + start, 0)); + } + + bool carry = false; + for (size_t index = 0; index < y.len(); index++) { + limb xi = x[index + start]; + limb yi = y[index]; + bool c1 = false; + bool c2 = false; + xi = scalar_add(xi, yi, c1); + if (carry) { + xi = scalar_add(xi, 1, c2); + } + x[index + start] = xi; + carry = c1 | c2; + } + + // handle overflow + if (carry) { + FASTFLOAT_TRY(small_add_from(x, 1, y.len() + start)); + } + return true; +} + +// add bigint to bigint. +template +fastfloat_really_inline bool large_add_from(stackvec& x, limb_span y) noexcept { + return large_add_from(x, y, 0); +} + +// grade-school multiplication algorithm +template +bool long_mul(stackvec& x, limb_span y) noexcept { + limb_span xs = limb_span(x.data, x.len()); + stackvec z(xs); + limb_span zs = limb_span(z.data, z.len()); + + if (y.len() != 0) { + limb y0 = y[0]; + FASTFLOAT_TRY(small_mul(x, y0)); + for (size_t index = 1; index < y.len(); index++) { + limb yi = y[index]; + stackvec zi; + if (yi != 0) { + // re-use the same buffer throughout + zi.set_len(0); + FASTFLOAT_TRY(zi.try_extend(zs)); + FASTFLOAT_TRY(small_mul(zi, yi)); + limb_span zis = limb_span(zi.data, zi.len()); + FASTFLOAT_TRY(large_add_from(x, zis, index)); + } + } + } + + x.normalize(); + return true; +} + +// grade-school multiplication algorithm +template +bool large_mul(stackvec& x, limb_span y) noexcept { + if (y.len() == 1) { + FASTFLOAT_TRY(small_mul(x, y[0])); + } else { + FASTFLOAT_TRY(long_mul(x, y)); + } + return true; +} + +// big integer type. implements a small subset of big integer +// arithmetic, using simple algorithms since asymptotically +// faster algorithms are slower for a small number of limbs. +// all operations assume the big-integer is normalized. +struct bigint { + // storage of the limbs, in little-endian order. + stackvec vec; + + bigint(): vec() {} + bigint(const bigint &) = delete; + bigint &operator=(const bigint &) = delete; + bigint(bigint &&) = delete; + bigint &operator=(bigint &&other) = delete; + + bigint(uint64_t value): vec() { +#ifdef FASTFLOAT_64BIT_LIMB + vec.push_unchecked(value); +#else + vec.push_unchecked(uint32_t(value)); + vec.push_unchecked(uint32_t(value >> 32)); +#endif + vec.normalize(); + } + + // get the high 64 bits from the vector, and if bits were truncated. + // this is to get the significant digits for the float. + uint64_t hi64(bool& truncated) const noexcept { +#ifdef FASTFLOAT_64BIT_LIMB + if (vec.len() == 0) { + return empty_hi64(truncated); + } else if (vec.len() == 1) { + return uint64_hi64(vec.rindex(0), truncated); + } else { + uint64_t result = uint64_hi64(vec.rindex(0), vec.rindex(1), truncated); + truncated |= vec.nonzero(2); + return result; + } +#else + if (vec.len() == 0) { + return empty_hi64(truncated); + } else if (vec.len() == 1) { + return uint32_hi64(vec.rindex(0), truncated); + } else if (vec.len() == 2) { + return uint32_hi64(vec.rindex(0), vec.rindex(1), truncated); + } else { + uint64_t result = uint32_hi64(vec.rindex(0), vec.rindex(1), vec.rindex(2), truncated); + truncated |= vec.nonzero(3); + return result; + } +#endif + } + + // compare two big integers, returning the large value. + // assumes both are normalized. if the return value is + // negative, other is larger, if the return value is + // positive, this is larger, otherwise they are equal. + // the limbs are stored in little-endian order, so we + // must compare the limbs in ever order. + int compare(const bigint& other) const noexcept { + if (vec.len() > other.vec.len()) { + return 1; + } else if (vec.len() < other.vec.len()) { + return -1; + } else { + for (size_t index = vec.len(); index > 0; index--) { + limb xi = vec[index - 1]; + limb yi = other.vec[index - 1]; + if (xi > yi) { + return 1; + } else if (xi < yi) { + return -1; + } + } + return 0; + } + } + + // shift left each limb n bits, carrying over to the new limb + // returns true if we were able to shift all the digits. + bool shl_bits(size_t n) noexcept { + // Internally, for each item, we shift left by n, and add the previous + // right shifted limb-bits. + // For example, we transform (for u8) shifted left 2, to: + // b10100100 b01000010 + // b10 b10010001 b00001000 + FASTFLOAT_DEBUG_ASSERT(n != 0); + FASTFLOAT_DEBUG_ASSERT(n < sizeof(limb) * 8); + + size_t shl = n; + size_t shr = limb_bits - shl; + limb prev = 0; + for (size_t index = 0; index < vec.len(); index++) { + limb xi = vec[index]; + vec[index] = (xi << shl) | (prev >> shr); + prev = xi; + } + + limb carry = prev >> shr; + if (carry != 0) { + return vec.try_push(carry); + } + return true; + } + + // move the limbs left by `n` limbs. + bool shl_limbs(size_t n) noexcept { + FASTFLOAT_DEBUG_ASSERT(n != 0); + if (n + vec.len() > vec.capacity()) { + return false; + } else if (!vec.is_empty()) { + // move limbs + limb* dst = vec.data + n; + const limb* src = vec.data; + ::memmove(dst, src, sizeof(limb) * vec.len()); + // fill in empty limbs + limb* first = vec.data; + limb* last = first + n; + ::std::fill(first, last, 0); + vec.set_len(n + vec.len()); + return true; + } else { + return true; + } + } + + // move the limbs left by `n` bits. + bool shl(size_t n) noexcept { + size_t rem = n % limb_bits; + size_t div = n / limb_bits; + if (rem != 0) { + FASTFLOAT_TRY(shl_bits(rem)); + } + if (div != 0) { + FASTFLOAT_TRY(shl_limbs(div)); + } + return true; + } + + // get the number of leading zeros in the bigint. + int ctlz() const noexcept { + if (vec.is_empty()) { + return 0; + } else { +#ifdef FASTFLOAT_64BIT_LIMB + return leading_zeroes(vec.rindex(0)); +#else + // no use defining a specialized leading_zeroes for a 32-bit type. + uint64_t r0 = vec.rindex(0); + return leading_zeroes(r0 << 32); +#endif + } + } + + // get the number of bits in the bigint. + int bit_length() const noexcept { + int lz = ctlz(); + return int(limb_bits * vec.len()) - lz; + } + + bool mul(limb y) noexcept { + return small_mul(vec, y); + } + + bool add(limb y) noexcept { + return small_add(vec, y); + } + + // multiply as if by 2 raised to a power. + bool pow2(uint32_t exp) noexcept { + return shl(exp); + } + + // multiply as if by 5 raised to a power. + bool pow5(uint32_t exp) noexcept { + // multiply by a power of 5 + static constexpr uint32_t large_step = 135; + static constexpr uint64_t small_power_of_5[] = { + 1UL, 5UL, 25UL, 125UL, 625UL, 3125UL, 15625UL, 78125UL, 390625UL, + 1953125UL, 9765625UL, 48828125UL, 244140625UL, 1220703125UL, + 6103515625UL, 30517578125UL, 152587890625UL, 762939453125UL, + 3814697265625UL, 19073486328125UL, 95367431640625UL, 476837158203125UL, + 2384185791015625UL, 11920928955078125UL, 59604644775390625UL, + 298023223876953125UL, 1490116119384765625UL, 7450580596923828125UL, + }; +#ifdef FASTFLOAT_64BIT_LIMB + constexpr static limb large_power_of_5[] = { + 1414648277510068013UL, 9180637584431281687UL, 4539964771860779200UL, + 10482974169319127550UL, 198276706040285095UL}; +#else + constexpr static limb large_power_of_5[] = { + 4279965485U, 329373468U, 4020270615U, 2137533757U, 4287402176U, + 1057042919U, 1071430142U, 2440757623U, 381945767U, 46164893U}; +#endif + size_t large_length = sizeof(large_power_of_5) / sizeof(limb); + limb_span large = limb_span(large_power_of_5, large_length); + while (exp >= large_step) { + FASTFLOAT_TRY(large_mul(vec, large)); + exp -= large_step; + } +#ifdef FASTFLOAT_64BIT_LIMB + uint32_t small_step = 27; + limb max_native = 7450580596923828125UL; +#else + uint32_t small_step = 13; + limb max_native = 1220703125U; +#endif + while (exp >= small_step) { + FASTFLOAT_TRY(small_mul(vec, max_native)); + exp -= small_step; + } + if (exp != 0) { + FASTFLOAT_TRY(small_mul(vec, limb(small_power_of_5[exp]))); + } + + return true; + } + + // multiply as if by 10 raised to a power. + bool pow10(uint32_t exp) noexcept { + FASTFLOAT_TRY(pow5(exp)); + return pow2(exp); + } +}; + +} // namespace fast_float + +#endif + +#ifndef FASTFLOAT_ASCII_NUMBER_H +#define FASTFLOAT_ASCII_NUMBER_H + +#include +#include +#include +#include + + +namespace fast_float { + +// Next function can be micro-optimized, but compilers are entirely +// able to optimize it well. +fastfloat_really_inline bool is_integer(char c) noexcept { return c >= '0' && c <= '9'; } + +fastfloat_really_inline uint64_t byteswap(uint64_t val) { + return (val & 0xFF00000000000000) >> 56 + | (val & 0x00FF000000000000) >> 40 + | (val & 0x0000FF0000000000) >> 24 + | (val & 0x000000FF00000000) >> 8 + | (val & 0x00000000FF000000) << 8 + | (val & 0x0000000000FF0000) << 24 + | (val & 0x000000000000FF00) << 40 + | (val & 0x00000000000000FF) << 56; +} + +fastfloat_really_inline uint64_t read_u64(const char *chars) { + uint64_t val; + ::memcpy(&val, chars, sizeof(uint64_t)); +#if FASTFLOAT_IS_BIG_ENDIAN == 1 + // Need to read as-if the number was in little-endian order. + val = byteswap(val); +#endif + return val; +} + +fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) { +#if FASTFLOAT_IS_BIG_ENDIAN == 1 + // Need to read as-if the number was in little-endian order. + val = byteswap(val); +#endif + ::memcpy(chars, &val, sizeof(uint64_t)); +} + +// credit @aqrit +fastfloat_really_inline uint32_t parse_eight_digits_unrolled(uint64_t val) { + const uint64_t mask = 0x000000FF000000FF; + const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32) + const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32) + val -= 0x3030303030303030; + val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8; + val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32; + return uint32_t(val); +} + +fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars) noexcept { + return parse_eight_digits_unrolled(read_u64(chars)); +} + +// credit @aqrit +fastfloat_really_inline bool is_made_of_eight_digits_fast(uint64_t val) noexcept { + return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) & + 0x8080808080808080)); +} + +fastfloat_really_inline bool is_made_of_eight_digits_fast(const char *chars) noexcept { + return is_made_of_eight_digits_fast(read_u64(chars)); +} + +typedef span byte_span; + +struct parsed_number_string { + int64_t exponent{0}; + uint64_t mantissa{0}; + const char *lastmatch{nullptr}; + bool negative{false}; + bool valid{false}; + bool too_many_digits{false}; + // contains the range of the significant digits + byte_span integer{}; // non-nullable + byte_span fraction{}; // nullable +}; + +// Assuming that you use no more than 19 digits, this will +// parse an ASCII string. +fastfloat_really_inline +parsed_number_string parse_number_string(const char *p, const char *pend, parse_options options) noexcept { + const chars_format fmt = options.format; + const char decimal_point = options.decimal_point; + + parsed_number_string answer; + answer.valid = false; + answer.too_many_digits = false; + answer.negative = (*p == '-'); + if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here + ++p; + if (p == pend) { + return answer; + } + if (!is_integer(*p) && (*p != decimal_point)) { // a sign must be followed by an integer or the dot + return answer; + } + } + const char *const start_digits = p; + + uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad) + + while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) { + i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok + p += 8; + } + while ((p != pend) && is_integer(*p)) { + // a multiplication by 10 is cheaper than an arbitrary integer + // multiplication + i = 10 * i + + uint64_t(*p - '0'); // might overflow, we will handle the overflow later + ++p; + } + const char *const end_of_integer_part = p; + int64_t digit_count = int64_t(end_of_integer_part - start_digits); + answer.integer = byte_span(start_digits, size_t(digit_count)); + int64_t exponent = 0; + if ((p != pend) && (*p == decimal_point)) { + ++p; + const char* before = p; + // can occur at most twice without overflowing, but let it occur more, since + // for integers with many digits, digit parsing is the primary bottleneck. + while ((std::distance(p, pend) >= 8) && is_made_of_eight_digits_fast(p)) { + i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok + p += 8; + } + while ((p != pend) && is_integer(*p)) { + uint8_t digit = uint8_t(*p - '0'); + ++p; + i = i * 10 + digit; // in rare cases, this will overflow, but that's ok + } + exponent = before - p; + answer.fraction = byte_span(before, size_t(p - before)); + digit_count -= exponent; + } + // we must have encountered at least one integer! + if (digit_count == 0) { + return answer; + } + int64_t exp_number = 0; // explicit exponential part + if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) { + const char * location_of_e = p; + ++p; + bool neg_exp = false; + if ((p != pend) && ('-' == *p)) { + neg_exp = true; + ++p; + } else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1) + ++p; + } + if ((p == pend) || !is_integer(*p)) { + if(!(fmt & chars_format::fixed)) { + // We are in error. + return answer; + } + // Otherwise, we will be ignoring the 'e'. + p = location_of_e; + } else { + while ((p != pend) && is_integer(*p)) { + uint8_t digit = uint8_t(*p - '0'); + if (exp_number < 0x10000000) { + exp_number = 10 * exp_number + digit; + } + ++p; + } + if(neg_exp) { exp_number = - exp_number; } + exponent += exp_number; + } + } else { + // If it scientific and not fixed, we have to bail out. + if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; } + } + answer.lastmatch = p; + answer.valid = true; + + // 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. + // + // We can deal with up to 19 digits. + if (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. + // We need to be mindful of the case where we only have zeroes... + // E.g., 0.000000000...000. + const char *start = start_digits; + while ((start != pend) && (*start == '0' || *start == decimal_point)) { + if(*start == '0') { digit_count --; } + start++; + } + if (digit_count > 19) { + answer.too_many_digits = true; + // Let us start again, this time, avoiding overflows. + // We don't need to check if is_integer, since we use the + // pre-tokenized spans from above. + i = 0; + p = answer.integer.ptr; + const char* int_end = p + answer.integer.len(); + const uint64_t minimal_nineteen_digit_integer{1000000000000000000}; + while((i < minimal_nineteen_digit_integer) && (p != int_end)) { + i = i * 10 + uint64_t(*p - '0'); + ++p; + } + if (i >= minimal_nineteen_digit_integer) { // We have a big integers + exponent = end_of_integer_part - p + exp_number; + } else { // We have a value with a fractional component. + p = answer.fraction.ptr; + const char* frac_end = p + answer.fraction.len(); + while((i < minimal_nineteen_digit_integer) && (p != frac_end)) { + i = i * 10 + uint64_t(*p - '0'); + ++p; + } + exponent = answer.fraction.ptr - p + exp_number; + } + // We have now corrected both exponent and i, to a truncated value + } + } + answer.exponent = exponent; + answer.mantissa = i; + return answer; +} + +} // namespace fast_float + +#endif + +#ifndef FASTFLOAT_DIGIT_COMPARISON_H +#define FASTFLOAT_DIGIT_COMPARISON_H + +#include +#include +#include +#include + + +namespace fast_float { + +// 1e0 to 1e19 +constexpr static uint64_t powers_of_ten_uint64[] = { + 1UL, 10UL, 100UL, 1000UL, 10000UL, 100000UL, 1000000UL, 10000000UL, 100000000UL, + 1000000000UL, 10000000000UL, 100000000000UL, 1000000000000UL, 10000000000000UL, + 100000000000000UL, 1000000000000000UL, 10000000000000000UL, 100000000000000000UL, + 1000000000000000000UL, 10000000000000000000UL}; + +// calculate the exponent, in scientific notation, of the number. +// this algorithm is not even close to optimized, but it has no practical +// effect on performance: in order to have a faster algorithm, we'd need +// to slow down performance for faster algorithms, and this is still fast. +fastfloat_really_inline int32_t scientific_exponent(parsed_number_string& num) noexcept { + uint64_t mantissa = num.mantissa; + int32_t exponent = int32_t(num.exponent); + while (mantissa >= 10000) { + mantissa /= 10000; + exponent += 4; + } + while (mantissa >= 100) { + mantissa /= 100; + exponent += 2; + } + while (mantissa >= 10) { + mantissa /= 10; + exponent += 1; + } + return exponent; +} + +// this converts a native floating-point number to an extended-precision float. +template +fastfloat_really_inline adjusted_mantissa to_extended(T value) noexcept { + adjusted_mantissa am; + int32_t bias = binary_format::mantissa_explicit_bits() - binary_format::minimum_exponent(); + if (std::is_same::value) { + constexpr uint32_t exponent_mask = 0x7F800000; + constexpr uint32_t mantissa_mask = 0x007FFFFF; + constexpr uint64_t hidden_bit_mask = 0x00800000; + uint32_t bits; + ::memcpy(&bits, &value, sizeof(T)); + if ((bits & exponent_mask) == 0) { + // denormal + am.power2 = 1 - bias; + am.mantissa = bits & mantissa_mask; + } else { + // normal + am.power2 = int32_t((bits & exponent_mask) >> binary_format::mantissa_explicit_bits()); + am.power2 -= bias; + am.mantissa = (bits & mantissa_mask) | hidden_bit_mask; + } + } else { + constexpr uint64_t exponent_mask = 0x7FF0000000000000; + constexpr uint64_t mantissa_mask = 0x000FFFFFFFFFFFFF; + constexpr uint64_t hidden_bit_mask = 0x0010000000000000; + uint64_t bits; + ::memcpy(&bits, &value, sizeof(T)); + if ((bits & exponent_mask) == 0) { + // denormal + am.power2 = 1 - bias; + am.mantissa = bits & mantissa_mask; + } else { + // normal + am.power2 = int32_t((bits & exponent_mask) >> binary_format::mantissa_explicit_bits()); + am.power2 -= bias; + am.mantissa = (bits & mantissa_mask) | hidden_bit_mask; + } + } + + return am; +} + +// get the extended precision value of the halfway point between b and b+u. +// we are given a native float that represents b, so we need to adjust it +// halfway between b and b+u. +template +fastfloat_really_inline adjusted_mantissa to_extended_halfway(T value) noexcept { + adjusted_mantissa am = to_extended(value); + am.mantissa <<= 1; + am.mantissa += 1; + am.power2 -= 1; + return am; +} + +// round an extended-precision float to the nearest machine float. +template +fastfloat_really_inline void round(adjusted_mantissa& am, callback cb) noexcept { + int32_t mantissa_shift = 64 - binary_format::mantissa_explicit_bits() - 1; + if (-am.power2 >= mantissa_shift) { + // have a denormal float + int32_t shift = -am.power2 + 1; + cb(am, std::min(shift, 64)); + // check for round-up: if rounding-nearest carried us to the hidden bit. + am.power2 = (am.mantissa < (uint64_t(1) << binary_format::mantissa_explicit_bits())) ? 