text: /*-------------------------------------------------------------------------
   *
   * int128.h
   *	  Roll-our-own 128-bit integer arithmetic.
   *
   * We make use of the native int128 type if there is one, otherwise
   * implement things the hard way based on two int64 halves.
   *
   * See src/tools/testint128.c for a simple test harness for this file.
   *
   * Copyright (c) 2017-2020, PostgreSQL Global Development Group
   *
   * src/include/common/int128.h
   *
   *-------------------------------------------------------------------------
   */
  #ifndef INT128_H
  #define INT128_H
  
  /*
   * For testing purposes, use of native int128 can be switched on/off by
   * predefining USE_NATIVE_INT128.
   */
  #ifndef USE_NATIVE_INT128
  #ifdef HAVE_INT128
  #define USE_NATIVE_INT128 1
  #else
  #define USE_NATIVE_INT128 0
  #endif
  #endif
  
  
  #if USE_NATIVE_INT128
  
  typedef int128 INT128;
  
  /*
   * Add an unsigned int64 value into an INT128 variable.
   */
  static inline void
  int128_add_uint64(INT128 *i128, uint64 v)
  {
  	*i128 += v;
  }
  
  /*
   * Add a signed int64 value into an INT128 variable.
   */
  static inline void
  int128_add_int64(INT128 *i128, int64 v)
  {
  	*i128 += v;
  }
  
  /*
   * Add the 128-bit product of two int64 values into an INT128 variable.
   *
   * XXX with a stupid compiler, this could actually be less efficient than
   * the other implementation; maybe we should do it by hand always?
   */
  static inline void
  int128_add_int64_mul_int64(INT128 *i128, int64 x, int64 y)
  {
  	*i128 += (int128) x * (int128) y;
  }
  
  /*
   * Compare two INT128 values, return -1, 0, or +1.
   */
  static inline int
  int128_compare(INT128 x, INT128 y)
  {
  	if (x < y)
  		return -1;
  	if (x > y)
  		return 1;
  	return 0;
  }
  
  /*
   * Widen int64 to INT128.
   */
  static inline INT128
  int64_to_int128(int64 v)
  {
  	return (INT128) v;
  }
  
  /*
   * Convert INT128 to int64 (losing any high-order bits).
   * This also works fine for casting down to uint64.
   */
  static inline int64
  int128_to_int64(INT128 val)
  {
  	return (int64) val;
  }
  
  #else							/* !USE_NATIVE_INT128 */
  
  /*
   * We lay out the INT128 structure with the same content and byte ordering
   * that a native int128 type would (probably) have.  This makes no difference
   * for ordinary use of INT128, but allows union'ing INT128 with int128 for
   * testing purposes.
   */
  typedef struct
  {
  #ifdef WORDS_BIGENDIAN
  	int64		hi;				/* most significant 64 bits, including sign */
  	uint64		lo;				/* least significant 64 bits, without sign */
  #else
  	uint64		lo;				/* least significant 64 bits, without sign */
  	int64		hi;				/* most significant 64 bits, including sign */
  #endif
  } INT128;
  
  /*
   * Add an unsigned int64 value into an INT128 variable.
   */
  static inline void
  int128_add_uint64(INT128 *i128, uint64 v)
  {
  	/*
  	 * First add the value to the .lo part, then check to see if a carry needs
  	 * to be propagated into the .hi part.  A carry is needed if both inputs
  	 * have high bits set, or if just one input has high bit set while the new
  	 * .lo part doesn't.  Remember that .lo part is unsigned; we cast to
  	 * signed here just as a cheap way to check the high bit.
  	 */
  	uint64		oldlo = i128->lo;
  
  	i128->lo += v;
  	if (((int64) v < 0 && (int64) oldlo < 0) ||
  		(((int64) v < 0 || (int64) oldlo < 0) && (int64) i128->lo >= 0))
  		i128->hi++;
  }
  
