4 ms·

When I went to university in 1982, one of the lower level courses was called "Numerical Methods". It went over all of the issues related to precision, stabilit

When I went to university in 1982, one of the lower level courses was called "Numerical Methods". It went over all of the issues related to precision, stability, as well as a host of common numerical integration and approximation methods. I'm just a sample size of one, but isn't this kind of class a requirement for CS majors?

Aeolun 8y ago
Not in many of the CS related majors. Though I guess it is for hard CS.
- jimmaswell 8y ago
  My CS course at a community college went over the limitations of floats in detail, in the CS class.
  - copperx 8y ago
    How detailed, if I may ask?
    - jimmaswell 8y ago
      I remember we learned how the representation worked bit-for-bit, and how it being stored in binary meant it couldn't perfectly represent everything in decimal. 1.01b meaning 12^0 + 02^-1 + 1*2^-2 for example.
kccqzy 8y ago
In my case, the CS class only covered the representation of floating point numbers (a sign bit, exponent bits, fraction bits, issues like bias etc) but not things like numerical approximation or integration methods. Those were in a separate class under the math department. And I think that's fair; after all those are really about scientific computing, not so much about computer science.
dzhiurgis 8y ago
CS isn’t really required for majority of developers.
sampo 8y ago
> isn't this kind of class a requirement for CS majors? I think most CS departments dropped numerical analysis from their requirements by the end of 1980s. Nowadays you are more likely to find such a course in some dusty corner of math or engineering departments.
- vlovich123 8y ago
  My university moved it from a 100 series course to a 200 series course but it's still being taught to ECE undergrads. The problem is more that we don't have the tools to track and understand how the errors are altered as we do the math (e.g. how would you even begin to try representing catastrophic cancellation at compile-time) and doing the numerical error analysis on the abstract math itself is hard once the math gets complex let alone trying to figure it out after you've optimized the code for performance & tweaked the algorithms for real-world data/discrete space. Now perhaps it could be possible to do it at runtime in some way but I suspect the performance of that is prohibitive to the point where arbitrary precision math or decimal numbers is going to be a better solution.
analog31 8y ago
I majored in math and physics. In math, our version of the course was called "numerical analysis," and we covered those things. In physics, the behavior of floating point math was covered in one of our lab courses. I don't know what's taught to CS majors, and as others have pointed out, programmers don't necessarily study CS. I believe the issue is just that the pitfalls of floating point are not apparent without a certain level of math education. But there may be one more pitfall, which is that those of us using FP regularly, also happen to be "scientific" or "exploratory" programmers who haven't learned a lot of formal software engineering discipline (including me). So we understand the math but might be more prone to making mistakes with it. I do kind of like the idea of flagging any number that is potentially exposed to a FP issue. We all make mistakes. Displaying all floats in exponential notation by default would be a good enough warning to the wary. We only display them as decimals for readability.
wwweston 8y ago
It wasn't required at my school a decade or two later. Floating point representations were touched on somewhat in the intro to computer architecture class where we wrote assembly for a MIPS simulator. I got an extra dose because I switched my major to Math, where there was an entire course on Numerical Methods (though it wasn't required by either the Math or CS depts). I'm a little amazed in retrospect that the Math department was where one had to go to get a class in the mechanical details of computing when as a subject it's usually considered (and often in practice is) notably up the ladder of abstraction. And this was a weird outlier as the single most practical upper division class offered by the Math department at the time...
svat 8y ago
From a 1998 interview with William Kahan, the “father” of IEEE-754 floating point (emphasis mine): > My reasoning was based on the requirements of a mass market: A lot of code involving a little floating-point will be written by many people who have never attended my (nor anyone else's) numerical analysis classes. We had to enhance the likelihood that their programs would get correct results. At the same time we had to ensure that people who really are expert in floating-point could write portable software and prove that it worked, since so many of us would have to rely upon it. There were a lot of almost conflicting requirements on the way to a balanced design. I imagine that the number of people writing code without having taken a numerical methods class has only increased since the late 1970s being talked about, or even in the two decades since that interview.

Aeolun 8y ago

Not in many of the CS related majors. Though I guess it is for hard CS.

jimmaswell 8y ago
My CS course at a community college went over the limitations of floats in detail, in the CS class.
- copperx 8y ago
  How detailed, if I may ask?
  - jimmaswell 8y ago
    I remember we learned how the representation worked bit-for-bit, and how it being stored in binary meant it couldn't perfectly represent everything in decimal. 1.01b meaning 12^0 + 02^-1 + 1*2^-2 for example.

kccqzy 8y ago

In my case, the CS class only covered the representation of floating point numbers (a sign bit, exponent bits, fraction bits, issues like bias etc) but not things like numerical approximation or integration methods. Those were in a separate class under the math department. And I think that's fair; after all those are really about scientific computing, not so much about computer science.

dzhiurgis 8y ago

CS isn’t really required for majority of developers.

sampo 8y ago

> isn't this kind of class a requirement for CS majors? I think most CS departments dropped numerical analysis from their requirements by the end of 1980s. Nowadays you are more likely to find such a course in some dusty corner of math or engineering departments.

vlovich123 8y ago
My university moved it from a 100 series course to a 200 series course but it's still being taught to ECE undergrads. The problem is more that we don't have the tools to track and understand how the errors are altered as we do the math (e.g. how would you even begin to try representing catastrophic cancellation at compile-time) and doing the numerical error analysis on the abstract math itself is hard once the math gets complex let alone trying to figure it out after you've optimized the code for performance & tweaked the algorithms for real-world data/discrete space. Now perhaps it could be possible to do it at runtime in some way but I suspect the performance of that is prohibitive to the point where arbitrary precision math or decimal numbers is going to be a better solution.

analog31 8y ago

I majored in math and physics. In math, our version of the course was called "numerical analysis," and we covered those things. In physics, the behavior of floating point math was covered in one of our lab courses. I don't know what's taught to CS majors, and as others have pointed out, programmers don't necessarily study CS. I believe the issue is just that the pitfalls of floating point are not apparent without a certain level of math education. But there may be one more pitfall, which is that those of us using FP regularly, also happen to be "scientific" or "exploratory" programmers who haven't learned a lot of formal software engineering discipline (including me). So we understand the math but might be more prone to making mistakes with it. I do kind of like the idea of flagging any number that is potentially exposed to a FP issue. We all make mistakes. Displaying all floats in exponential notation by default would be a good enough warning to the wary. We only display them as decimals for readability.

wwweston 8y ago

It wasn't required at my school a decade or two later. Floating point representations were touched on somewhat in the intro to computer architecture class where we wrote assembly for a MIPS simulator. I got an extra dose because I switched my major to Math, where there was an entire course on Numerical Methods (though it wasn't required by either the Math or CS depts). I'm a little amazed in retrospect that the Math department was where one had to go to get a class in the mechanical details of computing when as a subject it's usually considered (and often in practice is) notably up the ladder of abstraction. And this was a weird outlier as the single most practical upper division class offered by the Math department at the time...

svat 8y ago

From a 1998 interview with William Kahan, the “father” of IEEE-754 floating point (emphasis mine): > My reasoning was based on the requirements of a mass market: A lot of code involving a little floating-point will be written by many people who have never attended my (nor anyone else's) numerical analysis classes. We had to enhance the likelihood that their programs would get correct results. At the same time we had to ensure that people who really are expert in floating-point could write portable software and prove that it worked, since so many of us would have to rely upon it. There were a lot of almost conflicting requirements on the way to a balanced design. I imagine that the number of people writing code without having taken a numerical methods class has only increased since the late 1970s being talked about, or even in the two decades since that interview.