0 : 1; + return; + } + + // have a normal float, use the default shift. + cb(am, mantissa_shift); + + // check for carry + if (am.mantissa >= (uint64_t(2) << binary_format::mantissa_explicit_bits())) { + am.mantissa = (uint64_t(1) << binary_format::mantissa_explicit_bits()); + am.power2++; + } + + // check for infinite: we could have carried to an infinite power + am.mantissa &= ~(uint64_t(1) << binary_format::mantissa_explicit_bits()); + if (am.power2 >= binary_format::infinite_power()) { + am.power2 = binary_format::infinite_power(); + am.mantissa = 0; + } +} + +template +fastfloat_really_inline +void round_nearest_tie_even(adjusted_mantissa& am, int32_t shift, callback cb) noexcept { + uint64_t mask; + uint64_t halfway; + if (shift == 64) { + mask = UINT64_MAX; + } else { + mask = (uint64_t(1) << shift) - 1; + } + if (shift == 0) { + halfway = 0; + } else { + halfway = uint64_t(1) << (shift - 1); + } + uint64_t truncated_bits = am.mantissa & mask; + uint64_t is_above = truncated_bits > halfway; + uint64_t is_halfway = truncated_bits == halfway; + + // shift digits into position + if (shift == 64) { + am.mantissa = 0; + } else { + am.mantissa >>= shift; + } + am.power2 += shift; + + bool is_odd = (am.mantissa & 1) == 1; + am.mantissa += uint64_t(cb(is_odd, is_halfway, is_above)); +} + +fastfloat_really_inline void round_down(adjusted_mantissa& am, int32_t shift) noexcept { + if (shift == 64) { + am.mantissa = 0; + } else { + am.mantissa >>= shift; + } + am.power2 += shift; +} + +fastfloat_really_inline void skip_zeros(const char*& first, const char* last) noexcept { + uint64_t val; + while (std::distance(first, last) >= 8) { + ::memcpy(&val, first, sizeof(uint64_t)); + if (val != 0x3030303030303030) { + break; + } + first += 8; + } + while (first != last) { + if (*first != '0') { + break; + } + first++; + } +} + +// determine if any non-zero digits were truncated. +// all characters must be valid digits. +fastfloat_really_inline bool is_truncated(const char* first, const char* last) noexcept { + // do 8-bit optimizations, can just compare to 8 literal 0s. + uint64_t val; + while (std::distance(first, last) >= 8) { + ::memcpy(&val, first, sizeof(uint64_t)); + if (val != 0x3030303030303030) { + return true; + } + first += 8; + } + while (first != last) { + if (*first != '0') { + return true; + } + first++; + } + return false; +} + +fastfloat_really_inline bool is_truncated(byte_span s) noexcept { + return is_truncated(s.ptr, s.ptr + s.len()); +} + +fastfloat_really_inline +void parse_eight_digits(const char*& p, limb& value, size_t& counter, size_t& count) noexcept { + value = value * 100000000 + parse_eight_digits_unrolled(p); + p += 8; + counter += 8; + count += 8; +} + +fastfloat_really_inline +void parse_one_digit(const char*& p, limb& value, size_t& counter, size_t& count) noexcept { + value = value * 10 + limb(*p - '0'); + p++; + counter++; + count++; +} + +fastfloat_really_inline +void add_native(bigint& big, limb power, limb value) noexcept { + big.mul(power); + big.add(value); +} + +fastfloat_really_inline void round_up_bigint(bigint& big, size_t& count) noexcept { + // need to round-up the digits, but need to avoid rounding + // ....9999 to ...10000, which could cause a false halfway point. + add_native(big, 10, 1); + count++; +} + +// parse the significant digits into a big integer +inline void parse_mantissa(bigint& result, parsed_number_string& num, size_t max_digits, size_t& digits) noexcept { + // try to minimize the number of big integer and scalar multiplication. + // therefore, try to parse 8 digits at a time, and multiply by the largest + // scalar value (9 or 19 digits) for each step. + size_t counter = 0; + digits = 0; + limb value = 0; +#ifdef FASTFLOAT_64BIT_LIMB + size_t step = 19; +#else + size_t step = 9; +#endif + + // process all integer digits. + const char* p = num.integer.ptr; + const char* pend = p + num.integer.len(); + skip_zeros(p, pend); + // process all digits, in increments of step per loop + while (p != pend) { + while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) { + parse_eight_digits(p, value, counter, digits); + } + while (counter < step && p != pend && digits < max_digits) { + parse_one_digit(p, value, counter, digits); + } + if (digits == max_digits) { + // add the temporary value, then check if we've truncated any digits + add_native(result, limb(powers_of_ten_uint64[counter]), value); + bool truncated = is_truncated(p, pend); + if (num.fraction.ptr != nullptr) { + truncated |= is_truncated(num.fraction); + } + if (truncated) { + round_up_bigint(result, digits); + } + return; + } else { + add_native(result, limb(powers_of_ten_uint64[counter]), value); + counter = 0; + value = 0; + } + } + + // add our fraction digits, if they're available. + if (num.fraction.ptr != nullptr) { + p = num.fraction.ptr; + pend = p + num.fraction.len(); + if (digits == 0) { + skip_zeros(p, pend); + } + // process all digits, in increments of step per loop + while (p != pend) { + while ((std::distance(p, pend) >= 8) && (step - counter >= 8) && (max_digits - digits >= 8)) { + parse_eight_digits(p, value, counter, digits); + } + while (counter < step && p != pend && digits < max_digits) { + parse_one_digit(p, value, counter, digits); + } + if (digits == max_digits) { + // add the temporary value, then check if we've truncated any digits + add_native(result, limb(powers_of_ten_uint64[counter]), value); + bool truncated = is_truncated(p, pend); + if (truncated) { + round_up_bigint(result, digits); + } + return; + } else { + add_native(result, limb(powers_of_ten_uint64[counter]), value); + counter = 0; + value = 0; + } + } + } + + if (counter != 0) { + add_native(result, limb(powers_of_ten_uint64[counter]), value); + } +} + +template +inline adjusted_mantissa positive_digit_comp(bigint& bigmant, int32_t exponent) noexcept { + FASTFLOAT_ASSERT(bigmant.pow10(uint32_t(exponent))); + adjusted_mantissa answer; + bool truncated; + answer.mantissa = bigmant.hi64(truncated); + int bias = binary_format::mantissa_explicit_bits() - binary_format::minimum_exponent(); + answer.power2 = bigmant.bit_length() - 64 + bias; + + round(answer, [truncated](adjusted_mantissa& a, int32_t shift) { + round_nearest_tie_even(a, shift, [truncated](bool is_odd, bool is_halfway, bool is_above) -> bool { + return is_above || (is_halfway && truncated) || (is_odd && is_halfway); + }); + }); + + return answer; +} + +// the scaling here is quite simple: we have, for the real digits `m * 10^e`, +// and for the theoretical digits `n * 2^f`. Since `e` is always negative, +// to scale them identically, we do `n * 2^f * 5^-f`, so we now have `m * 2^e`. +// we then need to scale by `2^(f- e)`, and then the two significant digits +// are of the same magnitude. +template +inline adjusted_mantissa negative_digit_comp(bigint& bigmant, adjusted_mantissa am, int32_t exponent) noexcept { + bigint& real_digits = bigmant; + int32_t real_exp = exponent; + + // get the value of `b`, rounded down, and get a bigint representation of b+h + adjusted_mantissa am_b = am; + // gcc7 buf: use a lambda to remove the noexcept qualifier bug with -Wnoexcept-type. + round(am_b, [](adjusted_mantissa&a, int32_t shift) { round_down(a, shift); }); + T b; + to_float(false, am_b, b); + adjusted_mantissa theor = to_extended_halfway(b); + bigint theor_digits(theor.mantissa); + int32_t theor_exp = theor.power2; + + // scale real digits and theor digits to be same power. + int32_t pow2_exp = theor_exp - real_exp; + uint32_t pow5_exp = uint32_t(-real_exp); + if (pow5_exp != 0) { + FASTFLOAT_ASSERT(theor_digits.pow5(pow5_exp)); + } + if (pow2_exp > 0) { + FASTFLOAT_ASSERT(theor_digits.pow2(uint32_t(pow2_exp))); + } else if (pow2_exp < 0) { + FASTFLOAT_ASSERT(real_digits.pow2(uint32_t(-pow2_exp))); + } + + // compare digits, and use it to director rounding + int ord = real_digits.compare(theor_digits); + adjusted_mantissa answer = am; + round(answer, [ord](adjusted_mantissa& a, int32_t shift) { + round_nearest_tie_even(a, shift, [ord](bool is_odd, bool _, bool __) -> bool { + (void)_; // not needed, since we've done our comparison + (void)__; // not needed, since we've done our comparison + if (ord > 0) { + return true; + } else if (ord < 0) { + return false; + } else { + return is_odd; + } + }); + }); + + return answer; +} + +// parse the significant digits as a big integer to unambiguously round the +// the significant digits. here, we are trying to determine how to round +// an extended float representation close to `b+h`, halfway between `b` +// (the float rounded-down) and `b+u`, the next positive float. this +// algorithm is always correct, and uses one of two approaches. when +// the exponent is positive relative to the significant digits (such as +// 1234), we create a big-integer representation, get the high 64-bits, +// determine if any lower bits are truncated, and use that to direct +// rounding. in case of a negative exponent relative to the significant +// digits (such as 1.2345), we create a theoretical representation of +// `b` as a big-integer type, scaled to the same binary exponent as +// the actual digits. we then compare the big integer representations +// of both, and use that to direct rounding. +template +inline adjusted_mantissa digit_comp(parsed_number_string& num, adjusted_mantissa am) noexcept { + // remove the invalid exponent bias + am.power2 -= invalid_am_bias; + + int32_t sci_exp = scientific_exponent(num); + size_t max_digits = binary_format::max_digits(); + size_t digits = 0; + bigint bigmant; + parse_mantissa(bigmant, num, max_digits, digits); + // can't underflow, since digits is at most max_digits. + int32_t exponent = sci_exp + 1 - int32_t(digits); + if (exponent >= 0) { + return positive_digit_comp(bigmant, exponent); + } else { + return negative_digit_comp(bigmant, am, exponent); + } +} + +} // namespace fast_float + +#endif + +#ifndef FASTFLOAT_PARSE_NUMBER_H +#define FASTFLOAT_PARSE_NUMBER_H + + +#include +#include +#include +#include + +namespace fast_float { + + +namespace detail { +/** + * Special case +inf, -inf, nan, infinity, -infinity. + * The case comparisons could be made much faster given that we know that the + * strings a null-free and fixed. + **/ +template +from_chars_result parse_infnan(const char *first, const char *last, T &value) noexcept { + from_chars_result answer; + answer.ptr = first; + answer.ec = std::errc(); // be optimistic + bool minusSign = false; + if (*first == '-') { // assume first < last, so dereference without checks; C++17 20.19.3.(7.1) explicitly forbids '+' here + minusSign = true; + ++first; + } + if (last - first >= 3) { + if (fastfloat_strncasecmp(first, "nan", 3)) { + answer.ptr = (first += 3); + value = minusSign ? -std::numeric_limits::quiet_NaN() : std::numeric_limits::quiet_NaN(); + // Check for possible nan(n-char-seq-opt), C++17 20.19.3.7, C11 7.20.1.3.3. At least MSVC produces nan(ind) and nan(snan). + if(first != last && *first == '(') { + for(const char* ptr = first + 1; ptr != last; ++ptr) { + if (*ptr == ')') { + answer.ptr = ptr + 1; // valid nan(n-char-seq-opt) + break; + } + else if(!(('a' <= *ptr && *ptr <= 'z') || ('A' <= *ptr && *ptr <= 'Z') || ('0' <= *ptr && *ptr <= '9') || *ptr == '_')) + break; // forbidden char, not nan(n-char-seq-opt) + } + } + return answer; + } + if (fastfloat_strncasecmp(first, "inf", 3)) { + if ((last - first >= 8) && fastfloat_strncasecmp(first + 3, "inity", 5)) { + answer.ptr = first + 8; + } else { + answer.ptr = first + 3; + } + value = minusSign ? -std::numeric_limits::infinity() : std::numeric_limits::infinity(); + return answer; + } + } + answer.ec = std::errc::invalid_argument; + return answer; +} + +} // namespace detail + +template +from_chars_result from_chars(const char *first, const char *last, + T &value, chars_format fmt /*= chars_format::general*/) noexcept { + return from_chars_advanced(first, last, value, parse_options{fmt}); +} + +template +from_chars_result from_chars_advanced(const char *first, const char *last, + T &value, parse_options options) noexcept { + + static_assert (std::is_same::value || std::is_same::value, "only float and double are supported"); + + + from_chars_result answer; + if (first == last) { + answer.ec = std::errc::invalid_argument; + answer.ptr = first; + return answer; + } + parsed_number_string pns = parse_number_string(first, last, options); + if (!pns.valid) { + return detail::parse_infnan(first, last, value); + } + answer.ec = std::errc(); // be optimistic + answer.ptr = pns.lastmatch; + // Next is Clinger's fast path. + if (binary_format::min_exponent_fast_path() <= pns.exponent && pns.exponent <= binary_format::max_exponent_fast_path() && pns.mantissa <=binary_format::max_mantissa_fast_path() && !pns.too_many_digits) { + value = T(pns.mantissa); + if (pns.exponent < 0) { value = value / binary_format::exact_power_of_ten(-pns.exponent); } + else { value = value * binary_format::exact_power_of_ten(pns.exponent); } + if (pns.negative) { value = -value; } + return answer; + } + adjusted_mantissa am = compute_float>(pns.exponent, pns.mantissa); + if(pns.too_many_digits && am.power2 >= 0) { + if(am != compute_float>(pns.exponent, pns.mantissa + 1)) { + am = compute_error>(pns.exponent, pns.mantissa); + } + } + // If we called compute_float>(pns.exponent, pns.mantissa) and we have an invalid power (am.power2 < 0), + // then we need to go the long way around again. This is very uncommon. + if(am.power2 < 0) { am = digit_comp(pns, am); } + to_float(pns.negative, am, value); + return answer; +} + +} // namespace fast_float + +#endif + From patchwork Sun Jan 16 18:06:49 2022 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit X-Patchwork-Submitter: Patrick Palka X-Patchwork-Id: 50082 Return-Path: X-Original-To: patchwork@sourceware.org Delivered-To: patchwork@sourceware.org Received: from server2.sourceware.org (localhost [IPv6:::1]) by sourceware.org (Postfix) with ESMTP id A5CD2385842C for ; Sun, 16 Jan 2022 18:10:18 +0000 (GMT) DKIM-Filter: OpenDKIM Filter v2.11.0 sourceware.org A5CD2385842C DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gcc.gnu.org; s=default; t=1642356618; bh=SmuXr21uwjaZryx3WxHBrlNtpyvOylcCVAK1T/5Na1w=; h=To:Subject:Date:In-Reply-To:References:List-Id:List-Unsubscribe: List-Archive:List-Post:List-Help:List-Subscribe:From:Reply-To:Cc: From; b=UCLg/qajfSxO50p1M1ozobYTr3Y7x8KPFecpP+/1g4m0kiPjPUUQ7JfZhU0vL3Rrv ld3y+rK4aEqTQblZhyFW7zw4O6F4ofcmRXnlqx1OQBF4A8ojzHdzHbMHaSn6zLZu+K sDw2bbHLb+hrg7QBnrfXYQsm0UWJ3dENLSFPUwGk= X-Original-To: gcc-patches@gcc.gnu.org Delivered-To: gcc-patches@gcc.gnu.org Received: from us-smtp-delivery-124.mimecast.com (us-smtp-delivery-124.mimecast.com [170.10.129.124]) by sourceware.org (Postfix) with ESMTPS id 1013B3858C39 for ; Sun, 16 Jan 2022 18:07:03 +0000 (GMT) DMARC-Filter: OpenDMARC Filter v1.4.1 sourceware.org 1013B3858C39 Received: from mail-qk1-f200.google.com (mail-qk1-f200.google.com [209.85.222.200]) by relay.mimecast.com with ESMTP with STARTTLS (version=TLSv1.2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id us-mta-543-hLStsTKUO6y2xC2hN_0_CQ-1; Sun, 16 Jan 2022 13:06:59 -0500 X-MC-Unique: hLStsTKUO6y2xC2hN_0_CQ-1 Received: by mail-qk1-f200.google.com with SMTP id b189-20020a3780c6000000b0047b06f34f4cso1871647qkd.17 for ; Sun, 16 Jan 2022 10:06:59 -0800 (PST) X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20210112; h=x-gm-message-state:from:to:cc:subject:date:message-id:in-reply-to :references:mime-version:content-transfer-encoding; bh=SmuXr21uwjaZryx3WxHBrlNtpyvOylcCVAK1T/5Na1w=; b=J1WSMFcq641hCUcqQKnI8MzSieshwlxX24y4ENs9raPGrqKCbmgy1RhF4DsD9/90Gk sz7oB0kLsg3694hW6wuxdgEpel3AWLvInl4kItJVg3IM77tFqPyPW4cQyL1f55D2LAuG bPgL9tXO18pm1w+ciFWbBMSzmhc8fsJpXzCk6d+1HbF+1ktfZtVAfFr232NnK8B+6TCx TrSdvn22Ng3CKEd9MBW4xhNDpV3vnnT5vBE4QmyYS+3CMxw2+7V4Rrr5CGaMFYY/4hA5 gT29lUf6NXgp1ElvDZBjovTKLOJg1FSCBqe4vwZkunnXFC2AUq/KvXRccF43s2oFKL6t e4TQ== X-Gm-Message-State: AOAM533LT9GQWGCVyrEXmcEeMMDEEnNLDVRewxeQm9kn2Es8rbnvu2ND a+BzdNYerNXYgqMjE/SIE1GpSmAceEIJ0XbiE9tJ3yrtNOZduzTprR1y8jbtqQFOBSNp6e24gf3 gtlhE/H/UdcNRAWy0IEC4s+aPX5mDVvU5Vs6/BzHM5be/F8DmUuMUdw07bvegT5Ss7ik= X-Received: by 2002:ac8:7009:: with SMTP id x9mr14442865qtm.420.1642356418707; Sun, 16 Jan 2022 10:06:58 -0800 (PST) X-Google-Smtp-Source: ABdhPJyI+SulRav1fl8oT3Z97ZEaLn9CPDMiQm+1Muo0iVSS16roG6ge0vMe0URUNisIeKLXcjwOpQ== X-Received: by 2002:ac8:7009:: with SMTP id x9mr14442852qtm.420.1642356418398; Sun, 16 Jan 2022 10:06:58 -0800 (PST) Received: from localhost.localdomain (ool-18e40894.dyn.optonline.net. [24.228.8.148]) by smtp.gmail.com with ESMTPSA id o10sm7994149qtx.33.2022.01.16.10.06.57 (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Sun, 16 Jan 2022 10:06:57 -0800 (PST) To: gcc-patches@gcc.gnu.org Subject: [PATCH 3/6] libstdc++: Apply modifications to our local copy of fast_float Date: Sun, 16 Jan 2022 13:06:49 -0500 Message-Id: <20220116180652.3694791-3-ppalka@redhat.com> X-Mailer: git-send-email 2.35.0.rc1 In-Reply-To: <20220116180652.3694791-1-ppalka@redhat.com> References: <20220116180652.3694791-1-ppalka@redhat.com> MIME-Version: 1.0 X-Mimecast-Spam-Score: 0 X-Mimecast-Originator: redhat.com X-Spam-Status: No, score=-14.6 required=5.0 tests=BAYES_00, DKIMWL_WL_HIGH, DKIM_SIGNED, DKIM_VALID, DKIM_VALID_AU, DKIM_VALID_EF, GIT_PATCH_0, RCVD_IN_DNSWL_LOW, RCVD_IN_MSPIKE_H3, RCVD_IN_MSPIKE_WL, SPF_HELO_NONE, SPF_NONE, TXREP autolearn=unavailable autolearn_force=no version=3.4.4 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on server2.sourceware.org X-BeenThere: gcc-patches@gcc.gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Gcc-patches mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-Patchwork-Original-From: Patrick Palka via Gcc-patches From: Patrick Palka Reply-To: Patrick Palka Cc: libstdc++@gcc.gnu.org Errors-To: gcc-patches-bounces+patchwork=sourceware.org@gcc.gnu.org Sender: "Gcc-patches" This performs the following modifications to our local copy of fast_float in order to make it more readily usable in our std::from_chars implementation: * Remove system #includes * Replace stray call to assert * Use the standard chars_format and from_chars_result types libstdc++-v3/ChangeLog: * src/c++17/fast_float/LOCAL_PATCHES: Update. * src/c++17/fast_float/fast_float.h: Apply local modifications. --- .../src/c++17/fast_float/LOCAL_PATCHES | 1 + .../src/c++17/fast_float/fast_float.h | 62 ++----------------- 2 files changed, 7 insertions(+), 56 deletions(-) diff --git a/libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES b/libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES index e69de29bb2d..e9d7bba6195 100644 --- a/libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES +++ b/libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES @@ -0,0 +1 @@ +r12-???? diff --git a/libstdc++-v3/src/c++17/fast_float/fast_float.h b/libstdc++-v3/src/c++17/fast_float/fast_float.h index 8a45ebca8a8..c908719ec3a 100644 --- a/libstdc++-v3/src/c++17/fast_float/fast_float.h +++ b/libstdc++-v3/src/c++17/fast_float/fast_float.h @@ -42,21 +42,10 @@ #ifndef FASTFLOAT_FAST_FLOAT_H #define FASTFLOAT_FAST_FLOAT_H -#include - namespace fast_float { -enum chars_format { - scientific = 1<<0, - fixed = 1<<2, - hex = 1<<3, - general = fixed | scientific -}; - -struct from_chars_result { - const char *ptr; - std::errc ec; -}; +using std::chars_format; +using std::from_chars_result; struct parse_options { constexpr explicit parse_options(chars_format fmt = chars_format::general, @@ -105,11 +94,6 @@ from_chars_result from_chars_advanced(const char *first, const char *last, #ifndef FASTFLOAT_FLOAT_COMMON_H #define FASTFLOAT_FLOAT_COMMON_H -#include -#include -#include -#include - #if (defined(__x86_64) || defined(__x86_64__) || defined(_M_X64) \ || defined(__amd64) || defined(__aarch64__) || defined(_M_ARM64) \ || defined(__MINGW64__) \ @@ -233,7 +217,7 @@ struct value128 { /* result might be undefined when input_num is zero */ fastfloat_really_inline int leading_zeroes(uint64_t input_num) { - assert(input_num > 0); + FASTFLOAT_DEBUG_ASSERT(input_num > 0); #ifdef FASTFLOAT_VISUAL_STUDIO #if defined(_M_X64) || defined(_M_ARM64) unsigned long leading_zero = 0; @@ -468,11 +452,6 @@ fastfloat_really_inline void to_float(bool negative, adjusted_mantissa am, T &va #ifndef FASTFLOAT_ASCII_NUMBER_H #define FASTFLOAT_ASCII_NUMBER_H -#include -#include -#include -#include - namespace fast_float { @@ -610,7 +589,7 @@ parsed_number_string parse_number_string(const char *p, const char *pend, parse_ return answer; } int64_t exp_number = 0; // explicit exponential part - if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) { + if (bool(fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) { const char * location_of_e = p; ++p; bool neg_exp = false; @@ -621,7 +600,7 @@ parsed_number_string parse_number_string(const char *p, const char *pend, parse_ ++p; } if ((p == pend) || !is_integer(*p)) { - if(!