Float fminNormalized significand 1.0 Float fminNormalized exponent -1022
Float fminNormalized predecessor significand 1.9999999999999996 Float fminNormalized predecessor exponent -1023
But the significand only has 52 bits in this case of underflow. Gradual underflow is removing the leading 1, so that one should better be written like: Float fminNormalized predecessor = 2r0.1111111111111111111111111111111111111111111111111111e-1022 and that means that the exponent is still -1022 for gradual underflow (aka Float emin)...
And the smallest Float above zero is : Float fmin significand 1.0 Float fmin exponent -1074 or Float fmin = 2r0.0000000000000000000000000000000000000000000000000001e-1022
Nicolas
2014-11-25 18:42 GMT+01:00 Eliot Miranda eliot.miranda@gmail.com:
Hi All,
who wrote the Float class comment? Two things,
- first the comment mentions "I" and thanks several people, but there is
no comment stamp to reveal the author. It would be lovely if the author could "sign" this comment
- second, there seems to be a minor error (but I'm no expert), the comment
states
"It may help you to know that the basic format is... sign 1 bit exponent 11 bits with bias of 1023 (16r3FF) to produce an exponent in the range -1023 .. +1024
- 16r000:
significand = 0: Float zero significand ~= 0: Denormalized number (exp = -1024, no hidden '1' bit)
- 16r7FF:
significand = 0: Infinity significand ~= 0: Not A Number (NaN) representation mantissa 53 bits, but only 52 are stored (20 in the first word, 32 in the second). This is because a normalized mantissa, by definition, has a 1 to the right of its floating point, and IEEE-754 omits this redundant bit to gain an extra bit of precision instead. People talk about the mantissa without its leading one as the FRACTION, and with its leading 1 as the SIGNFICAND."
But if the significand has a leading zero then surely the section in the middle should read
sign 1 bit exponent 11 bits with bias of 1023 (16r3FF) to produce an exponent in the range -1023 .. +1024
- 16r000:
mantissa = 0: Float zero mantissa ~= 0: Denormalized number (exp = -1024, no hidden '1' bit)
- 16r7FF:
mantissa = 0: Infinity mantissa ~= 0: Not A Number (NaN) representation
Right?
best, Eliot