Added halfvec type

src/halfvec.c

@@ -0,0 +1,969 @@
+#include "postgres.h"
+
+#include <math.h>
+
+#include "catalog/pg_type.h"
+#include "common/shortest_dec.h"
+#include "fmgr.h"
+#include "halfvec.h"
+#include "lib/stringinfo.h"
+#include "libpq/pqformat.h"
+#include "port.h"				/* for strtof() */
+#include "utils/array.h"
+#include "utils/builtins.h"
+#include "utils/float.h"
+#include "utils/lsyscache.h"
+#include "utils/numeric.h"
+#include "vector.h"
+
+#if PG_VERSION_NUM < 130000
+#define TYPALIGN_DOUBLE 'd'
+#define TYPALIGN_INT 'i'
+#endif
+
+/*
+ * Check if half is NaN
+ */
+static inline bool
+HalfIsNan(half num)
+{
+#ifdef FLT16_SUPPORT
+	return isnan(num);
+#else
+	return (num & 0x7C00) == 0x7C00 && (num & 0x7FFF) != 0x7C00;
+#endif
+}
+
+/*
+ * Check if half is infinite
+ */
+static inline bool
+HalfIsInf(half num)
+{
+#ifdef FLT16_SUPPORT
+	return isinf(num);
+#else
+	return (num & 0x7FFF) == 0x7C00;
+#endif
+}
+
+/*
+ * Check if half is zero
+ */
+static inline bool
+HalfIsZero(half num)
+{
+#ifdef FLT16_SUPPORT
+	return num == 0;
+#else
+	return (num & 0x7FFF) == 0x0000;
+#endif
+}
+
+/*
+ * Get a half from a message buffer
+ */
+static half
+pq_getmsghalf(StringInfo msg)
+{
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swap;
+
+	swap.i = pq_getmsgint(msg, 2);
+	return swap.h;
+}
+
+/*
+ * Append a half to a StringInfo buffer
+ */
+static void
+pq_sendhalf(StringInfo buf, half h)
+{
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swap;
+
+	swap.h = h;
+	pq_sendint16(buf, swap.i);
+}
+
+/*
+ * Convert a half to a float4
+ */
+float
+HalfToFloat4(half num)
+{
+#ifdef FLT16_SUPPORT
+	return (float) num;
+#else
+	/* TODO Improve performance */
+
+	/* Assumes same endianness for floats and integers */
+	union
+	{
+		float		f;
+		uint32		i;
+	}			swapfloat;
+
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swaphalf;
+
+	uint16		bin;
+	uint32		exponent;
+	uint32		mantissa;
+	uint32		result;
+
+	swaphalf.h = num;
+	bin = swaphalf.i;
+	exponent = (bin & 0x7C00) >> 10;
+	mantissa = bin & 0x03FF;
+
+	/* Sign */
+	result = (bin & 0x8000) << 16;
+
+	if (exponent == 31)
+	{
+		if (mantissa == 0)
+		{
+			/* Infinite */
+			result |= 0x7F800000;
+		}
+		else
+		{
+			/* NaN */
+			result |= 0x7FC00000;
+			result |= mantissa << 13;
+		}
+	}
+	else if (exponent == 0)
+	{
+		/* Subnormal */
+		if (mantissa != 0)
+		{
+			exponent = -14;
+
+			for (int i = 0; i < 10; i++)
+			{
+				mantissa <<= 1;
+				exponent -= 1;
+
+				if ((mantissa >> 10) % 2 == 1)
+				{
+					mantissa &= 0x03ff;
+					break;
+				}
+			}
+
+			result |= (exponent + 127) << 23;
+			result |= mantissa << 13;
+		}
+	}
+	else
+	{
+		/* Normal */
+		result |= (exponent - 15 + 127) << 23;
+		result |= mantissa << 13;
+	}
+
+	swapfloat.i = result;
+	return swapfloat.f;
+#endif
+}
+
+/*
+ * Convert a float4 to a half
+ */
+half
+Float4ToHalfUnchecked(float num)
+{
+#ifdef FLT16_SUPPORT
+	return (_Float16) num;
+#else
+	/* TODO Improve performance */
+
+	/* Assumes same endianness for floats and integers */
+	union
+	{
+		float		f;
+		uint32		i;
+	}			swapfloat;
+
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swaphalf;
+
+	uint32		bin;
+	int			exponent;
+	int			mantissa;
+	uint16		result;
+
+	swapfloat.f = num;
+	bin = swapfloat.i;
+	exponent = (bin & 0x7F800000) >> 23;
+	mantissa = bin & 0x007FFFFF;
+
+	/* Sign */
+	result = (bin & 0x80000000) >> 16;
+
+	if (isinf(num))
+	{
+		/* Infinite */
+		result |= 0x7C00;
+	}
+	else if (isnan(num))
+	{
+		/* NaN */
