IEC559 totalOrder
Jonathan Wakely
jwakely@redhat.com
Wed Nov 13 22:13:00 GMT 2019
On 13/11/19 22:03 +0000, Jonathan Wakely wrote:
>On 09/11/19 08:40 +0100, Matthias Kretz wrote:
>>Here's an IEC559 totalOrder implementation that works with clang and GCC, for
>>float, double, long double, and __float128 (at least the non-clang branch
>>should work with float16, too):
>>https://godbolt.org/z/QzGWdB
>>
>>Note that I simplified the order reversal of negative values slightly, and
>>producing the bitmask for the sign is now "simpler".
>>
>>As Jakub noted on IRC, 32-bit x86's long double is a problem. Since it has
>>sizeof == 12 there's no *constexpr* way to cast it to an integer.
>>std::bit_cast also wouldn't help. It seems there's no way around a builtin for
>>this function. (Besides that, I ignored the presence of unnormal values in
>>long double - you still get a totalOrder, but I'm not sure IEC559 requests a
>>different behavior.)
>
>This is indistinguishable from magic, thanks!
>
>I've reworked your totalOrder as follows:
>
> template<floating_point _Fp> requires is_iec559<_Fp>
> constexpr strong_ordering
> __fp_strong_order(_Fp __e, _Fp __f)
> {
> struct _Selector : __make_unsigned_selector_base
> {
> using _Ints = _List<signed char, signed short, signed int,
> signed long, signed long long
>#ifdef __GLIBCXX_TYPE_INT_N_0
> , signed __GLIBCXX_TYPE_INT_N_0
>#endif
> >;
> using type = typename __select<sizeof(_Fp), _Ints>::__type;
> };
> using _Si = _Selector::type;
>
> auto __bit_cast = [](_Fp __x) -> _Si {
>#ifdef __clang__
> return __builtin_bit_cast(_Si, __x);
>#else
> using _Fp_v [[__gnu__::__vector_size__(sizeof(_Fp))]] = _Fp;
> using _Si_v [[__gnu__::__vector_size__(sizeof(_Fp))]] = _Si;
> return reinterpret_cast<_Si_v>(_Fp_v{__x})[0];
>#endif
> };
>
> constexpr int __unused_bits = sizeof(_Fp) <= 8
> ? 0
> : (sizeof(_Fp) - 8) * __CHAR_BIT__ - 1
> - __builtin_ctzll(_Si(__bit_cast(_Fp(-0.)) >> 8 * __CHAR_BIT__));
> constexpr _Si __signbit = __bit_cast(_Fp(-0.)) << __unused_bits;
> const _Si __ei = __bit_cast(__e) << __unused_bits;
> const _Si __fi = __bit_cast(__f) << __unused_bits;
> const _Si __e_cmp = __ei < 0 ? (~_Si(__ei ^ __signbit)) : __ei;
> const _Si __f_cmp = __fi < 0 ? (~_Si(__fi ^ __signbit)) : __fi;
> return __e_cmp <=> __f_cmp;
> }
>
>And then for the testsuite we can define totalOrder as:
>
> template<typename T>
> constexpr bool totalOrder(T e, T f)
> {
> return is_lteq(std::strong_order(e, f));
> }
>
>I *think* I've got casts in the right places in __fp_strong_order to
>avoid problems with integer promotions when sizeof(_Fp) < sizeof(int),
>so that it's safe to immediately do [0] on the vector type to convert
>back to a scalar.
>
>Does that look OK? Have I broken it somehow?
>
>I've also defined this, for the non-IEEE 60559 case:
>
> template<typename _Tp>
> concept is_iec559 = floating_point<_Tp>
> && numeric_limits<_Tp>::is_iec559
> // Exclude x86 12-byte long double:
> && ((sizeof(_Tp) & (sizeof(_Tp) - 1)) == 0);
>
> template<floating_point _Fp> requires (!is_iec559<_Fp>)
> constexpr strong_ordering
> __fp_strong_order(_Fp __e, _Fp __f)
> {
> auto __pord = __e <=> __f;
> if (is_lt(__pord))
> return strong_ordering::less;
> else if (is_gt(__pord))
> return strong_ordering::greater;
> else if (is_eq(__pord))
> return strong_ordering::equal;
> else
> return strong_ordering::equivalent;
> }
>
>A patch against current trunk is attached, although it fails some
>__float128 tests, because is_iec559 is false for that type:
>
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc: In instantiation of 'struct Test<__float128>':
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:128: required from here
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:107: error: non-constant condition for static assertion
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:107: in 'constexpr' expansion of 'totalOrder<__float128>(((__float128)(- Test<__float128>::qnan)), ((__float128)(+0.0)))'
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:88: in 'constexpr' expansion of 'std::__cmp_alg::strong_order.std::__cmp_cust::_Strong_order::operator()<__float128&, __float128&>(e, f)'
>.../libsupc++/compare:731: in 'constexpr' expansion of 'std::__cmp_cust::__fp_strong_order<__float128>(__e, __f)'
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:107: error: '(-QNaNf128 < 0.0f128)' is not a constant expression
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:108: error: non-constant condition for static assertion
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:108: in 'constexpr' expansion of 'totalOrder<__float128>(((__float128)(- Test<__float128>::qnan)), ((__float128)(- Test<__float128>::inf)))'
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:88: in 'constexpr' expansion of 'std::__cmp_alg::strong_order.std::__cmp_cust::_Strong_order::operator()<__float128&, __float128&>(e, f)'
>.../libsupc++/compare:731: in 'constexpr' expansion of 'std::__cmp_cust::__fp_strong_order<__float128>(__e, __f)'
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:108: error: '(-QNaNf128 < -Inff128)' is not a constant expression
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:117: error: static assertion failed
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:118: error: static assertion failed
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:119: error: static assertion failed
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:122: error: non-constant condition for static assertion
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:122: in 'constexpr' expansion of 'totalOrder<__float128>(((__float128)((double)Test<__float128>::qnan)), ((__float128)(- Test<__float128>::inf)))'
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:88: in 'constexpr' expansion of 'std::__cmp_alg::strong_order.std::__cmp_cust::_Strong_order::operator()<__float128&, __float128&>(e, f)'
>.../libsupc++/compare:731: in 'constexpr' expansion of 'std::__cmp_cust::__fp_strong_order<__float128>(__e, __f)'
>.../testsuite/18_support/comparisons/algorithms/strong_order.cc:122: error: '(+QNaNf128 < -Inff128)' is not a constant expression
>
>The same cases fail for long double on 32-bit x86, because that uses
>the !is_iec559 overload as well, which needs a built-in as you said.
>
>I think we still need a better implementation of the !is_iec559
>overload for the __float128 case. Alternatively, if the built-in
>handles all FP types (including non-IEEE ones) then we don't need a
>second overload anyway.
Here's another version of that patch that doesn't include unrelated
edits to __fp_weak_order, so is a bit easier to read.
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