Improve <cuda/std/bit> documentation (#3959)

docs/libcudacxx/standard_api/numerics_library/bit.rst

@@ -1,9 +1,36 @@
 .. _libcudacxx-standard-api-numerics-bit:
 
 ``<cuda/std/bit>``
-======================
+==================
 
-Extensions
-----------
+CUDA Performance Considerations
+-------------------------------
 
--  All features of ``<bit>`` are made available in C++11 onwards
+Given an unsigned integer with ``N`` bits and ``N <= 32``, the ``<bit>`` functions translate into the following SASS instructions. For some functions, the results is decorated with a compile-time assumption to restrict its range and allowing further optimizations.
+
+- ``bit_width()`` translates into a single ``FLO`` SASS instruction. The result is assumed to be in the range ``[0, N]``.
+- ``bit_ceil()`` translates into ``ADD, FLO, SHL, IMINMAX`` SASS instructions. The result is assumed to be greater than or equal to the input.
+- ``bit_floor()`` translates into ``FLO, SHL`` SASS instructions. The result is assumed to be less than or equal to the input.
+- ``byteswap()`` translates into a single ``PRMT`` SASS instruction.
+- ``popcount()`` translates into a single ``POPC`` SASS instruction. The result is assumed to be in the range ``[0, N]``.
+- ``has_single_bit()`` translates into ``POPC + ISETP`` SASS instructions.
+- ``rotl()/rotr()`` translate into a single ``SHF`` (funned shift) SASS instruction.
+- ``countl_zero()`` translates into ``FLO, IMINMAX`` SASS instructions. The result is assumed to be in the range ``[0, N]``.
+- ``countl_one()`` translates into ``LOP3, FLO, IMINMAX`` SASS instructions. The result is assumed to be in the range ``[0, N]``.
+- ``countr_zero()`` translates into ``BREV, FLO, IMINMAX`` SASS instructions. The result is assumed to be in the range ``[0, N]``.
+- ``countr_one()`` translates into ``LOP3, BREV, FLO, IMINMAX`` SASS instructions. The result is assumed to be in the range ``[0, N]``.
+
+Additional Notes
+----------------
+
+- All functions are marked ``[[nodiscard]]`` and ``noexcept``
+- All functions support 128-bit integer types
+- ``bit_ceil()`` checks for overflow in debug mode
+
+.. note::
+
+    When the input values are run-time values that the compiler can resolve at compile-time, e.g. an index of a loop with a fixed number of iterations, using the functions could not be optimal.
+
+.. note::
+
+    GCC <= 8 uses a slow path with more instructions even in CUDA