(fmt & chars_format::fixed)) { + if(!bool(fmt & chars_format::fixed)) { // We are in error. return answer; } @@ -640,7 +619,7 @@ parsed_number_string parse_number_string(const char *p, const char *pend, parse_ } } else { // If it scientific and not fixed, we have to bail out. - if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; } + if(bool(fmt & chars_format::scientific) && !bool(fmt & chars_format::fixed)) { return answer; } } answer.lastmatch = p; answer.valid = true; @@ -699,8 +678,6 @@ parsed_number_string parse_number_string(const char *p, const char *pend, parse_ #ifndef FASTFLOAT_FAST_TABLE_H #define FASTFLOAT_FAST_TABLE_H -#include - namespace fast_float { /** @@ -1399,13 +1376,6 @@ using powers = powers_template<>; #ifndef FASTFLOAT_DECIMAL_TO_BINARY_H #define FASTFLOAT_DECIMAL_TO_BINARY_H -#include -#include -#include -#include -#include -#include - namespace fast_float { // This will compute or rather approximate w * 5**q and return a pair of 64-bit words approximating @@ -1592,11 +1562,6 @@ adjusted_mantissa compute_float(int64_t q, uint64_t w) noexcept { #ifndef FASTFLOAT_BIGINT_H #define FASTFLOAT_BIGINT_H -#include -#include -#include -#include - namespace fast_float { @@ -2182,11 +2147,6 @@ struct bigint { #ifndef FASTFLOAT_ASCII_NUMBER_H #define FASTFLOAT_ASCII_NUMBER_H -#include -#include -#include -#include - namespace fast_float { @@ -2413,11 +2373,6 @@ parsed_number_string parse_number_string(const char *p, const char *pend, parse_ #ifndef FASTFLOAT_DIGIT_COMPARISON_H #define FASTFLOAT_DIGIT_COMPARISON_H -#include -#include -#include -#include - namespace fast_float { @@ -2835,11 +2790,6 @@ inline adjusted_mantissa digit_comp(parsed_number_string& num, adjusted_mantissa #define FASTFLOAT_PARSE_NUMBER_H -#include -#include -#include -#include - namespace fast_float { From patchwork Sun Jan 16 18:06:50 2022 Content-Type: text/plain; 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[24.228.8.148]) by smtp.gmail.com with ESMTPSA id o10sm7994149qtx.33.2022.01.16.10.06.58 (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Sun, 16 Jan 2022 10:06:58 -0800 (PST) To: gcc-patches@gcc.gnu.org Subject: [PATCH 4/6] libstdc++: Adjust fast_float's over/underflow behavior for conformnace Date: Sun, 16 Jan 2022 13:06:50 -0500 Message-Id: <20220116180652.3694791-4-ppalka@redhat.com> X-Mailer: git-send-email 2.35.0.rc1 In-Reply-To: <20220116180652.3694791-1-ppalka@redhat.com> References: <20220116180652.3694791-1-ppalka@redhat.com> MIME-Version: 1.0 X-Mimecast-Spam-Score: 0 X-Mimecast-Originator: redhat.com X-Spam-Status: No, score=-14.6 required=5.0 tests=BAYES_00, DKIMWL_WL_HIGH, DKIM_SIGNED, DKIM_VALID, DKIM_VALID_AU, DKIM_VALID_EF, GIT_PATCH_0, RCVD_IN_DNSWL_LOW, RCVD_IN_MSPIKE_H3, RCVD_IN_MSPIKE_WL, SPF_HELO_NONE, SPF_NONE, TXREP autolearn=ham autolearn_force=no version=3.4.4 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on server2.sourceware.org X-BeenThere: gcc-patches@gcc.gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Gcc-patches mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-Patchwork-Original-From: Patrick Palka via Gcc-patches From: Patrick Palka Reply-To: Patrick Palka Cc: libstdc++@gcc.gnu.org Errors-To: gcc-patches-bounces+patchwork=sourceware.org@gcc.gnu.org Sender: "Gcc-patches" This makes fast_float handle the situation where std::from_chars is specified to return result_out_of_range, i.e. when the parsed value is outside the representable range of the floating-point type. This adjusts fast_float's behavior in case of over/underflow: instead of returning errc{} and setting value to +-0 or +-infinity, return result_out_of_range and don't modify value, as per [charconv.from.chars]/1. libstdc++-v3/ChangeLog: * src/c++17/fast_float/LOCAL_PATCHES: Update. * src/c++17/fast_float/fast_float.h (from_chars_advanced): In case of over/underflow, return errc::result_out_of_range and don't modify 'value'. --- libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES | 1 + libstdc++-v3/src/c++17/fast_float/fast_float.h | 9 +++++++++ 2 files changed, 10 insertions(+) diff --git a/libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES b/libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES index e9d7bba6195..1f90f9d1d85 100644 --- a/libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES +++ b/libstdc++-v3/src/c++17/fast_float/LOCAL_PATCHES @@ -1 +1,2 @@ r12-???? +r12-???? diff --git a/libstdc++-v3/src/c++17/fast_float/fast_float.h b/libstdc++-v3/src/c++17/fast_float/fast_float.h index c908719ec3a..97d28940944 100644 --- a/libstdc++-v3/src/c++17/fast_float/fast_float.h +++ b/libstdc++-v3/src/c++17/fast_float/fast_float.h @@ -2884,6 +2884,15 @@ from_chars_result from_chars_advanced(const char *first, const char *last, // If we called compute_float>(pns.exponent, pns.mantissa) and we have an invalid power (am.power2 < 0), // then we need to go the long way around again. This is very uncommon. if(am.power2 < 0) { am = digit_comp(pns, am); } + + if((pns.mantissa != 0 && am.mantissa == 0 && am.power2 == 0) || am.power2 == binary_format::infinite_power()) { + // In case of over/underflow, return result_out_of_range and don't modify value, + // as per [charconv.from.chars]/1. Note that LWG 3081 wants to modify value in + // this case too. + answer.ec = std::errc::result_out_of_range; + return answer; + } + to_float(pns.negative, am, value); return answer; } From patchwork Sun Jan 16 18:06:51 2022 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit X-Patchwork-Submitter: Patrick Palka X-Patchwork-Id: 50083 Return-Path: X-Original-To: patchwork@sourceware.org Delivered-To: patchwork@sourceware.org Received: from server2.sourceware.org (localhost [IPv6:::1]) by sourceware.org (Postfix) with ESMTP id F2A893858427 for ; Sun, 16 Jan 2022 18:11:15 +0000 (GMT) DKIM-Filter: OpenDKIM Filter v2.11.0 sourceware.org F2A893858427 DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gcc.gnu.org; s=default; t=1642356676; bh=pzA9jREwHEoHqUIe98xV+KWAoNRjvl2rv6mj21B9u84=; h=To:Subject:Date:In-Reply-To:References:List-Id:List-Unsubscribe: List-Archive:List-Post:List-Help:List-Subscribe:From:Reply-To:Cc: From; b=VXGQYnOdBnCgZBEbFx9eRMgg5wJ9zxPbo6UwGynebXkN67WNYp886GqUlb9tNDo+i VZ2UXr8KgSS5dx/39Bioyv56zStkfHjyH3NJtYU1JXy+SHN1+hNYAea+sIufvhR4iU Ke1WXGr6u3gImfXQfF44FAdz5P66u11JpwxW9kTY= X-Original-To: gcc-patches@gcc.gnu.org Delivered-To: gcc-patches@gcc.gnu.org Received: from us-smtp-delivery-124.mimecast.com (us-smtp-delivery-124.mimecast.com [170.10.133.124]) by sourceware.org (Postfix) with ESMTPS id 60BDA3858400 for ; Sun, 16 Jan 2022 18:07:03 +0000 (GMT) DMARC-Filter: OpenDMARC Filter v1.4.1 sourceware.org 60BDA3858400 Received: from mail-qv1-f71.google.com (mail-qv1-f71.google.com [209.85.219.71]) by relay.mimecast.com with ESMTP with STARTTLS (version=TLSv1.2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id us-mta-62-4JzpmHn8PKW3Zd7eOYrPhg-1; Sun, 16 Jan 2022 13:07:01 -0500 X-MC-Unique: 4JzpmHn8PKW3Zd7eOYrPhg-1 Received: by mail-qv1-f71.google.com with SMTP id kd18-20020a056214401200b0041c3942383aso1664895qvb.9 for ; Sun, 16 Jan 2022 10:07:01 -0800 (PST) X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20210112; h=x-gm-message-state:from:to:cc:subject:date:message-id:in-reply-to :references:mime-version:content-transfer-encoding; bh=pzA9jREwHEoHqUIe98xV+KWAoNRjvl2rv6mj21B9u84=; b=GKJ5TzL3Eykz4gojvKz+VnnJMxZQe//qXb9dPwqyeY7NXyVsW56yRpgoXzRkp7LdG4 A0hBq0LrhKX+lHqhvvhBTCgEyaPur1LkrWEPm8j1Oki22a378JYCmOQ1Ku0MdzSfZeLV h/IR6RSlQhWgpiRjOHbei/c3Z2pfOxeewue6MzpuyQ1ePssK/dLFGuIob9CfkUZ223eH JVmdbpJZsAALp45w0uYf6TWTaD1HzHTnQuBWhDtx/YOy51VrhV2e7VtbmbAybqb8Q/8z VRfpE4fYpLCV/I1r+057Iu3B/bvFGVcDnpR9jFh60gZO6FnmyXL1zWKo6OqwIIQ6J6Ld 6JSQ== X-Gm-Message-State: AOAM532DLiQrpu6OjCf4Uw9Q+fOOINIEr/1tEafXnymp9b7yXE16zVCo QSK7oAx1dwf1GawfaG6f7dD7OrMV9gz/y1qnddcYFWw5Fy96GxQLM8LejJ/XYeg9CE6FyM6sG1v fgVVCJY0zlq6rkB5Ja+Ix8EdR/htyBJ7I0iwyJ88SgxxrEQxRlGdl1EA1qDqpm2EFVYg= X-Received: by 2002:a37:6144:: with SMTP id v65mr11953437qkb.528.1642356420930; Sun, 16 Jan 2022 10:07:00 -0800 (PST) X-Google-Smtp-Source: ABdhPJw9haCPKJyBBy+8Q0ww/uGIwGFeufjAbDOxdxWYNtC/DL5RZLU1t/grsviG6YbYlesjZpwsag== X-Received: by 2002:a37:6144:: with SMTP id v65mr11953421qkb.528.1642356420656; Sun, 16 Jan 2022 10:07:00 -0800 (PST) Received: from localhost.localdomain (ool-18e40894.dyn.optonline.net. [24.228.8.148]) by smtp.gmail.com with ESMTPSA id o10sm7994149qtx.33.2022.01.16.10.06.59 (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Sun, 16 Jan 2022 10:06:59 -0800 (PST) To: gcc-patches@gcc.gnu.org Subject: [PATCH 5/6] libstdc++: Use fast_float in std::from_chars for binary32/64 Date: Sun, 16 Jan 2022 13:06:51 -0500 Message-Id: <20220116180652.3694791-5-ppalka@redhat.com> X-Mailer: git-send-email 2.35.0.rc1 In-Reply-To: <20220116180652.3694791-1-ppalka@redhat.com> References: <20220116180652.3694791-1-ppalka@redhat.com> MIME-Version: 1.0 X-Mimecast-Spam-Score: 0 X-Mimecast-Originator: redhat.com X-Spam-Status: No, score=-14.4 required=5.0 tests=BAYES_00, DKIMWL_WL_HIGH, DKIM_SIGNED, DKIM_VALID, DKIM_VALID_AU, DKIM_VALID_EF, GIT_PATCH_0, KAM_NUMSUBJECT, RCVD_IN_DNSWL_LOW, RCVD_IN_MSPIKE_H3, RCVD_IN_MSPIKE_WL, SPF_HELO_NONE, SPF_NONE, TXREP autolearn=unavailable autolearn_force=no version=3.4.4 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on server2.sourceware.org X-BeenThere: gcc-patches@gcc.gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Gcc-patches mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-Patchwork-Original-From: Patrick Palka via Gcc-patches From: Patrick Palka Reply-To: Patrick Palka Cc: libstdc++@gcc.gnu.org Errors-To: gcc-patches-bounces+patchwork=sourceware.org@gcc.gnu.org Sender: "Gcc-patches" This makes our std::from_chars implementation use fast_float for parsing chars_format::scientific/fixed/general parsing into binary32/64 values. For other floating-point formats we still use the fallback implementation that goes through the strtod family of functions. libstdc++-v3/ChangeLog: * src/c++17/floating_from_chars.cc: (USE_LIB_FAST_FLOAT): Conditionally define, and use it to conditionally include fast_float. (from_chars): Use fast_float for float and double when USE_LIB_FAST_FLOAT. --- libstdc++-v3/src/c++17/floating_from_chars.cc | 31 ++++++++++++++++--- 1 file changed, 27 insertions(+), 4 deletions(-) diff --git a/libstdc++-v3/src/c++17/floating_from_chars.cc b/libstdc++-v3/src/c++17/floating_from_chars.cc index b186da9a955..c340eb18ea8 100644 --- a/libstdc++-v3/src/c++17/floating_from_chars.cc +++ b/libstdc++-v3/src/c++17/floating_from_chars.cc @@ -35,6 +35,7 @@ #include #include #include +#include #include #include #include @@ -53,6 +54,18 @@ extern "C" __ieee128 __strtoieee128(const char*, char**); #endif +#if _GLIBCXX_FLOAT_IS_IEEE_BINARY32 && _GLIBCXX_DOUBLE_IS_IEEE_BINARY64 +# define USE_LIB_FAST_FLOAT 1 +#endif + +#if USE_LIB_FAST_FLOAT +# define FASTFLOAT_DEBUG_ASSERT __glibcxx_assert +namespace +{ +# include "fast_float/fast_float.h" +} // anon namespace +#endif + #if _GLIBCXX_HAVE_USELOCALE namespace std _GLIBCXX_VISIBILITY(default) { @@ -775,8 +788,12 @@ from_chars(const char* first, const char* last, float& value, #if _GLIBCXX_FLOAT_IS_IEEE_BINARY32 && _GLIBCXX_DOUBLE_IS_IEEE_BINARY64 if (fmt == chars_format::hex) return __floating_from_chars_hex(first, last, value); -#endif - + else + { + static_assert(USE_LIB_FAST_FLOAT); + return fast_float::from_chars(first, last, value, fmt); + } +#else errc ec = errc::invalid_argument; #if _GLIBCXX_USE_CXX11_ABI buffer_resource mr; @@ -797,6 +814,7 @@ from_chars(const char* first, const char* last, float& value, fmt = chars_format{}; } return make_result(first, len, fmt, ec); +#endif } from_chars_result @@ -806,8 +824,12 @@ from_chars(const char* first, const char* last, double& value, #if _GLIBCXX_FLOAT_IS_IEEE_BINARY32 && _GLIBCXX_DOUBLE_IS_IEEE_BINARY64 if (fmt == chars_format::hex) return __floating_from_chars_hex(first, last, value); -#endif - + else + { + static_assert(USE_LIB_FAST_FLOAT); + return fast_float::from_chars(first, last, value, fmt); + } +#else errc ec = errc::invalid_argument; #if _GLIBCXX_USE_CXX11_ABI buffer_resource mr; @@ -828,6 +850,7 @@ from_chars(const char* first, const char* last, double& value, fmt = chars_format{}; } return make_result(first, len, fmt, ec); +#endif } from_chars_result From patchwork Sun Jan 16 18:06:52 2022 Content-Type: text/plain; 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[24.228.8.148]) by smtp.gmail.com with ESMTPSA id o10sm7994149qtx.33.2022.01.16.10.07.00 (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Sun, 16 Jan 2022 10:07:01 -0800 (PST) To: gcc-patches@gcc.gnu.org Subject: [PATCH 6/6] libstdc++: Import MSVC floating-point std::from_chars testcases Date: Sun, 16 Jan 2022 13:06:52 -0500 Message-Id: <20220116180652.3694791-6-ppalka@redhat.com> X-Mailer: git-send-email 2.35.0.rc1 In-Reply-To: <20220116180652.3694791-1-ppalka@redhat.com> References: <20220116180652.3694791-1-ppalka@redhat.com> MIME-Version: 1.0 X-Mimecast-Spam-Score: 0 X-Mimecast-Originator: redhat.com X-Spam-Status: No, score=-14.5 required=5.0 tests=BAYES_00, DKIMWL_WL_HIGH, DKIM_SIGNED, DKIM_VALID, DKIM_VALID_AU, DKIM_VALID_EF, GIT_PATCH_0, KAM_LOTSOFHASH, RCVD_IN_DNSWL_LOW, RCVD_IN_MSPIKE_H3, RCVD_IN_MSPIKE_WL, SPF_HELO_NONE, SPF_NONE, TXREP autolearn=ham autolearn_force=no version=3.4.4 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on server2.sourceware.org X-BeenThere: gcc-patches@gcc.gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Gcc-patches mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-Patchwork-Original-From: Patrick Palka via Gcc-patches From: Patrick Palka Reply-To: Patrick Palka Cc: libstdc++@gcc.gnu.org Errors-To: gcc-patches-bounces+patchwork=sourceware.org@gcc.gnu.org Sender: "Gcc-patches" libstdc++-v3/ChangeLog: * testsuite/20_util/from_chars/double.cc: New test, consisting of testcases extracted from the MSVC STL testsuite. * testsuite/20_util/from_chars/float.cc: New test. --- .../testsuite/20_util/from_chars/double.cc | 1674 +++++++++++++++++ .../testsuite/20_util/from_chars/float.cc | 290 +++ 2 files changed, 1964 insertions(+) create mode 100644 libstdc++-v3/testsuite/20_util/from_chars/double.cc create mode 100644 libstdc++-v3/testsuite/20_util/from_chars/float.cc diff --git a/libstdc++-v3/testsuite/20_util/from_chars/double.cc b/libstdc++-v3/testsuite/20_util/from_chars/double.cc new file mode 100644 index 00000000000..ce53a1c56c2 --- /dev/null +++ b/libstdc++-v3/testsuite/20_util/from_chars/double.cc @@ -0,0 +1,1674 @@ +// This file consists of testcases extracted from the MSVC STL testsuite. + +// Copyright (c) Microsoft Corporation. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception + +// { dg-do run { target c++17 } } +// { dg-require-effective-target ieee_floats } + +#include + +#include +#include +#include + +using namespace std; + +inline constexpr double double_inf = numeric_limits::infinity(); + +struct double_from_chars_testcase { + const char* input; + chars_format fmt; + size_t correct_idx; + errc correct_ec; + double correct_value; +}; + +inline constexpr double_from_chars_testcase double_from_chars_test_cases[] = { + {"1.000000000000a000", chars_format::hex, 18, errc{}, 0x1.000000000000ap0}, // exact + {"1.000000000000a001", chars_format::hex, 18, errc{}, 0x1.000000000000ap0}, // below midpoint, round down + {"1.000000000000a800", chars_format::hex, 18, errc{}, 0x1.000000000000ap0}, // midpoint, round down to even + {"1.000000000000a801", chars_format::hex, 18, errc{}, 0x1.000000000000bp0}, // above midpoint, round up + {"1.000000000000b000", chars_format::hex, 18, errc{}, 0x1.000000000000bp0}, // exact + {"1.000000000000b001", chars_format::hex, 18, errc{}, 0x1.000000000000bp0}, // below midpoint, round down + {"1.000000000000b800", chars_format::hex, 18, errc{}, 0x1.000000000000cp0}, // midpoint, round up to even + {"1.000000000000b801", chars_format::hex, 18, errc{}, 0x1.000000000000cp0}, // above midpoint, round up + + {"1.00000000000020", chars_format::hex, 16, errc{}, 0x1.0000000000002p0}, // exact + {"1.00000000000021", chars_format::hex, 16, errc{}, 0x1.0000000000002p0}, // below midpoint, round down + {"1.00000000000028", chars_format::hex, 16, errc{}, 0x1.0000000000002p0}, // midpoint, round down to even + {"1.00000000000029", chars_format::hex, 16, errc{}, 0x1.0000000000003p0}, // above midpoint, round up + {"1.00000000000030", chars_format::hex, 16, errc{}, 0x1.0000000000003p0}, // exact + {"1.00000000000031", chars_format::hex, 16, errc{}, 0x1.0000000000003p0}, // below midpoint, round down + {"1.00000000000038", chars_format::hex, 16, errc{}, 0x1.0000000000004p0}, // midpoint, round up to even + {"1.00000000000039", chars_format::hex, 16, errc{}, 0x1.0000000000004p0}, // above midpoint, round up + + {"1.00000000000000044408920985006261616945266723632812500000", chars_format::general, 58, errc{}, + 0x1.0000000000002p0}, // exact + {"1.00000000000000045796699765787707292474806308746337890625", chars_format::general, 58, errc{}, + 0x1.0000000000002p0}, // below midpoint, round down + {"1.00000000000000055511151231257827021181583404541015624999", chars_format::general, 58, errc{}, + 0x1.0000000000002p0}, // below midpoint, round down + {"1.00000000000000055511151231257827021181583404541015625000", chars_format::general, 58, errc{}, + 0x1.0000000000002p0}, // midpoint, round down to even + {"1.00000000000000055511151231257827021181583404541015625001", chars_format::general, 58, errc{}, + 0x1.0000000000003p0}, // above midpoint, round up + {"1.00000000000000056898930012039272696711122989654541015625", chars_format::general, 58, errc{}, + 0x1.0000000000003p0}, // above midpoint, round up + {"1.00000000000000066613381477509392425417900085449218750000", chars_format::general, 58, errc{}, + 0x1.0000000000003p0}, // exact + {"1.00000000000000068001160258290838100947439670562744140625", chars_format::general, 58, errc{}, + 