+		result |= 0x7E00;
+		result |= mantissa >> 13;
+	}
+	else if (exponent > 98)
+	{
+		int			m;
+		int			gr;
+		int			s;
+
+		exponent -= 127;
+		s = mantissa & 0x00000FFF;
+
+		/* Subnormal */
+		if (exponent < -14)
+		{
+			int			diff = -exponent - 14;
+
+			mantissa >>= diff;
+			mantissa += 1 << (23 - diff);
+			s |= mantissa & 0x00000FFF;
+		}
+
+		m = mantissa >> 13;
+
+		/* Round */
+		gr = (mantissa >> 12) % 4;
+		if (gr == 3 || (gr == 1 && s != 0))
+			m += 1;
+
+		if (m == 1024)
+		{
+			m = 0;
+			exponent += 1;
+		}
+
+		if (exponent > 15)
+		{
+			/* Infinite */
+			result |= 0x7C00;
+		}
+		else
+		{
+			if (exponent >= -14)
+				result |= (exponent + 15) << 10;
+
+			result |= m;
+		}
+	}
+
+	swaphalf.i = result;
+	return swaphalf.h;
+#endif
+}
+
+/*
+ * Convert a float4 to a half
+ */
+half
+Float4ToHalf(float num)
+{
+	half		result = Float4ToHalfUnchecked(num);
+
+	if (unlikely(HalfIsInf(result)) && !isinf(num))
+		float_overflow_error();
+	if (unlikely(HalfIsZero(result)) && num != 0.0)
+		float_underflow_error();
+
+	return result;
+}
+
+/*
+ * Ensure same dimensions
+ */
+static inline void
+CheckDims(HalfVector * a, HalfVector * b)
+{
+	if (a->dim != b->dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("different halfvec dimensions %d and %d", a->dim, b->dim)));
+}
+
+/*
+ * Ensure expected dimensions
+ */
+static inline void
+CheckExpectedDim(int32 typmod, int dim)
+{
+	if (typmod != -1 && typmod != dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected %d dimensions, not %d", typmod, dim)));
+}
+
+/*
+ * Ensure valid dimensions
+ */
+static inline void
+CheckDim(int dim)
+{
+	if (dim < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("halfvec must have at least 1 dimension")));
+
+	if (dim > HALFVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("halfvec cannot have more than %d dimensions", HALFVEC_MAX_DIM)));
+}
+
+/*
+ * Ensure finite element
+ */
+static inline void
+CheckElement(half value)
+{
+	if (HalfIsNan(value))
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("NaN not allowed in halfvec")));
+
+	if (HalfIsInf(value))
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("infinite value not allowed in halfvec")));
+}
+
+/*
+ * Allocate and initialize a new half vector
+ */
+HalfVector *
+InitHalfVector(int dim)
+{
+	HalfVector *result;
+	int			size;
+
+	size = HALFVEC_SIZE(dim);
+	result = (HalfVector *) palloc0(size);
+	SET_VARSIZE(result, size);
+	result->dim = dim;
+
+	return result;
+}
+
+/*
+ * Check for whitespace, since array_isspace() is static
+ */
+static inline bool
+halfvec_isspace(char ch)
+{
+	if (ch == ' ' ||
+		ch == '\t' ||
+		ch == '\n' ||
+		ch == '\r' ||
+		ch == '\v' ||
+		ch == '\f')
+		return true;
+	return false;
+}
+
+#if PG_VERSION_NUM < 120003
+static pg_noinline void
+float_overflow_error(void)
+{
+	ereport(ERROR,
+			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+			 errmsg("value out of range: overflow")));
+}
+
+static pg_noinline void
+float_underflow_error(void)
+{
+	ereport(ERROR,
+			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+			 errmsg("value out of range: underflow")));
+}
+#endif
+
+/*
+ * Convert textual representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_in);
+Datum
+halfvec_in(PG_FUNCTION_ARGS)
+{
+	char	   *lit = PG_GETARG_CSTRING(0);
+	int32		typmod = PG_GETARG_INT32(2);
+	half		x[HALFVEC_MAX_DIM];
+	int			dim = 0;
+	char	   *pt;
+	char	   *stringEnd;
+	HalfVector *result;
+	char	   *litcopy = pstrdup(lit);
+	char	   *str = litcopy;
