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Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient.
Note that C99 and C++ do not implement complex numbers in a code-compatible way – the latter instead provides the class std:: complex. All operations on complex numbers are defined in the <complex.h> header. As with the real-valued functions, an f or l suffix denotes the float complex or long double complex variant of the function.
In conclusion, the exact number of bits of precision needed in the significand of the intermediate result is somewhat data dependent but 64 bits is sufficient to avoid precision loss in the vast majority of exponentiation computations involving double-precision numbers. The number of bits needed for the exponent of the extended-precision format ...
Here we start with 0 in single precision (binary32) and repeatedly add 1 until the operation does not change the value. Since the significand for a single-precision number contains 24 bits, the first integer that is not exactly representable is 2 24 +1, and this value rounds to 2 24 in round to nearest, ties to even.
The range of a double-double remains essentially the same as the double-precision format because the exponent has still 11 bits, [4] significantly lower than the 15-bit exponent of IEEE quadruple precision (a range of 1.8 × 10 308 for double-double versus 1.2 × 10 4932 for binary128).
For numbers with a base-2 exponent part of 0, i.e. numbers with an absolute value higher than or equal to 1 but lower than 2, an ULP is exactly 2 −23 or about 10 −7 in single precision, and exactly 2 −53 or about 10 −16 in double precision. The mandated behavior of IEEE-compliant hardware is that the result be within one-half of a ULP.
In CORBA (from specification of 3.0, which uses "ANSI/IEEE Standard 754-1985" as its reference), "the long double data type represents an IEEE double-extended floating-point number, which has an exponent of at least 15 bits in length and a signed fraction of at least 64 bits", with GIOP/IIOP CDR, whose floating-point types "exactly follow the ...
FLT_MANT_DIG, DBL_MANT_DIG, LDBL_MANT_DIG – number of FLT_RADIX-base digits in the floating-point significand for types float, double, long double, respectively FLT_MIN_EXP , DBL_MIN_EXP , LDBL_MIN_EXP – minimum negative integer such that FLT_RADIX raised to a power one less than that number is a normalized float, double, long double ...