[Monetdb-developers] [Monetdb-checkins] MonetDB/src/gdk gdk.mx, , 1.279, 1.280 gdk_atoms.mx, , 1.161, 1.162 gdk_bat.mx, , 1.214, 1.215 gdk_batop.mx, , 1.170, 1.171 gdk_bbp.mx, , 1.252, 1.253 gdk_heap.mx, , 1.117, 1.118 gdk_qsort.mx, , 1.34, 1.35 gdk_ssort.mx, , 1.15, 1.16 gdk_utils.mx, , 1.246, 1.247

Sjoerd Mullender sjoerd at acm.org
Tue Apr 14 13:40:30 CEST 2009


Is this a backward compatible change?  In other words, can databases
created before this change be read by the new version?

I really want backward compatibility, so if it isn't, some kind of
conversion would be needed.

Peter Boncz wrote:
> Update of /cvsroot/monetdb/MonetDB/src/gdk
> In directory 23jxhf1.ch3.sourceforge.com:/tmp/cvs-serv5363/src/gdk
> 
> Modified Files:
> 	gdk.mx gdk_atoms.mx gdk_bat.mx gdk_batop.mx gdk_bbp.mx 
> 	gdk_heap.mx gdk_qsort.mx gdk_ssort.mx gdk_utils.mx 
> Log Message:
> support for 32GB string heaps in 64bits/oid32 mode
> (implies bat format change but ONLY for 64bits/oid32)
> 
> src/gdk/gdk.mx
> - introduce GDK_VARSHIFT, var_t (str indices) are to be shifted that
>   amount of bits to get to the real offset (padding is 8, in case 
>   of 64-bits and oid32 -- otherwise it is 0 => no change) 
> - clean up usage of var_t in HEAP_* interface
> 
> src/gdk/gdk_atoms.mx
> - str heaps with difficult double lim distrubution do not maintain 
>   a linked list (direct open hashing only)
> - allow internal string heap hash table pointers to be unsigned shorts 
>   instead of var_t (only switched on for 64bits/oid32)
> - double-elim string heaps scaled back to 64KB (from 256-512KB)
> - support for GDK_VARSHIFT 
> 
> src/gdk/gdk_bat.mx
> - bugfix in 64bits/oid32 offset calculation (precision loss averted)
> 
> src/gdk/gdk_batop.mx
> src/gdk/gdk_bbp.mx
> src/gdk/gdk_qsort.mx
> src/gdk/gdk_ssort.mx
> - support for GDK_VARSHIFT 
> 
> src/gdk/gdk_heap.mx
> - HEAPmargin allocates large VM area after a block alloc in 64-bits
>   (this to stimulate in-place HEAPextend without memcpy)
> - clean up use of var_t/size_t in HEAP_* functions, and support for GDK_VARSHIFT 
> 
> src/gdk/gdk_utils.mx
> - increase VM size for 64-bits systems to 4TB 
> 
> 
> 
> U gdk.mx
> Index: gdk.mx
> ===================================================================
> RCS file: /cvsroot/monetdb/MonetDB/src/gdk/gdk.mx,v
> retrieving revision 1.279
> retrieving revision 1.280
> diff -u -d -r1.279 -r1.280
> --- gdk.mx	3 Apr 2009 09:14:51 -0000	1.279
> +++ gdk.mx	13 Apr 2009 23:36:24 -0000	1.280
> @@ -1068,9 +1068,9 @@
>  @item void
>  HEAP_destroy     (Heap* h)
>  @item var_t
> -HEAP_malloc      (Heap* heap, var_t nbytes)
> +HEAP_malloc      (Heap* heap, size_t nbytes)
>  @item void
> -HEAP_free        (Heap *heap, size_t block)
> +HEAP_free        (Heap *heap, var_t block)
>  @item int
>  HEAP_private     (Heap* h)
>  @item void
> @@ -1111,7 +1111,7 @@
>  					int (*sizefcn) (ptr) /* BATatoms[].atomLen function */
>      );
>  
> -gdk_export var_t HEAP_malloc(Heap *heap, var_t nbytes);
> +gdk_export var_t HEAP_malloc(Heap *heap, size_t nbytes);
>  gdk_export void HEAP_free(Heap *heap, var_t block);
>  gdk_export var_t HEAP_private(Heap *h);
>  gdk_export void HEAP_checkformat(Heap *h);
> @@ -1350,12 +1350,37 @@
>  #define Hloc(b,p)	((b)->H->heap.base+((p)<<(b)->H->shift))
>  #define Tloc(b,p)	((b)->T->heap.base+((p)<<(b)->T->shift))
>  
> +#if SIZEOF_VAR_T < SIZEOF_VOID_P
> +/* NEW 11/4/2009: when compiled with 32-bits oids/var_t on 64-bits systems, align heap strings 
> + * on 8 byte boundaries always (wasting 4 padding bytes on avg). Note that in heaps where 
> + * duplicate elimination is succesful, such padding occurs anyway (as an aside, a better 
> + * implementation with two-bytes pointers in the string heap hash table, could reduce that 
> + * padding to avg 1 byte wasted -- see TODO below).
> + *
> + * This 8 byte alignment allows the offset in the fixed part of the BAT string column to be 
> + * interpreted as an index, which should be multiplied by 8 to get the position (VARSHIFT). The
> + * overall effect is that 32GB heaps can be addressed even when oids are limited to 4Gtuples.
> + *
> + * In the future, we might extend this such that the string alignment is set in the BAT header
> + * (columns with long strings take more storage space, but could tolerate more padding).
> + * It would mostly work, only the sort routine and strPut/strLocate (which do not see the BAT 
> + * header) extra parameters would be needed in their APIs.
> + */ 
> +typedef unsigned short stridx_t;
> +#define GDK_VARSHIFT 3 
> +#define GDK_VARALIGN (1<<GDK_VARSHIFT)
> +#else
> +typedef var_t stridx_t; /* TODO: should also be unsigned short, but kept at var_t not to break BAT images */
> +#define GDK_VARSHIFT 0 
> +#define GDK_VARALIGN sizeof(stridx_t)
> +#endif
> +
>  #define BUNhloc(bi,p)	Hloc((bi).b,p)
>  #define BUNtloc(bi,p)	Tloc((bi).b,p)
>  #define BUNhpos(bi,p)	(Hpos(&(bi),p))
>  #define BUNtpos(bi,p)	(Tpos(&(bi),p))
> -#define BUNhvar(bi,p)	((bi).b->htype?(Hbase((bi).b)+*((var_t*)BUNhloc(bi,p))):BUNhpos(bi,p))
> -#define BUNtvar(bi,p)	((bi).b->ttype?(Tbase((bi).b)+*((var_t*)BUNtloc(bi,p))):BUNtpos(bi,p))
> +#define BUNhvar(bi,p)	((bi).b->htype?(Hbase((bi).b)+((*(var_t*)BUNhloc(bi,p))<<GDK_VARSHIFT)):BUNhpos(bi,p))
> +#define BUNtvar(bi,p)	((bi).b->ttype?(Tbase((bi).b)+((*(var_t*)BUNtloc(bi,p))<<GDK_VARSHIFT)):BUNtpos(bi,p))
>  #define BUNhead(bi,p)	((bi).b->hvarsized?BUNhvar(bi,p):BUNhloc(bi,p))
>  #define BUNtail(bi,p)	((bi).b->tvarsized?BUNtvar(bi,p):BUNtloc(bi,p))
>  
> 
> U gdk_atoms.mx
> Index: gdk_atoms.mx
> ===================================================================
> RCS file: /cvsroot/monetdb/MonetDB/src/gdk/gdk_atoms.mx,v
> retrieving revision 1.161
> retrieving revision 1.162
> diff -u -d -r1.161 -r1.162
> --- gdk_atoms.mx	7 Apr 2009 11:53:22 -0000	1.161
> +++ gdk_atoms.mx	13 Apr 2009 23:36:24 -0000	1.162
> @@ -175,7 +175,6 @@
>  gdk_export int strLen(const char *s);
>  gdk_export int strCmp(str l, str r);
>  gdk_export int strNil(str s);
> -gdk_export void strHeapConvert(Heap *h, int directon);
>  gdk_export int strElimDoubles(Heap *h);
>  gdk_export var_t strLocate(Heap *h, str v);
>  gdk_export int strCmpNoNil(unsigned char *l, unsigned char *r);
> @@ -457,7 +456,7 @@
>  	 0, 0,
>  	 (var_t (*)(Heap *, var_t *, ptr)) strPut, 0,
>  	 (int (*)(ptr)) strLen, strHeap,
> -	 (void (*)(Heap *, int)) strHeapConvert, 0},
> +	 (void (*)(Heap *, int)) 0, 0},
>  };
>  int GDKatomcnt = TYPE_str + 1;
>  
> @@ -931,24 +930,25 @@
>  	}								\
>  } while (0)
>  
> -#define GDK_STRHASHTABLE	(1<<10)
> +/* string heaps:
> + * - strings are 8 byte aligned
> + * - start with a 1024 bucket hash table
> + * - heaps < 64KB are fully duplicate eliminated with this hash tables
> + * - heaps >= 64KB are opportunistically (imperfect) duplicate eliminated 
> + *   as only the last 128KB chunk is considered and there is no linked list
> + * - buckets and next pointers are unsigned short "indices"
> + * - indices should be multiplied by 8 and takes from ELIMBASE to get an offset
> + *
> + * Note that a 64KB chunk of the heap contains at most 8K 8-byte aligned
> + * strings. The 1K bucket list means that in worst load, the list length is 8 (OK).
> + */
> +#define GDK_STRHASHTABLE	(1<<10) /* 1024 */ 
>  #define GDK_STRHASHMASK		(GDK_STRHASHTABLE-1)
> -#define GDK_STRHASHSIZE		(GDK_STRHASHTABLE * sizeof(var_t))
> -#define GDK_STRHASHCREDIT(h)	(((var_t*) (h)->base)[GDK_STRHASHTABLE])
> +#define GDK_STRHASHSIZE		(GDK_STRHASHTABLE * sizeof(stridx_t))
> +#define GDK_ELIMPOWER		16 /* 64KB is the threshold */
>  #define GDK_ELIMDOUBLES(h)	((h)->free < GDK_ELIMLIMIT)
> -#define GDK_ELIMLIMIT		(1<<GDK_ELIMPOWER)
> +#define GDK_ELIMLIMIT		(1<<GDK_ELIMPOWER) /* equivalently: ELIMBASE == 0 */
>  #define GDK_ELIMBASE(x)		(((x) >> GDK_ELIMPOWER) << GDK_ELIMPOWER)
> -#if SIZEOF_SIZE_T == SIZEOF_INT
> -#define GDK_ELIMPOWER		16	/* makes for a max 64KB hash table 
> -					 * ie 256 string bytes per hash bucket 
> -					 * ~ 4 strings of UP4(8<=len<=11)=12 + 4 bytes 
> -					 */
> -#else
> -#define GDK_ELIMPOWER		17	/* makes for a max 128KB hash table 
> -					 * ie 512 string bytes per hash bucket 
> -					 * ~ 5 strings of UP8(8<=len<=15)=16 + 8 bytes 
> -					 */
> -#endif
>  
>  @- Atomic ADT functions
>  @c
> @@ -1767,46 +1767,34 @@
>  Because in many typical situations lots of double string values occur
>  in tables, the string insertion provides automatic double elimination.
>  To do this, a GDK_STRHASHTABLE(=1024) bucket hashtable is hidden in the first 
> -4096 (8192 on 64-bit architectures) bytes of the string heap, consisting of integer offsets of the first 
> -string hashing to that bucket in the heap. Furthermore, the first 4(8) bytes 
> -before each string in the heap is an integer offset to the next string hashing 
> -to the same number.
> +4096 bytes of the string heap, consisting an offset to the first string 
> +hashing to that bucket in the heap. 
> +These offsets are made small (stridx_t is an unsigned short) by exploiting 
> +the fact that the double elimination chunks are (now) 64KB, hence a short 
> +suffices.
>  
> -However, in many other situations the cardinality of string columns is large,
> +In many other situations the cardinality of string columns is large,
>  or the string values might even be unique. In those cases, our fixed-size hash 
>  table will start to overflow quickly. Therefore, after the hash table is full
>  (this is measured very simplistically by looking whether the string heap exceeds a 
> -heap size = GDK_ELIMLIMIT -- done this way to keep compatibility with old bat images) 
> -we flush the hash table. If one views the string heaps as consecutive chunks
> -of size GDK_ELIMLIMIT bytes, then all strings within one chunk are double-eliminated.
> -There is a macro GDK_ELIMBASE(offset) that computes the base of the chunk in which
> -a certain byte-offset falls.
> - at -
> -This is a departure from our previous policy of not looking at the hash tables at 
> -all after overflow occurred. The advantage of the new approach is that if we have 
> -a value distribution that is skewed (ie some values are very frequent), these 
> -values will always be double eliminated, saving a considerable amount of space. 
> -Disadvantage of the approach is that we always have to reserve space for the next 
> -pointer (4(8) byte integer offset) that is stored right in front of the string (and 
> -consequently have to keep all string chunks and offsets aligned to 4(8)). All this 
> -translates into some wasted space. However, if there are that many different strings 
> -that the hash table overflows, the strings must be relatively long and the relative 
> -storage overhead should be low.
> +heap size = GDK_ELIMLIMIT = 64KB) we flush the hash table. Even more, from that moment
> +on, we do not use a linked list, but a lossy hash table that just contains
> +the last position for each bucket. Basically, after exceeding GDK_ELIMLIMIT,
> +we get a probabilistic/opportunistic duplicate elimination mechanism,
> +that only looks at the last GDK_ELIMLIMIT chunk in the heap, in a lossy way.
> +
> +When comparing with the previous string implementation, the biggest difference
> +is that on 64-nbits bt with 32-bits oids, strings are always 8-byte aligned 
> +and var_t numbers are multiplied by 8 to get the true offset. The goal to do 
> +this is to allow 32-bits var_t on 64-bits systems to address 32GB (using string 
> +alignment=8).  For large database, the cost of padding (4 bytes avg) is offset 
> +by the savings in var_t (allowing to go from 64- to 32-bits). Nothing lost there, 
> +and 32-bits var_t also pay in smaller OIDs and smaller hash tables, reducing memory
> +pressure. For small duplicate eliminated heaps, the short indices
> +used in the hash table have now allowed more buckets (2K instead of 1K)
> +and average 2 bytes overhead for the next pointers instead of 6-12. Therefore
> +small heaps are now more compact than before.
>  @-
> -Notice that this mechanism enables to keep a certain linear storage property
> -in the string heaps. This is important if we want to take a BATslice on a BAT
> -by simply loading or @strong{mmap()}ping slices of the BAT files on disk into memory.
> -This is relevant in order to process a very large BAT iteratively by taking slices
> -in order to reduce memory consumption. Notice that if there are few different string 
> -values, the hash table has not overflowed, and the string heap size will be small 
> -(i.e. < GDK_ELIMLIMIT), so in those cases it is not a problem to load the entire string heap.
> -If the hash table @strong{has} overflowed, we want to be able to only map a slice of the 
> -string heap as well. Now, given that the first string in the BAT-slice is called F1 
> -and its heap offset is O1 and the last string in the slice is F2 and its 
> -offset is O2, then the slice we should take from the string heap is: 
> - at example
> -GDK_ELIMBASE(F1) .. MAX(GDK_ELIMBASE(F2)+GDK_ELIMLIMIT), O2+strlen(F2))
> - at end example
>  The routine strElimDoubles() can be used to check whether all 
>  strings are still being double-eliminated in the original hash-table.
>  Only then we know that unequal offset-integers in the BUN array means
> @@ -1877,16 +1865,12 @@
>  strHeap(Heap *d, size_t cap)
>  {
>  	size_t size;
> -	var_t *h, *e;
>  
>  	cap = MAX(cap, BATTINY);
> -	size = (GDK_STRHASHTABLE + 1) * sizeof(var_t) + MIN(GDK_ELIMLIMIT, cap * 12);
> +	size = GDK_STRHASHTABLE * sizeof(stridx_t) + MIN(GDK_ELIMLIMIT, cap * GDK_VARALIGN);
>  	if (HEAPalloc(d, size, 1) >= 0) {
> -		d->free = GDK_STRHASHTABLE * sizeof(var_t);
> -		h = (var_t *) d->base;
> -		for (e = h; e < h + GDK_STRHASHTABLE; e++) {
> -			*e = 0;
> -		}
> +		d->free = GDK_STRHASHTABLE * sizeof(stridx_t);
> +		memset(d->base, 0, d->free);
>  	}
>  }
>  
> @@ -1923,42 +1907,10 @@
>  void
>  strCleanHash(Heap *h, int rebuild)
>  {
> +	(void) rebuild;
>  	if (!GDK_ELIMDOUBLES(h)) {
>  		/* flush hash table for security */
>  		memset(h->base, 0, GDK_STRHASHSIZE);
> -	} else if (rebuild) {
> -		var_t xx, cur = 0, end = 0;
> -		str hash = (str) h->base;
> -
> -/* int cnt[GDK_STRHASHTABLE]; */
> -		/* collect all values in one big linked list */
> -		for (xx = 0; xx < GDK_STRHASHTABLE; xx++) {
> -			var_t yy = ((var_t *) hash)[xx];
> -
> -/* cnt[xx]=0; */
> -			((var_t *) hash)[xx] = 0;	/* clear hash table slot */
> -
> -			if (end) {
> -				*(var_t *) (hash + end) = yy;
> -			} else {
> -				cur = yy;
> -			}
> -			for (; yy; yy = *(var_t *) (hash + yy))
> -				end = yy;
> -		}
> -
> -		/* process the linked list, inserting the values again */
> -		for (; cur; cur = end) {
> -			str val = hash + cur;
> -			GDK_STRHASH(val + sizeof(var_t), xx);
> -			xx &= GDK_STRHASHMASK;
> -			end = *(var_t *) val;
> -			*(var_t *) val = ((var_t *) hash)[xx];
> -			((var_t *) hash)[xx] = cur;
> -/* cnt[xx]++; */
> -		}
