Hello Devs.

First of all, thanks for taking on this very important piece of work.

I'm using your 3.0 project on 32bit windows. I get some warnings that I'm uncomfortable with, given the operations involved.

Here they are (for the type posit<64,3>):

posit.hpp(159): warning C4244: 'argument': conversion from 'int64_t' to 'size_t', possible loss of data posit.hpp(176): warning C4244: 'argument': conversion from 'unsigned __int64' to 'size_t', possible loss of data

so on my platform size_t is 32 bit. I can understand that there might be a need to cast to size_t sometimes, but can't help thinking that e.g. defining any member variable (e.g. es) as size_t is unfortunate. Should std::uint32_t not be sufficient for es?

The first warning is in this code:

_exp[size_t(es - 1ull - i)]

so the problem here is the suffix ull. Writing ul should fix it. Maybe the size_t cast is not really needed.

The second warning appears in this code:

_frac[fbits - 1ull - (msb - i)]

here changing 1ull is not enough as msb is also 64bit.

I'm working with posit<16,1> at the moment. Modeling quire usage after the code in examples/blas/blas.hpp line 62, I have the following:

for(int row=0; row<n; ++row) {
     quireX sum = sw::unum::quire_mul(beta, ycoefs[row]); //sum is initially 0
     for(LocalOrdinalType i=Arowoffsets[row]; i<Arowoffsets[row+1]; ++i) {
          positX tempPosit; 
          sum += sw::unum::quire_mul(Acoefs[i], xcoefs[Acols[i]]);
          if (row > 263 && row < 269) {
               tempPosit.convert(sum.to_value());
               if (tempPosit < testCompare) {
                        std::cout <<"WRONG! Sum after += is less than -1.0: " << tempPosit <<", after taking sum (" << sumHolderPosit << ") += quire_mul("<<Acoefs[i] << ", " <<xcoefs[Acols[i]] << ")" << std::endl;
                        std::cout <<"We essentially took " << sumHolderPosit << " += " << tempQuireMultholder << " and somehow ended up with " << tempPosit << std::endl;
                        std::cout << "Incorrect sum as a quire: " << sum << std::endl;
                        std::cout << "Delta Quire: " << tempQuireMult << ", (as posit) = " << tempQuireMultholder << std::endl;
                        std::cout << "Row: " << row << ", Acoefs[i]: " << Acoefs[i] << ", Acols[i]: " << Acols[i] << ", xcoefs[" << Acols[i] << "]: " << xcoefs[Acols[i]] << std::endl;
               }
          }

The sum should never go below the value -1.0 - and if I run an alternate version of this code that does not use the quire feature, it doesn't. With the quire enabled, I get the following output - the WRONG! tag near the bottom is where the error occurs - I figured I'd include additional output prior to the error of the sum successfully reducing in size.

Row is 266. Acoefs[5334] = -0.016571, xcoefs[Acols[5334]] = 0.000999451
Sum before += quire_mul  1: 000000000000000000000000000000_000000000000000000000000000000000000000000000000000000000.00000000000001100000110001100000010000000000000000000000
Sum before += quire_mul (as posit)9.25064e-05
product of quire_mul = -1.66893e-05
Row is 266. Acoefs[5335] = -0.00828552, xcoefs[Acols[5335]] = 0.000999451
Sum before += quire_mul  1: 000000000000000000000000000000_000000000000000000000000000000000000000000000000000000000.00000000000001001111011010000011010000000000000000000000
Sum before += quire_mul (as posit)7.53403e-05
product of quire_mul = -8.10623e-06
Row is 266. Acoefs[5336] = -0.0165405, xcoefs[Acols[5336]] = 0.000999451
Sum before += quire_mul  1: 000000000000000000000000000000_000000000000000000000000000000000000000000000000000000000.00000000000001000110101110010100110000000000000000000000
Sum before += quire_mul (as posit)6.77109e-05
product of quire_mul = -1.66893e-05
Row is 266. Acoefs[5337] = 7.62939e-06, xcoefs[Acols[5337]] = 0.000999451
Sum before += quire_mul  1: 000000000000000000000000000000_000000000000000000000000000000000000000000000000000000000.00000000000000110101011000111010110000000000000000000000
Sum before += quire_mul (as posit)5.05447e-05
product of quire_mul = 1.49012e-08
Row is 266. Acoefs[5338] = -0.0165405, xcoefs[Acols[5338]] = 0.000999451
Sum before += quire_mul  1: 000000000000000000000000000000_000000000000000000000000000000000000000000000000000000000.00000000000000110101011001011011100000000000000000000000
Sum before += quire_mul (as posit)5.05447e-05
product of quire_mul = -1.66893e-05
Row is 266. Acoefs[5339] = -0.00828552, xcoefs[Acols[5339]] = 0.000999451
Sum before += quire_mul  1: 000000000000000000000000000000_000000000000000000000000000000000000000000000000000000000.00000000000000100100000100000001100000000000000000000000
Sum before += quire_mul (as posit)3.43323e-05
product of quire_mul = -8.10623e-06
Row is 266. Acoefs[5340] = -0.016571, xcoefs[Acols[5340]] = 0.000999451
Sum before += quire_mul  1: 000000000000000000000000000000_000000000000000000000000000000000000000000000000000000000.00000000000000011011011000010011000000000000000000000000
Sum before += quire_mul (as posit)2.6226e-05
product of quire_mul = -1.66893e-05
-------------------------------------------------------------------------------------------------------------------
WRONG! Sum after += is less than -1.0: -2.68435e+08, after taking sum (2.6226e-05) += quire_mul(-0.016571, 0.000999451)
We essentially took 2.6226e-05 += -1.66893e-05 and somehow ended up with -2.68435e+08 (= -maxpos)
Incorrect sum as a quire: -1: 111111111111111111111111111111_111111111111111111111111111111111111111111111111111111111.11111111111111110101111111001010000000000000000000000000
Delta Quire: -1: 000000000000000000000000000000_000000000000000000000000000000000000000000000000000000000.00000000000000010001010111011101000000000000000000000000, (as posit) = -1.66893e-05
Row: 266, Acoefs[i]: -0.016571, Acols[i]: 398, xcoefs[398]: 0.000999451
Row is 266. Acoefs[5341] = -0.00828552, xcoefs[Acols[5341]] = 0.000999451
-------------------------------------------------------------------------------------------------------------------

If you noticed, the value -2.68435e+08 is negative maxpos for a <16,1> posit. So what I'm wondering is, why does my quire suddenly explode from very small positive values to massive negative values?

My positX and quireX are declared as

namespace posit_shape {
    const uint es = UNUM_ES_SIZE; //1
    const uint nbits = UNUM_NBIT_SIZE; //16
}
namespace quire_shape {
    const uint es = UNUM_ES_SIZE;
    const uint nbits = UNUM_NBIT_SIZE;
    const uint capacity = UNUM_QUIRE_CAPACITY; //10 - as per stillwater example
}
typedef sw::unum::posit<posit_shape::nbits, posit_shape::es> positX;
typedef sw::unum::quire<quire_shape::nbits, quire_shape::es> quireX;

All evidence points to a bug in quire's +=, any feedback welcome.