+
+	while (halfvec_isspace(*str))
+		str++;
+
+	if (*str != '[')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("malformed halfvec literal: \"%s\"", lit),
+				 errdetail("Vector contents must start with \"[\".")));
+
+	str++;
+	pt = strtok(str, ",");
+	stringEnd = pt;
+
+	while (pt != NULL && *stringEnd != ']')
+	{
+		if (dim == HALFVEC_MAX_DIM)
+			ereport(ERROR,
+					(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+					 errmsg("halfvec cannot have more than %d dimensions", HALFVEC_MAX_DIM)));
+
+		while (halfvec_isspace(*pt))
+			pt++;
+
+		/* Check for empty string like float4in */
+		if (*pt == '\0')
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type halfvec: \"%s\"", lit)));
+
+		/* Use strtof like float4in to avoid a double-rounding problem */
+		x[dim] = Float4ToHalf(strtof(pt, &stringEnd));
+		CheckElement(x[dim]);
+		dim++;
+
+		if (stringEnd == pt)
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type halfvec: \"%s\"", lit)));
+
+		while (halfvec_isspace(*stringEnd))
+			stringEnd++;
+
+		if (*stringEnd != '\0' && *stringEnd != ']')
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type halfvec: \"%s\"", lit)));
+
+		pt = strtok(NULL, ",");
+	}
+
+	if (stringEnd == NULL || *stringEnd != ']')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("malformed halfvec literal: \"%s\"", lit),
+				 errdetail("Unexpected end of input.")));
+
+	stringEnd++;
+
+	/* Only whitespace is allowed after the closing brace */
+	while (halfvec_isspace(*stringEnd))
+		stringEnd++;
+
+	if (*stringEnd != '\0')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("malformed halfvec literal: \"%s\"", lit),
+				 errdetail("Junk after closing right brace.")));
+
+	/* Ensure no consecutive delimiters since strtok skips */
+	for (pt = lit + 1; *pt != '\0'; pt++)
+	{
+		if (pt[-1] == ',' && *pt == ',')
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("malformed halfvec literal: \"%s\"", lit)));
+	}
+
+	if (dim < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("halfvec must have at least 1 dimension")));
+
+	pfree(litcopy);
+
+	CheckExpectedDim(typmod, dim);
+
+	result = InitHalfVector(dim);
+	for (int i = 0; i < dim; i++)
+		result->x[i] = x[i];
+
+	PG_RETURN_POINTER(result);
+}
+
+#define AppendChar(ptr, c) (*(ptr)++ = (c))
+#define AppendFloat(ptr, f) ((ptr) += float_to_shortest_decimal_bufn((f), (ptr)))
+
+/*
+ * Convert internal representation to textual representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_out);
+Datum
+halfvec_out(PG_FUNCTION_ARGS)
+{
+	HalfVector *vector = PG_GETARG_HALFVEC_P(0);
+	int			dim = vector->dim;
+	char	   *buf;
+	char	   *ptr;
+
+	/*
+	 * Need:
+	 *
+	 * dim * (FLOAT_SHORTEST_DECIMAL_LEN - 1) bytes for
+	 * float_to_shortest_decimal_bufn
+	 *
+	 * dim - 1 bytes for separator
+	 *
+	 * 3 bytes for [, ], and \0
+	 */
+	buf = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN * dim + 2);
+	ptr = buf;
+
+	AppendChar(ptr, '[');
+
+	for (int i = 0; i < dim; i++)
+	{
+		if (i > 0)
+			AppendChar(ptr, ',');
+
+		AppendFloat(ptr, HalfToFloat4(vector->x[i]));
+	}
+
+	AppendChar(ptr, ']');
+	*ptr = '\0';
+
+	PG_FREE_IF_COPY(vector, 0);
+	PG_RETURN_CSTRING(buf);
+}
+
+/*
+ * Convert type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_typmod_in);
+Datum
+halfvec_typmod_in(PG_FUNCTION_ARGS)
+{
+	ArrayType  *ta = PG_GETARG_ARRAYTYPE_P(0);
+	int32	   *tl;
+	int			n;
+
+	tl = ArrayGetIntegerTypmods(ta, &n);
+
+	if (n != 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("invalid type modifier")));