> -/* for(xx=0; xx<GDK_STRHASHTABLE; xx++)
> -   if(cnt[xx]) stream_printf(GDKout, "%5d %6d", xx, cnt[xx]); */
>  	}
>  }
>  
> @@ -1970,90 +1922,63 @@
>  var_t
>  strLocate(Heap *h, str v)
>  {
> -	var_t *htab = (var_t *) h->base;
> -	var_t *l, *e;
> -	BUN idx;
> -
> -	GDK_STRHASH(v, idx);
> -	e = htab + (idx & GDK_STRHASHMASK);
> -	if (*e) {
> -		for (l = e; *l && *l < h->free; l = (var_t *) ((char *) h->base + *l)) {
> -			str x = (str) ((char *) h->base + *l + sizeof(var_t));
> -
> -			if (GDK_STRCMP(v, x) == 0) {
> -				return *l + (var_t) sizeof(var_t);
> -			}
> -		}
> -	}
> -	return 0;
> -}
> +	stridx_t *ref, *next;
>  
> -#if SIZEOF_SIZE_T == SIZEOF_INT
> -#define normal_vart_SWAP(x)	((var_t) normal_int_SWAP((int)x))
> -#else
> -#define normal_vart_SWAP(x)	((var_t) long_long_SWAP((lng)x))
> -#endif
> +	/* search hash-table, if double-elimination is still in place */
> +	BUN off; GDK_STRHASH(v, off);
> +	off &= GDK_STRHASHMASK;
>  
> -/* convert the integers in the implicit hash table structure */
> -void
> -strHeapConvert(Heap *h, int dir)
> -{
> -	var_t *htab = (var_t *) h->base;
> -	var_t *l, i, j;
> +	/* should only use strLocate iff fully double eliminated */
> +	assert(GDK_ELIMBASE(h->free) == 0);
>  
> -	if (dir == CONV_HTON) {
> -		for (i = 0; i < GDK_STRHASHTABLE; i++) {
> -			for (l = htab + i; (j = *l) != 0 && j < h->free; l = (var_t *) (h->base + j)) {
> -				*l = normal_vart_SWAP(j);
> -			}
> -		}
> -	} else {
> -		for (i = 0; i < GDK_STRHASHTABLE; i++) {
> -			for (l = htab + i; (j = *l) != 0 && j < h->free; l = (var_t *) (h->base + *l)) {
> -				*l = normal_vart_SWAP(j);
> -			}
> -		}
> +	/* search the linked list */
> +	for (ref = ((stridx_t *) h->base) + off; *ref; ref = next) { 
> +		next = (stridx_t*) (h->base + *ref);
> +		if (GDK_STRCMP(v, (str) (next+1)) == 0) 
> +			return (sizeof(stridx_t) + *ref) >> GDK_VARSHIFT; /* found */
>  	}
> +	return 0;
>  }
>  
>  var_t
>  strPut(Heap *h, var_t *dst, str v)
>  {
> -	var_t *l;
> -	size_t i = GDK_STRLEN(v);
> -	BUN off;
> -
> -	/* round up to var_t-byte alignment + var_t (next pointer) */
> -	size_t len = ((i + sizeof(var_t) - 1) & ~(sizeof(var_t) - 1)) + sizeof(var_t);
> -	size_t elimlimit = GDK_ELIMBASE(h->free) + GDK_ELIMLIMIT;
> +	size_t elimbase = GDK_ELIMBASE(h->free);
> +	size_t pad = GDK_VARALIGN - (h->free & (GDK_VARALIGN-1));
> +	size_t pos, len = GDK_STRLEN(v);
> +	stridx_t *bucket, *ref, *next;
>  
>  	/* search hash-table, if double-elimination is still in place */
> -	GDK_STRHASH(v, off);
> +	BUN off; GDK_STRHASH(v, off);
>  	off &= GDK_STRHASHMASK;
> -	for (l = ((var_t *) h->base) + off; *l && *l < h->free; l = (var_t *) (h->base + *l)) {
> -		str x = (str) (h->base + *l + sizeof(var_t));
> +	bucket = ((stridx_t *) h->base) + off; 
>  
> -		if (GDK_STRCMP(v, x) == 0) {
> -			*dst = *l + (var_t) sizeof(var_t);	/* already in heap; do not insert! */
> -			if (GDK_ELIMDOUBLES(h) == 0 && GDK_STRHASHCREDIT(h))
> -				GDK_STRHASHCREDIT(h) += 4;
> -			return *dst;
> +	if (elimbase == 0) { /* small string heap (<64KB) -- fully double eliminated */
> +		for (ref = bucket; *ref; ref = next) { /* search the linked list */
> +			next = (stridx_t*) (h->base + *ref);
> +			if (GDK_STRCMP(v, (str) (next+1)) == 0) { /* found */
> +				pos = sizeof(stridx_t) + *ref;
> +				return *dst = (pos >> GDK_VARSHIFT); 
> +			}
>  		}
> -	}
> -
> -	/* flush the hash table if it becomes too big (implies !GDK_ELIMDOUBLES) */
> -	if (h->free + len >= elimlimit) {
> -		/* if we are not hash-inserting anymore, h->free may no longer be var_t aligned */
> -		size_t mask = h->free & (sizeof(var_t) - 1);
> -
> -		if (mask)
> -			h->free += sizeof(var_t) - mask;	/* realign */
> -		memset(h->base, 0, GDK_STRHASHSIZE);	/* start over hash inserting in a pristine hash table */
> -		GDK_STRHASHCREDIT(h) = 32;	/* only tolerate limited misses in the future */
> +		/* is there room for the next pointer in the padding space? */
> +		if (pad < sizeof(stridx_t)) 
> +			pad += GDK_VARALIGN; /* if not, pad more */
> +	} else {
> +	        /* large string heap (>=64KB) -- opportunistic/probabilistic double elimination */
> +		pos = elimbase + *bucket;
> +		if (GDK_STRCMP(v, (str) (h->base + pos)) == 0) {
> +			return *dst = (pos >> GDK_VARSHIFT); /* already in heap; do not insert! */
> +		}
> +#if SIZEOF_VAR_T < SIZEOF_VOID_P
> +		pad &= (GDK_VARALIGN-1); /* a full VARALIGN pad can be omitted */
> +#else
> +		pad = 0; /* only 32-bits var_t in 64-bits needs padding */
> +#endif
>  	}
>  
>  	/* check heap for space (limited to a certain maximum after which nils are inserted) */
> -	if (h->free + len >= h->size) {
> +	if (h->free + pad + len >= h->size) {
>  		/* Something really strange happens here, In a special case
>  		   (Pentium II Klamath, gcc version 2.96 20000731,
>  		   GNU assembler version 2.10.90 using BFD version 2.10.0.18)
> @@ -2064,11 +1989,15 @@
>  		 */
>  		float batmargin = (float) BATMARGIN;
>  		float hnewsize = h->size * batmargin;
> -		size_t newsize = len + (size_t) hnewsize;
> +		size_t newsize = pad + len + (size_t) hnewsize;
>  
>  		assert(newsize);
>  
> -		if (h->free + len < h->maxsize) {
> +		if (h->free + pad + len >= (((size_t) VAR_MAX) << GDK_VARSHIFT)) {
> +			GDKerror("strPut: string heaps gets larger than %dGB.\n", (((size_t) VAR_MAX) << GDK_VARSHIFT) >> 30);
> +			return 0;
> +		}
> +		if (h->free + pad + len < h->maxsize) {
>  			/* if there is reserved space, first use the reserved space */
>  			newsize = MIN(newsize, h->maxsize);
>  		}
> @@ -2077,32 +2006,27 @@
>  		}
>  		/* fill should solve initialisation problems within valgrind */
>  		memset(h->base + h->free, 0, h->size - h->free);
> -	}
>  
> -	if (!GDK_ELIMDOUBLES(h)) {
> -		if (GDK_STRHASHCREDIT(h) == 0) {
> -			/* if credits are gone, we do not hash insert at all */
> -			if (h->free > VAR_MAX) {
> -				GDKerror("strPut: string heaps gets larger than 2GB -- too large for 32-bits oids.\n");
> -				return 0;
> -			}
> -			*dst = (var_t) h->free;
> -			memcpy(h->base + h->free, v, i);
> -			h->free += i;	/* in this case, we do not round to var_t either */
> -			return *dst;
> -		}
> -		GDK_STRHASHCREDIT(h)--;
> +		/* make bucket point into the enw heap */
> +		bucket = ((stridx_t *) h->base) + off; 
>  	}
>  
> -	/* insert string in hash table and copy into the heap */
> -	l = (var_t *) (h->base + h->free);
> -	*(l++) = ((var_t *) h->base)[off];
> -	assert(h->free + sizeof(var_t) <= VAR_MAX);
> -	((var_t *) h->base)[off] = (var_t) h->free;
> -	*dst = (var_t) (h->free + sizeof(var_t));
> -	h->free += len;
> -	memcpy((char *) l, v, i);
> +	/* insert string */
> +	pos = h->free + pad;
> +	*dst = pos >> GDK_VARSHIFT;
> +	memcpy(h->base + pos, v, len);
> +	h->free += pad + len;	
> +
> +	/* maintain hash table */
> +	if (elimbase == 0) { /* small string heap: link the next pointer */
> +		pos -= sizeof(stridx_t); /* the stridx_t next pointer directly precedes the string */
> +		*(stridx_t*) (h->base + pos) = *bucket;
> +	}
> +	*bucket = (stridx_t) (pos - elimbase); /* set bucket to the new string */
>  
> +	if (h->free >= elimbase + GDK_ELIMLIMIT) {
> +		memset(h->base, 0, GDK_STRHASHSIZE); /* flush hash table */	
> +	} 
>  	return *dst;
>  }
>  
> 
> U gdk_bbp.mx
> Index: gdk_bbp.mx
> ===================================================================
> RCS file: /cvsroot/monetdb/MonetDB/src/gdk/gdk_bbp.mx,v
> retrieving revision 1.252
> retrieving revision 1.253
> diff -u -d -r1.252 -r1.253
> --- gdk_bbp.mx	9 Apr 2009 15:29:18 -0000	1.252
> +++ gdk_bbp.mx	13 Apr 2009 23:36:24 -0000	1.253
> @@ -2965,9 +2965,9 @@
>  		BATsetcount(&bs->B, 0);
>  
>  		if (bs->H.vheap)
> -			memset(bs->H.vheap->base, 0, bs->H.vheap->free = GDK_STRHASHTABLE * sizeof(var_t));
> +			memset(bs->H.vheap->base, 0, bs->H.vheap->free = GDK_STRHASHTABLE * sizeof(stridx_t));
>  		if (bs->T.vheap)
> -			memset(bs->T.vheap->base, 0, bs->T.vheap->free = GDK_STRHASHTABLE * sizeof(var_t));
> +			memset(bs->T.vheap->base, 0, bs->T.vheap->free = GDK_STRHASHTABLE * sizeof(stridx_t));
>  		return bs;
>  	}
>  	BATDEBUG THRprintf(GDKout, "#BBPrecycle %d %d "SZFMT" (%d, %d %d %d) N2\n", ht, tt, cap, BATCACHE_NOTYPE(ht), BATCACHE_NOTYPE(tt), batcache_maxbuckets, bin);
> 
> U gdk_batop.mx
> Index: gdk_batop.mx
> ===================================================================
> RCS file: /cvsroot/monetdb/MonetDB/src/gdk/gdk_batop.mx,v
> retrieving revision 1.170
> retrieving revision 1.171
> diff -u -d -r1.170 -r1.171
> --- gdk_batop.mx	7 Jan 2009 14:13:48 -0000	1.170
> +++ gdk_batop.mx	13 Apr 2009 23:36:24 -0000	1.171
> @@ -1656,7 +1656,7 @@
>  				if (b->hkey == 0) {
>  					/* sorted and key? */
>  					while (cur < end) {
> -						char *val = base + *(((var_t *)b->H->heap.base)+ cur);
> +						char *val = base + (*(((var_t *)b->H->heap.base)+ cur) << GDK_VARSHIFT);
>  
>  						if (cmp(prv, val) @5= 0) {
>  							key = FALSE;
> @@ -1668,7 +1668,7 @@
>  				}
>  				/* sorted? */
>  				while (cur < end) {
> -					char *val = base + *(((var_t *)b->H->heap.base)+ cur);
> +					char *val = base + (*(((var_t *)b->H->heap.base)+ cur) << GDK_VARSHIFT);
>  
>  					if (cmp(prv, val) @5 0) {
>  						/* record negative position info */
> 
> U gdk_utils.mx
> Index: gdk_utils.mx
> ===================================================================
> RCS file: /cvsroot/monetdb/MonetDB/src/gdk/gdk_utils.mx,v
> retrieving revision 1.246
> retrieving revision 1.247
> diff -u -d -r1.246 -r1.247
> --- gdk_utils.mx	9 Apr 2009 18:48:25 -0000	1.246
> +++ gdk_utils.mx	13 Apr 2009 23:36:24 -0000	1.247
> @@ -382,7 +382,7 @@
>  #define GDK_MEM_NULLALLOWED
>  
>  #if SIZEOF_VOID_P==8
> -#define GDK_VM_MAXSIZE	LL_CONSTANT(137438953472)	/* :-) a 64-bit OS: 128 GB */
> +#define GDK_VM_MAXSIZE	LL_CONSTANT(4398046511104) /* :-) a 64-bit OS: 4TB */
>  #else
>  #define GDK_VM_MAXSIZE	LL_CONSTANT(1610612736)	/* :-| a 32-bit OS: 1.5GB */
>  #endif
> 
> U gdk_heap.mx
> Index: gdk_heap.mx
> ===================================================================
> RCS file: /cvsroot/monetdb/MonetDB/src/gdk/gdk_heap.mx,v
> retrieving revision 1.117
> retrieving revision 1.118
> diff -u -d -r1.117 -r1.118
> --- gdk_heap.mx	20 Mar 2009 11:59:57 -0000	1.117
> +++ gdk_heap.mx	13 Apr 2009 23:36:24 -0000	1.118
> @@ -75,8 +75,20 @@
>  nice).  
>  @{
>  @c
> -int
> -HEAPalloc(Heap *h, size_t nitems, size_t itemsize)
> +size_t HEAPmargin(size_t maxsize) {
> +	size_t ret;
> +#if SIZEOF_VOID_P == 8
> +	/* in 64-bits systems, try to enforce in-place realloc, but provoke the memcpy on 256MB, then 4GB */
> +	size_t use = GDKvm_cursize();
> +	ret = MIN(GDK_mem_maxsize, MAX(((size_t) 1) << 26, 16*maxsize));
> +	if ((ret+ret) > (GDK_vm_maxsize-MIN(GDK_vm_maxsize,use))) /* only if room */
> +#endif
> +	ret = ((double) BATMARGIN)*maxsize - 1; /* do not waste VM on 32-bits */
> +	return (1 + (MAX(maxsize,ret) >> 16)) << 16; /* round up to 64K */
> +}
> +
> +/* in 64-bits space, use very large margins to accomodate reallocations */
> +int HEAPalloc(Heap *h, size_t nitems, size_t itemsize)
>  {
>  	char nme[PATHLENGTH], *ext = NULL;
>  
> @@ -98,8 +110,7 @@
>  	/* when using anonymous vm we malloc we need 64K chunks, also we
>  	 * 20% extra malloc */
>  	if (h->size > GDK_mem_bigsize) {
> -		h->maxsize = (size_t) ((double) h->maxsize * BATMARGIN) - 1;
> -		h->maxsize = (1 + (h->maxsize >> 16)) << 16;
> +		h->maxsize = HEAPmargin(h->maxsize);
>  	}
>  	if (h->filename == NULL || (h->size < GDK_mmap_minsize)) {
>  		h->storage = STORE_MEM;
> @@ -169,17 +180,14 @@
>  		/* extend a malloced heap, possibly switching over to file-mapped storage */
>  		Heap bak = *h;
>  		int can_mmap = h->filename && (size >= GDK_mem_bigsize || h->newstorage != STORE_MEM);
> -		int must_mmap = can_mmap && (size >= GDK_mmap_minsize || h->newstorage != STORE_MEM);
> +		int small_cpy = (h->size*4 < size) && (size >= GDK_mmap_minsize);
> +		int must_mmap = can_mmap && (small_cpy || h->newstorage != STORE_MEM);
>  
>  		h->size = size;
>  
>  		if (can_mmap) {
>  			/* in anonymous vm, if have to realloc anyway, we reserve some extra space */
> -			if (size > h->maxsize) {
> -				h->maxsize = (size_t) ((double) size * BATMARGIN);
> -			}
> -			/* when using anonymous vm we malloc we need 64K chunks */
> -			h->maxsize = (1 + ((h->maxsize - 1) >> 16)) << 16;
> +			h->maxsize = HEAPmargin(MAX(size,h->maxsize));
>  		} else {
>  			h->maxsize = size;	/* for normal GDKmalloc, maxsize = size */
>  		}
> @@ -514,9 +522,9 @@
>  #define HEAPVERSION	20030408
>  
>  typedef struct heapheader {
> -	var_t head;		/* index to first free block            */
> +	size_t head;		/* index to first free block            */
>  	int alignment;		/* alignment of objects on heap         */
> -	var_t firstblock;	/* first block in heap                  */
> +	size_t firstblock;	/* first block in heap                  */
>  	int version;
>  	int (*sizefcn) (ptr);	/* ADT function to ask length           */
>  } HEADER32;
> @@ -524,8 +532,8 @@
>  typedef struct {
>  	int version;
>  	int alignment;
> -	var_t head;
> -	var_t firstblock;
> +	size_t head;
> +	size_t firstblock;
>  	int (*sizefcn) (ptr);
>  } HEADER64;
>  
> @@ -537,8 +545,8 @@
>  typedef HEADER64 HEADER_OTHER;
>  #endif
>  typedef struct hfblock {
> -	var_t size;		/* Size of this block in freelist        */
> -	var_t next;		/* index of next block                   */
> +	size_t size;		/* Size of this block in freelist        */
> +	size_t next;		/* index of next block                   */
>  } CHUNK;
>  
>  @c
> @@ -546,13 +554,13 @@
>  #define roundup_4(x)	(((x)+3)&~3)
>  #define blocksize(h,p)	((p)->size)
>  
> -static INLINE var_t
> -roundup_num(var_t number, int alignment)
> +static INLINE size_t
> +roundup_num(size_t number, int alignment)
>  {
> -	var_t rval;
> +	size_t rval;
>  
> -	rval = number + (var_t) alignment - 1;
> -	rval -= (rval % (var_t) alignment);
> +	rval = number + (size_t) alignment - 1;
> +	rval -= (rval % (size_t) alignment);
>  	return rval;
>  }
>  
> @@ -560,7 +568,7 @@
>  HEAP_private(Heap *h)
>  {
>  	(void) h;
> -	return (var_t) roundup_8(sizeof(HEADER));
> +	return (var_t) (roundup_8(sizeof(HEADER)) >> GDK_VARSHIFT);
>  }
>  
>  #ifdef TRACE
> @@ -568,7 +576,7 @@
>  HEAP_printstatus(Heap *heap)
>  {
>  	HEADER *hheader = HEAP_index(heap, 0, HEADER);
> -	var_t block, cur_free = hheader->head;
> +	size_t block, cur_free = hheader->head;
>  	CHUNK *blockp;
>  
>  	THRprintf(GDKout, "#HEAP has head " SZFMT " and alignment %d and size " SZFMT "\n",
> @@ -591,7 +599,7 @@
>  			cur_free = blockp->next;
>  			block += blockp->size;
>  		} else {
> -			var_t size = blocksize(hheader, blockp);
> +			size_t size = blocksize(hheader, blockp);
>  
>  			THRprintf(GDKout, "#   block at " SZFMT " with size " SZFMT "\n", block, size);
>  			block += size;
> @@ -611,7 +619,7 @@
>  	/*
>  	   // Calculate position of first and only free block.