Hi @Ravenwater !

I am working on the Bring Your Own DataTypes PR (https://github.com/apache/incubator-tvm/pull/5812), and unfortunately we are having trouble building because of warnings from this project.

I can open a new PR if you are okay with it

See: (https://ci.tvm.ai/blue/organizations/jenkins/tvm/detail/PR-5812/16/pipeline) or below:

/workspace/3rdparty/universal/posit/value.hpp: In function 'uint8_t Posit8es2Sqrt(uint8_t)':

/workspace/3rdparty/universal/posit/value.hpp:219:7: error: '_exponent' may be used uninitialized in this function [-Werror=maybe-uninitialized]

       _scale = _exponent - 1;

       ^

/workspace/3rdparty/universal/posit/value.hpp:217:11: note: '_exponent' was declared here

       int _exponent;

           ^

/workspace/3rdparty/universal/posit/value.hpp: In function 'uint16_t Posit16es2Sqrt(uint16_t)':

/workspace/3rdparty/universal/posit/value.hpp:219:7: error: '_exponent' may be used uninitialized in this function [-Werror=maybe-uninitialized]

       _scale = _exponent - 1;

       ^

/workspace/3rdparty/universal/posit/value.hpp:217:11: note: '_exponent' was declared here

       int _exponent;

           ^

/workspace/3rdparty/universal/posit/value.hpp: In function 'uint32_t Posit32es2Sqrt(uint32_t)':

/workspace/3rdparty/universal/posit/value.hpp:219:7: error: '_exponent' may be used uninitialized in this function [-Werror=maybe-uninitialized]

       _scale = _exponent - 1;

       ^

/workspace/3rdparty/universal/posit/value.hpp:217:11: note: '_exponent' was declared here

       int _exponent;

We don't have Apple gear to build on, so I am looking for folks that can keep a Mac build clean. We don't have Intel compiler gear, so I am looking for folks that can keep an Intel build clean. We do have ARM gear, so in this case, looking for collaborators to try to set up a cross compilation flow.

trying build on mac / clang etc. complains about popcntl, ctzl and __N can you hint where those should normally come from? tried searching but failed to find so far

I was trying to use pi/4 as the interval size / step size to show the difference in precision but I was having trouble with that. Take a look and let me know what you think :)

Kind of an annoyance for C projects is the fact that C++ code is full of references to things which in fact end up requiring their own support libraries. Exceptions, for example, require a support library, and the C api is going to be very cool for mixed C/C++ projects but a project where the maintainer wants to keep it in C is going to have a hard sell to adopt the codebase when it requires linking libstdc++, which by then they might as well just switch to C++ for their own code...

It is possible to write C++ code which doesn't use any of this, but you just need to be acutely aware of which features you're taking advantage of...

Here is the linker error from compiling a trivial program which calls posit_integer_assign128 when libstdc++ is not present, it shows the list of C++ symbols which the linker wants and why:

notgay:build user$ gcc-7 -o xxx ../xxx.c -L.//c_api/posit/ -std=c99 -Wall -Wextra -pedantic -lposit_c_api
../xxx.c: In function 'main':
../xxx.c:6:16: warning: unused variable 'four' [-Wunused-variable]
     posit128_t four = posit_integer_assign128(4);
                ^~~~
Undefined symbols for architecture x86_64:
  "std::runtime_error::what() const", referenced from:
      vtable for shift_too_large in libposit_c_api.a(posit_c_api.cpp.o)
      vtable for posit_internal_exception in libposit_c_api.a(posit_c_api.cpp.o)
      vtable for integer_divide_by_zero in libposit_c_api.a(posit_c_api.cpp.o)
      vtable for bitblock_arithmetic_exception in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::__basic_string_common<true>::__throw_length_error() const", referenced from:
      std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> >::str() const in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::locale::use_facet(std::__1::locale::id&) const", referenced from:
      std::__1::basic_ostream<char, std::__1::char_traits<char> >& std::__1::__put_character_sequence<char, std::__1::char_traits<char> >(std::__1::basic_ostream<char, std::__1::char_traits<char> >&, char const*, unsigned long) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::ios_base::getloc() const", referenced from:
      std::__1::basic_ostream<char, std::__1::char_traits<char> >& std::__1::__put_character_sequence<char, std::__1::char_traits<char> >(std::__1::basic_ostream<char, std::__1::char_traits<char> >&, char const*, unsigned long) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::logic_error::logic_error(char const*)", referenced from:
      std::__1::bitset<8ul>::set(unsigned long, bool) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<8ul, 0ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<16ul, 1ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<32ul, 2ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<8ul>& sw::unum::convert_to_bb<8ul, 0ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<8ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<16ul>& sw::unum::convert_to_bb<16ul, 1ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<16ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<32ul>& sw::unum::convert_to_bb<32ul, 2ul, 52ul>(bool, int, sw::unum::bitblock<52ul> const&, sw::unum::bitblock<32ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "std::out_of_range::~out_of_range()", referenced from:
      std::__1::bitset<8ul>::set(unsigned long, bool) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<8ul, 0ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<16ul, 1ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<32ul, 2ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<8ul>& sw::unum::convert_to_bb<8ul, 0ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<8ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<16ul>& sw::unum::convert_to_bb<16ul, 1ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<16ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<32ul>& sw::unum::convert_to_bb<32ul, 2ul, 52ul>(bool, int, sw::unum::bitblock<52ul> const&, sw::unum::bitblock<32ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "std::runtime_error::runtime_error(std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > const&)", referenced from:
      posit_internal_exception::posit_internal_exception(std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > const&) in libposit_c_api.a(posit_c_api.cpp.o)
      bitblock_arithmetic_exception::bitblock_arithmetic_exception(std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > const&) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::runtime_error::~runtime_error()", referenced from:
      shift_too_large::~shift_too_large() in libposit_c_api.a(posit_c_api.cpp.o)
      shift_too_large::~shift_too_large() in libposit_c_api.a(posit_c_api.cpp.o)
      posit_internal_exception::~posit_internal_exception() in libposit_c_api.a(posit_c_api.cpp.o)
      posit_internal_exception::~posit_internal_exception() in libposit_c_api.a(posit_c_api.cpp.o)
      integer_divide_by_zero::~integer_divide_by_zero() in libposit_c_api.a(posit_c_api.cpp.o)
      integer_divide_by_zero::~integer_divide_by_zero() in libposit_c_api.a(posit_c_api.cpp.o)
      bitblock_arithmetic_exception::~bitblock_arithmetic_exception() in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> >::__init(char const*, unsigned long)", referenced from:
      sw::unum::to_string(sw::unum::posit<8ul, 0ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<16ul, 1ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<32ul, 2ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<8ul, 0ul>(sw::unum::posit<8ul, 0ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<16ul, 1ul>(sw::unum::posit<16ul, 1ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<64ul, 3ul>(sw::unum::posit<64ul, 3ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<128ul, 4ul>(sw::unum::posit<128ul, 4ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> >::__init(unsigned long, char)", referenced from:
      std::__1::ostreambuf_iterator<char, std::__1::char_traits<char> > std::__1::__pad_and_output<char, std::__1::char_traits<char> >(std::__1::ostreambuf_iterator<char, std::__1::char_traits<char> >, char const*, char const*, char const*, std::__1::ios_base&, char) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> >::append(char const*, unsigned long)", referenced from:
      posit_internal_exception::posit_internal_exception(std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > const&) in libposit_c_api.a(posit_c_api.cpp.o)
      bitblock_arithmetic_exception::bitblock_arithmetic_exception(std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > const&) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> >::resize(unsigned long, char)", referenced from:
      std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> >::overflow(int) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> >::str(std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > const&) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> >::push_back(char)", referenced from:
      std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> >::overflow(int) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> >::~basic_string()", referenced from:
      sw::unum::to_string(sw::unum::posit<8ul, 0ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<16ul, 1ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<32ul, 2ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      _posit_format8 in libposit_c_api.a(posit_c_api.cpp.o)
      _posit_format16 in libposit_c_api.a(posit_c_api.cpp.o)
      _posit_format32 in libposit_c_api.a(posit_c_api.cpp.o)
      _posit_format64 in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> >::operator=(std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > const&)", referenced from:
      std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> >::str(std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > const&) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_istream<char, std::__1::char_traits<char> >::~basic_istream()", referenced from:
      construction vtable for std::__1::basic_istream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_istream<char, std::__1::char_traits<char> >::~basic_istream()", referenced from:
      construction vtable for std::__1::basic_istream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_ostream<char, std::__1::char_traits<char> >::sentry::sentry(std::__1::basic_ostream<char, std::__1::char_traits<char> >&)", referenced from:
      std::__1::basic_ostream<char, std::__1::char_traits<char> >& std::__1::__put_character_sequence<char, std::__1::char_traits<char> >(std::__1::basic_ostream<char, std::__1::char_traits<char> >&, char const*, unsigned long) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_ostream<char, std::__1::char_traits<char> >::sentry::~sentry()", referenced from:
      std::__1::basic_ostream<char, std::__1::char_traits<char> >& std::__1::__put_character_sequence<char, std::__1::char_traits<char> >(std::__1::basic_ostream<char, std::__1::char_traits<char> >&, char const*, unsigned long) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_ostream<char, std::__1::char_traits<char> >::~basic_ostream()", referenced from:
      construction vtable for std::__1::basic_ostream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_ostream<char, std::__1::char_traits<char> >::~basic_ostream()", referenced from:
      construction vtable for std::__1::basic_ostream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_ostream<char, std::__1::char_traits<char> >::operator<<(float)", referenced from:
      sw::unum::to_string(sw::unum::posit<8ul, 0ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<16ul, 1ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<32ul, 2ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_ostream<char, std::__1::char_traits<char> >::operator<<(unsigned long)", referenced from:
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<8ul, 0ul>(sw::unum::posit<8ul, 0ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<16ul, 1ul>(sw::unum::posit<16ul, 1ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<32ul, 2ul>(sw::unum::posit<32ul, 2ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<64ul, 3ul>(sw::unum::posit<64ul, 3ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<128ul, 4ul>(sw::unum::posit<128ul, 4ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_iostream<char, std::__1::char_traits<char> >::~basic_iostream()", referenced from:
      construction vtable for std::__1::basic_iostream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_iostream<char, std::__1::char_traits<char> >::~basic_iostream()", referenced from:
      construction vtable for std::__1::basic_iostream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_iostream<char, std::__1::char_traits<char> >::~basic_iostream()", referenced from:
      sw::unum::to_string(sw::unum::posit<8ul, 0ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<16ul, 1ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<32ul, 2ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> >::~basic_stringstream() in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<8ul, 0ul>(sw::unum::posit<8ul, 0ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<16ul, 1ul>(sw::unum::posit<16ul, 1ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<32ul, 2ul>(sw::unum::posit<32ul, 2ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "std::__1::basic_streambuf<char, std::__1::char_traits<char> >::sync()", referenced from:
      vtable for std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_streambuf<char, std::__1::char_traits<char> >::imbue(std::__1::locale const&)", referenced from:
      vtable for std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_streambuf<char, std::__1::char_traits<char> >::uflow()", referenced from:
      vtable for std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_streambuf<char, std::__1::char_traits<char> >::setbuf(char*, long)", referenced from:
      vtable for std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_streambuf<char, std::__1::char_traits<char> >::xsgetn(char*, long)", referenced from:
      vtable for std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_streambuf<char, std::__1::char_traits<char> >::xsputn(char const*, long)", referenced from:
      vtable for std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_streambuf<char, std::__1::char_traits<char> >::showmanyc()", referenced from:
      vtable for std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_streambuf<char, std::__1::char_traits<char> >::basic_streambuf()", referenced from:
      sw::unum::to_string(sw::unum::posit<8ul, 0ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<16ul, 1ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<32ul, 2ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<8ul, 0ul>(sw::unum::posit<8ul, 0ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<16ul, 1ul>(sw::unum::posit<16ul, 1ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<32ul, 2ul>(sw::unum::posit<32ul, 2ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<64ul, 3ul>(sw::unum::posit<64ul, 3ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "std::__1::basic_streambuf<char, std::__1::char_traits<char> >::~basic_streambuf()", referenced from:
      sw::unum::to_string(sw::unum::posit<8ul, 0ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<16ul, 1ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<32ul, 2ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> >::~basic_stringstream() in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<8ul, 0ul>(sw::unum::posit<8ul, 0ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<16ul, 1ul>(sw::unum::posit<16ul, 1ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<32ul, 2ul>(sw::unum::posit<32ul, 2ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "std::__1::ctype<char>::id", referenced from:
      std::__1::basic_ostream<char, std::__1::char_traits<char> >& std::__1::__put_character_sequence<char, std::__1::char_traits<char> >(std::__1::basic_ostream<char, std::__1::char_traits<char> >&, char const*, unsigned long) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::locale::~locale()", referenced from:
      std::__1::basic_ostream<char, std::__1::char_traits<char> >& std::__1::__put_character_sequence<char, std::__1::char_traits<char> >(std::__1::basic_ostream<char, std::__1::char_traits<char> >&, char const*, unsigned long) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::ios_base::__set_badbit_and_consider_rethrow()", referenced from:
      std::__1::basic_ostream<char, std::__1::char_traits<char> >& std::__1::__put_character_sequence<char, std::__1::char_traits<char> >(std::__1::basic_ostream<char, std::__1::char_traits<char> >&, char const*, unsigned long) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::ios_base::init(void*)", referenced from:
      sw::unum::to_string(sw::unum::posit<8ul, 0ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<16ul, 1ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<32ul, 2ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<8ul, 0ul>(sw::unum::posit<8ul, 0ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<16ul, 1ul>(sw::unum::posit<16ul, 1ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<32ul, 2ul>(sw::unum::posit<32ul, 2ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<64ul, 3ul>(sw::unum::posit<64ul, 3ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "std::__1::ios_base::clear(unsigned int)", referenced from:
      std::__1::basic_ostream<char, std::__1::char_traits<char> >& std::__1::__put_character_sequence<char, std::__1::char_traits<char> >(std::__1::basic_ostream<char, std::__1::char_traits<char> >&, char const*, unsigned long) in libposit_c_api.a(posit_c_api.cpp.o)
  "std::__1::basic_ios<char, std::__1::char_traits<char> >::~basic_ios()", referenced from:
      sw::unum::to_string(sw::unum::posit<8ul, 0ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<16ul, 1ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<32ul, 2ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> >::~basic_stringstream() in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<8ul, 0ul>(sw::unum::posit<8ul, 0ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<16ul, 1ul>(sw::unum::posit<16ul, 1ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<32ul, 2ul>(sw::unum::posit<32ul, 2ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "std::terminate()", referenced from:
      ___clang_call_terminate in libposit_c_api.a(posit_c_api.cpp.o)
  "typeinfo for std::__1::basic_istream<char, std::__1::char_traits<char> >", referenced from:
      construction vtable for std::__1::basic_istream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "typeinfo for std::__1::basic_ostream<char, std::__1::char_traits<char> >", referenced from:
      construction vtable for std::__1::basic_ostream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "typeinfo for std::__1::basic_iostream<char, std::__1::char_traits<char> >", referenced from:
      construction vtable for std::__1::basic_iostream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
      typeinfo for std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "typeinfo for std::__1::basic_streambuf<char, std::__1::char_traits<char> >", referenced from:
      typeinfo for std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "typeinfo for std::out_of_range", referenced from:
      std::__1::bitset<8ul>::set(unsigned long, bool) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<8ul, 0ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<16ul, 1ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<32ul, 2ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<8ul>& sw::unum::convert_to_bb<8ul, 0ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<8ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<16ul>& sw::unum::convert_to_bb<16ul, 1ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<16ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<32ul>& sw::unum::convert_to_bb<32ul, 2ul, 52ul>(bool, int, sw::unum::bitblock<52ul> const&, sw::unum::bitblock<32ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "typeinfo for std::runtime_error", referenced from:
      typeinfo for posit_internal_exception in libposit_c_api.a(posit_c_api.cpp.o)
      typeinfo for bitblock_arithmetic_exception in libposit_c_api.a(posit_c_api.cpp.o)
  "vtable for __cxxabiv1::__si_class_type_info", referenced from:
      typeinfo for std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
      typeinfo for std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
      typeinfo for posit_internal_exception in libposit_c_api.a(posit_c_api.cpp.o)
      typeinfo for shift_too_large in libposit_c_api.a(posit_c_api.cpp.o)
      typeinfo for bitblock_arithmetic_exception in libposit_c_api.a(posit_c_api.cpp.o)
      typeinfo for integer_divide_by_zero in libposit_c_api.a(posit_c_api.cpp.o)
  NOTE: a missing vtable usually means the first non-inline virtual member function has no definition.
  "vtable for std::out_of_range", referenced from:
      std::__1::bitset<8ul>::set(unsigned long, bool) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<8ul, 0ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<16ul, 1ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<32ul, 2ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<8ul>& sw::unum::convert_to_bb<8ul, 0ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<8ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<16ul>& sw::unum::convert_to_bb<16ul, 1ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<16ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<32ul>& sw::unum::convert_to_bb<32ul, 2ul, 52ul>(bool, int, sw::unum::bitblock<52ul> const&, sw::unum::bitblock<32ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  NOTE: a missing vtable usually means the first non-inline virtual member function has no definition.
  "non-virtual thunk to std::__1::basic_iostream<char, std::__1::char_traits<char> >::~basic_iostream()", referenced from:
      construction vtable for std::__1::basic_iostream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "non-virtual thunk to std::__1::basic_iostream<char, std::__1::char_traits<char> >::~basic_iostream()", referenced from:
      construction vtable for std::__1::basic_iostream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "virtual thunk to std::__1::basic_istream<char, std::__1::char_traits<char> >::~basic_istream()", referenced from:
      construction vtable for std::__1::basic_istream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "virtual thunk to std::__1::basic_istream<char, std::__1::char_traits<char> >::~basic_istream()", referenced from:
      construction vtable for std::__1::basic_istream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "virtual thunk to std::__1::basic_ostream<char, std::__1::char_traits<char> >::~basic_ostream()", referenced from:
      construction vtable for std::__1::basic_ostream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "virtual thunk to std::__1::basic_ostream<char, std::__1::char_traits<char> >::~basic_ostream()", referenced from:
      construction vtable for std::__1::basic_ostream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "virtual thunk to std::__1::basic_iostream<char, std::__1::char_traits<char> >::~basic_iostream()", referenced from:
      construction vtable for std::__1::basic_iostream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "virtual thunk to std::__1::basic_iostream<char, std::__1::char_traits<char> >::~basic_iostream()", referenced from:
      construction vtable for std::__1::basic_iostream<char, std::__1::char_traits<char> >-in-std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> > in libposit_c_api.a(posit_c_api.cpp.o)
  "operator delete(void*)", referenced from:
      std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> >::~basic_stringstream() in libposit_c_api.a(posit_c_api.cpp.o)
      non-virtual thunk to std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> >::~basic_stringstream() in libposit_c_api.a(posit_c_api.cpp.o)
      virtual thunk to std::__1::basic_stringstream<char, std::__1::char_traits<char>, std::__1::allocator<char> >::~basic_stringstream() in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> >::~basic_stringbuf() in libposit_c_api.a(posit_c_api.cpp.o)
      shift_too_large::~shift_too_large() in libposit_c_api.a(posit_c_api.cpp.o)
      posit_internal_exception::~posit_internal_exception() in libposit_c_api.a(posit_c_api.cpp.o)
      integer_divide_by_zero::~integer_divide_by_zero() in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "operator new(unsigned long)", referenced from:
      std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> >::str() const in libposit_c_api.a(posit_c_api.cpp.o)
  "___cxa_allocate_exception", referenced from:
      std::__1::bitset<8ul>::set(unsigned long, bool) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<8ul, 0ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<16ul, 1ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<32ul, 2ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<8ul>& sw::unum::convert_to_bb<8ul, 0ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<8ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<16ul>& sw::unum::convert_to_bb<16ul, 1ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<16ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<32ul>& sw::unum::convert_to_bb<32ul, 2ul, 52ul>(bool, int, sw::unum::bitblock<52ul> const&, sw::unum::bitblock<32ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "___cxa_begin_catch", referenced from:
      ___clang_call_terminate in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> >::overflow(int) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_ostream<char, std::__1::char_traits<char> >& std::__1::__put_character_sequence<char, std::__1::char_traits<char> >(std::__1::basic_ostream<char, std::__1::char_traits<char> >&, char const*, unsigned long) in libposit_c_api.a(posit_c_api.cpp.o)
  "___cxa_end_catch", referenced from:
      std::__1::basic_stringbuf<char, std::__1::char_traits<char>, std::__1::allocator<char> >::overflow(int) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_ostream<char, std::__1::char_traits<char> >& std::__1::__put_character_sequence<char, std::__1::char_traits<char> >(std::__1::basic_ostream<char, std::__1::char_traits<char> >&, char const*, unsigned long) in libposit_c_api.a(posit_c_api.cpp.o)
  "___cxa_free_exception", referenced from:
      std::__1::bitset<8ul>::set(unsigned long, bool) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<8ul, 0ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<16ul, 1ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<32ul, 2ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<8ul>& sw::unum::convert_to_bb<8ul, 0ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<8ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<16ul>& sw::unum::convert_to_bb<16ul, 1ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<16ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<32ul>& sw::unum::convert_to_bb<32ul, 2ul, 52ul>(bool, int, sw::unum::bitblock<52ul> const&, sw::unum::bitblock<32ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "___cxa_throw", referenced from:
      std::__1::bitset<8ul>::set(unsigned long, bool) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<8ul, 0ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<16ul, 1ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::regime<32ul, 2ul>::assign_regime_pattern(int) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<8ul>& sw::unum::convert_to_bb<8ul, 0ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<8ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<16ul>& sw::unum::convert_to_bb<16ul, 1ul, 23ul>(bool, int, sw::unum::bitblock<23ul> const&, sw::unum::bitblock<16ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::bitblock<32ul>& sw::unum::convert_to_bb<32ul, 2ul, 52ul>(bool, int, sw::unum::bitblock<52ul> const&, sw::unum::bitblock<32ul>&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
  "___gxx_personality_v0", referenced from:
      sw::unum::to_string(sw::unum::posit<8ul, 0ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<16ul, 1ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      sw::unum::to_string(sw::unum::posit<32ul, 2ul> const&, long) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<8ul, 0ul>(sw::unum::posit<8ul, 0ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<16ul, 1ul>(sw::unum::posit<16ul, 1ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<32ul, 2ul>(sw::unum::posit<32ul, 2ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      std::__1::basic_string<char, std::__1::char_traits<char>, std::__1::allocator<char> > sw::unum::posit_format<64ul, 3ul>(sw::unum::posit<64ul, 3ul> const&) in libposit_c_api.a(posit_c_api.cpp.o)
      ...
ld: symbol(s) not found for architecture x86_64
collect2: error: ld returned 1 exit status
notgay:build user$