+
+	if (*tl < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type halfvec must be at least 1")));
+
+	if (*tl > HALFVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type halfvec cannot exceed %d", HALFVEC_MAX_DIM)));
+
+	PG_RETURN_INT32(*tl);
+}
+
+/*
+ * Convert external binary representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_recv);
+Datum
+halfvec_recv(PG_FUNCTION_ARGS)
+{
+	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
+	int32		typmod = PG_GETARG_INT32(2);
+	HalfVector *result;
+	int16		dim;
+	int16		unused;
+
+	dim = pq_getmsgint(buf, sizeof(int16));
+	unused = pq_getmsgint(buf, sizeof(int16));
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	if (unused != 0)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected unused to be 0, not %d", unused)));
+
+	result = InitHalfVector(dim);
+	for (int i = 0; i < dim; i++)
+	{
+		result->x[i] = pq_getmsghalf(buf);
+		CheckElement(result->x[i]);
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert internal representation to the external binary representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_send);
+Datum
+halfvec_send(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	StringInfoData buf;
+
+	pq_begintypsend(&buf);
+	pq_sendint(&buf, vec->dim, sizeof(int16));
+	pq_sendint(&buf, vec->unused, sizeof(int16));
+	for (int i = 0; i < vec->dim; i++)
+		pq_sendhalf(&buf, vec->x[i]);
+
+	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
+}
+
+/*
+ * Convert half vector to half vector
+ * This is needed to check the type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec);
+Datum
+halfvec(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+
+	CheckExpectedDim(typmod, vec->dim);
+
+	PG_RETURN_POINTER(vec);
+}
+
+/*
+ * Convert array to half vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(array_to_halfvec);
+Datum
+array_to_halfvec(PG_FUNCTION_ARGS)
+{
+	ArrayType  *array = PG_GETARG_ARRAYTYPE_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	HalfVector *result;
+	int16		typlen;
+	bool		typbyval;
+	char		typalign;
+	Datum	   *elemsp;
+	int			nelemsp;
+
+	if (ARR_NDIM(array) > 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("array must be 1-D")));
+
+	if (ARR_HASNULL(array) && array_contains_nulls(array))
+		ereport(ERROR,
+				(errcode(ERRCODE_NULL_VALUE_NOT_ALLOWED),
+				 errmsg("array must not contain nulls")));
+
+	get_typlenbyvalalign(ARR_ELEMTYPE(array), &typlen, &typbyval, &typalign);
+	deconstruct_array(array, ARR_ELEMTYPE(array), typlen, typbyval, typalign, &elemsp, NULL, &nelemsp);
+
+	CheckDim(nelemsp);
+	CheckExpectedDim(typmod, nelemsp);
+
+	result = InitHalfVector(nelemsp);
+
+	if (ARR_ELEMTYPE(array) == INT4OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = Float4ToHalf(DatumGetInt32(elemsp[i]));
+	}
+	else if (ARR_ELEMTYPE(array) == FLOAT8OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = Float4ToHalf(DatumGetFloat8(elemsp[i]));
+	}
+	else if (ARR_ELEMTYPE(array) == FLOAT4OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = Float4ToHalf(DatumGetFloat4(elemsp[i]));
+	}
+	else if (ARR_ELEMTYPE(array) == NUMERICOID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = Float4ToHalf(DatumGetFloat4(DirectFunctionCall1(numeric_float4, elemsp[i])));
+	}
+	else
+	{
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("unsupported array type")));
+	}
+
+	/*
+	 * Free allocation from deconstruct_array. Do not free individual elements
+	 * when pass-by-reference since they point to original array.