>  	 */
> -	var_t head = roundup_num((var_t) (roundup_8(sizeof(HEADER)) + roundup_8(nprivate)), alignment);
> +	size_t head = roundup_num((size_t) (roundup_8(sizeof(HEADER)) + roundup_8(nprivate)), alignment);
>  	CHUNK *headp = HEAP_index(heap, head, CHUNK);
>  
>  	assert(roundup_8(sizeof(HEADER)) + roundup_8(nprivate) <= VAR_MAX);
> @@ -629,7 +637,7 @@
>  	   // Fill first free block.
>  	 */
>  	assert(heap->size - head <= VAR_MAX);
> -	headp->size = (var_t) (heap->size - head);
> +	headp->size = (size_t) (heap->size - head);
>  	headp->next = 0;
>  #ifdef TRACE
>  	THRprintf(GDKout, "#We created the following heap\n");
> @@ -669,9 +677,9 @@
>  
>  
>  var_t
> -HEAP_malloc(Heap *heap, var_t nbytes)
> +HEAP_malloc(Heap *heap, size_t nbytes)
>  {
> -	var_t block, trail, ttrail;
> +	size_t block, trail, ttrail;
>  	CHUNK *blockp;
>  	CHUNK *trailp;
>  	HEADER *hheader = HEAP_index(heap, 0, HEADER);
> @@ -682,15 +690,9 @@
>  
>  	/* add space for size field */
>  	nbytes += hheader->alignment;
> -	if (hheader->alignment == 8) {
> -		nbytes = roundup_8(nbytes);
> -	} else if (hheader->alignment == 4) {
> -		nbytes = roundup_4(nbytes);
> -	} else {
> -		GDKfatal("HEAP_malloc: Heap structure corrupt\n");
> -	}
> +	nbytes = roundup_8(nbytes);
>  	if (nbytes < sizeof(CHUNK))
> -		nbytes = (var_t) sizeof(CHUNK);
> +		nbytes = (size_t) sizeof(CHUNK);
>  
>  	/*
>  	   // block  -- points to block with acceptable size (if available).
> @@ -718,12 +720,12 @@
>  	   // If no block of acceptable size is found we try to enlarge the heap.
>  	 */
>  	if (block == 0) {
> -		var_t newsize;
> +		size_t newsize;
>  
>  		assert(heap->free + MAX(heap->free, nbytes) <= VAR_MAX);
> -		newsize = (var_t) roundup_8(heap->free + MAX(heap->free, nbytes));
> +		newsize = (size_t) roundup_8(heap->free + MAX(heap->free, nbytes));
>  		assert(heap->free <= VAR_MAX);
> -		block = (var_t) heap->free;	/* current end-of-heap */
> +		block = (size_t) heap->free;	/* current end-of-heap */
>  
>  #ifdef TRACE
>  		THRprintf(GDKout, "#No block found\n");
> @@ -747,7 +749,7 @@
>  
>  		blockp->next = 0;
>  		assert(heap->free - block <= VAR_MAX);
> -		blockp->size = (var_t) (heap->free - block);	/* determine size of allocated block */
> +		blockp->size = (size_t) (heap->free - block);	/* determine size of allocated block */
>  
>  		/*
>  		   // Try to join the last block in the freelist and the newly allocated
> @@ -778,7 +780,7 @@
>  	   // TUNE: use different amount than 2*sizeof(CHUNK)
>  	 */
>  	if (blockp->size >= nbytes + 2 * sizeof(CHUNK)) {
> -		var_t newblock = block + nbytes;
> +		size_t newblock = block + nbytes;
>  		CHUNK *newblockp = HEAP_index(heap, newblock, CHUNK);
>  
>  		newblockp->size = blockp->size - nbytes;
> @@ -800,17 +802,17 @@
>  	}
>  
>  	block += hheader->alignment;
> -	return block;
> +	return block >> GDK_VARSHIFT;
>  }
>  
>  void
> -HEAP_free(Heap *heap, var_t block)
> +HEAP_free(Heap *heap, var_t mem)
>  {
>  	HEADER *hheader = HEAP_index(heap, 0, HEADER);
>  	CHUNK *beforep;
>  	CHUNK *blockp;
>  	CHUNK *afterp;
> -	var_t after, before;
> +	size_t after, before, block = mem << GDK_VARSHIFT;
>  
>  	if (hheader->alignment != 8 && hheader->alignment != 4) {
>  		GDKfatal("HEAP_free: Heap structure corrupt\n");
> @@ -884,10 +886,10 @@
>  HEAP_check(Heap *heap, HeapRepair *hr)
>  {
>  	HEADER *hheader = HEAP_index(heap, 0, HEADER);
> -	var_t head = hheader->head, alignshift = 2;
> -	var_t block, nwords = (var_t) ((heap->free - 1) >> 7);
> +	size_t head = hheader->head, alignshift = 2;
> +	size_t block, nwords = (size_t) ((heap->free - 1) >> 7);
>  	int *freemask;
> -	var_t prevblock = 0;
> +	size_t prevblock = 0;
>  	CHUNK *blockp;
>  
>  	hr->alignment = hheader->alignment;
> @@ -922,8 +924,8 @@
>  	   // Walk the freelist; register them in freemask
>  	 */
>  	for (block = hheader->head; block != 0; block = HEAP_index(heap, block, CHUNK)->next) {
> -		var_t idx = block >> alignshift;
> -		var_t pos = idx >> 5;
> +		size_t idx = block >> alignshift;
> +		size_t pos = idx >> 5;
>  		int mask = 1 << (idx & 31);
>  
>  		if ((block <= prevblock) && (block != 0)) {
> @@ -942,8 +944,8 @@
>  	 */
>  	block = hheader->firstblock;
>  	while (block < heap->free) {
> -		var_t idx = block >> alignshift;
> -		var_t pos = idx >> 5;
> +		size_t idx = block >> alignshift;
> +		size_t pos = idx >> 5;
>  		int mask = 1 << (idx & 31);
>  
>  		hr->validmask[pos] |= mask;
> @@ -965,8 +967,8 @@