===>   Generating temporary packing list
[0/1] cd /usr/ports/math/universal/work/.build && /usr/local/bin/cmake -DCMAKE_INSTALL_DO_STRIP=1 -P cmake_install.cmake
-- Install configuration: "Release"
-- Up-to-date: /usr/ports/math/universal/work/stage/usr/local/share/Universal/universal-config.cmake
-- Up-to-date: /usr/ports/math/universal/work/stage/usr/local/share/Universal/universal-config-version.cmake
CMake Error at cmake_install.cmake:48 (file):
  file INSTALL cannot find
  "/usr/ports/math/universal/work/universal-1c244646b8f616881f8b5b95ee542c96e49e5580/universal":
  No such file or directory.

Right now, the core bit implementation is based on std::bitset<>. Some of the key operators on posits need to be implemented by bit searches in the bitset<>, which is particularly painful for big posits. The current lib runs in the 1MOPS range for small posit, but in the 100KOPS range for big posits.

Looking for help to create a fastPosit implementation that is based on integer arithmetic that will improve performance by several orders of magnitude. Should be a drop-in replacement, so that an application can swap out the two interfaces seamlessly.

Problem:

In include/universal/number/posit/math/minmax.hpp, expression sw::universal::posit<32,2>(std::pow(double(0.00978569), double(std::numeric_limits<sw::universal::posit<32,2>>::min()))) gives 1 rather than 0.00978569.

Compiling with Clang 8 on Mac:

/Users/gus/universal-llvm/./include/universal/posit/posit.hpp:1732:27: error: constexpr variable 'nbits' must be initialized by a constant expression
        constexpr size_t nbits = number.nbits;
                                 ^~~~~~~~~~~~
/Users/gus/universal-llvm/numerical/thin_triangle.cpp:223:35: note: in instantiation of function template specialization
      'sw::unum::to_binary<sw::unum::posit<32, 2> >' requested here
        ostr << "    a  = " << sw::unum::to_binary(a) << " " << sw::unum::to_base2_scientific(a) << " : " << std::showpos << a << std::noshowpos << std::endl;
                                         ^
/Users/gus/universal-llvm/numerical/thin_triangle.cpp:289:3: note: in instantiation of function template specialization
      'printTriangleConfiguration<sw::unum::posit<32, 2> >' requested here
                printTriangleConfiguration<Posit>(cout, a, b, c);
                ^

There are many instances of this same error. Any ideas?

The overloaded operator == returns incorrect results. As a test case:

sw::universal::blas::matrix<double> A = { { 5.0, 1.0, 0.0, 3.0}, { 0.0, -7.0, -1.0, -5.0}, { 0.0, -4.0, -8.0, -7.0}, { 0.0, 3.0, 3.0, 12.0 } };

std::cout << ((inv(A)*A) == I) << std::endl;

where I is the 4x4 identity matrix, returns false.

Others (e.g., MATLAB) have same issue due to rounding. Perhaps a better approach is to include a tolerance, that is equal within epsilon.

Hello!

I'm having some trouble using Universal for RISC-V. I have a small test project with the following directories:

test_universal/
    build/
    src/
        mymain.cpp
    CMakeLists.txt

The content of CMakeLists.txt is:

cmake_minimum_required(VERSION 3.0 FATAL_ERROR)
project(example)

set(CMAKE_CXX_COMPILER riscv64-unknown-elf-g++)

set(SRC_FOLDER "${CMAKE_CURRENT_LIST_DIR}/src")

include_directories("~/universal-3.52/include")

add_executable(test_posit ${SRC_FOLDER}/mymain.cpp)
set_property(TARGET test_posit PROPERTY CXX_STANDARD 17)

When executing:

mkdir build
cd build
cmake ..
make

I get the following errors:

[ 50%] Building CXX object CMakeFiles/test_posit.dir/src/mymain.cpp.o
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:406,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/gcc_long_double.hpp: In function 'void sw::universal::extract_fp_components(long double, bool&, int&, long double&, long long unsigned int&)':
/home/david/universal-3.52/include/universal/native/nonconstexpr/gcc_long_double.hpp:195:57: error: static assertion failed: This function only works when long double significant is <= 64 bit.
  195 |  static_assert(std::numeric_limits<long double>::digits <= 64, "This function only works when long double significant is <= 64 bit.");
      |                ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~
/home/david/universal-3.52/include/universal/native/nonconstexpr/gcc_long_double.hpp:203:9: error: 'frexpl' was not declared in this scope; did you mean 'frexpf'?
  203 |   _fr = frexpl(fp, &_exponent);
      |         ^~~~~~
      |         frexpf
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:407,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/riscv_long_double.hpp: At global scope:
/home/david/universal-3.52/include/universal/native/nonconstexpr/riscv_long_double.hpp:23:7: error: redefinition of 'union sw::universal::long_double_decoder'
   23 | union long_double_decoder {
      |       ^~~~~~~~~~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:406,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/gcc_long_double.hpp:23:7: note: previous definition of 'union sw::universal::long_double_decoder'
   23 | union long_double_decoder {
      |       ^~~~~~~~~~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:407,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/riscv_long_double.hpp:33:13: error: redefinition of 'void sw::universal::extractFields(long double, bool&, uint64_t&, uint64_t&)'
   33 | inline void extractFields(long double value, bool& s, uint64_t& rawExponentBits, uint64_t& rawFractionBits) {
      |             ^~~~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:406,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/gcc_long_double.hpp:33:13: note: 'void sw::universal::extractFields(long double, bool&, uint64_t&, uint64_t&)' previously defined here
   33 | inline void extractFields(long double value, bool& s, uint64_t& rawExponentBits, uint64_t& rawFractionBits) {
      |             ^~~~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:407,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/riscv_long_double.hpp:42:20: error: redefinition of 'std::string sw::universal::to_base2_scientific(long double)'
   42 | inline std::string to_base2_scientific(long double number) {
      |                    ^~~~~~~~~~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:406,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/gcc_long_double.hpp:42:20: note: 'std::string sw::universal::to_base2_scientific(long double)' previously defined here
   42 | inline std::string to_base2_scientific(long double number) {
      |                    ^~~~~~~~~~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:407,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/riscv_long_double.hpp:57:20: error: redefinition of 'std::string sw::universal::to_hex(long double)'
   57 | inline std::string to_hex(long double number) {
      |                    ^~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:406,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/gcc_long_double.hpp:57:20: note: 'std::string sw::universal::to_hex(long double)' previously defined here
   57 | inline std::string to_hex(long double number) {
      |                    ^~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:407,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/riscv_long_double.hpp:66:20: error: redefinition of 'std::string sw::universal::to_binary(long double, bool)'
   66 | inline std::string to_binary(long double number, bool bNibbleMarker = false) {
      |                    ^~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:406,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/gcc_long_double.hpp:66:20: note: 'std::string sw::universal::to_binary(long double, bool)' previously defined here
   66 | inline std::string to_binary(long double number, bool bNibbleMarker = false) {
      |                    ^~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:407,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/riscv_long_double.hpp:100:20: error: redefinition of 'std::string sw::universal::to_triple(long double)'
  100 | inline std::string to_triple(long double number) {
      |                    ^~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:406,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/gcc_long_double.hpp:100:20: note: 'std::string sw::universal::to_triple(long double)' previously defined here
  100 | inline std::string to_triple(long double number) {
      |                    ^~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:407,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/riscv_long_double.hpp:135:20: error: redefinition of 'std::string sw::universal::color_print(long double)'
  135 | inline std::string color_print(long double number) {
      |                    ^~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:406,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/gcc_long_double.hpp:135:20: note: 'std::string sw::universal::color_print(long double)' previously defined here
  135 | inline std::string color_print(long double number) {
      |                    ^~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:407,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/nonconstexpr/riscv_long_double.hpp: In function 'void sw::universal::extract_fp_components(long double, bool&, int&, long double&, uint64_t&)':
/home/david/universal-3.52/include/universal/native/nonconstexpr/riscv_long_double.hpp:181:31: error: static assertion failed: This function only works when long double is 128 bits.
  181 |  static_assert(sizeof(double) == 16, "This function only works when long double is 128 bits.");
      |                ~~~~~~~~~~~~~~~^~~~~
/home/david/universal-3.52/include/universal/native/nonconstexpr/riscv_long_double.hpp:183:8: error: 'frexpl' was not declared in this scope; did you mean 'frexpf'?
  183 |  _fr = frexpl(fp, &_exponent);
      |        ^~~~~~
      |        frexpf
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:20,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/error_and_gamma.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::erf(sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/error_and_gamma.hpp:16:30: error: 'erf' is not a member of 'std'; did you mean 'ref'?
   16 |  return posit<nbits,es>(std::erf(double(x)));
      |                              ^~~
      |                              ref
/home/david/universal-3.52/include/universal/number/posit/math/error_and_gamma.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::erfc(sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/error_and_gamma.hpp:22:30: error: 'erfc' is not a member of 'std'; did you mean 'errc'?
   22 |  return posit<nbits,es>(std::erfc(double(x)));
      |                              ^~~~
      |                              errc
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:21,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/exponent.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::exp2(sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/exponent.hpp:33:18: error: 'exp2' is not a member of 'std'; did you mean 'exp'?
   33 |  double d = std::exp2(double(x));
      |                  ^~~~
      |                  exp
/home/david/universal-3.52/include/universal/number/posit/math/exponent.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::expm1(sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/exponent.hpp:52:30: error: 'expm1' is not a member of 'std'; did you mean 'exp'?
   52 |  return posit<nbits,es>(std::expm1(double(x)));
      |                              ^~~~~
      |                              exp
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:22,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/fractional.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::remainder(sw::universal::posit<nbits, es>, sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/fractional.hpp:20:30: error: 'remainder' is not a member of 'std'
   20 |  return posit<nbits,es>(std::remainder(double(x), double(y)));
      |                              ^~~~~~~~~
/home/david/universal-3.52/include/universal/number/posit/math/fractional.hpp:20:30: note: suggested alternatives:
In file included from /home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/cmath:45,
                 from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:9,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/riscv/riscv64-unknown-elf/include/math.h:336:15: note:   'remainder'
  336 | extern double remainder (double, double);
      |               ^~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:22,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/fractional.hpp:19:17: note:   'sw::universal::remainder'
   19 | posit<nbits,es> remainder(posit<nbits,es> x, posit<nbits,es> y) {
      |                 ^~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:23,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/hyperbolic.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::atanh(sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/hyperbolic.hpp:37:45: error: no matching function for call to 'atanh(double)'
   37 |  return posit<nbits,es>(std::atanh(double(x)));
      |                                             ^
In file included from /home/david/universal-3.52/include/universal/number/posit/math/complex.hpp:7,
                 from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:19,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/complex:1833:5: note: candidate: 'template<class _Tp> std::complex<_Tp> std::atanh(const std::complex<_Tp>&)'
 1833 |     atanh(const std::complex<_Tp>& __z)
      |     ^~~~~
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/complex:1833:5: note:   template argument deduction/substitution failed:
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:23,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/hyperbolic.hpp:37:45: note:   mismatched types 'const std::complex<_Tp>' and 'double'
   37 |  return posit<nbits,es>(std::atanh(double(x)));
      |                                             ^
/home/david/universal-3.52/include/universal/number/posit/math/hyperbolic.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::acosh(sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/hyperbolic.hpp:43:45: error: no matching function for call to 'acosh(double)'
   43 |  return posit<nbits,es>(std::acosh(double(x)));
      |                                             ^
In file included from /home/david/universal-3.52/include/universal/number/posit/math/complex.hpp:7,
                 from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:19,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/complex:1750:5: note: candidate: 'template<class _Tp> std::complex<_Tp> std::acosh(const std::complex<_Tp>&)'
 1750 |     acosh(const std::complex<_Tp>& __z)
      |     ^~~~~
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/complex:1750:5: note:   template argument deduction/substitution failed:
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:23,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/hyperbolic.hpp:43:45: note:   mismatched types 'const std::complex<_Tp>' and 'double'
   43 |  return posit<nbits,es>(std::acosh(double(x)));
      |                                             ^
/home/david/universal-3.52/include/universal/number/posit/math/hyperbolic.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::asinh(sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/hyperbolic.hpp:49:45: error: no matching function for call to 'asinh(double)'
   49 |  return posit<nbits,es>(std::asinh(double(x)));
      |                                             ^
In file included from /home/david/universal-3.52/include/universal/number/posit/math/complex.hpp:7,
                 from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:19,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/complex:1789:5: note: candidate: 'template<class _Tp> std::complex<_Tp> std::asinh(const std::complex<_Tp>&)'
