47 // has a fixed-width mantissa and power of two exponent.  For example, a normal
48 // `double` has a 53-bit mantissa.  Because the high bit is always 1, it is not
57 // is represented as a subnormal with an all-bits-zero mantissa.)
59 // The code below, in calculations, represents the mantissa as a uint64_t.  The
80   // The number of mantissa bits in the given float type.  This includes the
84   // The largest supported IEEE exponent, in our integral mantissa
91   // The smallest supported IEEE normal exponent, in our integral mantissa
139   // This is intended to do the same operation as ldexp(mantissa, exponent),
146   // `mantissa` must either be exactly kTargetMantissaBits wide, in which case
150   static double Make(mantissa_t mantissa, int exponent, bool sign) {  in Make()
155     return sign ? -ldexp(mantissa, exponent) : ldexp(mantissa, exponent);  in Make()
160     if (mantissa > kMantissaMask) {  in Make()
163       // 52 due to the implied decimal point in the IEEE mantissa  in Make()
167       mantissa &= kMantissaMask;  in Make()
172     dbl += mantissa;  in Make()
210   static float Make(mantissa_t mantissa, int exponent, bool sign) {  in Make()
215     return sign ? -ldexpf(mantissa, exponent) : ldexpf(mantissa, exponent);  in Make()
220     if (mantissa > kMantissaMask) {  in Make()
223       // 23 due to the implied decimal point in the IEEE mantissa  in Make()
227       mantissa &= kMantissaMask;  in Make()
232     flt += mantissa;  in Make()
238 // Decimal-to-binary conversions require coercing powers of 10 into a mantissa
286 // Returns true if n is small enough that 10**n times a ParsedFloat mantissa
303 // The calculated number is mantissa * 2**exponent (mantissa is treated as an
304 // integer.)  `mantissa` is chosen to be the correct width for the IEEE float
305 // representation being calculated.  (`mantissa` will always have the same bit
311   uint64_t mantissa = 0;  member
326 // Calculates how far to the right a mantissa needs to be shifted to create a
327 // properly adjusted mantissa for an IEEE floating point number.
329 // `mantissa_width` is the bit width of the mantissa to be shifted, and
394   if (input.mantissa == 0) {  in HandleEdgeCase()
416   } else if (calculated.mantissa == 0 || calculated.exponent == kUnderflow) {  in EncodeResult()
423           calculated.mantissa),  in EncodeResult()
433 // be the correct bit-width for the target mantissa, which is strictly narrower
464     // mantissa (which represents underflow).  in ShiftRightAndRound()
517   // hundreds of digits of mantissa.)  in MustRoundUp()
572 // Constructs a CalculatedFloat from a given mantissa and exponent, but
575 // If rounding has caused mantissa to increase just past the allowed bit
580 // If mantissa is zero (representing a non-zero value not representable, even
583 CalculatedFloat CalculatedFloatFromRawValues(uint64_t mantissa, int exponent) {  in CalculatedFloatFromRawValues()  argument
585   if (mantissa == uint64_t{1} << FloatTraits<FloatType>::kTargetMantissaBits) {  in CalculatedFloatFromRawValues()
586     mantissa >>= 1;  in CalculatedFloatFromRawValues()
591   } else if (mantissa == 0) {  in CalculatedFloatFromRawValues()
595     result.mantissa = mantissa;  in CalculatedFloatFromRawValues()
603   uint64_t mantissa = parsed_hex.mantissa;  in CalculateFromParsedHexadecimal()  local
607   int mantissa_width = static_cast<int>(bit_width(mantissa));  in CalculateFromParsedHexadecimal()
611   mantissa = ShiftRightAndRound(mantissa, shift,  in CalculateFromParsedHexadecimal()
615   return CalculatedFloatFromRawValues<FloatType>(mantissa, exponent);  in CalculateFromParsedHexadecimal()
634   // mantissa, and multiply this by our parsed decimal mantissa.  in CalculateFromParsedDecimal()
635   uint128 wide_binary_mantissa = parsed_decimal.mantissa;  in CalculateFromParsedDecimal()
647     // Truncated mantissa  in CalculateFromParsedDecimal()
653     // Exact mantissa, truncated power of ten  in CalculateFromParsedDecimal()
664   // Shift into an FloatType-sized mantissa, and round to nearest.  in CalculateFromParsedDecimal()
692   uint64_t man = input.mantissa;  in EiselLemire()
722   // bias, 52 mantissa bits), but the same approach applies to single precision  in EiselLemire()
723   // (8 exponent bits with a -127 bias, 23 mantissa bits). Either way, the  in EiselLemire()
937     // A nullptr subrange_begin means that the decimal_parse.mantissa is exact  in FromCharsImpl()
969 // mantissa. The high bit is always on.
971 // kPower10MantissaLowTable extends that 64-bit mantissa to 128 bits.
985 // so we do not have to do further shifting to deduce the 128-bit mantissa: