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 // Copyright 2020-2023 Daniel Lemire
 // Copyright 2023 Matt Borland
 // Distributed under the Boost Software License, Version 1.0.
 // https://www.boost.org/LICENSE_1_0.txt
 
 #ifndef BOOST_CHARCONV_DETAIL_COMPUTE_FLOAT64_HPP
 #define BOOST_CHARCONV_DETAIL_COMPUTE_FLOAT64_HPP
 
 #include <boost/charconv/detail/config.hpp>
 #include <boost/charconv/detail/significand_tables.hpp>
 #include <boost/charconv/detail/emulated128.hpp>
 #include <boost/core/bit.hpp>
 #include <cstdint>
 #include <cfloat>
 #include <cstring>
 #include <cmath>
 
 namespace boost { namespace charconv { namespace detail { 
 
 static constexpr double powers_of_ten[] = {
     1e0,  1e1,  1e2,  1e3,  1e4,  1e5,  1e6,  1e7,  1e8,  1e9,  1e10, 1e11,
     1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22
 };
 
 // Attempts to compute i * 10^(power) exactly; and if "negative" is true, negate the result.
 // 
 // This function will only work in some cases, when it does not work, success is
 // set to false. This should work *most of the time* (like 99% of the time).
 // We assume that power is in the [-325, 308] interval.
 inline double compute_float64(std::int64_t power, std::uint64_t i, bool negative, bool& success) noexcept
 {
     static constexpr auto smallest_power = -325;
     static constexpr auto largest_power = 308;
 
     // We start with a fast path
     // It was described in Clinger WD. 
     // How to read floating point numbers accurately.
     // ACM SIGPLAN Notices. 1990
 #if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
     if (0 <= power && power <= 22 && i <= UINT64_C(9007199254740991))
 #else
     if (-22 <= power && power <= 22 && i <= UINT64_C(9007199254740991))
 #endif
     {
         // The general idea is as follows.
         // If 0 <= s < 2^53 and if 10^0 <= p <= 10^22 then
         // 1) Both s and p can be represented exactly as 64-bit floating-point
         // values
         // (binary64).
         // 2) Because s and p can be represented exactly as floating-point values,
         // then s * p
         // and s / p will produce correctly rounded values.
         
         auto d = static_cast<double>(i);
         
         if (power < 0) 
         {
             d = d / powers_of_ten[-power];
         } 
         else 
         {
             d = d * powers_of_ten[power];
         }
         
         if (negative) 
         {
             d = -d;
         }
 
         success = true;
         return d;
     }
 
     // When 22 < power && power <  22 + 16, we could
     // hope for another, secondary fast path.  It was
     // described by David M. Gay in  "Correctly rounded
     // binary-decimal and decimal-binary conversions." (1990)
     // If you need to compute i * 10^(22 + x) for x < 16,
     // first compute i * 10^x, if you know that result is exact
     // (e.g., when i * 10^x < 2^53),
     // then you can still proceed and do (i * 10^x) * 10^22.
     // Is this worth your time?
     // You need  22 < power *and* power <  22 + 16 *and* (i * 10^(x-22) < 2^53)
     // for this second fast path to work.
     // If you have 22 < power *and* power <  22 + 16, and then you
     // optimistically compute "i * 10^(x-22)", there is still a chance that you
     // have wasted your time if i * 10^(x-22) >= 2^53. It makes the use cases of
     // this optimization maybe less common than we would like. Source:
     // http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
     // also used in RapidJSON: https://rapidjson.org/strtod_8h_source.html
 
     if (i == 0 || power < smallest_power)
     {
         return negative ? -0.0 : 0.0;
     }
     else if (power > largest_power)
     {
         return negative ? -HUGE_VAL : HUGE_VAL;
     }
 
     const std::uint64_t factor_significand = significands_table::significand_64[power - smallest_power];
     const std::int64_t exponent = (((152170 + 65536) * power) >> 16) + 1024 + 63;
     int leading_zeros = boost::core::countl_zero(i);
     i <<= static_cast<std::uint64_t>(leading_zeros);
 
     uint128 product = umul128(i, factor_significand);
     std::uint64_t low = product.low;
     std::uint64_t high = product.high;
 
     // We know that upper has at most one leading zero because
     // both i and  factor_mantissa have a leading one. This means
     // that the result is at least as large as ((1<<63)*(1<<63))/(1<<64).
     // 
     // As long as the first 9 bits of "upper" are not "1", then we
     // know that we have an exact computed value for the leading
     // 55 bits because any imprecision would play out as a +1, in the worst case.
     // Having 55 bits is necessary because we need 53 bits for the mantissa,
     // but we have to have one rounding bit and, we can waste a bit if the most 
     // significant bit of the product is zero.
     // 
     // We expect this next branch to be rarely taken (say 1% of the time).
     // When (upper & 0x1FF) == 0x1FF, it can be common for
     // lower + i < lower to be true (proba. much higher than 1%).
     if (BOOST_UNLIKELY((high & 0x1FF) == 0x1FF) && (low + i < low))
     {
         const std::uint64_t factor_significand_low = significands_table::significand_128[power - smallest_power];
         product = umul128(i, factor_significand_low);
         //const std::uint64_t product_low = product.low;
         const std::uint64_t product_middle2 = product.high;
         const std::uint64_t product_middle1 = low;
         std::uint64_t product_high = high;
         const std::uint64_t product_middle = product_middle1 + product_middle2;
 
         if (product_middle < product_middle1)
         {
             product_high++;
         }
 
         // Commented out because possibly unneeded
         // See: https://arxiv.org/pdf/2212.06644.pdf
         /*
         // we want to check whether mantissa *i + i would affect our result
         // This does happen, e.g. with 7.3177701707893310e+15
         if (((product_middle + 1 == 0) && ((product_high & 0x1FF) == 0x1FF) && (product_low + i < product_low))) 
         {
             success = false;
             return 0;
         }
         */
 
         low = product_middle;
         high = product_high;
     }
 
     // The final significand should be 53 bits with a leading 1
     // We shift it so that it occupies 54 bits with a leading 1
     const std::uint64_t upper_bit = high >> 63;
     std::uint64_t significand = high >> (upper_bit + 9);
     leading_zeros += static_cast<int>(1 ^ upper_bit);
 
     // If we have lots of trailing zeros we may fall between two values
     if (BOOST_UNLIKELY((low == 0) && ((high & 0x1FF) == 0) && ((significand & 3) == 1)))
     {
         // if significand & 1 == 1 we might need to round up
         success = false;
         return 0;
     }
 
     significand += significand & 1;
     significand >>= 1;
 
     // Here the significand < (1<<53), unless there is an overflow
     if (significand >= (UINT64_C(1) << 53))
     {
         significand = (UINT64_C(1) << 52);
         leading_zeros--;
     }
 
     significand &= ~(UINT64_C(1) << 52);
     const auto real_exponent = static_cast<std::uint64_t>(exponent - leading_zeros);
 
     // We have to check that real_exponent is in range, otherwise fail
     if (BOOST_UNLIKELY((real_exponent < 1) || (real_exponent > 2046)))
     {
         success = false;
         return 0;
     }
 
     significand |= real_exponent << 52;
     significand |= ((static_cast<std::uint64_t>(negative) << 63));
     
     double d;
     std::memcpy(&d, &significand, sizeof(d));
 
     success = true;
     return d;
 }
 
 }}} // Namespaces
 
 #endif // BOOST_CHARCONV_DETAIL_COMPUTE_FLOAT64_HPP

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