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  2. Single-precision floating-point format - Wikipedia

    en.wikipedia.org/wiki/Single-precision_floating...

    If a decimal string with at most 6 significant digits is converted to the IEEE 754 single-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. If an IEEE 754 single-precision number is converted to a decimal string with at least 9 ...

  3. Floating-point arithmetic - Wikipedia

    en.wikipedia.org/wiki/Floating-point_arithmetic

    Converting a double-precision binary floating-point number to a decimal string is a common operation, but an algorithm producing results that are both accurate and minimal did not appear in print until 1990, with Steele and White's Dragon4. Some of the improvements since then include:

  4. Double-precision floating-point format - Wikipedia

    en.wikipedia.org/wiki/Double-precision_floating...

    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. If an IEEE 754 double-precision number is converted to a decimal string with at least ...

  5. Extended precision - Wikipedia

    en.wikipedia.org/wiki/Extended_precision

    Bounds on conversion between decimal and binary for the 80-bit format can be given as follows: If a decimal string with at most 18 significant digits is correctly rounded to an 80-bit IEEE 754 binary floating-point value (as on input) then converted back to the same number of significant decimal digits (as for output), then the final string ...

  6. IEEE 754 - Wikipedia

    en.wikipedia.org/wiki/IEEE_754

    For other binary formats, the required number of decimal digits is [h] + ⌈ ⁡ ⌉, where p is the number of significant bits in the binary format, e.g. 237 bits for binary256. When using a decimal floating-point format, the decimal representation will be preserved using:

  7. Quadruple-precision floating-point format - Wikipedia

    en.wikipedia.org/wiki/Quadruple-precision...

    If a decimal string with at most 33 significant digits is converted to the IEEE 754 quadruple-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. If an IEEE 754 quadruple-precision number is converted to a decimal string with at ...

  8. Arbitrary-precision arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arbitrary-precision_arithmetic

    Even floating-point numbers are soon outranged, so it may help to recast the calculations in terms of the logarithm of the number. But if exact values for large factorials are desired, then special software is required, as in the pseudocode that follows, which implements the classic algorithm to calculate 1, 1×2, 1×2×3, 1×2×3×4, etc. the ...

  9. Half-precision floating-point format - Wikipedia

    en.wikipedia.org/wiki/Half-precision_floating...

    In computing, half precision (sometimes called FP16 or float16) is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory. It is intended for storage of floating-point values in applications where higher precision is not essential, in particular image processing and neural networks .