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The integer is: 16777217 The float is: 16777216.000000 Their equality: 1 Note that 1 represents equality in the last line above. This odd behavior is caused by an implicit conversion of i_value to float when it is compared with f_value. The conversion causes loss of precision, which makes the values equal before the comparison. Important takeaways:
Usually, the 32-bit and 64-bit IEEE 754 binary floating-point formats are used for float and double respectively. The C99 standard includes new real floating-point types float_t and double_t, defined in <math.h>. They correspond to the types used for the intermediate results of floating-point expressions when FLT_EVAL_METHOD is 0, 1, or 2.
Conversion of the fractional part: Consider 0.375, the fractional part of 12.375. To convert it into a binary fraction, multiply the fraction by 2, take the integer part and repeat with the new fraction by 2 until a fraction of zero is found or until the precision limit is reached which is 23 fraction digits for IEEE 754 binary32 format.
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.
The F16C extension in 2012 allows x86 processors to convert half-precision floats to and from single-precision floats with a machine instruction. IEEE 754 half-precision binary floating-point format: binary16
A 2-bit float with 1-bit exponent and 1-bit mantissa would only have 0, 1, Inf, NaN values. If the mantissa is allowed to be 0-bit, a 1-bit float format would have a 1-bit exponent, and the only two values would be 0 and Inf. The exponent must be at least 1 bit or else it no longer makes sense as a float (it would just be a signed number).
Rounding is used when the exact result of a floating-point operation (or a conversion to floating-point format) would need more digits than there are digits in the significand. IEEE 754 requires correct rounding : that is, the rounded result is as if infinitely precise arithmetic was used to compute the value and then rounded (although in ...
Decimal floating-point (DFP) arithmetic refers to both a representation and operations on decimal floating-point numbers. Working directly with decimal (base-10) fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions (common in human-entered data, such as measurements or financial ...