 1789 |     asinh(const std::complex<_Tp>& __z)
      |     ^~~~~
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/complex:1789:5: note:   template argument deduction/substitution failed:
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:23,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/hyperbolic.hpp:49:45: note:   mismatched types 'const std::complex<_Tp>' and 'double'
   49 |  return posit<nbits,es>(std::asinh(double(x)));
      |                                             ^
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:24,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/hypot.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::hypot(sw::universal::posit<nbits, es>, sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/hypot.hpp:48:55: error: no matching function for call to 'hypot(double, double)'
   48 |  return posit<nbits,es>(std::hypot(double(x),double(y)));
      |                                                       ^
In file included from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:9,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/cmath:1868:3: note: candidate: 'float std::hypot(float, float, float)'
 1868 |   hypot(float __x, float __y, float __z)
      |   ^~~~~
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/cmath:1868:3: note:   candidate expects 3 arguments, 2 provided
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/cmath:1872:3: note: candidate: 'double std::hypot(double, double, double)'
 1872 |   hypot(double __x, double __y, double __z)
      |   ^~~~~
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/cmath:1872:3: note:   candidate expects 3 arguments, 2 provided
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/cmath:1876:3: note: candidate: 'long double std::hypot(long double, long double, long double)'
 1876 |   hypot(long double __x, long double __y, long double __z)
      |   ^~~~~
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/cmath:1876:3: note:   candidate expects 3 arguments, 2 provided
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/cmath:1881:5: note: candidate: 'template<class _Tp, class _Up, class _Vp> typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type std::hypot(_Tp, _Up, _Vp)'
 1881 |     hypot(_Tp __x, _Up __y, _Vp __z)
      |     ^~~~~
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/cmath:1881:5: note:   template argument deduction/substitution failed:
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:24,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/hypot.hpp:48:55: note:   candidate expects 3 arguments, 2 provided
   48 |  return posit<nbits,es>(std::hypot(double(x),double(y)));
      |                                                       ^
/home/david/universal-3.52/include/universal/number/posit/math/hypot.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::hypotf(sw::universal::posit<nbits, es>, sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/hypot.hpp:53:30: error: 'hypotf' is not a member of 'std'; did you mean 'hypot'?
   53 |  return posit<nbits,es>(std::hypotf(float(x),float(y)));
      |                              ^~~~~~
      |                              hypot
/home/david/universal-3.52/include/universal/number/posit/math/hypot.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::hypotl(sw::universal::posit<nbits, es>, sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/hypot.hpp:58:30: error: 'hypotl' is not a member of 'std'; did you mean 'hypot'?
   58 |  return posit<nbits,es>(std::hypotl((long double)(x),(long double)(y)));
      |                              ^~~~~~
      |                              hypot
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:25,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/logarithm.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::log2(sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/logarithm.hpp:22:30: error: 'log2' is not a member of 'std'; did you mean 'log'?
   22 |  return posit<nbits,es>(std::log2(double(x)));
      |                              ^~~~
      |                              log
/home/david/universal-3.52/include/universal/number/posit/math/logarithm.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::log1p(sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/logarithm.hpp:34:30: error: 'log1p' is not a member of 'std'; did you mean 'log10'?
   34 |  return posit<nbits,es>(std::log1p(double(x)));
      |                              ^~~~~
      |                              log10
In file included from /home/david/universal-3.52/include/universal/native/ieee754.hpp:49,
                 from /home/david/universal-3.52/include/universal/number/posit/math/sqrt.hpp:7,
                 from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:29,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/ieee754_riscv.hpp: At global scope:
/home/david/universal-3.52/include/universal/native/ieee754_riscv.hpp:15:7: error: redefinition of 'class sw::universal::ieee754_parameter<float>'
   15 | class ieee754_parameter<float> {
      |       ^~~~~~~~~~~~~~~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/ieee754.hpp:47,
                 from /home/david/universal-3.52/include/universal/number/posit/math/sqrt.hpp:7,
                 from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:29,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/ieee754_gcc.hpp:16:7: note: previous definition of 'class sw::universal::ieee754_parameter<float>'
   16 | class ieee754_parameter<float> {
      |       ^~~~~~~~~~~~~~~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/ieee754.hpp:49,
                 from /home/david/universal-3.52/include/universal/number/posit/math/sqrt.hpp:7,
                 from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:29,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/ieee754_riscv.hpp:32:7: error: redefinition of 'class sw::universal::ieee754_parameter<double>'
   32 | class ieee754_parameter<double> {
      |       ^~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/ieee754.hpp:47,
                 from /home/david/universal-3.52/include/universal/number/posit/math/sqrt.hpp:7,
                 from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:29,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/ieee754_gcc.hpp:38:7: note: previous definition of 'class sw::universal::ieee754_parameter<double>'
   38 | class ieee754_parameter<double> {
      |       ^~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/ieee754.hpp:49,
                 from /home/david/universal-3.52/include/universal/number/posit/math/sqrt.hpp:7,
                 from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:29,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/ieee754_riscv.hpp:52:7: error: redefinition of 'class sw::universal::ieee754_parameter<long double>'
   52 | class ieee754_parameter<long double> {
      |       ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/native/ieee754.hpp:47,
                 from /home/david/universal-3.52/include/universal/number/posit/math/sqrt.hpp:7,
                 from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:29,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/ieee754_gcc.hpp:63:7: note: previous definition of 'class sw::universal::ieee754_parameter<long double>'
   63 | class ieee754_parameter<long double> {
      |       ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/number/posit/math/sqrt.hpp:7,
                 from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:29,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/native/ieee754.hpp: In function 'Real sw::universal::ulp(const Real&)':
/home/david/universal-3.52/include/universal/native/ieee754.hpp:97:14: error: 'nextafter' is not a member of 'std'
   97 |  return std::nextafter(a, a + a/2.0f) - a;
      |              ^~~~~~~~~
/home/david/universal-3.52/include/universal/native/ieee754.hpp:97:14: note: suggested alternatives:
In file included from /home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/cmath:45,
                 from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:9,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/riscv/riscv64-unknown-elf/include/math.h:308:15: note:   'nextafter'
  308 | extern double nextafter (double, double);
      |               ^~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:27,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/next.hpp:27:17: note:   'sw::universal::nextafter'
   27 | posit<nbits,es> nextafter(posit<nbits,es> x, posit<nbits, es> target) {
      |                 ^~~~~~~~~
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:31,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/truncate.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::trunc(sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/truncate.hpp:16:30: error: 'trunc' is not a member of 'std'
   16 |  return posit<nbits,es>(std::trunc(double(x)));
      |                              ^~~~~
/home/david/universal-3.52/include/universal/number/posit/math/truncate.hpp:16:30: note: suggested alternatives:
In file included from /home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/cmath:45,
                 from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:9,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/riscv/riscv64-unknown-elf/include/math.h:321:15: note:   'trunc'
  321 | extern double trunc (double);
      |               ^~~~~
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:31,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/truncate.hpp:15:17: note:   'sw::universal::trunc'
   15 | posit<nbits,es> trunc(posit<nbits,es> x) {
      |                 ^~~~~
/home/david/universal-3.52/include/universal/number/posit/math/truncate.hpp: In function 'sw::universal::posit<nbits, es> sw::universal::round(sw::universal::posit<nbits, es>)':
/home/david/universal-3.52/include/universal/number/posit/math/truncate.hpp:22:30: error: 'round' is not a member of 'std'
   22 |  return posit<nbits,es>(std::round(double(x)));
      |                              ^~~~~
/home/david/universal-3.52/include/universal/number/posit/math/truncate.hpp:22:30: note: suggested alternatives:
In file included from /home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/cmath:45,
                 from /home/david/universal-3.52/include/universal/native/nonconstexpr754.hpp:9,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:12,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/riscv/riscv64-unknown-elf/include/math.h:318:15: note:   'round'
  318 | extern double round (double);
      |               ^~~~~
In file included from /home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/condition_variable:38,
                 from /home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/shared_mutex:37,
                 from /home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/memory_resource:40,
                 from /home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/regex:66,
                 from /home/david/universal-3.52/include/universal/number/posit/posit_parse.hpp:8,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:58,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/riscv/riscv64-unknown-elf/include/c++/10.2.0/chrono:853:7: note:   'std::chrono::round'
  853 |       round(const time_point<_Clock, _Dur>& __tp)
      |       ^~~~~
In file included from /home/david/universal-3.52/include/universal/number/posit/mathlib.hpp:31,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:89,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/number/posit/math/truncate.hpp:21:17: note:   'sw::universal::round'
   21 | posit<nbits,es> round(posit<nbits,es> x) {
      |                 ^~~~~
In file included from /home/david/universal-3.52/include/universal/number/posit/posit_impl.hpp:39,
                 from /home/david/universal-3.52/include/universal/number/posit/posit.hpp:59,
                 from /home/david/test_universal/src/mymain.cpp:3:
/home/david/universal-3.52/include/universal/internal/bitblock/bitblock.hpp:591:20: note:   'sw::universal::internal::round'
  591 | bitblock<tgt_size> round(const bitblock<src_size>& src, size_t n)
      |                    ^~~~~
make[2]: *** [CMakeFiles/test_posit.dir/build.make:63: CMakeFiles/test_posit.dir/src/mymain.cpp.o] Error 1
make[1]: *** [CMakeFiles/Makefile2:76: CMakeFiles/test_posit.dir/all] Error 2
make: *** [Makefile:84: all] Error 2

