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Floating-point pitfalls

Precision and accuracy

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.

Math library implementations

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.

Linear algebra

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.

Mixed-types operations

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.

Warnings and errors

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)