UNORM8 to half float validation

unorm8_to_half.sollya

/* -*- mode: c; -*- */

// multiply by recip: 10 aren't correctly rounded
print("multiply by 1/255");

for i from 0 to 255 do
{
  cr = HP(i/255);
  r  = HP(i*0x1.01p-8);

  if (cr != r) then {
      print(" ",i);
  };
};


// method of: https://marc-b-reynolds.github.io/math/2019/03/12/FpDiv.html
// requires FMA and denormals not flushing to zero
print("fma formulation");

k0 = 0x1.01p-8;
k1 = 0x1.00p-24;

for i from 0 to 255 do
{
  cr = HP(i/255);
  r  = HP(k0*i + HP(k1*i));

  if (cr != r) then {
      print(" ",i);
  };
};

// reworked to avoid denormals and FMAs are optional
// k0*(k1*i+i)
print("reworked: fma optional & no denormals");

k0 = 0x1.00p-8;
k1 = 0x1.01p-8;

for i from 0 to 255 do
{
  cr = HP(i/255);
  lo = HP(i*k1);
  r  = HP(k0 * HP(i+lo));

  if (cr != r) then {
      print(" ",i);
  };
};


// k0*fma(k1,i,i)
print("reworked: using fma");

k0 = 0x1.00p-8;
k1 = 0x1.01p-8;

for i from 0 to 255 do
{
  cr = HP(i/255);
  r  = HP(k0 * HP(k1*i+i));

  if (cr != r) then {
      print(" ",i);
  };
};