/* Set of hash utility functions to help maintaining the invariant that
    if a==b then hash(a)==hash(b)

   All the utility functions (_Py_Hash*()) return "-1" to signify an error.
*/
#include "Python.h"

#ifdef __APPLE__
#  include 
#elif defined(HAVE_LE64TOH) && defined(HAVE_ENDIAN_H)
#  include 
#elif defined(HAVE_LE64TOH) && defined(HAVE_SYS_ENDIAN_H)
#  include 
#endif

#ifdef __cplusplus
extern "C" {
#endif

_Py_HashSecret_t _Py_HashSecret = {{0}};

#if Py_HASH_ALGORITHM == Py_HASH_EXTERNAL
extern PyHash_FuncDef PyHash_Func;
#else
static PyHash_FuncDef PyHash_Func;
#endif

/* Count _Py_HashBytes() calls */
#ifdef Py_HASH_STATS
#define Py_HASH_STATS_MAX 32
static Py_ssize_t hashstats[Py_HASH_STATS_MAX + 1] = {0};
#endif

/* For numeric types, the hash of a number x is based on the reduction
   of x modulo the prime P = 2**_PyHASH_BITS - 1.  It's designed so that
   hash(x) == hash(y) whenever x and y are numerically equal, even if
   x and y have different types.

   A quick summary of the hashing strategy:

   (1) First define the 'reduction of x modulo P' for any rational
   number x; this is a standard extension of the usual notion of
   reduction modulo P for integers.  If x == p/q (written in lowest
   terms), the reduction is interpreted as the reduction of p times
   the inverse of the reduction of q, all modulo P; if q is exactly
   divisible by P then define the reduction to be infinity.  So we've
   got a well-defined map

      reduce : { rational numbers } -> { 0, 1, 2, ..., P-1, infinity }.

   (2) Now for a rational number x, define hash(x) by:

      reduce(x)   if x >= 0
      -reduce(-x) if x < 0

   If the result of the reduction is infinity (this is impossible for
   integers, floats and Decimals) then use the predefined hash value
   _PyHASH_INF for x >= 0, or -_PyHASH_INF for x < 0, instead.
   _PyHASH_INF and -_PyHASH_INF are also used for the
   hashes of float and Decimal infinities.

   NaNs hash with a pointer hash.  Having distinct hash values prevents
   catastrophic pileups from distinct NaN instances which used to always
   have the same hash value but would compare unequal.

   A selling point for the above strategy is that it makes it possible
   to compute hashes of decimal and binary floating-point numbers
   efficiently, even if the exponent of the binary or decimal number
   is large.  The key point is that

      reduce(x * y) == reduce(x) * reduce(y) (modulo _PyHASH_MODULUS)

   provided that {reduce(x), reduce(y)} != {0, infinity}.  The reduction of a
   binary or decimal float is never infinity, since the denominator is a power
   of 2 (for binary) or a divisor of a power of 10 (for decimal).  So we have,
   for nonnegative x,

      reduce(x * 2**e) == reduce(x) * reduce(2**e) % _PyHASH_MODULUS

      reduce(x * 10**e) == reduce(x) * reduce(10**e) % _PyHASH_MODULUS

   and reduce(10**e) can be computed efficiently by the usual modular
   exponentiation algorithm.  For reduce(2**e) it's even better: since
   P is of the form 2**n-1, reduce(2**e) is 2**(e mod n), and multiplication
   by 2**(e mod n) modulo 2**n-1 just amounts to a rotation of bits.

   */

Py_hash_t _Py_HashPointer(const void *);

Py_hash_t
_Py_HashDouble(PyObject *inst, double v)
{
    int e, sign;
    double m;
    Py_uhash_t x, y;

    if (!Py_IS_FINITE(v)) {
        if (Py_IS_INFINITY(v))
            return v > 0 ? _PyHASH_INF : -_PyHASH_INF;
        else
            return _Py_HashPointer(inst);
    }

    m = frexp(v, &e);

    sign = 1;
    if (m < 0) {
        sign = -1;
        m = -m;
    }

    /* process 28 bits at a time;  this should work well both for binary
       and hexadecimal floating point. */
    x = 0;
    while (m) {
        x = ((x > (_PyHASH_BITS - 28);
        m *= 268435456.0;  /* 2**28 */
        e -= 28;
        y = (Py_uhash_t)m;  /* pull out integer part */
        m -= y;
        x += y;
        if (x >= _PyHASH_MODULUS)
            x -= _PyHASH_MODULUS;
    }

    /* adjust for the exponent;  first reduce it modulo _PyHASH_BITS */
    e = e >= 0 ? e % _PyHASH_BITS : _PyHASH_BITS-1-((-1-e) % _PyHASH_BITS);
    x = ((x > (_PyHASH_BITS - e);

    x = x * sign;
    if (x == (Py_uhash_t)-1)
        x = (Py_uhash_t)-2;
    return (Py_hash_t)x;
}

Py_hash_t
_Py_HashPointerRaw(const void *p)
{
    size_t y = (size_t)p;
    /* bottom 3 or 4 bits are likely to be 0; rotate y by 4 to avoid
       excessive hash collisions for dicts and sets */
    y = (y >> 4) | (y