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I had a slightly similar experience at work. We deal a lot with angles and binary angles are often the most efficient representation. Many colleagues find it an

by yiyus 6y ago

I had a slightly similar experience at work. We deal a lot with angles and binary angles are often the most efficient representation. Many colleagues find it annoying because they insist on converting every binary angle to radian or degrees, but if you actually interpret the bits as successive divisions of a circumference, I actually find the binary representation way more intuitive than a floating point number.

a1369209993 6y ago
> they insist on converting every binary angle to [] degrees Bit of hypocrisy there, since degrees are literally the same thing, just with 360 sectors rather than (say) 256. Though the extra factors of 3 and 5 are sometimes useful.
- yiyus 6y ago
  The point is to not think of the bits as the representation of a decimal number. For example, if I need to know in which quadrant an angle is, I just need to look at the first two bits, independently of the precision (which we change just shifting and truncating). But I do not mind if 90 degrees are equal to 64 or 1073741824 "sectors". I think this is another good example where a binary representation (and a shift) can be a more natural way to approach the problem.
  - pdehaan 6y ago
    Not just more natural, it also lends itself to better accuracy and/or efficiency in some cases too. As a quick example, if you're writing a numerical approximation or even just a LUT for sin(x), you can get away with only approximating/storing values for a reduced range by using some bit twiddling. The top bit becomes sign of output if you XOR it out first, the next bit lets you take advantage of sin(pi/2-x) = sin(x+pi/2) to half the input range again, eek out symmetry for the next bit and you can nearly approximate sin(x) as a linear function for some use cases.
slavik81 6y ago
That method is exactly equivalent to using revolutions as the unit with a fixed-point numeric representation. Maybe your skeptical colleagues would find that perspective more palatable?
- yiyus 6y ago
  That's some good advice. Unfortunately, most of the people I work with do not have a computer science background (they are materials scientists and mechanical engineers), so they are not familiarized with fixed-point arithmetic neither.

by yiyus 6y ago

a1369209993 6y ago

> they insist on converting every binary angle to [] degrees Bit of hypocrisy there, since degrees are literally the same thing, just with 360 sectors rather than (say) 256. Though the extra factors of 3 and 5 are sometimes useful.

yiyus 6y ago
The point is to not think of the bits as the representation of a decimal number. For example, if I need to know in which quadrant an angle is, I just need to look at the first two bits, independently of the precision (which we change just shifting and truncating). But I do not mind if 90 degrees are equal to 64 or 1073741824 "sectors". I think this is another good example where a binary representation (and a shift) can be a more natural way to approach the problem.
- pdehaan 6y ago
  Not just more natural, it also lends itself to better accuracy and/or efficiency in some cases too. As a quick example, if you're writing a numerical approximation or even just a LUT for sin(x), you can get away with only approximating/storing values for a reduced range by using some bit twiddling. The top bit becomes sign of output if you XOR it out first, the next bit lets you take advantage of sin(pi/2-x) = sin(x+pi/2) to half the input range again, eek out symmetry for the next bit and you can nearly approximate sin(x) as a linear function for some use cases.

slavik81 6y ago

That method is exactly equivalent to using revolutions as the unit with a fixed-point numeric representation. Maybe your skeptical colleagues would find that perspective more palatable?

yiyus 6y ago
That's some good advice. Unfortunately, most of the people I work with do not have a computer science background (they are materials scientists and mechanical engineers), so they are not familiarized with fixed-point arithmetic neither.