3 ms·

Indeed! Given the effort and knowledge put into the question, the obvious answer seemed too... obvious for this poster to not already know it. I thought I must

Indeed! Given the effort and knowledge put into the question, the obvious answer seemed too... obvious for this poster to not already know it. I thought I must be missing something!

naniwaduni 3y ago
A striking reminder that fluency is not the same thing as competence...
sifar 3y ago
Perhaps because the poster seems to be historian and not a CS practioner. From the question "Why I am asking I am writing a history of the Fast Inverse Square Root, information about which is collected at 0x5f37642f.com. Part of investigating this as a historian means asking questions like this from the community. I do not have the expertise to distill, by myself, much of this because I am not a mathematician or a computer scientist."
cryptonector 3y ago
The key that TFA probably missed is that the bit pattern following the exponent (which is by definition an approximation of the logarithm) is the "linear" bit of the "piecewise linear approximation", while the exponent is the "piecewise" bit. That's really all the answer needed to explain in the end. "Why is an IEEE 754 positive [normal] number interpreted as an integer a piecewise linear approximation of its logarithm?" -> "Because the bit pattern for it will have an exponent followed by a mantissa, where the exponent by definition is a very rough approximation of the logarithm, and where the mantissa can be interpreted as a linear interpolation between the exponent and the next exponent, thus the two pieces as the "piecewise" (exponent) and "linear" (mantissa) approximation of the number's logarithm." The only remaining bits of interest is the bias of the exponent and the assumed-1 leading digit of the mantissa being left out. The latter is a compression technique (why wastefully include a bit that's always set or always reset?) that happens to help here (avoiding having to shift the mantissa bits by one). The former is easy enough to deal with.

Indeed! Given the effort and knowledge put into the question, the obvious answer seemed too... obvious for this poster to not already know it. I thought I must be missing something!

naniwaduni 3y ago

A striking reminder that fluency is not the same thing as competence...

sifar 3y ago

Perhaps because the poster seems to be historian and not a CS practioner. From the question "Why I am asking I am writing a history of the Fast Inverse Square Root, information about which is collected at 0x5f37642f.com. Part of investigating this as a historian means asking questions like this from the community. I do not have the expertise to distill, by myself, much of this because I am not a mathematician or a computer scientist."

cryptonector 3y ago

The key that TFA probably missed is that the bit pattern following the exponent (which is by definition an approximation of the logarithm) is the "linear" bit of the "piecewise linear approximation", while the exponent is the "piecewise" bit. That's really all the answer needed to explain in the end. "Why is an IEEE 754 positive [normal] number interpreted as an integer a piecewise linear approximation of its logarithm?" -> "Because the bit pattern for it will have an exponent followed by a mantissa, where the exponent by definition is a very rough approximation of the logarithm, and where the mantissa can be interpreted as a linear interpolation between the exponent and the next exponent, thus the two pieces as the "piecewise" (exponent) and "linear" (mantissa) approximation of the number's logarithm." The only remaining bits of interest is the bias of the exponent and the assumed-1 leading digit of the mantissa being left out. The latter is a compression technique (why wastefully include a bit that's always set or always reset?) that happens to help here (avoiding having to shift the mantissa bits by one). The former is easy enough to deal with.