The cpp file includes <universal/number/posit/posit.hpp>, and the same small code is working when compiling in Ubuntu by default without the

set(CMAKE_CXX_COMPILER riscv64-unknown-elf-g++)

line in CMakeLists.txt. I have also tried using clang++ with the same result. Any insights into how to solve this? Thanks!

For representation with posit in the command line, the decimal output does not have enough bits, which will confuse rounding results with accurate results.

For example:

posit 0.1

The output:

posit< 8,0>  = 00000110 : 0.09375
 posit< 8,1>  = 00010101 : 0.101562
 posit< 8,2>  = 00100101 : 0.101562
 posit< 8,3>  = 00110010 : 0.09375
 posit<16,1>  = 0001010011001101 : 0.10001
 posit<16,2>  = 0010010011001101 : 0.10001
 posit<16,3>  = 0011001001100110 : 0.099976
 posit<24,1>  = 000101001100110011001101 : 0.1
 posit<24,2>  = 001001001100110011001101 : 0.1
 posit<24,3>  = 001100100110011001100110 : 0.0999999
 posit<32,1>  = 00010100110011001100110011001101 : 0.1
 posit<32,2>  = 00100100110011001100110011001101 : 0.1
 posit<32,3>  = 00110010011001100110011001100110 : 0.0999999996
 posit<48,1>  = 000101001100110011001100110011001100110011001101 : 0.1
 posit<48,2>  = 001001001100110011001100110011001100110011001101 : 0.1
 posit<48,3>  = 001100100110011001100110011001100110011001100110 : 0.099999999999994
 posit<64,1>  = 0001010011001100110011001100110011001100110011001100110100000000 : 0.100000000000000006
 posit<64,2>  = 0010010011001100110011001100110011001100110011001100110100000000 : 0.100000000000000006
 posit<64,3>  = 0011001001100110011001100110011001100110011001100110011010000000 : 0.100000000000000006
 posit<64,4>  = 0011100100110011001100110011001100110011001100110011001101000000 : 0.100000000000000006

However, no posit can exactly represent 0.1. For instance, posit<32,2> (0.1) = 0.10000000009313226... not 0.1. The command line output seems to not have enough bits to cover the dynamic range of inaccurate representation.

Is it possible to convert posit to uint64_t which result the same as (uint64_t) &( posit to double) without converting to double first? In fact, I can't use xmm register at conversion.

Hi,

Looking through the codebase, it seems the SVD function is all commented, while the Jacobi solver isn't. Can I perform a SVD on a square posit matrix using universal, yet? How would i go from (for example) a 3x3 single precision to a 3x3 (32,2 for example) posit one? Any numbers on the performance of SVD/Jacobi on posits on CPU/GPU? Would the use of posits help to converge faster and/or more precisely?

Thanks in advance.

Hi,

I was looking for a posit implementation of the log and log1p functions, actually trying to benchmark how a posit32 (2,30?) would fare (precision and perf-wise) on a gpu or cpu (compared to a float binary32) - also trying to use (otherwise unused) int32 resources in a CUDA kernel.

Reading the code on elementary functions, they seem implemented as 'call std::log and convert to posit'? Did I miss anything?

If not present, is there a canonical posit log/log1p implementation I could start from?

Thanks in advance, Lionel