APPENDIX A: ANSI/IEEE Standard 754-1985
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APPENDIX A: ANSI/IEEE Standard 754-1985
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APPENDIX A: ANSI/IEEE Standard 754-1985
APPENDIX A: ANSI/IEEE Standard 754-1985
The definition of NaNs, signed zero and infinity, and denormalized
numbers from [3] is reproduced here for convenience. The definitions
for quadruple-precision floating point numbers are analogs of those
for single and double-precision floating point numbers, and are
defined in [3].
In the following, 'S' stands for the sign bit, 'E' for the exponent,
and 'F' for the fractional part. The symbol 'u' stands for an
undefined bit (0 or 1).
For single-precision floating point numbers:
Type S (1 bit) E (8 bits) F (23 bits)
---- --------- ---------- -----------
signalling NaN u 255 (max) .0uuuuu---u
(with at least
one 1 bit)
quiet NaN u 255 (max) .1uuuuu---u
negative infinity 1 255 (max) .000000---0
positive infinity 0 255 (max) .000000---0
negative zero 1 0 .000000---0
positive zero 0 0 .000000---0
For double-precision floating point numbers:
Type S (1 bit) E (11 bits) F (52 bits)
---- --------- ----------- -----------
signalling NaN u 2047 (max) .0uuuuu---u
(with at least
one 1 bit)
quiet NaN u 2047 (max) .1uuuuu---u
negative infinity 1 2047 (max) .000000---0
positive infinity 0 2047 (max) .000000---0
negative zero 1 0 .000000---0
positive zero 0 0 .000000---0
For quadruple-precision floating point numbers:
Type S (1 bit) E (15 bits) F (112 bits)
---- --------- ----------- ------------
signalling NaN u 32767 (max) .0uuuuu---u
(with at least
one 1 bit)
quiet NaN u 32767 (max) .1uuuuu---u
negative infinity 1 32767 (max) .000000---0
positive infinity 0 32767 (max) .000000---0
negative zero 1 0 .000000---0
positive zero 0 0 .000000---0
Subnormal numbers are represented as follows:
Precision Exponent Value
--------- -------- -----
Single 0 (-1)**S * 2**(-126) * 0.F
Double 0 (-1)**S * 2**(-1022) * 0.F
Quadruple 0 (-1)**S * 2**(-16382) * 0.F
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APPENDIX A: ANSI/IEEE Standard 754-1985
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