int128.h

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/*-------------------------------------------------------------------------
 *
 * 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/test/modules/test_int128 for a simple test harness for this file.
 *
 * Copyright (c) 2017-2026, 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 native int128 support is enabled, INT128 is just int128. Otherwise, it
 * is a structure with separate 64-bit high and low parts.
 *
 * 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.
 *
 * PG_INT128_HI_INT64 and PG_INT128_LO_UINT64 allow the (signed) high and
 * (unsigned) low 64-bit integer parts to be extracted portably on all
 * platforms.
 */
#if USE_NATIVE_INT128
 
typedef int128 INT128;
 
#define PG_INT128_HI_INT64(i128)    ((int64) ((i128) >> 64))
#define PG_INT128_LO_UINT64(i128)   ((uint64) (i128))
 
#else
 
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;
 
#define PG_INT128_HI_INT64(i128)    ((i128).hi)
#define PG_INT128_LO_UINT64(i128)   ((i128).lo)
 
#endif
 
/*
 * Construct an INT128 from (signed) high and (unsigned) low 64-bit integer
 * parts.
 */
static inline INT128
make_int128(int64 hi, uint64 lo)
{
#if USE_NATIVE_INT128
    return (((int128) hi) << 64) + lo;
#else
    INT128      val;
 
    val.hi = hi;
    val.lo = lo;
    return val;
#endif
}
 
/*
 * Add an unsigned int64 value into an INT128 variable.
 */
static inline void
int128_add_uint64(INT128 *i128, uint64 v)
{
#if USE_NATIVE_INT128
    *i128 += v;
#else
    /*
     * First add the value to the .lo part, then check to see if a carry needs
     * to be propagated into the .hi part.  Since this is unsigned integer
     * arithmetic, which is just modular arithmetic, a carry is needed if the
     * new .lo part is less than the old .lo part (i.e., if modular
     * wrap-around occurred).  Writing this in the form below, rather than
     * using an "if" statement causes modern compilers to produce branchless
     * machine code identical to the native code.
     */
    uint64      oldlo = i128->lo;
 
    i128->lo += v;
    i128->hi += (i128->lo < oldlo);
#endif
}
 
/*
 * Add a signed int64 value into an INT128 variable.
 */
static inline void
int128_add_int64(INT128 *i128, int64 v)
{
#if USE_NATIVE_INT128
    *i128 += v;
#else
    /*
     * This is much like the above except that the carry logic differs for
     * negative v -- we need to subtract 1 from the .hi part if the new .lo
     * value is greater than the old .lo value.  That can be achieved without
     * any branching by adding the sign bit from v (v >> 63 = 0 or -1) to the
     * previous result (for negative v, if the new .lo value is less than the
     * old .lo value, the two terms cancel and we leave the .hi part
     * unchanged, otherwise we subtract 1 from the .hi part).  With modern
     * compilers this often produces machine code identical to the native
     * code.
     */
    uint64      oldlo = i128->lo;
 
    i128->lo += v;
    i128->hi += (i128->lo < oldlo) + (v >> 63);
#endif
}
 
/*
 * Add an INT128 value into an INT128 variable.
 */
static inline void
int128_add_int128(INT128 *i128, INT128 v)
{
#if USE_NATIVE_INT128
    *i128 += v;
#else
    int128_add_uint64(i128, v.lo);
    i128->hi += v.hi;
#endif
}
 
/*
 * Subtract an unsigned int64 value from an INT128 variable.
 */
static inline void
int128_sub_uint64(INT128 *i128, uint64 v)
{
#if USE_NATIVE_INT128
    *i128 -= v;
#else
    /*
     * This is like int128_add_uint64(), except we must propagate a borrow to
     * (subtract 1 from) the .hi part if the new .lo part is greater than the
     * old .lo part.
     */
    uint64      oldlo = i128->lo;
 
