4 ms·

In case anyone else wasn't quite following this, I think the idea is e^x = e^(a+b+c+d) (where abcd are the bytes of x) = e^a * e^b * e^d * e*d and then you

by evmar 2y ago

In case anyone else wasn't quite following this, I think the idea is e^x = e^(a+b+c+d) (where abcd are the bytes of x) = e^a * e^b * e^d * e*d and then you make a lookup table for each of those e^a, e^b values. (I fudged "a" here, where it's really more like "high byte << 24", but I think you just make your lookup table for e^a be a map from a => e^(a<<24), and similar for the other bytes.)

dekhn 2y ago
When I took Huffman's Cybernetics course as an undergrad, his tests were full of multiplication and you couldn't use a calculator, so he provided a table of exponents and logarithms, and you'd look up in one table, sum the values, then look up the result in another table. I was not a fan.
- gdevenyi 2y ago
  This is literally what a sliderule is.
  - bigbacaloa 2y ago
    In their day, slide rules were the most efficient easily available option.
    - bluenose69 2y ago
      Slide rules were a great teaching aide, because they required you to (1) keep track of powers of 10 for yourself, and (2) understand the exponential difficulty of seeking more digits in a result. The first point lets you guess the order of magnitude of a result before doing the detailed calculation, and that is a great way to find errors. The second one reveals why teachers get so annoyed when 9-digit answers are given to problems with 2-digit data. I do wish some company would start producing cheap plastic slide rules again, so my students could try them out. The online ones are not as effective as actually seeing something in the real world, squinting your eyes to guess where the cursor lies between two lines on the rule. (Hm, I can get more digits on the left end of the rule than I can on the right ...)
      - abecedarius 2y ago
        ThinkGeek sold a cheap plastic slide rule once. Its motion was too sticky for me to, well, stick with learning to use it. I agree there's a good product idea here if you can do it better.
  - acc_297 2y ago
    A good YouTube channel “Welch labs” recently did a good history of the logarithm and how it revolutionized the speed at which people could do math

by evmar 2y ago

dekhn 2y ago

When I took Huffman's Cybernetics course as an undergrad, his tests were full of multiplication and you couldn't use a calculator, so he provided a table of exponents and logarithms, and you'd look up in one table, sum the values, then look up the result in another table. I was not a fan.

gdevenyi 2y ago
This is literally what a sliderule is.
- bigbacaloa 2y ago
  In their day, slide rules were the most efficient easily available option.
  - bluenose69 2y ago
    Slide rules were a great teaching aide, because they required you to (1) keep track of powers of 10 for yourself, and (2) understand the exponential difficulty of seeking more digits in a result. The first point lets you guess the order of magnitude of a result before doing the detailed calculation, and that is a great way to find errors. The second one reveals why teachers get so annoyed when 9-digit answers are given to problems with 2-digit data. I do wish some company would start producing cheap plastic slide rules again, so my students could try them out. The online ones are not as effective as actually seeing something in the real world, squinting your eyes to guess where the cursor lies between two lines on the rule. (Hm, I can get more digits on the left end of the rule than I can on the right ...)
    - abecedarius 2y ago
      ThinkGeek sold a cheap plastic slide rule once. Its motion was too sticky for me to, well, stick with learning to use it. I agree there's a good product idea here if you can do it better.
- acc_297 2y ago
  A good YouTube channel “Welch labs” recently did a good history of the logarithm and how it revolutionized the speed at which people could do math