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Exp, Log: Estrin polynomial evaluation in RELAXED mode #18

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Exp, Log: Estrin polynomial evaluation in RELAXED mode #18

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103 changes: 68 additions & 35 deletions include/FastSIMD/ToolSet/Generic/Functions.h
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Original file line number Diff line number Diff line change
Expand Up @@ -556,19 +556,33 @@ namespace FS
value -= fx * RegisterF( 0.693359375f );
value -= fx * RegisterF( -2.12194440e-4f );

RegisterF y( 1.9875691500E-4f );
y *= value;
y += RegisterF( 1.3981999507E-3f );
y *= value;
y += RegisterF( 8.3334519073E-3f );
y *= value;
y += RegisterF( 4.1665795894E-2f );
y *= value;
y += RegisterF( 1.6666665459E-1f );
y *= value;
y += RegisterF( 5.0000001201E-1f );
y *= value * value;
y += value + RegisterF( 1 );
RegisterF y;
if constexpr( FastSIMD::IsRelaxed<SIMD>() )
{
/* Estrin's scheme: about half the dependency chain of Horner's, rounds slightly differently */
RegisterF x2 = value * value;
RegisterF r01 = FMulAdd( RegisterF( 1.6666665459E-1f ), value, RegisterF( 5.0000001201E-1f ) );
RegisterF r23 = FMulAdd( RegisterF( 8.3334519073E-3f ), value, RegisterF( 4.1665795894E-2f ) );
RegisterF r45 = FMulAdd( RegisterF( 1.9875691500E-4f ), value, RegisterF( 1.3981999507E-3f ) );
y = FMulAdd( r45, x2 * x2, FMulAdd( r23, x2, r01 ) );
y = FMulAdd( y, x2, value + RegisterF( 1 ) );
}
else
{
y = RegisterF( 1.9875691500E-4f );
y *= value;
y += RegisterF( 1.3981999507E-3f );
y *= value;
y += RegisterF( 8.3334519073E-3f );
y *= value;
y += RegisterF( 4.1665795894E-2f );
y *= value;
y += RegisterF( 1.6666665459E-1f );
y *= value;
y += RegisterF( 5.0000001201E-1f );
y *= value * value;
y += value + RegisterF( 1 );
}

/* build 2^n */
RegisterI i = Convert<std::int32_t>( fx );
Expand Down Expand Up @@ -613,29 +627,48 @@ namespace FS
value -= RegisterF( 1 );
e = MaskedDecrement( mask, e );

RegisterF y = RegisterF( 7.0376836292E-2f );
y *= value;
y += RegisterF( -1.1514610310E-1f );
y *= value;
y += RegisterF( 1.1676998740E-1f );
y *= value;
y += RegisterF( -1.2420140846E-1f );
y *= value;
y += RegisterF( 1.4249322787E-1f );
y *= value;
y += RegisterF( -1.6668057665E-1f );
y *= value;
y += RegisterF( 2.0000714765E-1f );
y *= value;
y += RegisterF( -2.4999993993E-1f );
y *= value;
y += RegisterF( 3.3333331174E-1f );
y *= value;

RegisterF xx = value * value;
y *= xx;
y += e * RegisterF( -2.12194440e-4f );
y -= xx * RegisterF( 0.5f );
RegisterF y;
if constexpr( FastSIMD::IsRelaxed<SIMD>() )
{
/* Estrin's scheme (with the -x^2/2 term folded in): about half the dependency chain of Horner's,
rounds slightly differently */
RegisterF x4 = xx * xx;
RegisterF q01 = FMulAdd( RegisterF( 3.3333331174E-1f ), value, RegisterF( -0.5f ) );
RegisterF q23 = FMulAdd( RegisterF( 2.0000714765E-1f ), value, RegisterF( -2.4999993993E-1f ) );
RegisterF q45 = FMulAdd( RegisterF( 1.4249322787E-1f ), value, RegisterF( -1.6668057665E-1f ) );
RegisterF q67 = FMulAdd( RegisterF( 1.1676998740E-1f ), value, RegisterF( -1.2420140846E-1f ) );
RegisterF q89 = FMulAdd( RegisterF( 7.0376836292E-2f ), value, RegisterF( -1.1514610310E-1f ) );
y = FMulAdd( FMulAdd( q67, xx, q45 ), x4, FMulAdd( q23, xx, q01 ) );
y = FMulAdd( q89, x4 * x4, y );
y *= xx;
y += e * RegisterF( -2.12194440e-4f );
}
else
{
y = RegisterF( 7.0376836292E-2f );
y *= value;
y += RegisterF( -1.1514610310E-1f );
y *= value;
y += RegisterF( 1.1676998740E-1f );
y *= value;
y += RegisterF( -1.2420140846E-1f );
y *= value;
y += RegisterF( 1.4249322787E-1f );
y *= value;
y += RegisterF( -1.6668057665E-1f );
y *= value;
y += RegisterF( 2.0000714765E-1f );
y *= value;
y += RegisterF( -2.4999993993E-1f );
y *= value;
y += RegisterF( 3.3333331174E-1f );
y *= value;

y *= xx;
y += e * RegisterF( -2.12194440e-4f );
y -= xx * RegisterF( 0.5f );
}

value += y;
value += e * RegisterF( 0.693359375f );
Expand Down
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