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Fix error in float trig. function range reduction 

The single-precision trigonometric functions show rather high errors in
specific ranges starting at about 30000 radians. For example the sinf
procedure produces an error of 7626.55 ULP with the input
5.195880078125e+04 (0x474AF6CD) (compared with MPFR in 128bit
precision). For the test we used 100k values evenly spaced in the range
of [30k, 70k]. The issues are periodic at higher ranges.

This error was introduced when the double precision range reduction was
first converted to float. The shift by 8 bits always returns 0 as iq is
never higher than 255.

The fix reduces the error of the example above to 0.45 ULP, highest
error within the test set fell to 1.31 ULP, which is not perfect, but
still a significant improvement. Testing other previously erroneous
ranges no longer show particularly large accuracy errors.
This commit is contained in:
Fabian Schriever 2020-03-03 14:49:06 +01:00 committed by Corinna Vinschen
parent ecf27dd2e0
commit d4bcecb3e9
1 changed files with 1 additions and 1 deletions
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2
newlib/libm/math/kf_rem_pio2.c
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@ -101,7 +101,7 @@ recompute:
iq[jz-1] -= i<<(8-q0);
ih = iq[jz-1]>>(7-q0);
}
else if(q0==0) ih = iq[jz-1]>>8;
else if(q0==0) ih = iq[jz-1]>>7;
else if(z>=(float)0.5) ih=2;
if(ih>0) { /* q > 0.5 */