0x1.0000000000003p0}, // below midpoint, round down + {"1.00000000000000077715611723760957829654216766357421874999", chars_format::general, 58, errc{}, + 0x1.0000000000003p0}, // below midpoint, round down + {"1.00000000000000077715611723760957829654216766357421875000", chars_format::general, 58, errc{}, + 0x1.0000000000004p0}, // midpoint, round up to even + {"1.00000000000000077715611723760957829654216766357421875001", chars_format::general, 58, errc{}, + 0x1.0000000000004p0}, // above midpoint, round up + {"1.00000000000000079103390504542403505183756351470947265625", chars_format::general, 58, errc{}, + 0x1.0000000000004p0}, // above midpoint, round up + + // https://www.exploringbinary.com/nondeterministic-floating-point-conversions-in-java/ + {"0.0000008p-1022", chars_format::hex, 15, errc{}, 0x0.0000008p-1022}, + + // VSO-838635 ": from_chars() mishandles certain subnormals" + // These values change on half-ulp boundaries: + // 1 * 2^-1075 ~= 2.47e-324 (half-ulp between zero and min subnormal) + // 2 * 2^-1075 ~= 4.94e-324 (min subnormal) + // 3 * 2^-1075 ~= 7.41e-324 (half-ulp between min subnormal and next subnormal) + // 4 * 2^-1075 ~= 9.88e-324 (next subnormal) + {"1." + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111e-324", + chars_format::scientific, 1007, errc::result_out_of_range, 0x0.0000000000000p+0}, + {"2." + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222e-324", + chars_format::scientific, 1007, errc::result_out_of_range, 0x0.0000000000000p+0}, + {"3." + "3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333" + "3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333" + "3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333" + "3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333" + "3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333" + "3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333" + "3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333" + "3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333" + "3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333" + "3333333333333333333e-324", + chars_format::scientific, 1007, errc{}, 0x0.0000000000001p-1022}, + {"4." + "4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444" + "4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444" + "4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444" + "4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444" + "4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444" + "4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444" + "4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444" + "4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444" + "4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444" + "4444444444444444444e-324", + chars_format::scientific, 1007, errc{}, 0x0.0000000000001p-1022}, + {"5." + "5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555" + "5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555" + "5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555" + "5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555" + "5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555" + "5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555" + "5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555" + "5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555" + "5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555" + "5555555555555555555e-324", + chars_format::scientific, 1007, errc{}, 0x0.0000000000001p-1022}, + {"6." + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666e-324", + chars_format::scientific, 1007, errc{}, 0x0.0000000000001p-1022}, + {"7." + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777e-324", + chars_format::scientific, 1007, errc{}, 0x0.0000000000002p-1022}, + {"8." + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888e-324", + chars_format::scientific, 1007, errc{}, 0x0.0000000000002p-1022}, + {"9." + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999e-324", + chars_format::scientific, 1007, errc{}, 0x0.0000000000002p-1022}, + + // VSO-852024: Test cases for round-to-nearest, ties-to-even. + // Consider the values: + // A: 0x1.0000000000000p+0 == 1.0000000000000000000000000000000000000000000000000000 + // X: (1 + 2^-53) * 2^0 == 1.00000000000000011102230246251565404236316680908203125 + // B: 0x1.0000000000001p+0 == 1.0000000000000002220446049250313080847263336181640625 + // X is equidistant from A and B. Because they're tied for being nearest, we need to round to even. + // That means rounding down to A, because A's least significant hexit 0 is even. + // However, values between X and B aren't tied - they're simply nearer to B, so they need to round up to B. + // We need to handle tricky cases like the digits of X, followed by a million 0 digits, followed by a 1 digit. + // Similarly: + // E: 0x1.ffffffffffffep+0 == 1.999999999999999555910790149937383830547332763671875 + // Y: (1 + 1 - 3 * 2^-53) * 2^0 == 1.99999999999999966693309261245303787291049957275390625 + // F: 0x1.fffffffffffffp+0 == 1.9999999999999997779553950749686919152736663818359375 + // The hexit E is 14 and even, while F is 15 and odd. + + // just below (0 + 2^-53) * 2^-1022: decremented last digit, then appended three 9 digits + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002470" + "3282292062327208828439643411068618252990130716238221279284125033775363510437593264991818081799618989828234772" + "2858865463328355177969898199387398005390939063150356595155702263922908583924491051844359318028499365361525003" + "1937045767824921936562366986365848075700158576926990370631192827955855133292783433840935197801553124659726357" + "9574622766465272827220056374006485499977096599470454020828166226237857393450736339007967761930577506740176324" + "6736009689513405355374585166611342237666786041621596804619144672918403005300575308490487653917113865916462395" + "2491262365388187963623937328042389101867234849766823508986338858792562830275599565752445550725518931369083625" + "4779186948667994968324049705821028513185451396213837722826145437693412532098591327667236328124999", + chars_format::fixed, 1080, errc::result_out_of_range, 0x0.0000000000000p+0}, + + // (0 + 2^-53) * 2^-1022 exactly + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002470" + "3282292062327208828439643411068618252990130716238221279284125033775363510437593264991818081799618989828234772" + "2858865463328355177969898199387398005390939063150356595155702263922908583924491051844359318028499365361525003" + "1937045767824921936562366986365848075700158576926990370631192827955855133292783433840935197801553124659726357" + "9574622766465272827220056374006485499977096599470454020828166226237857393450736339007967761930577506740176324" + "6736009689513405355374585166611342237666786041621596804619144672918403005300575308490487653917113865916462395" + "2491262365388187963623937328042389101867234849766823508986338858792562830275599565752445550725518931369083625" + "4779186948667994968324049705821028513185451396213837722826145437693412532098591327667236328125", + chars_format::fixed, 1077, errc::result_out_of_range, 0x0.0000000000000p+0}, + + // (0 + 2^-53) * 2^-1022 exactly, followed by a thousand 0 digits + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002470" + "3282292062327208828439643411068618252990130716238221279284125033775363510437593264991818081799618989828234772" + "2858865463328355177969898199387398005390939063150356595155702263922908583924491051844359318028499365361525003" + "1937045767824921936562366986365848075700158576926990370631192827955855133292783433840935197801553124659726357" + "9574622766465272827220056374006485499977096599470454020828166226237857393450736339007967761930577506740176324" + "6736009689513405355374585166611342237666786041621596804619144672918403005300575308490487653917113865916462395" + "2491262365388187963623937328042389101867234849766823508986338858792562830275599565752445550725518931369083625" + "4779186948667994968324049705821028513185451396213837722826145437693412532098591327667236328125000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000", + chars_format::fixed, 2077, errc::result_out_of_range, 0x0.0000000000000p+0}, + + // above (0 + 2^-53) * 2^-1022: appended a thousand 0 digits followed by a 1 digit + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002470" + "3282292062327208828439643411068618252990130716238221279284125033775363510437593264991818081799618989828234772" + "2858865463328355177969898199387398005390939063150356595155702263922908583924491051844359318028499365361525003" + "1937045767824921936562366986365848075700158576926990370631192827955855133292783433840935197801553124659726357" + "9574622766465272827220056374006485499977096599470454020828166226237857393450736339007967761930577506740176324" + "6736009689513405355374585166611342237666786041621596804619144672918403005300575308490487653917113865916462395" + "2491262365388187963623937328042389101867234849766823508986338858792562830275599565752445550725518931369083625" + "4779186948667994968324049705821028513185451396213837722826145437693412532098591327667236328125000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00001", + chars_format::fixed, 2078, errc{}, 0x0.0000000000001p-1022}, + + // above (0 + 2^-53) * 2^-1022: appended a 1 digit + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002470" + "3282292062327208828439643411068618252990130716238221279284125033775363510437593264991818081799618989828234772" + "2858865463328355177969898199387398005390939063150356595155702263922908583924491051844359318028499365361525003" + "1937045767824921936562366986365848075700158576926990370631192827955855133292783433840935197801553124659726357" + "9574622766465272827220056374006485499977096599470454020828166226237857393450736339007967761930577506740176324" + "6736009689513405355374585166611342237666786041621596804619144672918403005300575308490487653917113865916462395" + "2491262365388187963623937328042389101867234849766823508986338858792562830275599565752445550725518931369083625" + "47791869486679949683240497058210285131854513962138377228261454376934125320985913276672363281251", + chars_format::fixed, 1078, errc{}, 0x0.0000000000001p-1022}, + + // above (0 + 2^-53) * 2^-1022: incremented last digit + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002470" + "3282292062327208828439643411068618252990130716238221279284125033775363510437593264991818081799618989828234772" + "2858865463328355177969898199387398005390939063150356595155702263922908583924491051844359318028499365361525003" + "1937045767824921936562366986365848075700158576926990370631192827955855133292783433840935197801553124659726357" + "9574622766465272827220056374006485499977096599470454020828166226237857393450736339007967761930577506740176324" + "6736009689513405355374585166611342237666786041621596804619144672918403005300575308490487653917113865916462395" + "2491262365388187963623937328042389101867234849766823508986338858792562830275599565752445550725518931369083625" + "4779186948667994968324049705821028513185451396213837722826145437693412532098591327667236328126", + chars_format::fixed, 1077, errc{}, 0x0.0000000000001p-1022}, + + // just below (0 + 1 - 3 * 2^-53) * 2^-1022: decremented last digit, then appended three 9 digits + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072006419" + "9176395546258779936602667813027328296362349540005779643539444484102225369938322261431279727704724131030539099" + "2976863718870946851468024222968583977359185141028540361975476844303195813273469348201130421165308554532083149" + "3676067608324920106709384047261543474082573017216837765643921010648239116172158852475760231303527077156200284" + "1775343298712758123539074213191978739083589771549597066404661620550578925994422322342444472859570416955675758" + "5423752417124134805999073137808018133811049489046686648944255834488901008259721496147104204399198556535697531" + "0055231935448663898095485089604066035268185282450207861510244351362091237759797852153577038777504570568436147" + "5530270683064113556748943345076587312006145811358486831521563686919762403704226016998291015624999", + chars_format::fixed, 1080, errc{}, 0x0.ffffffffffffep-1022}, + + // (0 + 1 - 3 * 2^-53) * 2^-1022 exactly + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072006419" + "9176395546258779936602667813027328296362349540005779643539444484102225369938322261431279727704724131030539099" + "2976863718870946851468024222968583977359185141028540361975476844303195813273469348201130421165308554532083149" + "3676067608324920106709384047261543474082573017216837765643921010648239116172158852475760231303527077156200284" + "1775343298712758123539074213191978739083589771549597066404661620550578925994422322342444472859570416955675758" + "5423752417124134805999073137808018133811049489046686648944255834488901008259721496147104204399198556535697531" + "0055231935448663898095485089604066035268185282450207861510244351362091237759797852153577038777504570568436147" + "5530270683064113556748943345076587312006145811358486831521563686919762403704226016998291015625", + chars_format::fixed, 1077, errc{}, 0x0.ffffffffffffep-1022}, + + // (0 + 1 - 3 * 2^-53) * 2^-1022 exactly, followed by a thousand 0 digits + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072006419" + "9176395546258779936602667813027328296362349540005779643539444484102225369938322261431279727704724131030539099" + "2976863718870946851468024222968583977359185141028540361975476844303195813273469348201130421165308554532083149" + "3676067608324920106709384047261543474082573017216837765643921010648239116172158852475760231303527077156200284" + "1775343298712758123539074213191978739083589771549597066404661620550578925994422322342444472859570416955675758" + "5423752417124134805999073137808018133811049489046686648944255834488901008259721496147104204399198556535697531" + "0055231935448663898095485089604066035268185282450207861510244351362091237759797852153577038777504570568436147" + "5530270683064113556748943345076587312006145811358486831521563686919762403704226016998291015625000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000", + chars_format::fixed, 2077, errc{}, 0x0.ffffffffffffep-1022}, + + // above (0 + 1 - 3 * 2^-53) * 2^-1022: appended a thousand 0 digits followed by a 1 digit + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072006419" + "9176395546258779936602667813027328296362349540005779643539444484102225369938322261431279727704724131030539099" + "2976863718870946851468024222968583977359185141028540361975476844303195813273469348201130421165308554532083149" + "3676067608324920106709384047261543474082573017216837765643921010648239116172158852475760231303527077156200284" + "1775343298712758123539074213191978739083589771549597066404661620550578925994422322342444472859570416955675758" + "5423752417124134805999073137808018133811049489046686648944255834488901008259721496147104204399198556535697531" + "0055231935448663898095485089604066035268185282450207861510244351362091237759797852153577038777504570568436147" + "5530270683064113556748943345076587312006145811358486831521563686919762403704226016998291015625000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00001", + chars_format::fixed, 2078, errc{}, 0x0.fffffffffffffp-1022}, + + // above (0 + 1 - 3 * 2^-53) * 2^-1022: appended a 1 digit + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072006419" + "9176395546258779936602667813027328296362349540005779643539444484102225369938322261431279727704724131030539099" + "2976863718870946851468024222968583977359185141028540361975476844303195813273469348201130421165308554532083149" + "3676067608324920106709384047261543474082573017216837765643921010648239116172158852475760231303527077156200284" + "1775343298712758123539074213191978739083589771549597066404661620550578925994422322342444472859570416955675758" + "5423752417124134805999073137808018133811049489046686648944255834488901008259721496147104204399198556535697531" + "0055231935448663898095485089604066035268185282450207861510244351362091237759797852153577038777504570568436147" + "55302706830641135567489433450765873120061458113584868315215636869197624037042260169982910156251", + chars_format::fixed, 1078, errc{}, 0x0.fffffffffffffp-1022}, + + // above (0 + 1 - 3 * 2^-53) * 2^-1022: incremented last digit + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072006419" + "9176395546258779936602667813027328296362349540005779643539444484102225369938322261431279727704724131030539099" + "2976863718870946851468024222968583977359185141028540361975476844303195813273469348201130421165308554532083149" + "3676067608324920106709384047261543474082573017216837765643921010648239116172158852475760231303527077156200284" + "1775343298712758123539074213191978739083589771549597066404661620550578925994422322342444472859570416955675758" + "5423752417124134805999073137808018133811049489046686648944255834488901008259721496147104204399198556535697531" + "0055231935448663898095485089604066035268185282450207861510244351362091237759797852153577038777504570568436147" + "5530270683064113556748943345076587312006145811358486831521563686919762403704226016998291015626", + chars_format::fixed, 1077, errc{}, 0x0.fffffffffffffp-1022}, + + // just below (1 + 2^-53) * 2^-1022: decremented last digit, then appended three 9 digits + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072016301" + "2305563795567615250361241457301801308322872404958664760675944619203679411688695321398552054903200090343478188" + "4412325572184367563347617020518175998922941393629966742598285899994830148971433555578567693279306015978183162" + "1424250679624607852958851992724935776883207324924799248168692322471659649343292587839501022509739575795105716" + "0073834364573849432419299709217920738991976169431413149717326525502008499797367678374315520581880443916381057" + "2367791175177756227497413804253387084478193655533073867420834526162513029462022730109054820067654020201547112" + "0020281397001415752591234401773622442737124681517501897455599786532342558862196115163359241679580296044770649" + "4647018477736093430045142168360701364747951396213837722826145437693412532098591327667236328124999", + chars_format::fixed, 1080, errc{}, 0x1.0000000000000p-1022}, + + // (1 + 2^-53) * 2^-1022 exactly + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072016301" + "2305563795567615250361241457301801308322872404958664760675944619203679411688695321398552054903200090343478188" + "4412325572184367563347617020518175998922941393629966742598285899994830148971433555578567693279306015978183162" + "1424250679624607852958851992724935776883207324924799248168692322471659649343292587839501022509739575795105716" + "0073834364573849432419299709217920738991976169431413149717326525502008499797367678374315520581880443916381057" + "2367791175177756227497413804253387084478193655533073867420834526162513029462022730109054820067654020201547112" + "0020281397001415752591234401773622442737124681517501897455599786532342558862196115163359241679580296044770649" + "4647018477736093430045142168360701364747951396213837722826145437693412532098591327667236328125", + chars_format::fixed, 