.. _libcudacxx-standard-api-numerics-complex:

``<cuda/std/complex>``
======================

Omissions
---------

  When using libcu++ with NVCC, ``complex`` does not support ``long double`` or ``complex`` literals (``_i``, ``_if``, and ``_il``).
  NVCC warns on any usage of ``long double`` in device code, because ``long double`` will be demoted to ``double`` in device code.
  This warning can be suppressed silenced with ``#pragma``\ s, but only globally, not just when using ``complex``.
  User-defined floating-point literals must be specified in terms of ``long double``, so they lead to warnings
  that are unable to be suppressed.

Extensions
--------------

- Handling of infinities

  Our implementation by default recovers infinite values during multiplication and division. This adds a significant runtime overhead,
  so we allow disabling that canonicalization if it is not desired.

  Definition of ``LIBCUDACXX_ENABLE_SIMPLIFIED_COMPLEX_OPERATIONS`` disables canonicalization for both multiplication *and* division.

  Definition of ``LIBCUDACXX_ENABLE_SIMPLIFIED_COMPLEX_MULTIPLICATION`` or ``LIBCUDACXX_ENABLE_SIMPLIFIED_COMPLEX_DIVISION`` disables
  canonicalization for multiplication or division individually.

- Support for half and bfloat16 (since libcu++ 2.4.0)

  Our implementation includes support for the ``__half`` type from ``<cuda_fp16.h>``, when the CUDA toolkit version is at
  least 12.2, and when ``CCCL_DISABLE_FP16_SUPPORT`` is **not** defined.

  This is detected automatically when compiling through NVCC. If you are compiling a host-only translation unit directly
  with the host compiler, you must define the macro ``LIBCUDACXX_ENABLE_HOST_NVFP16`` prior to including any libcu++ headers,
  and you must ensure that the ``<cuda_fp16.h>`` header that's found by the compiler comes from a CUDA toolkit version
  12.2 or higher.

  Our implementation includes support for the ``__nv_bfloat16`` type from ``<cuda_bf16.h>``, when the conditions for the
  support of ``__half`` are fulfilled, and when ``CCCL_DISABLE_BF16_SUPPORT`` and ``CCCL_DISABLE_FP16_SUPPORT`` are **not** defined.

- C++20 constexpr ``<complex>`` is available in C++14.