  /*
   * Add a signed int64 value into an INT128 variable.
   */
  static inline void
  int128_add_int64(INT128 *i128, int64 v)
  {
  	/*
  	 * This is much like the above except that the carry logic differs for
  	 * negative v.  Ordinarily we'd need to subtract 1 from the .hi part
  	 * (corresponding to adding the sign-extended bits of v to it); but if
  	 * there is a carry out of the .lo part, that cancels and we do nothing.
  	 */
  	uint64		oldlo = i128->lo;
  
  	i128->lo += v;
  	if (v >= 0)
  	{
  		if ((int64) oldlo < 0 && (int64) i128->lo >= 0)
  			i128->hi++;
  	}
  	else
  	{
  		if (!((int64) oldlo < 0 || (int64) i128->lo >= 0))
  			i128->hi--;
  	}
  }
  
  /*
   * INT64_AU32 extracts the most significant 32 bits of int64 as int64, while
   * INT64_AL32 extracts the least significant 32 bits as uint64.
   */
  #define INT64_AU32(i64) ((i64) >> 32)
  #define INT64_AL32(i64) ((i64) & UINT64CONST(0xFFFFFFFF))
  
  /*
   * Add the 128-bit product of two int64 values into an INT128 variable.
   */
  static inline void
  int128_add_int64_mul_int64(INT128 *i128, int64 x, int64 y)
  {
  	/* INT64_AU32 must use arithmetic right shift */
  	StaticAssertStmt(((int64) -1 >> 1) == (int64) -1,
  					 "arithmetic right shift is needed");
  
  	/*----------
  	 * Form the 128-bit product x * y using 64-bit arithmetic.
  	 * Considering each 64-bit input as having 32-bit high and low parts,
  	 * we can compute
  	 *
  	 *	 x * y = ((x.hi << 32) + x.lo) * (((y.hi << 32) + y.lo)
  	 *		   = (x.hi * y.hi) << 64 +
  	 *			 (x.hi * y.lo) << 32 +
  	 *			 (x.lo * y.hi) << 32 +
  	 *			 x.lo * y.lo
  	 *
  	 * Each individual product is of 32-bit terms so it won't overflow when
  	 * computed in 64-bit arithmetic.  Then we just have to shift it to the
  	 * correct position while adding into the 128-bit result.  We must also
  	 * keep in mind that the "lo" parts must be treated as unsigned.
  	 *----------
  	 */
  
  	/* No need to work hard if product must be zero */
  	if (x != 0 && y != 0)
  	{
  		int64		x_u32 = INT64_AU32(x);
  		uint64		x_l32 = INT64_AL32(x);
  		int64		y_u32 = INT64_AU32(y);
  		uint64		y_l32 = INT64_AL32(y);
  		int64		tmp;
  
  		/* the first term */
  		i128->hi += x_u32 * y_u32;
  
  		/* the second term: sign-extend it only if x is negative */
  		tmp = x_u32 * y_l32;
  		if (x < 0)
  			i128->hi += INT64_AU32(tmp);
  		else
  			i128->hi += ((uint64) tmp) >> 32;
  		int128_add_uint64(i128, ((uint64) INT64_AL32(tmp)) << 32);
  
  		/* the third term: sign-extend it only if y is negative */
  		tmp = x_l32 * y_u32;
  		if (y < 0)
  			i128->hi += INT64_AU32(tmp);
  		else
  			i128->hi += ((uint64) tmp) >> 32;
  		int128_add_uint64(i128, ((uint64) INT64_AL32(tmp)) << 32);
  
  		/* the fourth term: always unsigned */
  		int128_add_uint64(i128, x_l32 * y_l32);
  	}
  }
  
  /*
   * Compare two INT128 values, return -1, 0, or +1.
   */
  static inline int
  int128_compare(INT128 x, INT128 y)
  {
  	if (x.hi < y.hi)
  		return -1;
  	if (x.hi > y.hi)
  		return 1;
  	if (x.lo < y.lo)
  		return -1;
  	if (x.lo > y.lo)
  		return 1;
  	return 0;
  }
  
  /*
   * Widen int64 to INT128.
   */
  static inline INT128
  int64_to_int128(int64 v)
  {
  	INT128		val;
  
  	val.lo = (uint64) v;
  	val.hi = (v < 0) ? -INT64CONST(1) : INT64CONST(0);
  	return val;
  }
  
  /*
   * Convert INT128 to int64 (losing any high-order bits).
   * This also works fine for casting down to uint64.
   */
  static inline int64
  int128_to_int64(INT128 val)
  {
  	return (int64) val.lo;
  }
  
  #endif							/* USE_NATIVE_INT128 */
  
  #endif							/* INT128_H */
  