How does this function compute the absolute value of a float through a NOT and AND operation?
absolute-value, bit-manipulation, c++, simd, sse
Solution
`-0.0` is represented as `1000...000`1. Therefore `_mm_andnot_ps(-0.0, x)`2 is equivalent to `0111...111 & x`. This forces the MSB (which is the sign bit) to 0.
1. In IEEE-754, at least.
2. The `_mm_andnot_ps` intrinsic does not mean "NAND"; see e.g. http://msdn.microsoft.com/en-us/library/68h7wd02(v=vs.90).aspx.
Problem
I am trying to understand how the following code snippet works. This program uses SIMD vector instructions (Intel SSE) to calculate the absolute value of 4 floats (so, basically, a vectorized "fabs()" function). Here is the snippet: ``` #include <iostream> #include "xmmintrin.h" template <typename T> struct alignas(16) sse_t { T data[16/sizeof(T)]; }; int main() { sse_t<float> x; x.data[0] = -4.; x.data[1] = -20.; x.data[2] = 15.; x.data[3] = -143.; __m128 a = _mm_set_ps1(-0.0); // ??? __m128 xv = _mm_load_ps(x.data); xv = _mm_andnot_ps(a,xv); // <-- Computes absolute value sse_t<float> result; _mm_store_ps(result.data, xv); std::cout << "x[0]: " << result.data[0] << std::endl; std::cout << "x[1]: " << result.data[1] << std::endl; std::cout << "x[2]: " << result.data[2] << std::endl; std::cout << "x[3]: " << result.data[3] << std::endl; } ``` Now, I know it works, since I ran the program myself to test it. When compiled with g++ 4.8.2, the result is: ``` x[0]: 4 x[1]: 20 x[2]: 15 x[3]: 143 ``` Three (related) questions puzzle me: First, how is it even possible to take a bitwise function and apply it on a float? If I try this in vanilla C++, it informs me that this only works for integral types (which makes sense). But, second, and more importantly: How does it even work? How does taking a NOT and an AND even help you here? Trying this in Python with an integral type just gives you the expected result: any integral number AND -1 (which is NOT 0), simply gives you that number back, but doesn't change the sign. So how does it work here? Third, I noticed that if I change the value of the float used for the NAND operation (marked with three ???), from -0.0 to 0.0, the program doesn't give me the absolute value anymore. But how can a -0.0 even exist and how does it help? Helpful references: Intel intrinsics guide