Adding upstream version 3.45.1.upstream/3.45.1

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 884 insertions, 0 deletions

diff --git a/ext/misc/decimal.c b/ext/misc/decimal.c
new file mode 100644
index 0000000..9365ae6
--- /dev/null
+++ b/ext/misc/decimal.c
@@ -0,0 +1,884 @@
+/*
+** 2020-06-22
+**
+** The author disclaims copyright to this source code.  In place of
+** a legal notice, here is a blessing:
+**
+**    May you do good and not evil.
+**    May you find forgiveness for yourself and forgive others.
+**    May you share freely, never taking more than you give.
+**
+******************************************************************************
+**
+** Routines to implement arbitrary-precision decimal math.
+**
+** The focus here is on simplicity and correctness, not performance.
+*/
+#include "sqlite3ext.h"
+SQLITE_EXTENSION_INIT1
+#include <assert.h>
+#include <string.h>
+#include <ctype.h>
+#include <stdlib.h>
+
+/* Mark a function parameter as unused, to suppress nuisance compiler
+** warnings. */
+#ifndef UNUSED_PARAMETER
+# define UNUSED_PARAMETER(X)  (void)(X)
+#endif
+
+
+/* A decimal object */
+typedef struct Decimal Decimal;
+struct Decimal {
+  char sign;        /* 0 for positive, 1 for negative */
+  char oom;         /* True if an OOM is encountered */
+  char isNull;      /* True if holds a NULL rather than a number */
+  char isInit;      /* True upon initialization */
+  int nDigit;       /* Total number of digits */
+  int nFrac;        /* Number of digits to the right of the decimal point */
+  signed char *a;   /* Array of digits.  Most significant first. */
+};
+
+/*
+** Release memory held by a Decimal, but do not free the object itself.
+*/
+static void decimal_clear(Decimal *p){
+  sqlite3_free(p->a);
+}
+
+/*
+** Destroy a Decimal object
+*/
+static void decimal_free(Decimal *p){
+  if( p ){
+    decimal_clear(p);
+    sqlite3_free(p);
+  }
+}
+
+/*
+** Allocate a new Decimal object initialized to the text in zIn[].
+** Return NULL if any kind of error occurs.
+*/
+static Decimal *decimalNewFromText(const char *zIn, int n){
+  Decimal *p = 0;
+  int i;
+  int iExp = 0;
+
+  p = sqlite3_malloc( sizeof(*p) );
+  if( p==0 ) goto new_from_text_failed;
+  p->sign = 0;
+  p->oom = 0;
+  p->isInit = 1;
+  p->isNull = 0;
+  p->nDigit = 0;
+  p->nFrac = 0;
+  p->a = sqlite3_malloc64( n+1 );
+  if( p->a==0 ) goto new_from_text_failed;
+  for(i=0; isspace(zIn[i]); i++){}
+  if( zIn[i]=='-' ){
+    p->sign = 1;
+    i++;
+  }else if( zIn[i]=='+' ){
+    i++;
+  }
+  while( i<n && zIn[i]=='0' ) i++;
+  while( i<n ){
+    char c = zIn[i];
+    if( c>='0' && c<='9' ){
+      p->a[p->nDigit++] = c - '0';
+    }else if( c=='.' ){
+      p->nFrac = p->nDigit + 1;
+    }else if( c=='e' || c=='E' ){
+      int j = i+1;
+      int neg = 0;
+      if( j>=n ) break;
+      if( zIn[j]=='-' ){
+        neg = 1;
+        j++;
+      }else if( zIn[j]=='+' ){
+        j++;
+      }
+      while( j<n && iExp<1000000 ){
+        if( zIn[j]>='0' && zIn[j]<='9' ){
+          iExp = iExp*10 + zIn[j] - '0';
+        }
+        j++;
+      }
+      if( neg ) iExp = -iExp;
+      break;
+    }
+    i++;
+  }
+  if( p->nFrac ){
+    p->nFrac = p->nDigit - (p->nFrac - 1);
+  }
+  if( iExp>0 ){
+    if( p->nFrac>0 ){
+      if( iExp<=p->nFrac ){
+        p->nFrac -= iExp;
+        iExp = 0;
+      }else{
+        iExp -= p->nFrac;
+        p->nFrac = 0;
+      }
+    }
+    if( iExp>0 ){   
+      p->a = sqlite3_realloc64(p->a, p->nDigit + iExp + 1 );
+      if( p->a==0 ) goto new_from_text_failed;
+      memset(p->a+p->nDigit, 0, iExp);
+      p->nDigit += iExp;
+    }
+  }else if( iExp<0 ){
+    int nExtra;
+    iExp = -iExp;
+    nExtra = p->nDigit - p->nFrac - 1;
+    if( nExtra ){
+      if( nExtra>=iExp ){
+        p->nFrac += iExp;
+        iExp  = 0;
+      }else{
+        iExp -= nExtra;
+        p->nFrac = p->nDigit - 1;
+      }
+    }
+    if( iExp>0 ){
+      p->a = sqlite3_realloc64(p->a, p->nDigit + iExp + 1 );
+      if( p->a==0 ) goto new_from_text_failed;
+      memmove(p->a+iExp, p->a, p->nDigit);
+      memset(p->a, 0, iExp);
+      p->nDigit += iExp;
+      p->nFrac += iExp;
+    }
+  }
+  return p;
+
+new_from_text_failed:
+  if( p ){
+    if( p->a ) sqlite3_free(p->a);
+    sqlite3_free(p);
+  }
+  return 0;
+}
+
+/* Forward reference */
+static Decimal *decimalFromDouble(double);
+
+/*
+** Allocate a new Decimal object from an sqlite3_value.  Return a pointer
+** to the new object, or NULL if there is an error.  If the pCtx argument
+** is not NULL, then errors are reported on it as well.