    i128->lo -= v;
    i128->hi -= (i128->lo > oldlo);
#endif
}
 
/*
 * Subtract a signed int64 value from an INT128 variable.
 */
static inline void
int128_sub_int64(INT128 *i128, int64 v)
{
#if USE_NATIVE_INT128
    *i128 -= v;
#else
    /* Like int128_add_int64() with the sign of v inverted */
    uint64      oldlo = i128->lo;
 
    i128->lo -= v;
    i128->hi -= (i128->lo > oldlo) + (v >> 63);
#endif
}
 
/*
 * INT64_HI_INT32 extracts the most significant 32 bits of int64 as int32.
 * INT64_LO_UINT32 extracts the least significant 32 bits as uint32.
 */
#define INT64_HI_INT32(i64)     ((int32) ((i64) >> 32))
#define INT64_LO_UINT32(i64)    ((uint32) (i64))
 
/*
 * 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)
{
#if USE_NATIVE_INT128
    /*
     * XXX with a stupid compiler, this could actually be less efficient than
     * the non-native implementation; maybe we should do it by hand always?
     */
    *i128 += (int128) x * (int128) y;
#else
    /* INT64_HI_INT32 must use arithmetic right shift */
    StaticAssertDecl(((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)
    {
        int32       x_hi = INT64_HI_INT32(x);
        uint32      x_lo = INT64_LO_UINT32(x);
        int32       y_hi = INT64_HI_INT32(y);
        uint32      y_lo = INT64_LO_UINT32(y);
        int64       tmp;
 
        /* the first term */
        i128->hi += (int64) x_hi * (int64) y_hi;
 
        /* the second term: sign-extended with the sign of x */
        tmp = (int64) x_hi * (int64) y_lo;
        i128->hi += INT64_HI_INT32(tmp);
        int128_add_uint64(i128, ((uint64) INT64_LO_UINT32(tmp)) << 32);
 
        /* the third term: sign-extended with the sign of y */
        tmp = (int64) x_lo * (int64) y_hi;
        i128->hi += INT64_HI_INT32(tmp);
        int128_add_uint64(i128, ((uint64) INT64_LO_UINT32(tmp)) << 32);
 
        /* the fourth term: always unsigned */
        int128_add_uint64(i128, (uint64) x_lo * (uint64) y_lo);
    }
#endif
}
 
/*
 * Subtract the 128-bit product of two int64 values from an INT128 variable.
 */
static inline void
int128_sub_int64_mul_int64(INT128 *i128, int64 x, int64 y)
{
#if USE_NATIVE_INT128
    *i128 -= (int128) x * (int128) y;
#else
    /* As above, except subtract the 128-bit product */
    if (x != 0 && y != 0)
    {
        int32       x_hi = INT64_HI_INT32(x);
        uint32      x_lo = INT64_LO_UINT32(x);
        int32       y_hi = INT64_HI_INT32(y);
        uint32      y_lo = INT64_LO_UINT32(y);
        int64       tmp;
 
        /* the first term */
        i128->hi -= (int64) x_hi * (int64) y_hi;
 
        /* the second term: sign-extended with the sign of x */
        tmp = (int64) x_hi * (int64) y_lo;
        i128->hi -= INT64_HI_INT32(tmp);
        int128_sub_uint64(i128, ((uint64) INT64_LO_UINT32(tmp)) << 32);
 
        /* the third term: sign-extended with the sign of y */
        tmp = (int64) x_lo * (int64) y_hi;
        i128->hi -= INT64_HI_INT32(tmp);
        int128_sub_uint64(i128, ((uint64) INT64_LO_UINT32(tmp)) << 32);
 
        /* the fourth term: always unsigned */
        int128_sub_uint64(i128, (uint64) x_lo * (uint64) y_lo);
    }
#endif
}
 
/*
 * Divide an INT128 variable by a signed int32 value, returning the quotient
 * and remainder.  The remainder will have the same sign as *i128.
 *
 * Note: This provides no protection against dividing by 0, or dividing
 * INT128_MIN by -1, which overflows.  It is the caller's responsibility to
 * guard against those.
 */
static inline void
int128_div_mod_int32(INT128 *i128, int32 v, int32 *remainder)
{
#if USE_NATIVE_INT128
    int128      old_i128 = *i128;
 
