Add exp/log optimization documentation
This PDF file details the techniques that were used to optimize the
exp2() and log2() implementations, as well as their relaxed precision
variants.
Legacy implementations have been removed since they're unused and no
longer contain useful techniques not already incorporated into the new
versions or superseded by superior ones in terms of precision and/or
performance, as explained by the document.
Bug: b/169754022
Change-Id: I4e137fd6a35ebba8976310f9e168e20b5223f4ef
Reviewed-on: https://swiftshader-review.googlesource.com/c/SwiftShader/+/64250
Tested-by: Nicolas Capens <nicolascapens@google.com>
Kokoro-Result: kokoro <noreply+kokoro@google.com>
Reviewed-by: Alexis Hétu <sugoi@google.com>
diff --git a/docs/Exp-Log-Optimization.pdf b/docs/Exp-Log-Optimization.pdf
new file mode 100644
index 0000000..a2424d0
--- /dev/null
+++ b/docs/Exp-Log-Optimization.pdf
Binary files differ
diff --git a/tests/MathUnitTests/unittests.cpp b/tests/MathUnitTests/unittests.cpp
index de2a16b..5b92f48 100644
--- a/tests/MathUnitTests/unittests.cpp
+++ b/tests/MathUnitTests/unittests.cpp
@@ -202,31 +202,6 @@
CPUID::setFlushToZero(false);
}
-float Log2_legacy(float x)
-{
- float x0;
- float x1;
- float x2;
- float x3;
-
- x0 = x;
-
- x1 = bit_cast<float>(bit_cast<int>(x0) & int(0x7F800000));
- x1 = bit_cast<float>(bit_cast<unsigned int>(x1) >> 8);
- x1 = bit_cast<float>(bit_cast<int>(x1) | bit_cast<int>(float(1.0f)));
- x1 = (x1 - float(1.4960938f)) * float(256.0f); // FIXME: (x1 - 1.4960938f) * 256.0f;
- x0 = bit_cast<float>((bit_cast<int>(x0) & int(0x007FFFFF)) | bit_cast<int>(float(1.0f)));
-
- x2 = (float(9.5428179e-2f) * x0 + float(4.7779095e-1f)) * x0 + float(1.9782813e-1f);
- x3 = ((float(1.6618466e-2f) * x0 + float(2.0350508e-1f)) * x0 + float(2.7382900e-1f)) * x0 + float(4.0496687e-2f);
- x2 /= x3;
-
- x1 += (x0 - float(1.0f)) * x2;
-
- int pos_inf_x = (bit_cast<int>(x) == int(0x7F800000)) ? 0xFFFFFFFF : 0x00000000;
- return bit_cast<float>((pos_inf_x & bit_cast<int>(x)) | (~pos_inf_x & bit_cast<int>(x1)));
-}
-
// lolremez --float -d 7 -r "0:1" "(log2(x+1)-x)/x" "1/x"
// ULP-32: 1.69571960, abs: 0.360798746
float Pl(float x)
@@ -316,35 +291,6 @@
CPUID::setFlushToZero(false);
}
-// ULP-32: 3.36676240, Vulkan margin: 1.0737335
-float Exp2_legacy(float x)
-{
- // This implementation is based on 2^(i + f) = 2^i * 2^f,
- // where i is the integer part of x and f is the fraction.
-
- // For 2^i we can put the integer part directly in the exponent of
- // the IEEE-754 floating-point number. Clamp to prevent overflow
- // past the representation of infinity.
- float x0 = x;
- // x0 = Min(x0, bit_cast<float>(int(0x43010000))); // 129.00000e+0f
- // x0 = Max(x0, bit_cast<float>(int(0xC2FDFFFF))); // -126.99999e+0f
-
- int i = (int)round(x0 - 0.5f);
- float ii = bit_cast<float>((i + int(127)) << 23); // Add single-precision bias, and shift into exponent.
-
- // For the fractional part use a polynomial
- // which approximates 2^f in the 0 to 1 range.
- float f = x0 - float(i);
- float ff = bit_cast<float>(int(0x3AF61905)); // 1.8775767e-3f
- ff = ff * f + bit_cast<float>(int(0x3C134806)); // 8.9893397e-3f
- ff = ff * f + bit_cast<float>(int(0x3D64AA23)); // 5.5826318e-2f
- ff = ff * f + bit_cast<float>(int(0x3E75EAD4)); // 2.4015361e-1f
- ff = ff * f + bit_cast<float>(int(0x3F31727B)); // 6.9315308e-1f
- ff = ff * f + float(1.0f);
-
- return ii * ff;
-}
-
// lolremez --float -d 4 -r "0:1" "(2^x-x-1)/x" "1/x"
// ULP_32: 2.14694786, Vulkan margin: 0.686957061
float P(float x)
