Real Computing Made Real

What Hacker News says

1. PaulHouleApr 2025
   (1) Maybe I'm just a little too young but my impression was that the 360 and it's successors were not that big in scientific computing, certainly there were some big academic installations but I saw a lot more DEC machines (PDP-8 in the experimental lab, PDP-10, PDP-11 and VAX elsewhere) and by the time I went to college circa 1990 you were likely to see Motorola 68k-based "workstations" that were quickly replaced by RISC architectures like SPARC and PA-RISC which in turn failed to compete with the PC.

   Cornell had one of very few IBM 3090s with a vector unit (to compete with the Cray) just before I showed up, but when I did IBM had donated a message-passing based supercomputer based on the Power PC architecture. I only saw a 3090 (no vector unit) at New Hampshire Insurance which I got to use as a Computer Explorer.

   (2) I was taught in grad school in the 1990s to use floats if at all possible to reduce the memory requirements of scientific codes if not actually speed up the computation. (In the 1990s floats were twice as fast as doubles on most architectures but not the x86). I really enjoyed taking a course on numerics from Saul Teukolsky, what stood out in the class as opposed my reading to the Numerical Recipes book which he was a co-author of, was the part about the numerical stability of discretizing and integrating partial differential equations. If you did it wrong, unphysical artifacts of the discretization would wreck your calculation. Depending on how you did things rounding errors can be made better or worse, Foreman Action's Numerical Methods that Work and later Real Computing Made Real reveal techniques for managing these errors that let you accomplish a lot with floats and some would point out that going to doubles doesn't win you that much slack to do things wrong.

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2. jostylrApr 2018
   From the book "real computing made real" by Acton, the suggestion is to first view (not always!) the quadratic as x^2 + 2bx + c, so its roots are -b +/- sqrt(b^2 - c). The product of the roots is c and therefore we can compute the root that does not do the subtraction and then divide c by that root to get the other root.

   This avoids any of the bad subtraction.

   Some sample js code that corresponds to quadratic in the post:

       b = 5e7
       c = 1
   
       d = b*b - c
   
       if (d >= 0) {
           m = Math.sqrt(d)   
           if ( b> 0) {
               r = -b - m
               s = c/r
           } else if ( b <  0) {
               s = -b + m
               r = c/s
           } else {
               r = m
               s = -r
           }
           console.log(r, s)
       } else {
           console.log("no real roots");
       }
   

   This gives the correct roots for this problem in one go.
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