utils.c

OTP是开放电信平台的简称

/*                                                                           *\
 *                                                                           *
\* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

/* make a hash index from an erlang term */

/*
** There are three hash functions.
** make_broken_hash: the one used for backward compatibility
** is called from the bif erlang:hash/2. Should never be used
** as it a) hashes only a part of binaries, b) hashes bignums really poorly,
** c) hashes bignums differently on different endian processors and d) hashes 
** small integers with different weights on different bytes.
**
** make_hash: A hash function that will give the same values for the same
** terms regardless of the internal representation. Small integers are 
** hashed using the same algorithm as bignums and bignums are hashed 
** independent of the CPU endianess. 
** Make_hash also hashes pids, ports and references like 32 bit numbers 
** (but with different constants). 
** make_hash() is called from the bif erlang:phash/2
**
** The idea behind the hash algorithm is to produce values suitable for 
** linear dynamic hashing. We cannot choose the range at all while hashing 
** (it's not even supplied to the hashing functions). The good old algorithm
** [H = H*C+X mod M, where H is the hash value, C is a "random" constant(or M),
** M is the range, preferably a prime, and X is each byte value] is therefore 
** modified to:
** H = H*C+X mod 2^32, where C is a large prime. This gives acceptable 
** "spreading" of the hashes, so that later modulo calculations also will give
** acceptable "spreading" in the range. 
** We really need to hash on bytes, otherwise the 
** upper bytes of a word will be less significant than the lower ones. That's 
** not acceptable at all. For internal use one could maybe optimize by using
** another hash function, that is less strict but faster. That is, however, not
** implemented.
**
** Short semi-formal description of make_hash:
**
** In make_hash, the number N is treated like this:
**  Abs(N) is hashed bytewise with the least significant byte, B(0), first.
**  The number of bytes (J) to calculate hash on in N is 
**  (the number of _32_ bit words needed to store the unsigned 
**   value of abs(N)) * 4.
**  X = FUNNY_NUMBER2
**  If N < 0, Y = FUNNY_NUMBER4 else Y = FUNNY_NUMBER3.
**  The hash value is Y*h(J) mod 2^32 where h(J) is calculated like
**  h(0) = <initial hash> 
**  h(i) = h(i-i)*X + B(i-1)
** The above should hold regardless of internal representation.
** Pids are hashed like small numbers but with differrent constants, as are
** ports.
** References are hashed like ports but only on the least significant byte.
** Binaries are hashed on all bytes (not on the 15 first as in 
** make_broken_hash()).
** Bytes in lists (possibly text strings) use a simpler multiplication inlined
** in the handling of lists, that is an optimization.
** Everything else is like in the old hash (make_broken_hash()).
**
** make_hash2() is faster than make_hash, in particular for bignums
** and binaries, and produces better hash values. 
*/

/* some prime numbers just above 2 ^ 28 */

#define FUNNY_NUMBER1  268440163
#define FUNNY_NUMBER2  268439161
#define FUNNY_NUMBER3  268435459
#define FUNNY_NUMBER4  268436141
#define FUNNY_NUMBER5  268438633
#define FUNNY_NUMBER6  268437017
#define FUNNY_NUMBER7  268438039
#define FUNNY_NUMBER8  268437511
#define FUNNY_NUMBER9  268439627
#define FUNNY_NUMBER10 268440479
#define FUNNY_NUMBER11 268440577

static Uint32
hash_binary_bytes(Eterm bin, Uint sz, Uint32 hash)
{
    byte* ptr;
    Uint bitoffs;
    Uint bitsize;

    if (sz > 0) {
	ERTS_GET_BINARY_BYTES(bin, ptr, bitoffs, bitsize);
	if (bitoffs == 0) {
	    while (sz--) {
		hash = hash*FUNNY_NUMBER1 + *ptr++;
	    }
	} else {
	    Uint previous = *ptr++;
	    Uint b;
	    Uint lshift = bitoffs;
	    Uint rshift = 8 - lshift;
	    
	    while (sz--) {
		b = (previous << lshift) & 0xFF;
		previous = *ptr++;
		b |= previous >> rshift;
		hash = hash*FUNNY_NUMBER1 + b;
	    }
	}
    }
    return hash;
}