+**
+** If the pIn argument is SQLITE_TEXT or SQLITE_INTEGER, it is converted
+** directly into a Decimal.  For SQLITE_FLOAT or for SQLITE_BLOB of length
+** 8 bytes, the resulting double value is expanded into its decimal equivalent.
+** If pIn is NULL or if it is a BLOB that is not exactly 8 bytes in length,
+** then NULL is returned.
+*/
+static Decimal *decimal_new(
+  sqlite3_context *pCtx,       /* Report error here, if not null */
+  sqlite3_value *pIn,          /* Construct the decimal object from this */
+  int bTextOnly                /* Always interpret pIn as text if true */
+){
+  Decimal *p = 0;
+  int eType = sqlite3_value_type(pIn);
+  if( bTextOnly && (eType==SQLITE_FLOAT || eType==SQLITE_BLOB) ){
+    eType = SQLITE_TEXT;
+  }
+  switch( eType ){
+    case SQLITE_TEXT:
+    case SQLITE_INTEGER: {
+      const char *zIn = (const char*)sqlite3_value_text(pIn);
+      int n = sqlite3_value_bytes(pIn);
+      p = decimalNewFromText(zIn, n);
+      if( p==0 ) goto new_failed;
+      break;
+    }
+
+    case SQLITE_FLOAT: {
+      p = decimalFromDouble(sqlite3_value_double(pIn));
+      break;
+    }
+
+    case SQLITE_BLOB: {
+      const unsigned char *x;
+      unsigned int i;
+      sqlite3_uint64 v = 0;
+      double r;
+
+      if( sqlite3_value_bytes(pIn)!=sizeof(r) ) break;
+      x = sqlite3_value_blob(pIn);
+      for(i=0; i<sizeof(r); i++){
+        v = (v<<8) | x[i];
+      }
+      memcpy(&r, &v, sizeof(r));
+      p = decimalFromDouble(r);
+      break;
+    }
+
+    case SQLITE_NULL: {
+      break;
+    }
+  }
+  return p;
+
+new_failed:
+  if( pCtx ) sqlite3_result_error_nomem(pCtx);
+  sqlite3_free(p);
+  return 0;
+}
+
+/*
+** Make the given Decimal the result.
+*/
+static void decimal_result(sqlite3_context *pCtx, Decimal *p){
+  char *z;
+  int i, j;
+  int n;
+  if( p==0 || p->oom ){
+    sqlite3_result_error_nomem(pCtx);
+    return;
+  }
+  if( p->isNull ){
+    sqlite3_result_null(pCtx);
+    return;
+  }
+  z = sqlite3_malloc( p->nDigit+4 );
+  if( z==0 ){
+    sqlite3_result_error_nomem(pCtx);
+    return;
+  }
+  i = 0;
+  if( p->nDigit==0 || (p->nDigit==1 && p->a[0]==0) ){
+    p->sign = 0;
+  }
+  if( p->sign ){
+    z[0] = '-';
+    i = 1;
+  }
+  n = p->nDigit - p->nFrac;
+  if( n<=0 ){
+    z[i++] = '0';
+  }
+  j = 0;
+  while( n>1 && p->a[j]==0 ){
+    j++;
+    n--;
+  }
+  while( n>0  ){
+    z[i++] = p->a[j] + '0';
+    j++;
+    n--;
+  }
+  if( p->nFrac ){
+    z[i++] = '.';
+    do{
+      z[i++] = p->a[j] + '0';
+      j++;
+    }while( j<p->nDigit );
+  }
+  z[i] = 0;
+  sqlite3_result_text(pCtx, z, i, sqlite3_free);
+}
+
+/*
+** Make the given Decimal the result in an format similar to  '%+#e'.
