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The outgoing license was MIT only. The new dual license allows
using the code under Apache-2.0 WITH LLVM-exception license too.
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gcc-12 -frounding-math started using runtime rounding mode for
converting double constants to float, so abstop12(pio4) is no longer
a compile time constant (this is required by iso c). Use float pio4f
instead to make the generated code the same as before and avoid
regressions on gcc-12.
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Scripted copyright year updates based on git committer date.
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math/single contained code for systems without double precision fpu
and rem_pio2 is not used currently and likely will be designed
differently when double precision trigonometric functions are added.
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Improve comments. Use TOINT_INTRINSICS rather than HAVE_FAST_ROUND.
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Use const sincos_t for clarity instead of making the typedef const.
Use __inv_pi4 and __sincosf_table to avoid namespace issues with
static linking.
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Whitespace changes only.
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This patch is a complete rewrite of sinf, cosf and sincosf. The new version
is significantly faster, as well as simple and accurate.
The worst-case ULP is 0.56072, maximum relative error is 0.5303p-23 over all
4 billion inputs. In non-nearest rounding modes the error is 1ULP.
The algorithm uses 3 main cases: small inputs which don't need argument
reduction, small inputs which need a simple range reduction and large inputs
requiring complex range reduction. The code uses approximate integer
comparisons to quickly decide between these cases - on some targets this may
be slow, so this can be configured to use floating point comparisons.
The small range reducer uses a single reduction step to handle values up to
120.0. It is fastest on targets which support inlined round instructions.
The large range reducer uses integer arithmetic for simplicity. It does a
32x96 bit multiply to compute a 64-bit modulo result. This is more than
accurate enough to handle the worst-case cancellation for values close to
an integer multiple of PI/4. It could be further optimized, however it is
already much faster than necessary.
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