Uint32
make_hash(Eterm term, Uint32 hash)
{
    /* 
    ** Convenience macro for calculating a bytewise hash on an unsigned 32 bit 
    ** integer.
    ** If the endianess is known, we could be smarter here, 
    ** but that gives no significant speedup (on a sparc at least) 
    */
#define UINT32_HASH_STEP(Expr, Prime1)					\
	do {								\
	    Uint32 x = (Uint32) (Expr);	                                \
	    hash =							\
		(((((hash)*(Prime1) + (x & 0xFF)) * (Prime1) + 	        \
		((x >> 8) & 0xFF)) * (Prime1) + 			\
		((x >> 16) & 0xFF)) * (Prime1) + 			\
		 (x >> 24));						\
	} while(0)

#define UINT32_HASH_RET(Expr, Prime1, Prime2)   			\
	do {								\
	    UINT32_HASH_STEP(Expr, Prime1);				\
	    return hash * (Prime2);					\
	} while(0)

#define SINT32_HASH_RET(Expr, Prime1, Prime2, Prime3)	\
	do {						\
	    Sint32 y = (Sint32) Expr;			\
	    if (y < 0) {				\
		UINT32_HASH_RET(-y, Prime1, Prime3);	\
	    } 						\
	    UINT32_HASH_RET(y, Prime1, Prime2);		\
	} while(0)
		
	    
    /* 
     * Significant additions needed for real 64 bit port with larger fixnums.
     */	    

    /* 
     * Note, for the simple 64bit port, not utilizing the 
     * larger word size this function will work without modification. 
     */

    switch (tag_val_def(term)) {
    case NIL_DEF:
	return hash*FUNNY_NUMBER3 + 1;

    case ATOM_DEF:
	return hash*FUNNY_NUMBER1 + 
	    (atom_tab(atom_val(term))->slot.bucket.hvalue);

    case SMALL_DEF:
	{
	    Sint y1 = signed_val(term);
	    Uint y2 = y1 < 0 ? -(Uint)y1 : y1;

	    UINT32_HASH_STEP(y2, FUNNY_NUMBER2);
#ifdef ARCH_64
	    if (y2 >> 32)
		UINT32_HASH_STEP(y2 >> 32, FUNNY_NUMBER2);
#endif
	    return hash * (y1 < 0 ? FUNNY_NUMBER4 : FUNNY_NUMBER3);
	}

    case BINARY_DEF:
	{
	    Uint sz = binary_size(term);

	    hash = hash_binary_bytes(term, sz, hash);
	    return hash*FUNNY_NUMBER4 + sz;
	}

    case EXPORT_DEF:
	{
	    Export* ep = (Export *) (export_val(term))[1];

	    hash = hash * FUNNY_NUMBER11 + ep->code[2];
	    hash = hash*FUNNY_NUMBER1 + 
		(atom_tab(atom_val(ep->code[0]))->slot.bucket.hvalue);
	    hash = hash*FUNNY_NUMBER1 + 
		(atom_tab(atom_val(ep->code[1]))->slot.bucket.hvalue);
	    return hash;
	}

    case FUN_DEF:
	{
	    ErlFunThing* funp = (ErlFunThing *) fun_val(term);
	    Uint num_free = funp->num_free;
	    Uint i;

	    hash = hash * FUNNY_NUMBER10 + num_free;
	    hash = hash*FUNNY_NUMBER1 + 
		(atom_tab(atom_val(funp->fe->module))->slot.bucket.hvalue);
	    hash = hash*FUNNY_NUMBER2 + funp->fe->old_index;
	    hash = hash*FUNNY_NUMBER2 + funp->fe->old_uniq;
	    for (i = 0; i < num_free; i++) {
		hash = make_hash(funp->env[i], hash);
	    }
	    return hash;
	}