+** In other words, show exponential notation with leading and trailing
+** zeros omitted.
+*/
+static void decimal_result_sci(sqlite3_context *pCtx, Decimal *p){
+  char *z;       /* The output buffer */
+  int i;         /* Loop counter */
+  int nZero;     /* Number of leading zeros */
+  int nDigit;    /* Number of digits not counting trailing zeros */
+  int nFrac;     /* Digits to the right of the decimal point */
+  int exp;       /* Exponent value */
+  signed char zero;     /* Zero value */
+  signed char *a;       /* Array of digits */
+
+  if( p==0 || p->oom ){
+    sqlite3_result_error_nomem(pCtx);
+    return;
+  }
+  if( p->isNull ){
+    sqlite3_result_null(pCtx);
+    return;
+  }
+  for(nDigit=p->nDigit; nDigit>0 && p->a[nDigit-1]==0; nDigit--){}
+  for(nZero=0; nZero<nDigit && p->a[nZero]==0; nZero++){}
+  nFrac = p->nFrac + (nDigit - p->nDigit);
+  nDigit -= nZero;
+  z = sqlite3_malloc( nDigit+20 );
+  if( z==0 ){
+    sqlite3_result_error_nomem(pCtx);
+    return;
+  }
+  if( nDigit==0 ){
+    zero = 0;
+    a = &zero;
+    nDigit = 1;
+    nFrac = 0;
+  }else{
+    a = &p->a[nZero];
+  }
+  if( p->sign && nDigit>0 ){
+    z[0] = '-';
+  }else{
+    z[0] = '+';
+  }
+  z[1] = a[0]+'0';
+  z[2] = '.';
+  if( nDigit==1 ){
+    z[3] = '0';
+    i = 4;
+  }else{
+    for(i=1; i<nDigit; i++){
+      z[2+i] = a[i]+'0';
+    }
+    i = nDigit+2;
+  }
+  exp = nDigit - nFrac - 1;
+  sqlite3_snprintf(nDigit+20-i, &z[i], "e%+03d", exp);
+  sqlite3_result_text(pCtx, z, -1, sqlite3_free);
+}
+
+/*
+** Compare to Decimal objects.  Return negative, 0, or positive if the
+** first object is less than, equal to, or greater than the second.
+**
+** Preconditions for this routine:
+**
+**    pA!=0
+**    pA->isNull==0
+**    pB!=0
+**    pB->isNull==0
+*/
+static int decimal_cmp(const Decimal *pA, const Decimal *pB){
+  int nASig, nBSig, rc, n;
+  if( pA->sign!=pB->sign ){
+    return pA->sign ? -1 : +1;
+  }
+  if( pA->sign ){
+    const Decimal *pTemp = pA;
+    pA = pB;
+    pB = pTemp;
+  }
+  nASig = pA->nDigit - pA->nFrac;
+  nBSig = pB->nDigit - pB->nFrac;
+  if( nASig!=nBSig ){
+    return nASig - nBSig;
+  }
+  n = pA->nDigit;
+  if( n>pB->nDigit ) n = pB->nDigit;
+  rc = memcmp(pA->a, pB->a, n);
+  if( rc==0 ){
+    rc = pA->nDigit - pB->nDigit;
+  }
+  return rc;
+}
+
+/*
+** SQL Function:   decimal_cmp(X, Y)
+**
+** Return negative, zero, or positive if X is less then, equal to, or
+** greater than Y.
+*/
+static void decimalCmpFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  Decimal *pA = 0, *pB = 0;
+  int rc;
+
+  UNUSED_PARAMETER(argc);
+  pA = decimal_new(context, argv[0], 1);
+  if( pA==0 || pA->isNull ) goto cmp_done;
+  pB = decimal_new(context, argv[1], 1);
+  if( pB==0 || pB->isNull ) goto cmp_done;
+  rc = decimal_cmp(pA, pB);
+  if( rc<0 ) rc = -1;
+  else if( rc>0 ) rc = +1;
+  sqlite3_result_int(context, rc);
+cmp_done:
+  decimal_free(pA);
+  decimal_free(pB);
+}
+
+/*
+** Expand the Decimal so that it has a least nDigit digits and nFrac
+** digits to the right of the decimal point.