1077, errc{}, 0x1.0000000000000p-1022}, + + // (1 + 2^-53) * 2^-1022 exactly, followed by a thousand 0 digits + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072016301" + "2305563795567615250361241457301801308322872404958664760675944619203679411688695321398552054903200090343478188" + "4412325572184367563347617020518175998922941393629966742598285899994830148971433555578567693279306015978183162" + "1424250679624607852958851992724935776883207324924799248168692322471659649343292587839501022509739575795105716" + "0073834364573849432419299709217920738991976169431413149717326525502008499797367678374315520581880443916381057" + "2367791175177756227497413804253387084478193655533073867420834526162513029462022730109054820067654020201547112" + "0020281397001415752591234401773622442737124681517501897455599786532342558862196115163359241679580296044770649" + "4647018477736093430045142168360701364747951396213837722826145437693412532098591327667236328125000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000", + chars_format::fixed, 2077, errc{}, 0x1.0000000000000p-1022}, + + // above (1 + 2^-53) * 2^-1022: appended a thousand 0 digits followed by a 1 digit + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072016301" + "2305563795567615250361241457301801308322872404958664760675944619203679411688695321398552054903200090343478188" + "4412325572184367563347617020518175998922941393629966742598285899994830148971433555578567693279306015978183162" + "1424250679624607852958851992724935776883207324924799248168692322471659649343292587839501022509739575795105716" + "0073834364573849432419299709217920738991976169431413149717326525502008499797367678374315520581880443916381057" + "2367791175177756227497413804253387084478193655533073867420834526162513029462022730109054820067654020201547112" + "0020281397001415752591234401773622442737124681517501897455599786532342558862196115163359241679580296044770649" + "4647018477736093430045142168360701364747951396213837722826145437693412532098591327667236328125000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00001", + chars_format::fixed, 2078, errc{}, 0x1.0000000000001p-1022}, + + // above (1 + 2^-53) * 2^-1022: appended a 1 digit + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072016301" + "2305563795567615250361241457301801308322872404958664760675944619203679411688695321398552054903200090343478188" + "4412325572184367563347617020518175998922941393629966742598285899994830148971433555578567693279306015978183162" + "1424250679624607852958851992724935776883207324924799248168692322471659649343292587839501022509739575795105716" + "0073834364573849432419299709217920738991976169431413149717326525502008499797367678374315520581880443916381057" + "2367791175177756227497413804253387084478193655533073867420834526162513029462022730109054820067654020201547112" + "0020281397001415752591234401773622442737124681517501897455599786532342558862196115163359241679580296044770649" + "46470184777360934300451421683607013647479513962138377228261454376934125320985913276672363281251", + chars_format::fixed, 1078, errc{}, 0x1.0000000000001p-1022}, + + // above (1 + 2^-53) * 2^-1022: incremented last digit + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000022250738585072016301" + "2305563795567615250361241457301801308322872404958664760675944619203679411688695321398552054903200090343478188" + "4412325572184367563347617020518175998922941393629966742598285899994830148971433555578567693279306015978183162" + "1424250679624607852958851992724935776883207324924799248168692322471659649343292587839501022509739575795105716" + "0073834364573849432419299709217920738991976169431413149717326525502008499797367678374315520581880443916381057" + "2367791175177756227497413804253387084478193655533073867420834526162513029462022730109054820067654020201547112" + "0020281397001415752591234401773622442737124681517501897455599786532342558862196115163359241679580296044770649" + "4647018477736093430045142168360701364747951396213837722826145437693412532098591327667236328126", + chars_format::fixed, 1077, errc{}, 0x1.0000000000001p-1022}, + + // just below (1 + 1 - 3 * 2^-53) * 2^-1022: decremented last digit, then appended three 9 digits + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000044501477170144020250" + "8199667279499186358524265859260511351695091228726223124931264069530541271189424317838013700808305231545782515" + "4530323827726959236845743044099361970891187471508150509418060480375117378320411851935338796416115205148741308" + "3163272520124606023105869053620631175265621765214646643181420505164043632222668006474326056011713528291579642" + "2274554896821334728738317548403413978098469341510556195293821919814730032341053661708792231510873354131880491" + "1055533902788485678121901775450062980622457102958163711745945687733011032421168917765671370549738710820782247" + "7584250967061891687062782163335299376138075114200886249979505279101870966346394401564490729731565935244123171" + "5398102212132212018470035807616260163568645811358486831521563686919762403704226016998291015624999", + chars_format::fixed, 1080, errc{}, 0x1.ffffffffffffep-1022}, + + // (1 + 1 - 3 * 2^-53) * 2^-1022 exactly + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000044501477170144020250" + "8199667279499186358524265859260511351695091228726223124931264069530541271189424317838013700808305231545782515" + "4530323827726959236845743044099361970891187471508150509418060480375117378320411851935338796416115205148741308" + "3163272520124606023105869053620631175265621765214646643181420505164043632222668006474326056011713528291579642" + "2274554896821334728738317548403413978098469341510556195293821919814730032341053661708792231510873354131880491" + "1055533902788485678121901775450062980622457102958163711745945687733011032421168917765671370549738710820782247" + "7584250967061891687062782163335299376138075114200886249979505279101870966346394401564490729731565935244123171" + "5398102212132212018470035807616260163568645811358486831521563686919762403704226016998291015625", + chars_format::fixed, 1077, errc{}, 0x1.ffffffffffffep-1022}, + + // (1 + 1 - 3 * 2^-53) * 2^-1022 exactly, followed by a thousand 0 digits + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000044501477170144020250" + "8199667279499186358524265859260511351695091228726223124931264069530541271189424317838013700808305231545782515" + "4530323827726959236845743044099361970891187471508150509418060480375117378320411851935338796416115205148741308" + "3163272520124606023105869053620631175265621765214646643181420505164043632222668006474326056011713528291579642" + "2274554896821334728738317548403413978098469341510556195293821919814730032341053661708792231510873354131880491" + "1055533902788485678121901775450062980622457102958163711745945687733011032421168917765671370549738710820782247" + "7584250967061891687062782163335299376138075114200886249979505279101870966346394401564490729731565935244123171" + "5398102212132212018470035807616260163568645811358486831521563686919762403704226016998291015625000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000", + chars_format::fixed, 2077, errc{}, 0x1.ffffffffffffep-1022}, + + // above (1 + 1 - 3 * 2^-53) * 2^-1022: appended a thousand 0 digits followed by a 1 digit + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000044501477170144020250" + "8199667279499186358524265859260511351695091228726223124931264069530541271189424317838013700808305231545782515" + "4530323827726959236845743044099361970891187471508150509418060480375117378320411851935338796416115205148741308" + "3163272520124606023105869053620631175265621765214646643181420505164043632222668006474326056011713528291579642" + "2274554896821334728738317548403413978098469341510556195293821919814730032341053661708792231510873354131880491" + "1055533902788485678121901775450062980622457102958163711745945687733011032421168917765671370549738710820782247" + "7584250967061891687062782163335299376138075114200886249979505279101870966346394401564490729731565935244123171" + "5398102212132212018470035807616260163568645811358486831521563686919762403704226016998291015625000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00001", + chars_format::fixed, 2078, errc{}, 0x1.fffffffffffffp-1022}, + + // above (1 + 1 - 3 * 2^-53) * 2^-1022: appended a 1 digit + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000044501477170144020250" + "8199667279499186358524265859260511351695091228726223124931264069530541271189424317838013700808305231545782515" + "4530323827726959236845743044099361970891187471508150509418060480375117378320411851935338796416115205148741308" + "3163272520124606023105869053620631175265621765214646643181420505164043632222668006474326056011713528291579642" + "2274554896821334728738317548403413978098469341510556195293821919814730032341053661708792231510873354131880491" + "1055533902788485678121901775450062980622457102958163711745945687733011032421168917765671370549738710820782247" + "7584250967061891687062782163335299376138075114200886249979505279101870966346394401564490729731565935244123171" + "53981022121322120184700358076162601635686458113584868315215636869197624037042260169982910156251", + chars_format::fixed, 1078, errc{}, 0x1.fffffffffffffp-1022}, + + // above (1 + 1 - 3 * 2^-53) * 2^-1022: incremented last digit + {"0." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000044501477170144020250" + "8199667279499186358524265859260511351695091228726223124931264069530541271189424317838013700808305231545782515" + "4530323827726959236845743044099361970891187471508150509418060480375117378320411851935338796416115205148741308" + "3163272520124606023105869053620631175265621765214646643181420505164043632222668006474326056011713528291579642" + "2274554896821334728738317548403413978098469341510556195293821919814730032341053661708792231510873354131880491" + "1055533902788485678121901775450062980622457102958163711745945687733011032421168917765671370549738710820782247" + "7584250967061891687062782163335299376138075114200886249979505279101870966346394401564490729731565935244123171" + "5398102212132212018470035807616260163568645811358486831521563686919762403704226016998291015626", + chars_format::fixed, 1077, errc{}, 0x1.fffffffffffffp-1022}, + + // just below (1 + 2^-53) * 2^-33: decremented last digit, then appended three 9 digits + {"0.00000000011641532182693482737782207114105741986576081359316958696581423282623291015624999", chars_format::fixed, + 91, errc{}, 0x1.0000000000000p-33}, + + // (1 + 2^-53) * 2^-33 exactly + {"0.00000000011641532182693482737782207114105741986576081359316958696581423282623291015625", chars_format::fixed, + 88, errc{}, 0x1.0000000000000p-33}, + + // (1 + 2^-53) * 2^-33 exactly, followed by a thousand 0 digits + {"0." + "0000000001164153218269348273778220711410574198657608135931695869658142328262329101562500000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + chars_format::fixed, 1088, errc{}, 0x1.0000000000000p-33}, + + // above (1 + 2^-53) * 2^-33: appended a thousand 0 digits followed by a 1 digit + {"0." + "0000000001164153218269348273778220711410574198657608135931695869658142328262329101562500000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", + chars_format::fixed, 1089, errc{}, 0x1.0000000000001p-33}, + + // above (1 + 2^-53) * 2^-33: appended a 1 digit + {"0.000000000116415321826934827377822071141057419865760813593169586965814232826232910156251", chars_format::fixed, + 89, errc{}, 0x1.0000000000001p-33}, + + // above (1 + 2^-53) * 2^-33: incremented last digit + {"0.00000000011641532182693482737782207114105741986576081359316958696581423282623291015626", chars_format::fixed, + 88, errc{}, 0x1.0000000000001p-33}, + + // just below (1 + 1 - 3 * 2^-53) * 2^-33: decremented last digit, then appended three 9 digits + {"0.00000000023283064365386959013215878657682774040271755922049123910255730152130126953124999", chars_format::fixed, + 91, errc{}, 0x1.ffffffffffffep-33}, + + // (1 + 1 - 3 * 2^-53) * 2^-33 exactly + {"0.00000000023283064365386959013215878657682774040271755922049123910255730152130126953125", chars_format::fixed, + 88, errc{}, 0x1.ffffffffffffep-33}, + + // (1 + 1 - 3 * 2^-53) * 2^-33 exactly, followed by a thousand 0 digits + {"0." + "0000000002328306436538695901321587865768277404027175592204912391025573015213012695312500000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + chars_format::fixed, 1088, errc{}, 0x1.ffffffffffffep-33}, + + // above (1 + 1 - 3 * 2^-53) * 2^-33: appended a thousand 0 digits followed by a 1 digit + {"0." + "0000000002328306436538695901321587865768277404027175592204912391025573015213012695312500000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", + chars_format::fixed, 1089, errc{}, 0x1.fffffffffffffp-33}, + + // above (1 + 1 - 3 * 2^-53) * 2^-33: appended a 1 digit + {"0.000000000232830643653869590132158786576827740402717559220491239102557301521301269531251", chars_format::fixed, + 89, errc{}, 0x1.fffffffffffffp-33}, + + // above (1 + 1 - 3 * 2^-53) * 2^-33: incremented last digit + {"0.00000000023283064365386959013215878657682774040271755922049123910255730152130126953126", chars_format::fixed, + 88, errc{}, 0x1.fffffffffffffp-33}, + + // just below (1 + 2^-53) * 2^0: decremented last digit, then appended three 9 digits + {"1.00000000000000011102230246251565404236316680908203124999", chars_format::fixed, 58, errc{}, + 0x1.0000000000000p+0}, + + // (1 + 2^-53) * 2^0 exactly + {"1.00000000000000011102230246251565404236316680908203125", chars_format::fixed, 55, errc{}, 0x1.0000000000000p+0}, + + // (1 + 2^-53) * 2^0 exactly, followed by a thousand 0 digits + {"1." + "0000000000000001110223024625156540423631668090820312500000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "000000000000000000000000000000000000000000000000000000000000000000000000", + chars_format::fixed, 1055, errc{}, 0x1.0000000000000p+0}, + + // above (1 + 2^-53) * 2^0: appended a thousand 0 digits followed by a 1 digit + {"1." + "0000000000000001110223024625156540423631668090820312500000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000001", + chars_format::fixed, 1056, errc{}, 0x1.0000000000001p+0}, + + // above (1 + 2^-53) * 2^0: appended a 1 digit + {"1.000000000000000111022302462515654042363166809082031251", chars_format::fixed, 56, errc{}, 0x1.0000000000001p+0}, + + // above (1 + 2^-53) * 2^0: incremented last digit + {"1.00000000000000011102230246251565404236316680908203126", chars_format::fixed, 55, errc{}, 0x1.0000000000001p+0}, + + // just below (1 + 1 - 3 * 2^-53) * 2^0: decremented last digit, then appended three 9 digits + {"1.99999999999999966693309261245303787291049957275390624999", chars_format::fixed, 58, errc{}, + 0x1.ffffffffffffep+0}, + + // (1 + 1 - 3 * 2^-53) * 2^0 exactly + {"1.99999999999999966693309261245303787291049957275390625", chars_format::fixed, 55, errc{}, 0x1.ffffffffffffep+0}, + + // (1 + 1 - 3 * 2^-53) * 2^0 exactly, followed by a thousand 0 digits + {"1." + "9999999999999996669330926124530378729104995727539062500000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "000000000000000000000000000000000000000000000000000000000000000000000000", + chars_format::fixed, 1055, errc{}, 0x1.ffffffffffffep+0}, + + // above (1 + 1 - 3 * 2^-53) * 2^0: appended a thousand 0 digits followed by a 1 digit + {"1." + "9999999999999996669330926124530378729104995727539062500000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000001", + chars_format::fixed, 1056, errc{}, 0x1.fffffffffffffp+0}, + + // above (1 + 1 - 3 * 2^-53) * 2^0: appended a 1 digit + {"1.999999999999999666933092612453037872910499572753906251", chars_format::fixed, 56, errc{}, 0x1.fffffffffffffp+0}, + + // above (1 + 1 - 3 * 2^-53) * 2^0: incremented last digit + {"1.99999999999999966693309261245303787291049957275390626", chars_format::fixed, 55, errc{}, 0x1.fffffffffffffp+0}, + + // just below (1 + 2^-53) * 2^33: decremented last digit, then appended three 9 digits + {"8589934592.00000095367431640624999", chars_format::fixed, 34, errc{}, 0x1.0000000000000p+33}, + + // (1 + 2^-53) * 2^33 exactly + {"8589934592.00000095367431640625", chars_format::fixed, 31, errc{}, 0x1.0000000000000p+33}, + + // (1 + 2^-53) * 2^33 exactly, followed by a thousand 0 digits + {"8589934592." + "0000009536743164062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "000000000000000000000000000000000000000", + chars_format::fixed, 1031, errc{}, 0x1.0000000000000p+33}, + + // above (1 + 2^-53) * 2^33: appended a thousand 0 digits followed by a 1 digit + {"8589934592." + "0000009536743164062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000001", + chars_format::fixed, 1032, errc{}, 0x1.0000000000001p+33}, + + // above (1 + 2^-53) * 2^33: appended a 1 digit + {"8589934592.000000953674316406251", chars_format::fixed, 32, errc{}, 0x1.0000000000001p+33}, + + // above (1 + 2^-53) * 2^33: incremented last digit + {"8589934592.00000095367431640626", chars_format::fixed, 31, errc{}, 0x1.0000000000001p+33}, + + // just below (1 + 1 - 3 * 2^-53) * 2^33: decremented last digit, then appended three 9 digits + {"17179869183.99999713897705078124999", chars_format::fixed, 35, errc{}, 0x1.ffffffffffffep+33}, + + // (1 + 1 - 3 * 2^-53) * 2^33 exactly + {"17179869183.99999713897705078125", chars_format::fixed, 32, errc{}, 0x1.ffffffffffffep+33}, + + // (1 + 1 - 3 * 2^-53) * 2^33 exactly, followed by a thousand 0 digits + {"17179869183." + "9999971389770507812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "000000000000000000000000000000000000000", + chars_format::fixed, 1032, errc{}, 0x1.ffffffffffffep+33}, + + // above (1 + 1 - 3 * 2^-53) * 2^33: appended a thousand 0 digits followed by a 1 digit + {"17179869183." + "9999971389770507812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000001", + chars_format::fixed, 1033, errc{}, 0x1.fffffffffffffp+33}, + + // above (1 + 1 - 3 * 2^-53) * 2^33: appended a 1 digit + {"17179869183.999997138977050781251", chars_format::fixed, 33, errc{}, 0x1.fffffffffffffp+33}, + + // above (1 + 1 - 3 * 2^-53) * 2^33: incremented last digit + {"17179869183.99999713897705078126", chars_format::fixed, 32, errc{}, 0x1.fffffffffffffp+33}, + + // just below (1 + 2^-53) * 2^77: decremented last digit, then appended three 9 digits + {"151115727451828663615487.999", chars_format::fixed, 28, errc{}, 0x1.0000000000000p+77}, + + // (1 + 2^-53) * 2^77 exactly + {"151115727451828663615488", chars_format::fixed, 24, errc{}, 0x1.0000000000000p+77}, + + // (1 + 2^-53) * 2^77 exactly, followed by a thousand 0 digits + {"151115727451828663615488." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000", + chars_format::fixed, 1025, errc{}, 0x1.0000000000000p+77}, + + // above (1 + 2^-53) * 2^77: appended a thousand 0 digits followed by a 1 digit + {"151115727451828663615488." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000001", + chars_format::fixed, 1026, errc{}, 0x1.0000000000001p+77}, + + // above (1 + 2^-53) * 2^77: appended a 1 digit + {"151115727451828663615488.1", chars_format::fixed, 26, errc{}, 0x1.0000000000001p+77}, + + // above (1 + 2^-53) * 2^77: incremented last digit + {"151115727451828663615489", chars_format::fixed, 24, errc{}, 0x1.0000000000001p+77}, + + // just below (1 + 1 - 3 * 2^-53) * 2^77: decremented last digit, then appended three 9 digits + {"302231454903657243344895.999", chars_format::fixed, 28, errc{}, 0x1.ffffffffffffep+77}, + + // (1 + 1 - 3 * 2^-53) * 2^77 exactly + {"302231454903657243344896", chars_format::fixed, 24, errc{}, 0x1.ffffffffffffep+77}, + + // (1 + 1 - 3 * 2^-53) * 2^77 exactly, followed by a thousand 0 digits + {"302231454903657243344896." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000", + chars_format::fixed, 1025, errc{}, 0x1.ffffffffffffep+77}, + + // above (1 + 1 - 3 * 2^-53) * 2^77: appended a thousand 0 digits followed by a 1 digit + {"302231454903657243344896." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000001", + chars_format::fixed, 1026, errc{}, 0x1.fffffffffffffp+77}, + + // above (1 + 1 - 3 * 2^-53) * 2^77: appended a 1 digit + {"302231454903657243344896.1", chars_format::fixed, 26, errc{}, 0x1.fffffffffffffp+77}, + + // above (1 + 1 - 3 * 2^-53) * 2^77: incremented last digit + {"302231454903657243344897", chars_format::fixed, 24, errc{}, 0x1.fffffffffffffp+77}, + + // just below (1 + 2^-53) * 2^1023: decremented last digit, then appended three 9 digits + {"8988465674311580536566680721305029496276241413130815897397134275615404541548669375241369800602409693534988440" + "3114202125541629105369684531108613657287705365884742938136589844238179474556051429647415148697857438797685859" + "063890851407391008830874765563025951597582513936655578157348020066364210154316532161708031.999", + chars_format::fixed, 312, errc{}, 0x1.0000000000000p+1023}, + + // (1 + 2^-53) * 2^1023 exactly + {"8988465674311580536566680721305029496276241413130815897397134275615404541548669375241369800602409693534988440" + "3114202125541629105369684531108613657287705365884742938136589844238179474556051429647415148697857438797685859" + "063890851407391008830874765563025951597582513936655578157348020066364210154316532161708032", + chars_format::fixed, 308, errc{}, 0x1.0000000000000p+1023}, + + // (1 + 2^-53) * 2^1023 exactly, followed by a thousand 0 digits + {"8988465674311580536566680721305029496276241413130815897397134275615404541548669375241369800602409693534988440" + "3114202125541629105369684531108613657287705365884742938136589844238179474556051429647415148697857438797685859" + "063890851407391008830874765563025951597582513936655578157348020066364210154316532161708032." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000", + chars_format::fixed, 1309, errc{}, 0x1.0000000000000p+1023}, + + // above (1 + 2^-53) * 2^1023: appended a thousand 0 digits followed by a 1 digit + {"8988465674311580536566680721305029496276241413130815897397134275615404541548669375241369800602409693534988440" + "3114202125541629105369684531108613657287705365884742938136589844238179474556051429647415148697857438797685859" + "063890851407391008830874765563025951597582513936655578157348020066364210154316532161708032." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000001", + chars_format::fixed, 1310, errc{}, 0x1.0000000000001p+1023}, + + // above (1 + 2^-53) * 2^1023: appended a 1 digit + {"8988465674311580536566680721305029496276241413130815897397134275615404541548669375241369800602409693534988440" + "3114202125541629105369684531108613657287705365884742938136589844238179474556051429647415148697857438797685859" + "063890851407391008830874765563025951597582513936655578157348020066364210154316532161708032.1", + chars_format::fixed, 310, errc{}, 0x1.0000000000001p+1023}, + + // above (1 + 2^-53) * 2^1023: incremented last digit + {"8988465674311580536566680721305029496276241413130815897397134275615404541548669375241369800602409693534988440" + "3114202125541629105369684531108613657287705365884742938136589844238179474556051429647415148697857438797685859" + "063890851407391008830874765563025951597582513936655578157348020066364210154316532161708033", + chars_format::fixed, 308, errc{}, 0x1.0000000000001p+1023}, + + // just below (1 + 1 - 3 * 2^-53) * 2^1023: decremented last digit, then appended three 9 digits + {"1797693134862315608353258760581052985162070023416521662616611746258695532672923265745300992879465492467506314" + "9033587701752208710592698796290627760473556921329019091915239418047621712533496094635638726128664019802903779" + "9514183602981511756283727771403830521483963923935633133642802139091669457927874464075218943.999", + chars_format::fixed, 313, errc{}, 0x1.ffffffffffffep+1023}, + + // (1 + 1 - 3 * 2^-53) * 2^1023 exactly + {"1797693134862315608353258760581052985162070023416521662616611746258695532672923265745300992879465492467506314" + "9033587701752208710592698796290627760473556921329019091915239418047621712533496094635638726128664019802903779" + "9514183602981511756283727771403830521483963923935633133642802139091669457927874464075218944", + chars_format::fixed, 309, errc{}, 0x1.ffffffffffffep+1023}, + + // (1 + 1 - 3 * 2^-53) * 2^1023 exactly, followed by a thousand 0 digits + {"1797693134862315608353258760581052985162070023416521662616611746258695532672923265745300992879465492467506314" + "9033587701752208710592698796290627760473556921329019091915239418047621712533496094635638726128664019802903779" + "9514183602981511756283727771403830521483963923935633133642802139091669457927874464075218944." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000", + chars_format::fixed, 1310, errc{}, 0x1.ffffffffffffep+1023}, + + // above (1 + 1 - 3 * 2^-53) * 2^1023: appended a thousand 0 digits followed by a 1 digit + {"1797693134862315608353258760581052985162070023416521662616611746258695532672923265745300992879465492467506314" + "9033587701752208710592698796290627760473556921329019091915239418047621712533496094635638726128664019802903779" + "9514183602981511756283727771403830521483963923935633133642802139091669457927874464075218944." + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000001", + chars_format::fixed, 1311, errc{}, 0x1.fffffffffffffp+1023}, + + // above (1 + 1 - 3 * 2^-53) * 2^1023: appended a 1 digit + {"1797693134862315608353258760581052985162070023416521662616611746258695532672923265745300992879465492467506314" + "9033587701752208710592698796290627760473556921329019091915239418047621712533496094635638726128664019802903779" + "9514183602981511756283727771403830521483963923935633133642802139091669457927874464075218944.1", + chars_format::fixed, 311, errc{}, 0x1.fffffffffffffp+1023}, + + // above (1 + 1 - 3 * 2^-53) * 2^1023: incremented last digit + {"1797693134862315608353258760581052985162070023416521662616611746258695532672923265745300992879465492467506314" + "9033587701752208710592698796290627760473556921329019091915239418047621712533496094635638726128664019802903779" + "9514183602981511756283727771403830521483963923935633133642802139091669457927874464075218945", + chars_format::fixed, 309, errc{}, 0x1.fffffffffffffp+1023}, + + // VSO-852024 also affected hexfloats. + {"0.00000000000008p-1022", chars_format::hex, 22, errc::result_out_of_range, 0x0.0000000000000p+0}, + {"0." + "0000000000000800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000001p-1022", + chars_format::hex, 1023, errc{}, 0x0.0000000000001p-1022}, + + {"0.ffffffffffffe8p-1022", chars_format::hex, 22, errc{}, 0x0.ffffffffffffep-1022}, + {"0." + "ffffffffffffe800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000001p-1022", + chars_format::hex, 1023, errc{}, 0x0.fffffffffffffp-1022}, + + {"1.00000000000008p+0", chars_format::hex, 19, errc{}, 0x1.0000000000000p+0}, + {"1." + "0000000000000800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000001p+0", + chars_format::hex, 1020, errc{}, 0x1.0000000000001p+0}, + + {"1.ffffffffffffe8p+0", chars_format::hex, 19, errc{}, 0x1.ffffffffffffep+0}, + {"1." + "ffffffffffffe800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000001p+0", + chars_format::hex, 1020, errc{}, 0x1.fffffffffffffp+0}, + + {"1.00000000000008p+1023", chars_format::hex, 22, errc{}, 0x1.0000000000000p+1023}, + {"1." + "0000000000000800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000001p+1023", + chars_format::hex, 1023, errc{}, 0x1.0000000000001p+1023}, + + {"1.ffffffffffffe8p+1023", chars_format::hex, 22, errc{}, 0x1.ffffffffffffep+1023}, + {"1." + "ffffffffffffe800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000001p+1023", + chars_format::hex, 1023, errc{}, 0x1.fffffffffffffp+1023}, + + // VSO-733765 ": [Feedback] double std::from_chars behavior on exponent out of range" + // LWG-3081 "Floating point from_chars API does not distinguish between overflow and underflow" + // These test cases exercise every overflow/underflow codepath. + {"1e+1000", chars_format::scientific, 7, errc::result_out_of_range, double_inf}, + {"1e-1000", chars_format::scientific, 7, errc::result_out_of_range, 0.0}, + {"1.fffffffffffff8p+1023", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"1e+2000", chars_format::scientific, 7, errc::result_out_of_range, double_inf}, + {"1e-2000", chars_format::scientific, 7, errc::result_out_of_range, 0.0}, + {"1e+9999", chars_format::scientific, 7, errc::result_out_of_range, double_inf}, + {"1e-9999", chars_format::scientific, 7, errc::result_out_of_range, 0.0}, + {"10e+5199", chars_format::scientific, 8, errc::result_out_of_range, double_inf}, + {"0.001e-5199", chars_format::scientific, 11, errc::result_out_of_range, 0.0}, + + // GH-931 ": hex from_chars(\"0.fffffffffffff8p-1022\") is incorrect" + // Test cases for values close to std::numeric_limits::min() and std::numeric_limits::max() + {"0.fffffffffffffp-1022", chars_format::hex, 21, errc{}, 0x0.fffffffffffffp-1022}, + {"1.0000000000000p-1022", chars_format::hex, 21, errc{}, 0x1.0000000000000p-1022}, + + {"1.ffffffffffffep-1023", chars_format::hex, 21, errc{}, 0x0.fffffffffffffp-1022}, + {"1.fffffffffffffp-1023", chars_format::hex, 21, errc{}, 0x1.0000000000000p-1022}, + {"2.0000000000000p-1023", chars_format::hex, 21, errc{}, 0x1.0000000000000p-1022}, + + {"3.ffffffffffffcp-1024", chars_format::hex, 21, errc{}, 0x0.fffffffffffffp-1022}, + {"3.ffffffffffffdp-1024", chars_format::hex, 21, errc{}, 0x0.fffffffffffffp-1022}, + {"3.ffffffffffffep-1024", chars_format::hex, 21, errc{}, 0x1.0000000000000p-1022}, + {"3.fffffffffffffp-1024", chars_format::hex, 21, errc{}, 0x1.0000000000000p-1022}, + {"4.0000000000000p-1024", chars_format::hex, 21, errc{}, 0x1.0000000000000p-1022}, + + {"7.ffffffffffff8p-1025", chars_format::hex, 21, errc{}, 0x0.fffffffffffffp-1022}, + {"7.ffffffffffff9p-1025", chars_format::hex, 21, errc{}, 0x0.fffffffffffffp-1022}, + {"7.ffffffffffffbp-1025", chars_format::hex, 21, errc{}, 0x0.fffffffffffffp-1022}, + {"7.ffffffffffffcp-1025", chars_format::hex, 21, errc{}, 0x1.0000000000000p-1022}, + {"7.ffffffffffffdp-1025", chars_format::hex, 21, errc{}, 0x1.0000000000000p-1022}, + {"7.ffffffffffffep-1025", chars_format::hex, 21, errc{}, 0x1.0000000000000p-1022}, + {"7.fffffffffffffp-1025", chars_format::hex, 21, errc{}, 0x1.0000000000000p-1022}, + {"8.0000000000000p-1025", chars_format::hex, 21, errc{}, 0x1.0000000000000p-1022}, + + {"0.fffffffffffff0p-1022", chars_format::hex, 22, errc{}, 0x0.fffffffffffffp-1022}, + {"0.fffffffffffff1p-1022", chars_format::hex, 22, errc{}, 0x0.fffffffffffffp-1022}, + {"0.fffffffffffff7p-1022", chars_format::hex, 22, errc{}, 0x0.fffffffffffffp-1022}, + {"0.fffffffffffff8p-1022", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"0.fffffffffffff9p-1022", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"0.fffffffffffffbp-1022", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"0.fffffffffffffcp-1022", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"0.fffffffffffffdp-1022", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"0.ffffffffffffffp-1022", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"1.00000000000000p-1022", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + + {"1.ffffffffffffe0p-1023", chars_format::hex, 22, errc{}, 0x0.fffffffffffffp-1022}, + {"1.ffffffffffffe1p-1023", chars_format::hex, 22, errc{}, 0x0.fffffffffffffp-1022}, + {"1.ffffffffffffefp-1023", chars_format::hex, 22, errc{}, 0x0.fffffffffffffp-1022}, + {"1.fffffffffffff0p-1023", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"1.fffffffffffff1p-1023", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"1.fffffffffffff7p-1023", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"1.fffffffffffff8p-1023", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"1.fffffffffffff9p-1023", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"1.ffffffffffffffp-1023", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"2.00000000000000p-1023", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + + {"3.ffffffffffffc0p-1024", chars_format::hex, 22, errc{}, 0x0.fffffffffffffp-1022}, + {"3.ffffffffffffc1p-1024", chars_format::hex, 22, errc{}, 0x0.fffffffffffffp-1022}, + {"3.ffffffffffffdfp-1024", chars_format::hex, 22, errc{}, 0x0.fffffffffffffp-1022}, + {"3.ffffffffffffe0p-1024", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"3.ffffffffffffe1p-1024", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"3.ffffffffffffefp-1024", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"3.fffffffffffff0p-1024", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"3.fffffffffffff1p-1024", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"3.ffffffffffffffp-1024", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"4.00000000000000p-1024", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + + {"7.ffffffffffff80p-1025", chars_format::hex, 22, errc{}, 0x0.fffffffffffffp-1022}, + {"7.ffffffffffff81p-1025", chars_format::hex, 22, errc{}, 0x0.fffffffffffffp-1022}, + {"7.ffffffffffffbfp-1025", chars_format::hex, 22, errc{}, 0x0.fffffffffffffp-1022}, + {"7.ffffffffffffc0p-1025", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"7.ffffffffffffc1p-1025", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"7.ffffffffffffdfp-1025", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"7.ffffffffffffe0p-1025", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"7.ffffffffffffe1p-1025", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"7.ffffffffffffffp-1025", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + {"8.00000000000000p-1025", chars_format::hex, 22, errc{}, 0x1.0000000000000p-1022}, + + {"1.fffffffffffffp+1023", chars_format::hex, 21, errc{}, 0x1.fffffffffffffp+1023}, + {"2.0000000000000p+1023", chars_format::hex, 21, errc::result_out_of_range, double_inf}, + + {"3.ffffffffffffep+1022", chars_format::hex, 21, errc{}, 0x1.fffffffffffffp+1023}, + {"3.fffffffffffffp+1022", chars_format::hex, 21, errc::result_out_of_range, double_inf}, + {"4.0000000000000p+1022", chars_format::hex, 21, errc::result_out_of_range, double_inf}, + + {"7.ffffffffffffcp+1021", chars_format::hex, 21, errc{}, 0x1.fffffffffffffp+1023}, + {"7.ffffffffffffdp+1021", chars_format::hex, 21, errc{}, 0x1.fffffffffffffp+1023}, + {"7.ffffffffffffep+1021", chars_format::hex, 21, errc::result_out_of_range, double_inf}, + {"7.fffffffffffffp+1021", chars_format::hex, 21, errc::result_out_of_range, double_inf}, + {"8.0000000000000p+1021", chars_format::hex, 21, errc::result_out_of_range, double_inf}, + + {"0.fffffffffffff8p+1024", chars_format::hex, 22, errc{}, 0x1.fffffffffffffp+1023}, + {"0.fffffffffffff9p+1024", chars_format::hex, 22, errc{}, 0x1.fffffffffffffp+1023}, + {"0.fffffffffffffbp+1024", chars_format::hex, 22, errc{}, 0x1.fffffffffffffp+1023}, + {"0.fffffffffffffcp+1024", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"0.fffffffffffffdp+1024", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"0.ffffffffffffffp+1024", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"1.00000000000000p+1024", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + + {"1.fffffffffffff0p+1023", chars_format::hex, 22, errc{}, 0x1.fffffffffffffp+1023}, + {"1.fffffffffffff1p+1023", chars_format::hex, 22, errc{}, 0x1.fffffffffffffp+1023}, + {"1.fffffffffffff7p+1023", chars_format::hex, 22, errc{}, 0x1.fffffffffffffp+1023}, + {"1.fffffffffffff8p+1023", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"1.fffffffffffff9p+1023", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"1.ffffffffffffffp+1023", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"2.00000000000000p+1023", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + + {"3.ffffffffffffe0p+1022", chars_format::hex, 22, errc{}, 0x1.fffffffffffffp+1023}, + {"3.ffffffffffffe1p+1022", chars_format::hex, 22, errc{}, 0x1.fffffffffffffp+1023}, + {"3.ffffffffffffefp+1022", chars_format::hex, 22, errc{}, 0x1.fffffffffffffp+1023}, + {"3.fffffffffffff0p+1022", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"3.fffffffffffff1p+1022", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"3.ffffffffffffffp+1022", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"4.00000000000000p+1022", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + + {"7.ffffffffffffc0p+1021", chars_format::hex, 22, errc{}, 0x1.fffffffffffffp+1023}, + {"7.ffffffffffffc1p+1021", chars_format::hex, 22, errc{}, 0x1.fffffffffffffp+1023}, + {"7.ffffffffffffdfp+1021", chars_format::hex, 22, errc{}, 0x1.fffffffffffffp+1023}, + {"7.ffffffffffffe0p+1021", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"7.ffffffffffffe1p+1021", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"7.ffffffffffffffp+1021", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + {"8.00000000000000p+1021", chars_format::hex, 22, errc::result_out_of_range, double_inf}, + + {"0.fffffffffffff80p+1024", chars_format::hex, 23, errc{}, 0x1.fffffffffffffp+1023}, + {"0.fffffffffffff81p+1024", chars_format::hex, 23, errc{}, 0x1.fffffffffffffp+1023}, + {"0.fffffffffffffbfp+1024", chars_format::hex, 23, errc{}, 0x1.fffffffffffffp+1023}, + {"0.fffffffffffffc0p+1024", chars_format::hex, 23, errc::result_out_of_range, double_inf}, + {"0.fffffffffffffc1p+1024", chars_format::hex, 23, errc::result_out_of_range, double_inf}, + {"0.fffffffffffffffp+1024", chars_format::hex, 23, errc::result_out_of_range, double_inf}, + {"1.000000000000000p+1024", chars_format::hex, 23, errc::result_out_of_range, double_inf}, + + // (0 + 1 - 2 * 2^-53) * 2^-1022 exactly + {"2." + "22507385850720088902458687608585988765042311224095946549352480256244000922823569517877588880375915526423097809504" + "34312085877387158357291821993020294379224223559819827501242041788969571311791082261043971979604000454897391938079" + "19893608152561311337614984204327175103362739154978273159414382813627511383860409424946494228631669542910508020181" + "59266421349966065178030950759130587198464239060686371020051087232827846788436319445158661350412234790147923695852" + "08321597621066375401613736583044193603714778355306682834535634005074073040135602968046375918583163124224521599262" + "54649430083685186171942241764645513713542013221703137049658321015465406803539741790602258950302350193751977303094" + "5763173210852507299305089761582519159720757232455434770912461317493580281734466552734375e-308", + chars_format::scientific, 773, errc{}, 0x0.fffffffffffffp-1022}, + + // (0 + 1 - 2 * 2^-53) * 2^-1022 exactly, followed by a thousand 0 digits + {"2." + "22507385850720088902458687608585988765042311224095946549352480256244000922823569517877588880375915526423097809504" + "34312085877387158357291821993020294379224223559819827501242041788969571311791082261043971979604000454897391938079" + "19893608152561311337614984204327175103362739154978273159414382813627511383860409424946494228631669542910508020181" + "59266421349966065178030950759130587198464239060686371020051087232827846788436319445158661350412234790147923695852" + "08321597621066375401613736583044193603714778355306682834535634005074073040135602968046375918583163124224521599262" + "54649430083685186171942241764645513713542013221703137049658321015465406803539741790602258950302350193751977303094" + "57631732108525072993050897615825191597207572324554347709124613174935802817344665527343750000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000e-308", + chars_format::scientific, 1773, errc{}, 0x0.fffffffffffffp-1022}, + + // above (0 + 1 - 2 * 2^-53) * 2^-1022, appended a thousand 0 digits followed by a 1 digit + {"2." + "22507385850720088902458687608585988765042311224095946549352480256244000922823569517877588880375915526423097809504" + "34312085877387158357291821993020294379224223559819827501242041788969571311791082261043971979604000454897391938079" + "19893608152561311337614984204327175103362739154978273159414382813627511383860409424946494228631669542910508020181" + "59266421349966065178030950759130587198464239060686371020051087232827846788436319445158661350412234790147923695852" + "08321597621066375401613736583044193603714778355306682834535634005074073040135602968046375918583163124224521599262" + "54649430083685186171942241764645513713542013221703137049658321015465406803539741790602258950302350193751977303094" + "57631732108525072993050897615825191597207572324554347709124613174935802817344665527343750000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "000000000000000000000000000000000000000000000000000000000000000000000001e-308", + chars_format::scientific, 1774, errc{}, 0x0.fffffffffffffp-1022}, + + // above (0 + 1 - 2 * 2^-53) * 2^-1022: appended a 1 digit + {"2." + "22507385850720088902458687608585988765042311224095946549352480256244000922823569517877588880375915526423097809504" + "34312085877387158357291821993020294379224223559819827501242041788969571311791082261043971979604000454897391938079" + "19893608152561311337614984204327175103362739154978273159414382813627511383860409424946494228631669542910508020181" + "59266421349966065178030950759130587198464239060686371020051087232827846788436319445158661350412234790147923695852" + "08321597621066375401613736583044193603714778355306682834535634005074073040135602968046375918583163124224521599262" + "54649430083685186171942241764645513713542013221703137049658321015465406803539741790602258950302350193751977303094" + "57631732108525072993050897615825191597207572324554347709124613174935802817344665527343751e-308", + chars_format::scientific, 774, errc{}, 0x0.fffffffffffffp-1022}, + + // above (0 + 1 - 2 * 2^-53) * 2^-1022: incremented last digit + {"2." + "22507385850720088902458687608585988765042311224095946549352480256244000922823569517877588880375915526423097809504" + "34312085877387158357291821993020294379224223559819827501242041788969571311791082261043971979604000454897391938079" + "19893608152561311337614984204327175103362739154978273159414382813627511383860409424946494228631669542910508020181" + "59266421349966065178030950759130587198464239060686371020051087232827846788436319445158661350412234790147923695852" + "08321597621066375401613736583044193603714778355306682834535634005074073040135602968046375918583163124224521599262" + "54649430083685186171942241764645513713542013221703137049658321015465406803539741790602258950302350193751977303094" + "5763173210852507299305089761582519159720757232455434770912461317493580281734466552734376e-308", + chars_format::scientific, 773, errc{}, 0x0.fffffffffffffp-1022}, + + // below (0 + 1 - 2^-53) * 2^-1022: decremented last digit, then appended three 9 digits + {"2." + "22507385850720113605740979670913197593481954635164564802342610972482222202107694551652952390813508791414915891303" + "96211068700864386945946455276572074078206217433799881410632673292535522868813721490129811224514518898490572223072" + "85255133155755015914397476397983411801999323962548289017107081850690630666655994938275772572015763062690663332647" + "56530000924588831643303777979186961204949739037782970490505108060994073026293712895895000358379996720725430436028" + "40788957717961509455167482434710307026091446215722898802581825451803257070188608721131280795122334262883686223215" + "03775666622503982534335974568884423900265498198385487948292206894721689831099698365846814022854243330660339850886" + "44580400103493397042756718644338377048603786162277173854562306587467901408672332763671874999e-308", + chars_format::scientific, 777, errc{}, 0x0.fffffffffffffp-1022}, + + // (0 + 1 - 2^-53) * 2^-1022 exactly + {"2." + "22507385850720113605740979670913197593481954635164564802342610972482222202107694551652952390813508791414915891303" + "96211068700864386945946455276572074078206217433799881410632673292535522868813721490129811224514518898490572223072" + "85255133155755015914397476397983411801999323962548289017107081850690630666655994938275772572015763062690663332647" + "56530000924588831643303777979186961204949739037782970490505108060994073026293712895895000358379996720725430436028" + "40788957717961509455167482434710307026091446215722898802581825451803257070188608721131280795122334262883686223215" + "03775666622503982534335974568884423900265498198385487948292206894721689831099698365846814022854243330660339850886" + "44580400103493397042756718644338377048603786162277173854562306587467901408672332763671875e-308", + chars_format::scientific, 774, errc{}, 0x1.0000000000000p-1022}, + + // (0 + 1 - 2^-53) * 2^-1022 exactly, followed by a thousand 0 digits + {"2." + "22507385850720113605740979670913197593481954635164564802342610972482222202107694551652952390813508791414915891303" + "96211068700864386945946455276572074078206217433799881410632673292535522868813721490129811224514518898490572223072" + "85255133155755015914397476397983411801999323962548289017107081850690630666655994938275772572015763062690663332647" + "56530000924588831643303777979186961204949739037782970490505108060994073026293712895895000358379996720725430436028" + "40788957717961509455167482434710307026091446215722898802581825451803257070188608721131280795122334262883686223215" + "03775666622503982534335974568884423900265498198385487948292206894721689831099698365846814022854243330660339850886" + "44580400103493397042756718644338377048603786162277173854562306587467901408672332763671875000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "000000000000000000000000000000000000000000000000000000000000000000000000e-308", + chars_format::scientific, 1774, errc{}, 0x1.0000000000000p-1022}, + + // above (0 + 1 - 2^-53) * 2^-1022: append a thousand 0 digits followed by a 1 digit + {"2." + "22507385850720113605740979670913197593481954635164564802342610972482222202107694551652952390813508791414915891303" + "96211068700864386945946455276572074078206217433799881410632673292535522868813721490129811224514518898490572223072" + "85255133155755015914397476397983411801999323962548289017107081850690630666655994938275772572015763062690663332647" + "56530000924588831643303777979186961204949739037782970490505108060994073026293712895895000358379996720725430436028" + "40788957717961509455167482434710307026091446215722898802581825451803257070188608721131280795122334262883686223215" + "03775666622503982534335974568884423900265498198385487948292206894721689831099698365846814022854243330660339850886" + "44580400103493397042756718644338377048603786162277173854562306587467901408672332763671875000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000001e-308", + chars_format::scientific, 1775, errc{}, 0x1.0000000000000p-1022}, + + // above (0 + 1 - 2^-53) * 2^-1022: appended a 1 digit + {"2." + "22507385850720113605740979670913197593481954635164564802342610972482222202107694551652952390813508791414915891303" + "96211068700864386945946455276572074078206217433799881410632673292535522868813721490129811224514518898490572223072" + "85255133155755015914397476397983411801999323962548289017107081850690630666655994938275772572015763062690663332647" + "56530000924588831643303777979186961204949739037782970490505108060994073026293712895895000358379996720725430436028" + "40788957717961509455167482434710307026091446215722898802581825451803257070188608721131280795122334262883686223215" + "03775666622503982534335974568884423900265498198385487948292206894721689831099698365846814022854243330660339850886" + "445804001034933970427567186443383770486037861622771738545623065874679014086723327636718751e-308", + chars_format::scientific, 775, errc{}, 0x1.0000000000000p-1022}, + + // above (0 + 1 - 2^-53) * 2^-1022: incremented last digit + {"2." + "22507385850720113605740979670913197593481954635164564802342610972482222202107694551652952390813508791414915891303" + "96211068700864386945946455276572074078206217433799881410632673292535522868813721490129811224514518898490572223072" + "85255133155755015914397476397983411801999323962548289017107081850690630666655994938275772572015763062690663332647" + "56530000924588831643303777979186961204949739037782970490505108060994073026293712895895000358379996720725430436028" + "40788957717961509455167482434710307026091446215722898802581825451803257070188608721131280795122334262883686223215" + "03775666622503982534335974568884423900265498198385487948292206894721689831099698365846814022854243330660339850886" + "44580400103493397042756718644338377048603786162277173854562306587467901408672332763671876e-308", + chars_format::scientific, 774, errc{}, 0x1.0000000000000p-1022}, + + // below (0 + 1 - 0.5 * 2^-53) * 2^-1022: decremented last digit, then appended three 9 digits + {"2." + "22507385850720125957382125702076802007701776340698873928837676330601332841749757068540634146032305423910824932203" + "77160560112603001240273771918347963927697214370789908365327989044318498647325041104672730846969778120287162365569" + "67935895657351868202788722494811530151317616366333296945953431369222190308053787694940411743707809822580740988880" + "55161790711900214875940191589215148208192489026331270225732118475077186145222409621263169862363877686014183806116" + "57022637766409076481944355360543363737279780145931006786604921175167849085215111597673733233391919832213268535191" + "28338784891913380715532840971003878993627240686726663397609149834349831344879676653469091559130189899114521124782" + "380547341009775590676096291585949697743018930811385869272811532937339507043361663818359374999e-308", + chars_format::scientific, 778, errc{}, 0x1.0000000000000p-1022}, + + // (0 + 1 - 0.5 * 2^-53) * 2^-1022 exactly + {"2." + "22507385850720125957382125702076802007701776340698873928837676330601332841749757068540634146032305423910824932203" + "77160560112603001240273771918347963927697214370789908365327989044318498647325041104672730846969778120287162365569" + "67935895657351868202788722494811530151317616366333296945953431369222190308053787694940411743707809822580740988880" + "55161790711900214875940191589215148208192489026331270225732118475077186145222409621263169862363877686014183806116" + "57022637766409076481944355360543363737279780145931006786604921175167849085215111597673733233391919832213268535191" + "28338784891913380715532840971003878993627240686726663397609149834349831344879676653469091559130189899114521124782" + "380547341009775590676096291585949697743018930811385869272811532937339507043361663818359375e-308", + chars_format::scientific, 775, errc{}, 0x1.0000000000000p-1022}, + + // (0 + 1 - 0.5 * 2^-53) * 2^-1022 exactly, followed by a thousand 0 digits + {"2." + "22507385850720125957382125702076802007701776340698873928837676330601332841749757068540634146032305423910824932203" + "77160560112603001240273771918347963927697214370789908365327989044318498647325041104672730846969778120287162365569" + "67935895657351868202788722494811530151317616366333296945953431369222190308053787694940411743707809822580740988880" + "55161790711900214875940191589215148208192489026331270225732118475077186145222409621263169862363877686014183806116" + "57022637766409076481944355360543363737279780145931006786604921175167849085215111597673733233391919832213268535191" + "28338784891913380715532840971003878993627240686726663397609149834349831344879676653469091559130189899114521124782" + "38054734100977559067609629158594969774301893081138586927281153293733950704336166381835937500000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000e-308", + chars_format::scientific, 1775, errc{}, 0x1.0000000000000p-1022}, + + // above (0 + 1 - 0.5 * 2^-53) * 2^-1022: append a thousand 0 digits followed by a 1 digit + {"2." + "22507385850720125957382125702076802007701776340698873928837676330601332841749757068540634146032305423910824932203" + "77160560112603001240273771918347963927697214370789908365327989044318498647325041104672730846969778120287162365569" + "67935895657351868202788722494811530151317616366333296945953431369222190308053787694940411743707809822580740988880" + "55161790711900214875940191589215148208192489026331270225732118475077186145222409621263169862363877686014183806116" + "57022637766409076481944355360543363737279780145931006786604921175167849085215111597673733233391919832213268535191" + "28338784891913380715532840971003878993627240686726663397609149834349831344879676653469091559130189899114521124782" + "38054734100977559067609629158594969774301893081138586927281153293733950704336166381835937500000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000001e-308", + chars_format::scientific, 1776, errc{}, 0x1.0000000000000p-1022}, + + // above (0 + 1 - 0.5 * 2^-53) * 2^-1022: appended a 1 digit + {"2." + "22507385850720125957382125702076802007701776340698873928837676330601332841749757068540634146032305423910824932203" + "77160560112603001240273771918347963927697214370789908365327989044318498647325041104672730846969778120287162365569" + "67935895657351868202788722494811530151317616366333296945953431369222190308053787694940411743707809822580740988880" + "55161790711900214875940191589215148208192489026331270225732118475077186145222409621263169862363877686014183806116" + "57022637766409076481944355360543363737279780145931006786604921175167849085215111597673733233391919832213268535191" + "28338784891913380715532840971003878993627240686726663397609149834349831344879676653469091559130189899114521124782" + "3805473410097755906760962915859496977430189308113858692728115329373395070433616638183593751e-308", + chars_format::scientific, 776, errc{}, 0x1.0000000000000p-1022}, + + // above (0 + 1 - 0.5 * 2^-53) * 2^-1022: incremented last digit + {"2." + "22507385850720125957382125702076802007701776340698873928837676330601332841749757068540634146032305423910824932203" + "77160560112603001240273771918347963927697214370789908365327989044318498647325041104672730846969778120287162365569" + "67935895657351868202788722494811530151317616366333296945953431369222190308053787694940411743707809822580740988880" + "55161790711900214875940191589215148208192489026331270225732118475077186145222409621263169862363877686014183806116" + "57022637766409076481944355360543363737279780145931006786604921175167849085215111597673733233391919832213268535191" + "28338784891913380715532840971003878993627240686726663397609149834349831344879676653469091559130189899114521124782" + "380547341009775590676096291585949697743018930811385869272811532937339507043361663818359376e-308", + chars_format::scientific, 775, errc{}, 0x1.0000000000000p-1022}, + + // below 1 * 2^-1022: decremented last digit, then appended three 9 digits + {"2." + "22507385850720138309023271733240406421921598046233183055332741688720443481391819585428315901251102056406733973103" + "58110051524341615534601088560123853777188211307779935320023304796101474425836360719215650469425037342083752508066" + "50616658158948720491179968591639648500635908770118304874799780887753749949451580451605050915399856582470818645113" + "53793580499211598108576605199243335211435239014879569960959128889160299264151106346631339366347758651302937176204" + "73256317814856643508721228286376420448468114076139114770628016898532441100241614474216185671661505401542850847167" + "52901903161322778896729707373123334086988983175067838846926092773977972858659654941091369095406136467568702398678" + "315290680984617210924625396728515624999e-308", + chars_format::scientific, 724, errc{}, 0x1.0000000000000p-1022}, + + // 1 * 2^-1022 exactly + {"2." + "22507385850720138309023271733240406421921598046233183055332741688720443481391819585428315901251102056406733973103" + "58110051524341615534601088560123853777188211307779935320023304796101474425836360719215650469425037342083752508066" + "50616658158948720491179968591639648500635908770118304874799780887753749949451580451605050915399856582470818645113" + "53793580499211598108576605199243335211435239014879569960959128889160299264151106346631339366347758651302937176204" + "73256317814856643508721228286376420448468114076139114770628016898532441100241614474216185671661505401542850847167" + "52901903161322778896729707373123334086988983175067838846926092773977972858659654941091369095406136467568702398678" + "315290680984617210924625396728515625e-308", + chars_format::scientific, 721, errc{}, 0x1.0000000000000p-1022}, + + // (1 + 1 - 2 * 2^-53) * 2^1023 exactly + {"17976931348623157081452742373170435679807056752584499659891747680315726078002853876058955863276687817154045895351" + "43824642343213268894641827684675467035375169860499105765512820762454900903893289440758685084551339423045832369032" + "22948165808559332123348274797826204144723168738177180919299881250404026184124858368", + chars_format::fixed, 309, errc{}, 0x1.fffffffffffffp+1023}, + + // (1 + 1 - 2 * 2^-53) * 2^1023 exactly, followed by a thousand 0 digits + {"17976931348623157081452742373170435679807056752584499659891747680315726078002853876058955863276687817154045895351" + "43824642343213268894641827684675467035375169860499105765512820762454900903893289440758685084551339423045832369032" + "22948165808559332123348274797826204144723168738177180919299881250404026184124858368." + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + chars_format::fixed, 1310, errc{}, 0x1.fffffffffffffp+1023}, + + // above (1 + 1 - 2 * 2^-53) * 2^1023, appended a thousand 0 digits followed by a 1 digit + {"17976931348623157081452742373170435679807056752584499659891747680315726078002853876058955863276687817154045895351" + "43824642343213268894641827684675467035375169860499105765512820762454900903893289440758685084551339423045832369032" + "22948165808559332123348274797826204144723168738177180919299881250404026184124858368." + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", + chars_format::fixed, 1311, errc{}, 0x1.fffffffffffffp+1023}, + + // above (1 + 1 - 