    *i128 /= v;
    *remainder = (int32) (old_i128 - *i128 * v);
#else
    /*
     * To avoid any intermediate values overflowing (as happens if INT64_MIN
     * is divided by -1), we first compute the quotient abs(*i128) / abs(v)
     * using unsigned 64-bit arithmetic, and then fix the signs up at the end.
     *
     * The quotient is computed using the short division algorithm described
     * in Knuth volume 2, section 4.3.1 exercise 16 (cf. div_var_int() in
     * numeric.c).  Since the absolute value of the divisor is known to be at
     * most 2^31, the remainder carried from one digit to the next is at most
     * 2^31 - 1, and so there is no danger of overflow when this is combined
     * with the next digit (a 32-bit unsigned integer).
     */
    uint64      n_hi;
    uint64      n_lo;
    uint32      d;
    uint64      q;
    uint64      r;
    uint64      tmp;
 
    /* numerator: absolute value of *i128 */
    if (i128->hi < 0)
    {
        n_hi = 0 - ((uint64) i128->hi);
        n_lo = 0 - i128->lo;
        if (n_lo != 0)
            n_hi--;
    }
    else
    {
        n_hi = i128->hi;
        n_lo = i128->lo;
    }
 
    /* denominator: absolute value of v */
    d = abs(v);
 
    /* quotient and remainder of high 64 bits */
    q = n_hi / d;
    r = n_hi % d;
    n_hi = q;
 
    /* quotient and remainder of next 32 bits (upper half of n_lo) */
    tmp = (r << 32) + (n_lo >> 32);
    q = tmp / d;
    r = tmp % d;
 
    /* quotient and remainder of last 32 bits (lower half of n_lo) */
    tmp = (r << 32) + (uint32) n_lo;
    n_lo = q << 32;
    q = tmp / d;
    r = tmp % d;
    n_lo += q;
 
    /* final remainder should have the same sign as *i128 */
    *remainder = i128->hi < 0 ? (int32) (0 - r) : (int32) r;
 
    /* store the quotient in *i128, negating it if necessary */
    if ((i128->hi < 0) != (v < 0))
    {
        n_hi = 0 - n_hi;
        n_lo = 0 - n_lo;
        if (n_lo != 0)
            n_hi--;
    }
    i128->hi = (int64) n_hi;
    i128->lo = n_lo;
#endif
}
 
/*
 * Test if an INT128 value is zero.
 */
static inline bool
int128_is_zero(INT128 x)
{
#if USE_NATIVE_INT128
    return x == 0;
#else
    return x.hi == 0 && x.lo == 0;
#endif
}
 
/*
 * Return the sign of an INT128 value (returns -1, 0, or +1).
 */
static inline int
int128_sign(INT128 x)
{
#if USE_NATIVE_INT128
    if (x < 0)
        return -1;
    if (x > 0)
        return 1;
    return 0;
#else
    if (x.hi < 0)
        return -1;
    if (x.hi > 0)
        return 1;
    if (x.lo > 0)
        return 1;
    return 0;
#endif
}
 
/*
 * Compare two INT128 values, return -1, 0, or +1.
 */
static inline int
int128_compare(INT128 x, INT128 y)
{
#if USE_NATIVE_INT128
    if (x < y)
        return -1;
    if (x > y)
        return 1;
    return 0;
#else
    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;
#endif
}
 
/*
 * Widen int64 to INT128.
 */
static inline INT128
int64_to_int128(int64 v)
{
#if USE_NATIVE_INT128
    return (INT128) v;
#else
    INT128      val;
 
    val.lo = (uint64) v;
    val.hi = (v < 0) ? -INT64CONST(1) : INT64CONST(0);
    return val;
#endif
}
 
/*
 * 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)
{
#if USE_NATIVE_INT128
    return (int64) val;
#else
    return (int64) val.lo;
#endif
}
 
#endif                          /* INT128_H */