For some operations, Numba may use a different algorithm than Python or Numpy. The results may not be bit-by-bit compatible. The difference should generally be small and within reasonable expectations. However, small accumulated differences might produce large differences at the end, especially if a divergent function is involved.
Numba supports a variety of platforms and operating systems, each of which
has its own math library implementation (referred to as libm from here
in). The majority of math functions included in libm have specific
requirements as set out by the IEEE 754 standard (like sin(), exp()
etc.), but each implementation may have bugs. Thus, on some platforms
Numba has to exercise special care in order to workaround known libm
issues.
Another typical problem is when an operating system’s libm function
set is incomplete and needs to be supplemented by additional functions.
These are provided with reference to the IEEE 754 and C99 standards
and are often implemented in Numba in a manner similar to equivalent
CPython functions.
Numpy forces some linear algebra operations to run in double-precision mode
even when a float32 input is given. Numba will always observe
the input’s precision, and invoke single-precision linear algebra routines
when all inputs are float32 or complex64.
The implementations of the numpy.linalg routines in Numba only support the
floating point types that are used in the LAPACK functions that provide
the underlying core functionality. As a result only float32, float64,
complex64 and complex128 types are supported. If a user has e.g. an
int32 type, an appropriate type conversion must be performed to a
floating point type prior to its use in these routines. The reason for this
decision is to essentially avoid having to replicate type conversion choices
made in Numpy and to also encourage the user to choose the optimal floating
point type for the operation they are undertaking.
Numpy will most often return a float64 as a result of a computation
with mixed integer and floating-point operands (a typical example is the
power operator **). Numba by contrast will select the highest precision
amongst the floating-point operands, so for example float32 ** int32
will return a float32, regardless of the input values. This makes
performance characteristics easier to predict, but you should explicitly
cast the input to float64 if you need the extra precision.
When calling a ufunc created with vectorize(),
Numpy will determine whether an error occurred by examining the FPU
error word. It may then print out a warning or raise an exception
(such as RuntimeWarning: divide by zero encountered),
depending on the current error handling settings.
Depending on how LLVM optimized the ufunc’s code, however, some spurious
warnings or errors may appear. If you get caught by this issue, we
recommend you call numpy.seterr() to change Numpy’s error handling
settings, or the numpy.errstate context manager to switch them
temporarily:
with np.errstate(all='ignore'):
x = my_ufunc(y)