    case PID_DEF:
	UINT32_HASH_RET(internal_pid_number(term),FUNNY_NUMBER5,FUNNY_NUMBER6);
    case EXTERNAL_PID_DEF:
	UINT32_HASH_RET(external_pid_number(term),FUNNY_NUMBER5,FUNNY_NUMBER6);

    case PORT_DEF:
	UINT32_HASH_RET(internal_port_number(term),FUNNY_NUMBER9,FUNNY_NUMBER10);
    case EXTERNAL_PORT_DEF:
	UINT32_HASH_RET(external_port_number(term),FUNNY_NUMBER9,FUNNY_NUMBER10);

    case REF_DEF:
	UINT32_HASH_RET(internal_ref_numbers(term)[0],FUNNY_NUMBER9,FUNNY_NUMBER10);
    case EXTERNAL_REF_DEF:
	UINT32_HASH_RET(external_ref_numbers(term)[0],FUNNY_NUMBER9,FUNNY_NUMBER10);

    case FLOAT_DEF: 
	{
	    FloatDef ff;
	    GET_DOUBLE(term, ff);
	    return hash*FUNNY_NUMBER6 + (ff.fw[0] ^ ff.fw[1]);
	}
	break;

    case LIST_DEF:
	{
	    Eterm* list = list_val(term);
	    while(1) {
		if (is_byte(*list)) {
		    /* Optimization for strings. 
		    ** Note that this hash is different from a 'small' hash,
		    ** as multiplications on a Sparc is so slow.
		    */

		    hash = hash*FUNNY_NUMBER2 + unsigned_val(*list);
		} else {
		    hash = make_hash(*list, hash);
		}
		if (is_not_list(CDR(list)))
		    return make_hash(CDR(list),hash)*FUNNY_NUMBER8;
		list = list_val(CDR(list));
	    }
	}
	break;

    case BIG_DEF:
	/* Note that this is the exact same thing as the hashing of smalls.*/
	{
	  /* FIXED: __alpha__ this was remade to be backwards +
	   * compaible with 32 bit implmentation 
	   */
	    Eterm* ptr  = big_val(term);
	    Uint n = BIG_SIZE(ptr);
	    int is_neg = BIG_SIGN(ptr);
	    Uint i;

	    if (D_EXP < 32 && (n & 1)) /* emulate 32 bit behaviour (add a MSB 0 :-( )*/
	      n++;

	    for (i = 0; i < n; i++)  {
	      digit_t d = BIG_DIGIT(ptr, i);
	      int j;
	      for(j = 0; j < sizeof(digit_t); ++j) {
		  hash = (hash*FUNNY_NUMBER2) + (d & 0xff);
		  d >>= 8;
	      }
	    }
	    if (is_neg) {
		return hash*FUNNY_NUMBER4;
	    }
	    else {
	      return hash*FUNNY_NUMBER3;
	    }
	}
	break;

    case TUPLE_DEF: 
	{
	    Eterm* ptr = tuple_val(term);
	    Uint arity = arityval(*ptr);
	    int i = arity;

	    ptr++;
	    while(i--)
		hash = make_hash(*ptr++, hash);
	    return hash*FUNNY_NUMBER9 + arity;
	}
	break;

    default:
	erl_exit(1, "Invalid tag in make_hash(0x%X)\n", term);
	return 0;
    }
#undef UINT32_HASH_STEP
#undef UINT32_HASH_RET
#undef SINT32_HASH_RET
}

/* Hash function suggested by Bob Jenkins. */

#define MIX(a,b,c)                 \
do {                               \
  a -= b; a -= c; a ^= (c>>13);    \
  b -= c; b -= a; b ^= (a<<8);     \
  c -= a; c -= b; c ^= (b>>13);    \
  a -= b; a -= c; a ^= (c>>12);    \
  b -= c; b -= a; b ^= (a<<16);    \
  c -= a; c -= b; c ^= (b>>5);     \
  a -= b; a -= c; a ^= (c>>3);     \
  b -= c; b -= a; b ^= (a<<10);    \
  c -= a; c -= b; c ^= (b>>15);    \
} while(0)

