module gfm.integers.half;

import std.traits,
	   std.string;

/**

  16-bits floating point type (Half).
  Implements conversion from ftp://www.fox-toolkit.org/pub/fasthalffloatconversion.pdf
  by Jeroen van der Zijp.

  Supports builtin operations that float support, but computations are performed in 32-bits
  float and converted back.

  Bugs: rounding is not IEEE compliant.

 */
struct half
{
	public
	{
		ushort value;

		/// Construct a half from a float.
		@nogc this(float n) pure nothrow
		{
			opAssign!float(n);
		}

		/// Construct a half from another half.
		@nogc this(half h) pure nothrow
		{
			opAssign!half(h);
		}

		/// Converts to a pretty string.
		string toString() const
		{
			return format("%s", value);
		}

		@nogc float opCast() pure const nothrow
		{
			return halfToFloat(value);
		}

		/// Converts to a float.
		@nogc float toFloat() pure const nothrow
		{
			return halfToFloat(value);
		}

		/// Assign with float.
		@nogc ref half opAssign(T)(T other) pure nothrow if (is(T: float))
		{
			value = floatToHalf(other);
			return this;
		}

		/// Assign with another half.
		@nogc ref half opAssign(T)(T other) pure nothrow if (is(Unqual!T == half))
		{
			value = other.value;
			return this;
		}

		@nogc half opBinary(string op, T)(T o) pure const nothrow if (is(Unqual!T == half))
		{
			return opBinary!(op, float)(o.toFloat());
		}

		@nogc half opBinary(string op, T)(T o) pure const nothrow if (is(T: float))
		{
			half res = void;
			mixin("res.value = floatToHalf(toFloat() " ~ op ~ "o);");
			return res;
		}

		@nogc ref half opOpAssign(string op, T)(T o) pure nothrow
		{
			half res = opBinary!(op, T)(o);
			this = res;
			return this;
		}

		@nogc half opUnary(string op)() pure const nothrow if (op == "+" || op == "-")
		{
			static if (op == "-")
			{
				half h = this;
				h.value ^= 0x8000; // flip sign bit
				return h;
			}
			else static if (op == "+")
				return this;
		}


		@nogc bool opEquals(T)(T other) pure const nothrow if (!is(Unqual!T == half))
		{
			return this == half(other);
		}

		@nogc bool opEquals(T)(T other) pure const nothrow if (is(Unqual!T == half))
		{
			return value == other.value;
		}
	}
}

static assert (half.sizeof == 2);


// Conversions.

private union uint_float
{
	float f;
	uint ui;
}

/// Converts from float to half.
@nogc ushort floatToHalf(float f) pure nothrow
{
	uint_float uf = void;
	uf.f = f;
	uint idx = (uf.ui >> 23) & 0x1ff;
	return cast(ushort)(basetable[idx] + ((uf.ui & 0x007fffff) >> shifttable[idx]));
}

/// Converts from half to float.
@nogc float halfToFloat(ushort h) pure nothrow
{
	uint_float uf = void;
	uf.ui = mantissatable[offsettable[h>>10] + (h & 0x3ff)] + exponenttable[h>>10];
	return uf.f;
}

unittest
{
	half a = 1.0f;
	assert (a == 1);
	half b = 2.0f;
	assert (a * 2 == b);
	half c = a + b;
	half d = (b / a - c) ;
	assert (-d == 1);
}

private
{
	// build tables through CTFE

	static immutable uint[2048] mantissatable =
	(){
		uint[2048] t;
		t[0] = 0;
		for (uint i = 1; i < 1024; ++i)
		{
			uint m = i << 13;            // zero pad mantissa bits
			uint e = 0;                  // zero exponent
			while(0 == (m & 0x00800000)) // while not normalized
			{
				e -= 0x00800000;         // decrement exponent (1<<23)
				m = m << 1;              // shift mantissa
			}

			m = m & (~0x00800000);       // clear leading 1 bit
			e += 0x38800000;             // adjust bias ((127-14)<<23)
			t[i] = m | e;                // return combined number
		}

		for (uint i = 1024; i < 2047; ++i)
			t[i] = 0x38000000 + ((i-1024) << 13);

		return t;
	}();

	static immutable uint[64] exponenttable =
	(){
		uint[64] t;
		t[0] = 0;
		for (uint i = 1; i <= 30; ++i)
			t[i] = i << 23;
		t[31] = 0x47800000;
		t[32] = 0x80000000;
		for (uint i = 33; i <= 62; ++i)
			t[i] = 0x80000000 + ((i - 32) << 23);

		t[63] = 0xC7800000;
		return t;
	}();

	static immutable ushort[64] offsettable =
	(){
		ushort[64] t;
		t[] = 1024;
		t[0] = t[32] = 0;
		return t;
	}();

	static immutable ushort[512] basetable =
	(){
		ushort[512] t;
		for (uint i = 0; i < 256; ++i)
		{
			int e = cast(int)i - 127;
			if (e < -24)
			{
				t[i | 0x000] = 0x0000;
				t[i | 0x100] = 0x8000;
			}
			else if(e < -14)
			{
				t[i | 0x000] = (0x0400 >> (-e - 14));
				t[i | 0x100] = (0x0400 >> (-e - 14)) | 0x8000;
			}
			else if(e <= 15)
			{
				t[i | 0x000] = cast(ushort)((e + 15) << 10);
				t[i | 0x100] = cast(ushort)((e + 15) << 10) | 0x8000;
			}
			else
			{
				t[i | 0x000] = 0x7C00;
				t[i | 0x100] = 0xFC00;
			}
		}
		return t;
	}();

	static immutable ubyte[512] shifttable =
	(){
		ubyte[512] t;

		for (uint i = 0; i < 256; ++i)
		{
			int e = cast(int)i - 127;
			if (e < -24)
			{
				t[i | 0x000] = 24;
				t[i | 0x100] = 24;
			}
			else if(e < -14)
			{
				t[i | 0x000] = cast(ubyte)(-e - 1);
				t[i | 0x100] = cast(ubyte)(-e - 1);
			}
			else if(e <= 15)
			{
				t[i | 0x000]=13;
				t[i | 0x100]=13;
			}
			else if (e < 128)
			{
				t[i | 0x000]=24;
				t[i | 0x100]=24;
			}
			else
			{
				t[i | 0x000] = 13;
				t[i | 0x100] = 13;
			}
		}

		return t;
	}();
}