Floating-Point Comparison
IEEE 754 floating point numbers are ordered because
- Sign bit is most significant
⇒quick test of signed ‘<’. - Exponent value and its binary representation have same ordering because exponent uses a biased representation.
- Placing exponent before the fraction field orders the magnitude because
- Larger exponent
⇒larger magnitude and - For equal exponents, larger fraction
⇒larger magnitude.
- Larger exponent
0 < 0.F2×21-Bias < 1.F2×2E-Bias < ∞Denormalized Numbers
IEEE standard uses denormalized numbers to
- Fill the gap between 0 and the smallest normalized float (
1.02×2-126), and - Provide gradual underflow to zero.
E=0 and fraction F≠0.
Implicit 1. before the fraction now becomes 0 (not normalized).
| S | 0 | F = f1 f2 f3 f4 ... |
Value of denormalized number
(S,0,F) is as follows:
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βIn fact, the mere act of opening the box will determine the state of the cat, although in this case there were three determinate states the cat could be in: these being Alive, Dead, and Bloody Furious.β β Terry Pratchett, Lords and Ladies |