#define HCONST 0x9e3779b9UL /* the golden ratio; an arbitrary value */

Uint32
block_hash(byte *k, unsigned length, Uint32 initval)
{
   Uint32 a,b,c;
   unsigned len;

   /* Set up the internal state */
   len = length;
   a = b = HCONST;
   c = initval;           /* the previous hash value */

   while (len >= 12)
   {
      a += (k[0] +((Uint32)k[1]<<8) +((Uint32)k[2]<<16) +((Uint32)k[3]<<24));
      b += (k[4] +((Uint32)k[5]<<8) +((Uint32)k[6]<<16) +((Uint32)k[7]<<24));
      c += (k[8] +((Uint32)k[9]<<8) +((Uint32)k[10]<<16)+((Uint32)k[11]<<24));
      MIX(a,b,c);
      k += 12; len -= 12;
   }

   c += length;
   switch(len)              /* all the case statements fall through */
   {
   case 11: c+=((Uint32)k[10]<<24);
   case 10: c+=((Uint32)k[9]<<16);
   case 9 : c+=((Uint32)k[8]<<8);
      /* the first byte of c is reserved for the length */
   case 8 : b+=((Uint32)k[7]<<24);
   case 7 : b+=((Uint32)k[6]<<16);
   case 6 : b+=((Uint32)k[5]<<8);
   case 5 : b+=k[4];
   case 4 : a+=((Uint32)k[3]<<24);
   case 3 : a+=((Uint32)k[2]<<16);
   case 2 : a+=((Uint32)k[1]<<8);
   case 1 : a+=k[0];
     /* case 0: nothing left to add */
   }
   MIX(a,b,c);
   return c;
}

Uint32
make_hash2(Eterm term)
{
    Uint32 hash;
    Eterm tmp_big[2];

/* (HCONST * {2, ..., 14}) mod 2^32 */
#define HCONST_2 0x3c6ef372UL
#define HCONST_3 0xdaa66d2bUL
#define HCONST_4 0x78dde6e4UL
#define HCONST_5 0x1715609dUL
#define HCONST_6 0xb54cda56UL
#define HCONST_7 0x5384540fUL
#define HCONST_8 0xf1bbcdc8UL
#define HCONST_9 0x8ff34781UL
#define HCONST_10 0x2e2ac13aUL
#define HCONST_11 0xcc623af3UL
#define HCONST_12 0x6a99b4acUL
#define HCONST_13 0x08d12e65UL
#define HCONST_14 0xa708a81eUL

#define UINT32_HASH_2(Expr1, Expr2, AConst)       \
         do {                                     \
	    Uint32 a,b;                           \
	    a = AConst + (Uint32) (Expr1);        \
	    b = AConst + (Uint32) (Expr2);        \
	    MIX(a,b,hash);                        \
	 } while(0)

#define UINT32_HASH(Expr, AConst) UINT32_HASH_2(Expr, 0, AConst)

#define SINT32_HASH(Expr, AConst)                 \
	do {					  \
            Sint32 y = (Sint32) (Expr);           \
	    if (y < 0) {			  \
		UINT32_HASH(-y, AConst);          \
                /* Negative numbers are unnecessarily mixed twice. */ \
	    } 					  \
	    UINT32_HASH(y, AConst);          	  \
	} while(0)

#define IS_SSMALL28(x) (((Uint) (((x) >> (28-1)) + 1)) < 2)

    /* Optimization. Simple cases before declaration of estack. */
    if (primary_tag(term) == TAG_PRIMARY_IMMED1) {
	switch (term & _TAG_IMMED1_MASK) {
	case _TAG_IMMED1_IMMED2:
	    switch (term & _TAG_IMMED2_MASK) {
	    case _TAG_IMMED2_ATOM:
		return atom_tab(atom_val(term))->slot.bucket.hvalue;
	    }
	    break;
	case _TAG_IMMED1_SMALL:
	  {
	      Sint x = signed_val(term);

	      if (SMALL_BITS > 28 && !IS_SSMALL28(x)) {
		  term = small_to_big(x, tmp_big);
		  break;
	      }
	      hash = 0;
	      SINT32_HASH(x, HCONST);
	      return hash;
	  }
	}
    };
    {
    Eterm tmp;
    DECLARE_ESTACK(s);

    hash = 0;
    for (;;) {
	switch (primary_tag(term)) {
	case TAG_PRIMARY_LIST:
	{
	    int c = 0;
	    Uint32 s = 0;
	    Eterm* ptr = list_val(term);
	    while (is_byte(*ptr)) {
		/* Optimization for strings. */
		s = (s << 8) + unsigned_val(*ptr);
		if (c == 3) {
		    UINT32_HASH(s, HCONST_4);
		    c = s = 0;
		} else {
		    c++;
		}
		term = CDR(ptr);
		if (is_not_list(term))
		    break;
		ptr = list_val(term);
	    }
	    if (c > 0)
		UINT32_HASH(s, HCONST_4);
	    if (is_list(term)) {
		term = *ptr;
		tmp = *++ptr;
		ESTACK_PUSH(s, tmp);	    
	    }
	}
	break;
	case TAG_PRIMARY_BOXED:
	{
	    Eterm hdr = *boxed_val(term);
	    ASSERT(is_header(hdr));
	    switch (hdr & _TAG_HEADER_MASK) {
	    case ARITYVAL_SUBTAG:
	    {
		int i;
		int arity = header_arity(hdr);
		Eterm* elem = tuple_val(term);
		UINT32_HASH(arity, HCONST_9);
		if (arity == 0) /* Empty tuple */ 
		    goto hash2_common;
		for (i = arity; i >= 2; i--) {
		    tmp = elem[i];
		    ESTACK_PUSH(s, tmp);
		}
		term = elem[1];
	    }
	    break;
	    case EXPORT_SUBTAG:
	    {
		Export* ep = (Export *) (export_val(term))[1];

		UINT32_HASH_2
		    (ep->code[2], 
		     atom_tab(atom_val(ep->code[0]))->slot.bucket.hvalue,
		     HCONST);
		UINT32_HASH
		    (atom_tab(atom_val(ep->code[1]))->slot.bucket.hvalue,
		     HCONST_14);
		goto hash2_common;
	    }

	    case FUN_SUBTAG:
	    {
		ErlFunThing* funp = (ErlFunThing *) fun_val(term);
		Uint num_free = funp->num_free;

		UINT32_HASH_2
		    (num_free, 
		     atom_tab(atom_val(funp->fe->module))->slot.bucket.hvalue,
		     HCONST);
		UINT32_HASH_2
		    (funp->fe->old_index, funp->fe->old_uniq, HCONST);
		if (num_free == 0) {
		    goto hash2_common;
		} else {
		    Eterm* bptr = funp->env + num_free - 1;
		    while (num_free-- > 1) {
			term = *bptr--;
			ESTACK_PUSH(s, term);
		    }
		    term = *bptr;
		}
	    }
	    break;
	    case REFC_BINARY_SUBTAG:
	    case HEAP_BINARY_SUBTAG:
	    case SUB_BINARY_SUBTAG:
	    {
		byte* bptr;
		unsigned sz = binary_size(term);
		Uint32 con = HCONST_13 + hash;

		if (sz == 0) {
		    hash = con;
		} else {
		    Uint bitoffs;
		    Uint bitsize;

		    ERTS_GET_BINARY_BYTES(term, bptr, bitoffs, bitsize);
		    if (bitoffs == 0) {
			hash = block_hash(bptr, sz, con);
		    } else {
			byte* buf = (byte *) erts_alloc(ERTS_ALC_T_TMP, sz);
			erts_copy_bits(bptr, bitoffs, 1, buf, 0, 1, sz*8);
			hash = block_hash(buf, sz, con);
			erts_free(ERTS_ALC_T_TMP, (void *) buf);
		    }
		}
		goto hash2_common;
	    }
	    break;
	    case POS_BIG_SUBTAG:
	    case NEG_BIG_SUBTAG:
	    {
		Eterm* ptr = big_val(term);