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Double oblique hyphen in a Fraktur typeface. In Latin script, the double hyphen ⹀ is a punctuation mark that consists of two parallel hyphens (‐). It was a development of the earlier double oblique hyphen ⸗, which developed from a Central European variant of the virgule slash, originally a form of scratch comma.
If a decimal string with at most 15 significant digits is converted to the IEEE 754 double-precision format, giving a normal number, and then converted back to a decimal string with the same number of digits, the final result should match the original string.
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.
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.
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 ...
As the magnitude of the value decreases, the amount of extra precision also decreases. Therefore, the smallest number in the normalized range is narrower than double precision. The smallest number with full precision is 1000...0 2 (106 zeros) × 2 −1074, or 1.000...0 2 (106 zeros) × 2 −968. Numbers whose magnitude is smaller than 2 −1021 ...
Hyphenate all numbers under 100 that need more than one word. For example, $73 is written as “seventy-three,” and the words for $43.50 are “Forty-three and 50/100.”
On some PowerPC systems, [11] long double is implemented as a double-double arithmetic, where a long double value is regarded as the exact sum of two double-precision values, giving at least a 106-bit precision; with such a format, the long double type does not conform to the IEEE floating-point standard.