sin(x) and cos(x) have increasing error for |x|>128

[dpgeorge]

When using single precision float, sin(x) and cos(x) (and possibly sincos and tan) are accurate for |x| < 128 (here, |x| means absolute value of x) but show increasing error as |x| grows beyond 128.

Here is a plot of the error of sin(x) as a function of x (compared to the single-precision float musl implementation of sin):

You can see that the error grows linearly beyond -128 / +128.

Looking at the code, there's a wrapper function that reduces the argument down to within +/- 128 and then calls the ROM code: https://github.com/raspberrypi/pico-sdk/blob/master/src/rp2_common/pico_float/float_aeabi.S#L637-L664 . That reduction is probably introducing a small floating point error for each loop of the reduction (that's a guess, I did not investigate further).

(Note: this was found running MicroPython's tests/float/cmath_fun.py test, which fails on a Pico board due to the above problem.)

[znmeb]

One should never call sin (x) or cos(x) with |x| greater than 128! And code for sin(x) and cos(x) should take advantage of trigonometric identities to reduce the range of the argument. See https://realtimecollisiondetection.net/blog/?p=9, for example. The graph tells me the code may have range reduction but it's broken.

[kilograham]

it is indeed broken ;-) oops.

[dpgeorge]

@kilograham did you intend to close this?

[kilograham]

nope (wrong button)