+	 */
+	pfree(elemsp);
+
+	/* Check elements */
+	for (int i = 0; i < result->dim; i++)
+		CheckElement(result->x[i]);
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert half vector to float4[]
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_to_float4);
+Datum
+halfvec_to_float4(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	Datum	   *datums;
+	ArrayType  *result;
+
+	datums = (Datum *) palloc(sizeof(Datum) * vec->dim);
+
+	for (int i = 0; i < vec->dim; i++)
+		datums[i] = Float4GetDatum(HalfToFloat4(vec->x[i]));
+
+	/* Use TYPALIGN_INT for float4 */
+	result = construct_array(datums, vec->dim, FLOAT4OID, sizeof(float4), true, TYPALIGN_INT);
+
+	pfree(datums);
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert vector to half vec
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_to_halfvec);
+Datum
+vector_to_halfvec(PG_FUNCTION_ARGS)
+{
+	Vector	   *vec = PG_GETARG_VECTOR_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	HalfVector *result;
+
+	CheckDim(vec->dim);
+	CheckExpectedDim(typmod, vec->dim);
+
+	result = InitHalfVector(vec->dim);
+
+	for (int i = 0; i < vec->dim; i++)
+	{
+		result->x[i] = Float4ToHalfUnchecked(vec->x[i]);
+		/* TODO Better error for overflow */
+		CheckElement(result->x[i]);
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Get the L2 distance between half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_l2_distance);
+Datum
+halfvec_l2_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+	{
+		float		diff = HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]);
+
+		distance += diff * diff;
+	}
+
+	PG_RETURN_FLOAT8(sqrt((double) distance));
+}
+
+/*
+ * Get the L2 squared distance between half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_l2_squared_distance);
+Datum
+halfvec_l2_squared_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+	{
+		float		diff = HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]);
+
+		distance += diff * diff;
+	}
+
+	PG_RETURN_FLOAT8((double) distance);
+}
+
+/*
+ * Get the inner product of two half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_inner_product);
+Datum
+halfvec_inner_product(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		distance += HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]);
+
+	PG_RETURN_FLOAT8((double) distance);
+}
+
+/*
+ * Get the negative inner product of two half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_negative_inner_product);
+Datum
+halfvec_negative_inner_product(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		distance += HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]);
+
+	PG_RETURN_FLOAT8((double) distance * -1);
+}
+
+/*
+ * Get the cosine distance between two half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_cosine_distance);
+Datum
+halfvec_cosine_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+	float		norma = 0.0;
+	float		normb = 0.0;
+	double		similarity;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+	{
+		float		axi = HalfToFloat4(ax[i]);
+		float		bxi = HalfToFloat4(bx[i]);
+
+		distance += axi * bxi;
+		norma += axi * axi;
+		normb += bxi * bxi;
+	}
+
+	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
+	similarity = (double) distance / sqrt((double) norma * (double) normb);
+
+#ifdef _MSC_VER
+	/* /fp:fast may not propagate NaN */
+	if (isnan(similarity))
+		PG_RETURN_FLOAT8(NAN);
+#endif
+
+	/* Keep in range */
+	if (similarity > 1)
+		similarity = 1;
+	else if (similarity < -1)
+		similarity = -1;
+
+	PG_RETURN_FLOAT8(1 - similarity);
+}
+
+/*
+ * Get the L1 distance between two half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_l1_distance);
+Datum
+halfvec_l1_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		distance += fabsf(HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]));
+
+	PG_RETURN_FLOAT8((double) distance);
+}
+
+/*
+ * Get the L2 norm of a half vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_norm);
+Datum
+halfvec_norm(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	half	   *ax = a->x;
+	double		norm = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+	{
+		double		axi = (double) HalfToFloat4(ax[i]);
+
+		norm += axi * axi;
+	}
+
+	PG_RETURN_FLOAT8(sqrt(norm));
+}