2 * 2^-53) * 2^1023: appended a 1 digit + {"17976931348623157081452742373170435679807056752584499659891747680315726078002853876058955863276687817154045895351" + "43824642343213268894641827684675467035375169860499105765512820762454900903893289440758685084551339423045832369032" + "22948165808559332123348274797826204144723168738177180919299881250404026184124858368.1", + chars_format::fixed, 311, errc{}, 0x1.fffffffffffffp+1023}, + + // above (1 + 1 - 2 * 2^-53) * 2^1023: incremented last digit + {"17976931348623157081452742373170435679807056752584499659891747680315726078002853876058955863276687817154045895351" + "43824642343213268894641827684675467035375169860499105765512820762454900903893289440758685084551339423045832369032" + "22948165808559332123348274797826204144723168738177180919299881250404026184124858369", + chars_format::fixed, 309, errc{}, 0x1.fffffffffffffp+1023}, + + // below (1 + 1 - 2^-53) * 2^1023: decremented last digit, then appended three 9 digits + {"17976931348623158079372897140530341507993413271003782693617377898044496829276475094664901797758720709633028641669" + "28879109465555478519404026306574886715058206819089020007083836762738548458177115317644757302700698555713669596228" + "42914819860834936475292719074168444365510704342711559699508093042880177904174497791.999", + chars_format::fixed, 313, errc{}, 0x1.fffffffffffffp+1023}, + + // (1 + 1 - 2^-53) * 2^1023 exactly + {"17976931348623158079372897140530341507993413271003782693617377898044496829276475094664901797758720709633028641669" + "28879109465555478519404026306574886715058206819089020007083836762738548458177115317644757302700698555713669596228" + "42914819860834936475292719074168444365510704342711559699508093042880177904174497792", + chars_format::fixed, 309, errc::result_out_of_range, double_inf}, + + // (1 + 1 - 2^-53) * 2^1023 exactly, followed by a thousand 0 digits + {"17976931348623158079372897140530341507993413271003782693617377898044496829276475094664901797758720709633028641669" + "28879109465555478519404026306574886715058206819089020007083836762738548458177115317644757302700698555713669596228" + "42914819860834936475292719074168444365510704342711559699508093042880177904174497792." + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + chars_format::fixed, 1310, errc::result_out_of_range, double_inf}, + + // above (1 + 1 - 2^-53) * 2^1023: append a thousand 0 digits followed by a 1 digit + {"17976931348623158079372897140530341507993413271003782693617377898044496829276475094664901797758720709633028641669" + "28879109465555478519404026306574886715058206819089020007083836762738548458177115317644757302700698555713669596228" + "42914819860834936475292719074168444365510704342711559699508093042880177904174497792." + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", + chars_format::fixed, 1311, errc::result_out_of_range, double_inf}, + + // above (1 + 1 - 2^-53) * 2^1023: appended a 1 digit + {"17976931348623158079372897140530341507993413271003782693617377898044496829276475094664901797758720709633028641669" + "28879109465555478519404026306574886715058206819089020007083836762738548458177115317644757302700698555713669596228" + "42914819860834936475292719074168444365510704342711559699508093042880177904174497792.1", + chars_format::fixed, 311, errc::result_out_of_range, double_inf}, + + // above (1 + 1 - 2^-53) * 2^1023: incremented last digit + {"17976931348623158079372897140530341507993413271003782693617377898044496829276475094664901797758720709633028641669" + "28879109465555478519404026306574886715058206819089020007083836762738548458177115317644757302700698555713669596228" + "42914819860834936475292719074168444365510704342711559699508093042880177904174497792", + chars_format::fixed, 309, errc::result_out_of_range, double_inf}, + + // below 1 * 2^1024: decremented last digit, then appended three 9 digits + {"17976931348623159077293051907890247336179769789423065727343008115773267580550096313270847732240753602112011387987" + "13933576587897688144166224928474306394741243777678934248654852763022196012460941194530829520850057688381506823424" + "62881473913110540827237163350510684586298239947245938479716304835356329624224137215.999", + chars_format::fixed, 313, errc::result_out_of_range, double_inf}, + + // 1 * 2^1024 exactly + {"17976931348623159077293051907890247336179769789423065727343008115773267580550096313270847732240753602112011387987" + "13933576587897688144166224928474306394741243777678934248654852763022196012460941194530829520850057688381506823424" + "62881473913110540827237163350510684586298239947245938479716304835356329624224137216", + chars_format::fixed, 309, errc::result_out_of_range, double_inf}, +}; + +int +main() +{ + for (const auto [input,fmt,correct_end,correct_ec,correct_value] + : double_from_chars_test_cases) + { + double value = -1.2345; + const auto [ptr,ec] = from_chars(input, input + strlen(input), value, fmt); + VERIFY( correct_ec == ec ); + VERIFY( ptr == input + correct_end ); + if (ec == errc{}) + VERIFY( value == correct_value ); + else + VERIFY( value == -1.2345 ); + } +} diff --git a/libstdc++-v3/testsuite/20_util/from_chars/float.cc b/libstdc++-v3/testsuite/20_util/from_chars/float.cc new file mode 100644 index 00000000000..13909e4c5d9 --- /dev/null +++ b/libstdc++-v3/testsuite/20_util/from_chars/float.cc @@ -0,0 +1,290 @@ +// This file consists of testcases extracted from the MSVC STL testsuite. + +// Copyright (c) Microsoft Corporation. +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception + +// { dg-do run { target c++17 } } +// { dg-require-effective-target ieee_floats } + +#include + +#include +#include +#include + +using namespace std; + +inline constexpr float float_inf = numeric_limits::infinity(); + +struct float_to_chars_testcase { + const char* input; + chars_format fmt; + size_t correct_idx; + errc correct_ec; + float correct_value; +}; + +inline constexpr float_to_chars_testcase float_from_chars_test_cases[] = { + {"1.a0000400", chars_format::hex, 10, errc{}, 0x1.a00004p0f}, // exact + {"1.a0000401", chars_format::hex, 10, errc{}, 0x1.a00004p0f}, // below midpoint, round down + {"1.a0000500", chars_format::hex, 10, errc{}, 0x1.a00004p0f}, // midpoint, round down to even + {"1.a0000501", chars_format::hex, 10, errc{}, 0x1.a00006p0f}, // above midpoint, round up + {"1.a0000600", chars_format::hex, 10, errc{}, 0x1.a00006p0f}, // exact + {"1.a0000601", chars_format::hex, 10, errc{}, 0x1.a00006p0f}, // below midpoint, round down + {"1.a0000700", chars_format::hex, 10, errc{}, 0x1.a00008p0f}, // midpoint, round up to even + {"1.a0000701", chars_format::hex, 10, errc{}, 0x1.a00008p0f}, // above midpoint, round up + + {"1.0000040", chars_format::hex, 9, errc{}, 0x1.000004p0f}, // exact + {"1.0000041", chars_format::hex, 9, errc{}, 0x1.000004p0f}, // below midpoint, round down + {"1.0000050", chars_format::hex, 9, errc{}, 0x1.000004p0f}, // midpoint, round down to even + {"1.0000051", chars_format::hex, 9, errc{}, 0x1.000006p0f}, // above midpoint, round up + {"1.0000060", chars_format::hex, 9, errc{}, 0x1.000006p0f}, // exact + {"1.0000061", chars_format::hex, 9, errc{}, 0x1.000006p0f}, // below midpoint, round down + {"1.0000070", chars_format::hex, 9, errc{}, 0x1.000008p0f}, // midpoint, round up to even + {"1.0000071", chars_format::hex, 9, errc{}, 0x1.000008p0f}, // above midpoint, round up + + {"1.0000002384185791015625000000", chars_format::general, 30, errc{}, 0x1.000004p0f}, // exact + {"1.0000002421438694000244140625", chars_format::general, 30, errc{}, 0x1.000004p0f}, // below midpoint, round down + {"1.0000002980232238769531249999", chars_format::general, 30, errc{}, 0x1.000004p0f}, // below midpoint, round down + {"1.0000002980232238769531250000", chars_format::general, 30, errc{}, + 0x1.000004p0f}, // midpoint, round down to even + {"1.0000002980232238769531250001", chars_format::general, 30, errc{}, 0x1.000006p0f}, // above midpoint, round up + {"1.0000003017485141754150390625", chars_format::general, 30, errc{}, 0x1.000006p0f}, // above midpoint, round up + {"1.0000003576278686523437500000", chars_format::general, 30, errc{}, 0x1.000006p0f}, // exact + {"1.0000003613531589508056640625", chars_format::general, 30, errc{}, 0x1.000006p0f}, // below midpoint, round down + {"1.0000004172325134277343749999", chars_format::general, 30, errc{}, 0x1.000006p0f}, // below midpoint, round down + {"1.0000004172325134277343750000", chars_format::general, 30, errc{}, 0x1.000008p0f}, // midpoint, round up to even + {"1.0000004172325134277343750001", chars_format::general, 30, errc{}, 0x1.000008p0f}, // above midpoint, round up + {"1.0000004209578037261962890625", chars_format::general, 30, errc{}, 0x1.000008p0f}, // above midpoint, round up + + // VSO-838635 ": from_chars() mishandles certain subnormals" + // This bug didn't actually affect float, but we should have similar test cases. + // These values change on half-ulp boundaries: + // 1 * 2^-150 ~= 7.01e-46 (half-ulp between zero and min subnormal) + // 2 * 2^-150 ~= 1.40e-45 (min subnormal) + // 3 * 2^-150 ~= 2.10e-45 (half-ulp between min subnormal and next subnormal) + // 4 * 2^-150 ~= 2.80e-45 (next subnormal) + {"6." + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666" + "6666666666666666666e-46", + chars_format::scientific, 1006, errc::result_out_of_range, 0x0.000000p+0f}, + {"7." + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777" + "7777777777777777777e-46", + chars_format::scientific, 1006, errc{}, 0x0.000002p-126f}, + {"8." + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888" + "8888888888888888888e-46", + chars_format::scientific, 1006, errc{}, 0x0.000002p-126f}, + {"9." + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" + "9999999999999999999e-46", + chars_format::scientific, 1006, errc{}, 0x0.000002p-126f}, + {"1." + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111" + "1111111111111111111e-45", + chars_format::scientific, 1006, errc{}, 0x0.000002p-126f}, + {"2." + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222" + "2222222222222222222e-45", + chars_format::scientific, 1006, errc{}, 0x0.000004p-126f}, + + // VSO-733765 ": [Feedback] double std::from_chars behavior on exponent out of range" + // LWG-3081 "Floating point from_chars API does not distinguish between overflow and underflow" + // These test cases exercise every overflow/underflow codepath. + {"1e+1000", chars_format::scientific, 7, errc::result_out_of_range, float_inf}, + {"1e-1000", chars_format::scientific, 7, errc::result_out_of_range, 0.0f}, + {"1.ffffffp+127", chars_format::hex, 13, errc::result_out_of_range, float_inf}, + {"1e+2000", chars_format::scientific, 7, errc::result_out_of_range, float_inf}, + {"1e-2000", chars_format::scientific, 7, errc::result_out_of_range, 0.0f}, + {"1e+9999", chars_format::scientific, 7, errc::result_out_of_range, float_inf}, + {"1e-9999", chars_format::scientific, 7, errc::result_out_of_range, 0.0f}, + {"10e+5199", chars_format::scientific, 8, errc::result_out_of_range, float_inf}, + {"0.001e-5199", chars_format::scientific, 11, errc::result_out_of_range, 0.0f}, + + // GH-931 ": hex from_chars(\"0.fffffffffffff8p-1022\") is incorrect" + // Test cases for values close to std::numeric_limits::min() and std::numeric_limits::max() + {"7.fffffp-129", chars_format::hex, 12, errc{}, 0x0.fffffep-126f}, + {"8.00000p-129", chars_format::hex, 12, errc{}, 0x1.000000p-126f}, + + {"0.fffffep-126", chars_format::hex, 13, errc{}, 0x0.fffffep-126f}, + {"0.ffffffp-126", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"1.000000p-126", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + + {"1.fffffcp-127", chars_format::hex, 13, errc{}, 0x0.fffffep-126f}, + {"1.fffffdp-127", chars_format::hex, 13, errc{}, 0x0.fffffep-126f}, + {"1.fffffep-127", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"1.ffffffp-127", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"2.000000p-127", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + + {"3.fffff8p-128", chars_format::hex, 13, errc{}, 0x0.fffffep-126f}, + {"3.fffff9p-128", chars_format::hex, 13, errc{}, 0x0.fffffep-126f}, + {"3.fffffbp-128", chars_format::hex, 13, errc{}, 0x0.fffffep-126f}, + {"3.fffffcp-128", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"3.fffffdp-128", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"3.fffffep-128", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"3.ffffffp-128", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"4.000000p-128", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + + {"7.fffff0p-129", chars_format::hex, 13, errc{}, 0x0.fffffep-126f}, + {"7.fffff1p-129", chars_format::hex, 13, errc{}, 0x0.fffffep-126f}, + {"7.fffff7p-129", chars_format::hex, 13, errc{}, 0x0.fffffep-126f}, + {"7.fffff8p-129", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"7.fffff9p-129", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"7.fffffbp-129", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"7.fffffcp-129", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"7.fffffdp-129", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"7.ffffffp-129", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + {"8.000000p-129", chars_format::hex, 13, errc{}, 0x1.000000p-126f}, + + {"0.fffffe0p-126", chars_format::hex, 14, errc{}, 0x0.fffffep-126f}, + {"0.fffffe1p-126", chars_format::hex, 14, errc{}, 0x0.fffffep-126f}, + {"0.fffffefp-126", chars_format::hex, 14, errc{}, 0x0.fffffep-126f}, + {"0.ffffff0p-126", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"0.ffffff1p-126", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"0.ffffff7p-126", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"0.ffffff8p-126", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"0.ffffff9p-126", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"0.fffffffp-126", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"1.0000000p-126", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + + {"1.fffffc0p-127", chars_format::hex, 14, errc{}, 0x0.fffffep-126f}, + {"1.fffffc1p-127", chars_format::hex, 14, errc{}, 0x0.fffffep-126f}, + {"1.fffffdfp-127", chars_format::hex, 14, errc{}, 0x0.fffffep-126f}, + {"1.fffffe0p-127", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"1.fffffe1p-127", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"1.fffffefp-127", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"1.ffffff0p-127", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"1.ffffff1p-127", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"1.fffffffp-127", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"2.0000000p-127", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + + {"3.fffff80p-128", chars_format::hex, 14, errc{}, 0x0.fffffep-126f}, + {"3.fffff81p-128", chars_format::hex, 14, errc{}, 0x0.fffffep-126f}, + {"3.fffffbfp-128", chars_format::hex, 14, errc{}, 0x0.fffffep-126f}, + {"3.fffffc0p-128", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"3.fffffc1p-128", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"3.fffffdfp-128", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"3.fffffe0p-128", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"3.fffffe1p-128", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"3.fffffffp-128", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + {"4.0000000p-128", chars_format::hex, 14, errc{}, 0x1.000000p-126f}, + + {"0.ffffffp+128", chars_format::hex, 13, errc{}, 0x1.fffffep+127f}, + {"1.000000p+128", chars_format::hex, 13, errc::result_out_of_range, float_inf}, + + {"1.fffffep+127", chars_format::hex, 13, errc{}, 0x1.fffffep+127f}, + {"1.ffffffp+127", chars_format::hex, 13, errc::result_out_of_range, float_inf}, + {"2.000000p+127", chars_format::hex, 13, errc::result_out_of_range, float_inf}, + + {"3.fffffcp+126", chars_format::hex, 13, errc{}, 0x1.fffffep+127f}, + {"3.fffffdp+126", chars_format::hex, 13, errc{}, 0x1.fffffep+127f}, + {"3.fffffep+126", chars_format::hex, 13, errc::result_out_of_range, float_inf}, + {"3.ffffffp+126", chars_format::hex, 13, errc::result_out_of_range, float_inf}, + {"4.000000p+126", chars_format::hex, 13, errc::result_out_of_range, float_inf}, + + {"7.fffff8p+125", chars_format::hex, 13, errc{}, 0x1.fffffep+127f}, + {"7.fffff9p+125", chars_format::hex, 13, errc{}, 0x1.fffffep+127f}, + {"7.fffffbp+125", chars_format::hex, 13, errc{}, 0x1.fffffep+127f}, + {"7.fffffcp+125", chars_format::hex, 13, errc::result_out_of_range, float_inf}, + {"7.fffffdp+125", chars_format::hex, 13, errc::result_out_of_range, float_inf}, + {"7.ffffffp+125", chars_format::hex, 13, errc::result_out_of_range, float_inf}, + {"8.000000p+125", chars_format::hex, 13, errc::result_out_of_range, float_inf}, + + {"0.ffffff0p+128", chars_format::hex, 14, errc{}, 0x1.fffffep+127f}, + {"0.ffffff1p+128", chars_format::hex, 14, errc{}, 0x1.fffffep+127f}, + {"0.ffffff7p+128", chars_format::hex, 14, errc{}, 0x1.fffffep+127f}, + {"0.ffffff8p+128", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + {"0.ffffff9p+128", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + {"0.fffffffp+128", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + {"1.0000000p+128", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + + {"1.fffffe0p+127", chars_format::hex, 14, errc{}, 0x1.fffffep+127f}, + {"1.fffffe1p+127", chars_format::hex, 14, errc{}, 0x1.fffffep+127f}, + {"1.fffffefp+127", chars_format::hex, 14, errc{}, 0x1.fffffep+127f}, + {"1.ffffff0p+127", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + {"1.ffffff1p+127", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + {"1.fffffffp+127", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + {"2.0000000p+127", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + + {"3.fffffc0p+126", chars_format::hex, 14, errc{}, 0x1.fffffep+127f}, + {"3.fffffc1p+126", chars_format::hex, 14, errc{}, 0x1.fffffep+127f}, + {"3.fffffdfp+126", chars_format::hex, 14, errc{}, 0x1.fffffep+127f}, + {"3.fffffe0p+126", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + {"3.fffffe1p+126", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + {"3.fffffffp+126", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + {"4.0000000p+126", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + + {"7.fffff80p+125", chars_format::hex, 14, errc{}, 0x1.fffffep+127f}, + {"7.fffff81p+125", chars_format::hex, 14, errc{}, 0x1.fffffep+127f}, + {"7.fffffbfp+125", chars_format::hex, 14, errc{}, 0x1.fffffep+127f}, + {"7.fffffc0p+125", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + {"7.fffffc1p+125", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + {"7.fffffffp+125", chars_format::hex, 14, errc::result_out_of_range, float_inf}, + {"8.0000000p+125", chars_format::hex, 14, errc::result_out_of_range, float_inf}, +}; + +int +main() +{ + for (const auto [input,fmt,correct_end,correct_ec,correct_value] + : float_from_chars_test_cases) + { + float value = -1.2345f; + const auto [ptr,ec] = from_chars(input, input + strlen(input), value, fmt); + VERIFY( correct_ec == ec ); + VERIFY( ptr == input + correct_end ); + if (ec == errc{}) + VERIFY( value == correct_value ); + else + VERIFY( value == -1.2345f ); + } +}