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$emin$ shall be $1 − emax$ for all formats (section 3.3, page 17),
when biased exponent $E = 0$ and trailing significand $T \neq 0$, the number is subnormal and the corresponding value is $v = (-1)^S \times 2^{emin} \times (0 + 2^{1-p} \times T)$ (section 3.4, page 19),
As a consequence for 32 bits precision the value of subnormal numbers shall be $v = (-1)^S \times 2^{-126} \times (0 + 2^{-23} \times T)$. The Floating Point Representation tool apparently has a different interpretation and displays equation $v = (-1)^S \times 2^{-127} \times 2^{-23} \times T$. The first screenshot below shows the tool for $S = 0, E = 0, T = 1$. Still, it displays the correct scientific notation: 1.4E-45 instead of the wrong $v = 2^{-127} \times 2^{-23} = 2^{-150} \approx 7e^{-46}$.
I suggest to replace $0 - 127$ with $-126$, $2^{-127}$ with $2^{-126}$ and, while we are at it, denormalized with the new standard subnormal term. Pull request submitted, new screenshot added with the correct display.
The text was updated successfully, but these errors were encountered:
According IEEE 754-2019:
As a consequence for 32 bits precision the value of subnormal numbers shall be$v = (-1)^S \times 2^{-126} \times (0 + 2^{-23} \times T)$ . The Floating Point Representation tool apparently has a different interpretation and displays equation $v = (-1)^S \times 2^{-127} \times 2^{-23} \times T$ . The first screenshot below shows the tool for $S = 0, E = 0, T = 1$ . Still, it displays the correct scientific notation: $v = 2^{-127} \times 2^{-23} = 2^{-150} \approx 7e^{-46}$ .
1.4E-45
instead of the wrongI suggest to replace$0 - 127$ with $-126$ , $2^{-127}$ with $2^{-126}$ and, while we are at it, denormalized with the new standard subnormal term. Pull request submitted, new screenshot added with the correct display.
The text was updated successfully, but these errors were encountered: