Fix the Floating Point

Pun intended

I had two bugs that cancelled each other out and made a self consistent float that was wrong except for all the ones I compared it to!

David helped fix it.

diff --git a/src/tests/represent.cpp b/src/tests/represent.cpp
index e5abef5..c576802 100644 (file)
--- a/src/tests/represent.cpp
+++ b/src/tests/represent.cpp
@@ -70,13 +70,8 @@ template <size_t EMAX, size_t PREC, size_t BASE = 2> Real BitsToReal(void * data
 
        // Calculate the actual mantissa from the IEEE style encoding of the mantissa (sigh)
        // This is obviously horribly inefficient but I guess that encoding not designed for ... whatever it is I'm doing here
-       Real M = (exponent != 0);
-       for (size_t i = 1; i < PREC; ++i)
-       {
-               if ((mantissa >> PREC-i) & 1)
-                       M += Real(1) / powl(BASE, i);
-       }
-       
+       // NOW WITH LESS TERRIBLE LOOPING THAT GIVES SLIGHTLY WRONG RESULTS! Order a copy today.
+       Real M = (((exponent != 0) << PREC) + (uint64_t)(mantissa))/powl(BASE,PREC);
        
        //Debug("Mantissa: %x = %lf", mantissa, Float(M));
        //Debug("Exponent: %x = %u => %lf", exponent, exponent, Float(Real(exponent + 1) - Real(1LL << (EMAX-1))));
@@ -174,45 +169,51 @@ template <size_t EMAX, size_t PREC, size_t BASE = 2> void BitsFromReal(Real x, v
        uint64_t mantissa = 0LL;
        int64_t biased_exponent = 0LL;
        
-       // Combine integer and fraction into mantissa
-       if (integer == 0)
+       size_t integer_leading_zeroes = 0;
+       for (integer_leading_zeroes = 0; integer_leading_zeroes < max_bits; ++integer_leading_zeroes)
        {
-               //Debug("0. %lx (%d)", fraction, fraction_leading_zeroes);
-               // Mantissa must have leading '1'; shift to get leading 1, then shift back to mantissa position
-               mantissa = (fraction << fraction_leading_zeroes) >> (max_bits - PREC);
-               biased_exponent -= fraction_leading_zeroes;
-               // If the unbiased exponent would be negative use a denormalised number instead
-               if (biased_exponent < -(1LL << (EMAX-1))+1)
-               {
-                       mantissa = mantissa >> (-(1LL << (EMAX-1))+1 - biased_exponent);
-                       biased_exponent = -(1LL << (EMAX-1))+1;
-               }
+               if ((integer >> (max_bits-1-integer_leading_zeroes)) & 1LL)
+                       break;
+       }
+
+       // 0|011 11|00 0000 0001
+       // 0001
+       // 0000 0000 0100
+       // 10000 0000 0100
+       if (integer != 0)
+       {
+               mantissa = (integer << (integer_leading_zeroes));
+               mantissa |= (fraction >> (max_bits - integer_leading_zeroes));
        }
        else
        {
-
-               size_t integer_leading_zeroes = 0;
-               for (integer_leading_zeroes = 0; integer_leading_zeroes < max_bits; ++integer_leading_zeroes)
-               {
-                       if ((integer >> (max_bits-1-integer_leading_zeroes)) & 1LL)
-                               break;
-               }
-               //Debug("%.16lx . %.16lx (%li, %li)", integer,fraction,  integer_leading_zeroes, fraction_leading_zeroes);
-
-               mantissa = (integer << (integer_leading_zeroes)); // shift integer part
-               mantissa |= (fraction >> (max_bits-integer_leading_zeroes)); // append the fraction after it
-               //Debug("%.16lx (%.16lx << %i)", mantissa,  fraction, (fraction_leading_zeroes - max_bits + integer_leading_zeroes));
-               mantissa = mantissa >> (max_bits - PREC); // shift back to the mantissa position
-               biased_exponent = (max_bits - integer_leading_zeroes); // calculate exponent
+               mantissa = (fraction << (fraction_leading_zeroes));
+       }
+       //Debug("Mantissa with fraction %.16lx (%.16lx >><>?<< %lu)", mantissa, fraction, fraction_leading_zeroes);
+       mantissa = (mantissa >> (max_bits - PREC - 1));
+       //Debug("Mantissa is %.16lx (%.16lx . %.16lx)", mantissa, fraction, integer);
+       biased_exponent = (integer != 0) ? (max_bits - integer_leading_zeroes) : (-fraction_leading_zeroes);
+       if (biased_exponent < -(1LL << (EMAX-1))+1)
+       {
+               //Debug("Denormalising for glory or death! %li , %li", biased_exponent, -(1LL << (EMAX-1)) - biased_exponent + 1);
+               mantissa = mantissa >> (-(1LL << (EMAX-1)) - biased_exponent + 1);
+               biased_exponent = -(1LL << (EMAX-1))+1;
        }
+       //Debug("Biased exponent is %li", biased_exponent);
 
        // If the unbiased exponent would be non-zero, the IEEE has the leading 1 as implied; remove it and decrease exponent to compensate
        if (biased_exponent != -(1LL << (EMAX-1))+1)
        {
-               mantissa &= ~(1LL << max_bits - PREC);
-               mantissa = mantissa << 1;
+               //Debug("Implied 1 in mantissa %.16lx", mantissa);
+               mantissa &= ~(1LL << (PREC));
+               //Debug("Implied 1 in mantissa %.16lx", mantissa);
                biased_exponent -= 1;
        }
+       else
+       {
+               mantissa >>= 1;
+       }
+       //Debug("%.16lx", mantissa);
 
        uint64_t exponent = (uint64_t)(biased_exponent + (1LL << (EMAX-1))-1); // offset the exponent
 
@@ -241,17 +242,21 @@ int main(int argc, char ** argv)
        printf("# Convert custom floats to a Real\n");
        printf("# a\thex(a)\tReal(a)\tdelta(last2)\n");
 
-       typedef pair<uint16_t, Real> Pear;
+       typedef uint16_t Bits;
+       typedef pair<Bits, Real> Pear;
+       const uint8_t E = 5;
+       const uint8_t P = 10;
+       
        list<Pear> space;
-       uint16_t a0 = 0x0000;
-       for (uint16_t a = a0; a < 0xFFFF; ++a)
+       Bits a0 = 0x0000;
+       for (Bits a = a0; a < 0xFFFF; ++a)
        {
-               Real x = BitsToReal<5,10>(&a);
-               uint16_t b = 0; BitsFromReal<5,10>(x, &b);
-               Real y = BitsToReal<5,10>(&b);
+               Real x = BitsToReal<E,P>(&a);
+               Bits b = 0; BitsFromReal<E,P>(x, &b);
+               Real y = BitsToReal<E,P>(&b);
                if (y != x)
                {
-                       Fatal("%x -> %lf -> %x -> %lf", a, Float(x), b, Float(y));
+                       Fatal("%x -> %.10lf -> %x -> %.10lf", a, Float(x), b, Float(y));
                }
                space.push_back(Pear(a, x));
        }
@@ -266,3 +271,7 @@ int main(int argc, char ** argv)
                prev = i->second;        
        }
 }
+
+//0|011 11|00 0000 0001 
+
+//0|000 01|00 0000 0000
\ No newline at end of file