>  	   // Check if there are left over free blocks
>  	 */
>  	for (block = hheader->head; block != 0; block = HEAP_index(heap, block, CHUNK)->next) {
> -		var_t idx = block >> alignshift;
> -		var_t pos = idx >> 5;
> +		size_t idx = block >> alignshift;
> +		size_t pos = idx >> 5;
>  		int mask = 1 << (idx & 31);
>  
>  		if (freemask[pos] & mask) {
> @@ -1046,14 +1048,14 @@
>  	if (hheader->head > heap->free) {
>  		hheader->head = 0;	/* cut off free block */
>  	} else if (hheader->head) {
> -		var_t idx = hheader->head;
> +		size_t idx = hheader->head;
>  
>  		while (idx) {
>  			CHUNK *blk = HEAP_index(heap, idx, CHUNK);
>  
>  			if (idx + blk->size > heap->free) {
>  				assert(heap->free - idx <= VAR_MAX);
> -				blk->size = (var_t) (heap->free - idx);	/* cut off illegal tail of block */
> +				blk->size = (size_t) (heap->free - idx);	/* cut off illegal tail of block */
>  			}
>  			if (blk->next > heap->free || blk->next < (idx + blk->size) || (blk->next & (hheader->alignment - 1))) {
>  				blk->next = 0;	/* cut off next block */
> 
> U gdk_qsort.mx
> Index: gdk_qsort.mx
> ===================================================================
> RCS file: /cvsroot/monetdb/MonetDB/src/gdk/gdk_qsort.mx,v
> retrieving revision 1.34
> retrieving revision 1.35
> diff -u -d -r1.34 -r1.35
> --- gdk_qsort.mx	7 Jan 2009 14:13:48 -0000	1.34
> +++ gdk_qsort.mx	13 Apr 2009 23:36:24 -0000	1.35
> @@ -86,6 +86,7 @@
>  	char *offst;		/* NULL or start of varsized heap */
>  	int hshift;		/* log2 of hs */
>  	int tshift;		/* log2 of hs */
> +	int vshift;		/* shift to be applied on var_ offsets */
>  	unsigned hs;		/* width of head record */
>  	unsigned ts;		/* width of tail record */
>  	void *h;		/* start of head buns */		
> @@ -189,7 +190,7 @@
>  #endif
>  #endif
>  
> -#define offset(p)		(buf->offst + *(var_t*) (p))
> +#define offset(p)		(buf->offst + ((*(var_t*) (p)) << buf->vshift))
>  #define direct(p)		(p)
>  
>  #define any_LE(a,b)		((buf->cmp)(a,b) <= 0)
> @@ -432,6 +433,7 @@
>  	buf.ts = (unsigned) ts;
>  	buf.hshift = ATOMelmshift(hs);
>  	buf.tshift = ATOMelmshift(ts);
> +	buf.vshift = ATOMvarsized(tpe)?GDK_VARSHIFT:0;
>  	buf.h = h;
>  	if (!t)
>  		t = &x;
> 
> U gdk_bat.mx
> Index: gdk_bat.mx
> ===================================================================
> RCS file: /cvsroot/monetdb/MonetDB/src/gdk/gdk_bat.mx,v
> retrieving revision 1.214
> retrieving revision 1.215
> diff -u -d -r1.214 -r1.215
> --- gdk_bat.mx	3 Apr 2009 09:14:52 -0000	1.214
> +++ gdk_bat.mx	13 Apr 2009 23:36:24 -0000	1.215
> @@ -434,7 +434,7 @@
>  BAT *
>  BATextend(BAT *b, BUN newcap)
>  {
> -	size_t hheap_size, theap_size;
> +	size_t hheap_size = newcap, theap_size = newcap;
>  
>  	assert(newcap <= BUN_MAX);
>  	BATcheck(b, "BATextend");
> @@ -453,10 +453,10 @@
>  
>  	b->batCapacity = newcap;
>  
> -	hheap_size = Hsize(b) * newcap;
> +	hheap_size *= Hsize(b);
>  	if (b->H->heap.base && HEAPextend(&b->H->heap, hheap_size) < 0)
>  		return NULL;
> -	theap_size = Tsize(b) * newcap;
> +	theap_size *= Tsize(b);
>  	if (b->T->heap.base && HEAPextend(&b->T->heap, theap_size) < 0)
>  		return NULL;
>  	HASHdestroy(b);
> 
> U gdk_ssort.mx
> Index: gdk_ssort.mx
> ===================================================================
> RCS file: /cvsroot/monetdb/MonetDB/src/gdk/gdk_ssort.mx,v
> retrieving revision 1.15
> retrieving revision 1.16
> diff -u -d -r1.15 -r1.16
> --- gdk_ssort.mx	7 Jan 2009 14:13:48 -0000	1.15
> +++ gdk_ssort.mx	13 Apr 2009 23:36:24 -0000	1.16
> @@ -203,8 +203,8 @@
>  		}						\
>  	} while (0)
>  
> -#define ISLT_any(X, Y, ms)  (((ms)->heap ? (*(ms)->compare)((ms)->heap + * (var_t *) (X), (ms)->heap + * (var_t *) (Y)) : (*(ms)->compare)((X), (Y))) < 0)
> -#define ISLT_any_rev(X, Y, ms)  (((ms)->heap ? (*(ms)->compare)((ms)->heap + * (var_t *) (X), (ms)->heap + * (var_t *) (Y)) : (*(ms)->compare)((X), (Y))) > 0)
> +#define ISLT_any(X, Y, ms)  (((ms)->heap ? (*(ms)->compare)((ms)->heap + ((*(var_t*) (X)) << GDK_VARSHIFT), (ms)->heap + ((*(var_t*) (Y)) << GDK_VARSHIFT)) : (*(ms)->compare)((X), (Y))) < 0)
> +#define ISLT_any_rev(X, Y, ms)  (((ms)->heap ? (*(ms)->compare)((ms)->heap + ((*(var_t*) (X)) << GDK_VARSHIFT), (ms)->heap + ((*(var_t*) (Y)) << GDK_VARSHIFT)) : (*(ms)->compare)((X), (Y))) > 0)
>  @= islt
>  #define ISLT_ at 1@2(X, Y, ms)	(* (@1 *) (X) @3 * (@1 *) (Y))
>  
> 
> 
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-- 
Sjoerd Mullender

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