# math.sin-cos

Sine and cosine of an angle in radians, computed together with nothing but
`+`, `-`, `*` and `/`, so TypeScript, Python and Rust return the same doubles.
Used for arcs and pie slices, where a coordinate that lands on x.xx5 must round
the same way in every language. See `math.ln` for why the platform's `sin` and
`cos` cannot promise that.

## Method

1. Reduce: k = the nearest whole number of quarter turns, r = x - k pi/2, with
   pi/2 in two parts (fdlibm's `pio2_1`, 33 bits, and `pio2_1t`), so that
   k x pio2_1 is exact for every k the permitted range needs.
2. sin r and cos r by Taylor series to r^17 and r^18 on |r| <= pi/4, where they
   converge to well below an ulp.
3. Rotate by the quadrant k mod 4.

Results are within about 2e-16 of the true values. `sinCos(pi / 2).cos` is
6.1e-17, not 0, because pi/2 as a double is not exactly pi/2; every library
says the same. No `-0` is returned.

The angle must be within ±1,000,000 radians: beyond that the two-part pi/2 no
longer reduces exactly, and an angle that large is almost always a bug (degrees
passed as radians many times over).

Sources: W. J. Cody and W. Waite, *Software Manual for the Elementary
Functions* (1980); Sun Microsystems fdlibm, `e_rem_pio2.c` (the constants).

## Notices

Derived from fdlibm e_rem_pio2.c.
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
Developed at SunSoft, a Sun Microsystems, Inc. business.
Permission to use, copy, modify, and distribute this
software is freely granted, provided that this notice
is preserved.

The same notice heads each implementation file.

1.0.1 adds its attribution notices (NOTICE). The code is unchanged apart from that notice at the top of each implementation file; the tests are unchanged.