+*/
+static void decimal_expand(Decimal *p, int nDigit, int nFrac){
+  int nAddSig;
+  int nAddFrac;
+  if( p==0 ) return;
+  nAddFrac = nFrac - p->nFrac;
+  nAddSig = (nDigit - p->nDigit) - nAddFrac;
+  if( nAddFrac==0 && nAddSig==0 ) return;
+  p->a = sqlite3_realloc64(p->a, nDigit+1);
+  if( p->a==0 ){
+    p->oom = 1;
+    return;
+  }
+  if( nAddSig ){
+    memmove(p->a+nAddSig, p->a, p->nDigit);
+    memset(p->a, 0, nAddSig);
+    p->nDigit += nAddSig;
+  }
+  if( nAddFrac ){
+    memset(p->a+p->nDigit, 0, nAddFrac);
+    p->nDigit += nAddFrac;
+    p->nFrac += nAddFrac;
+  }
+}
+
+/*
+** Add the value pB into pA.   A := A + B.
+**
+** Both pA and pB might become denormalized by this routine.
+*/
+static void decimal_add(Decimal *pA, Decimal *pB){
+  int nSig, nFrac, nDigit;
+  int i, rc;
+  if( pA==0 ){
+    return;
+  }
+  if( pA->oom || pB==0 || pB->oom ){
+    pA->oom = 1;
+    return;
+  }
+  if( pA->isNull || pB->isNull ){
+    pA->isNull = 1;
+    return;
+  }
+  nSig = pA->nDigit - pA->nFrac;
+  if( nSig && pA->a[0]==0 ) nSig--;
+  if( nSig<pB->nDigit-pB->nFrac ){
+    nSig = pB->nDigit - pB->nFrac;
+  }
+  nFrac = pA->nFrac;
+  if( nFrac<pB->nFrac ) nFrac = pB->nFrac;
+  nDigit = nSig + nFrac + 1;
+  decimal_expand(pA, nDigit, nFrac);
+  decimal_expand(pB, nDigit, nFrac);
+  if( pA->oom || pB->oom ){
+    pA->oom = 1;
+  }else{
+    if( pA->sign==pB->sign ){
+      int carry = 0;
+      for(i=nDigit-1; i>=0; i--){
+        int x = pA->a[i] + pB->a[i] + carry;
+        if( x>=10 ){
+          carry = 1;
+          pA->a[i] = x - 10;
+        }else{
+          carry = 0;
+          pA->a[i] = x;
+        }
+      }
+    }else{
+      signed char *aA, *aB;
+      int borrow = 0;
+      rc = memcmp(pA->a, pB->a, nDigit);
+      if( rc<0 ){
+        aA = pB->a;
+        aB = pA->a;
+        pA->sign = !pA->sign;
+      }else{
+        aA = pA->a;
+        aB = pB->a;
+      }
+      for(i=nDigit-1; i>=0; i--){
+        int x = aA[i] - aB[i] - borrow;
+        if( x<0 ){
+          pA->a[i] = x+10;
+          borrow = 1;
+        }else{
+          pA->a[i] = x;
+          borrow = 0;
+        }
+      }
+    }
+  }
+}
+
+/*
+** Multiply A by B.   A := A * B
+**
+** All significant digits after the decimal point are retained.
+** Trailing zeros after the decimal point are omitted as long as
+** the number of digits after the decimal point is no less than
+** either the number of digits in either input.
+*/
+static void decimalMul(Decimal *pA, Decimal *pB){
+  signed char *acc = 0;
+  int i, j, k;
+  int minFrac;
+
+  if( pA==0 || pA->oom || pA->isNull
+   || pB==0 || pB->oom || pB->isNull 
+  ){
+    goto mul_end;
+  }
+  acc = sqlite3_malloc64( pA->nDigit + pB->nDigit + 2 );
+  if( acc==0 ){
+    pA->oom = 1;
+    goto mul_end;
+  }
+  memset(acc, 0, pA->nDigit + pB->nDigit + 2);
+  minFrac = pA->nFrac;
+  if( pB->nFrac<minFrac ) minFrac = pB->nFrac;
+  for(i=pA->nDigit-1; i>=0; i--){
+    signed char f = pA->a[i];
+    int carry = 0, x;
+    for(j=pB->nDigit-1, k=i+j+3; j>=0; j--, k--){
+      x = acc[k] + f*pB->a[j] + carry;
+      acc[k] = x%10;
+      carry = x/10;
+    }
+    x = acc[k] + carry;
+    acc[k] = x%10;
+    acc[k-1] += x/10;
+  }
+  sqlite3_free(pA->a);
+  pA->a = acc;
+  acc = 0;
+  pA->nDigit += pB->nDigit + 2;
+  pA->nFrac += pB->nFrac;
+  pA->sign ^= pB->sign;
+  while( pA->nFrac>minFrac && pA->a[pA->nDigit-1]==0 ){
+    pA->nFrac--;
+    pA->nDigit--;
+  }
+
+mul_end:
+  sqlite3_free(acc);
+}
+
+/*
+** Create a new Decimal object that contains an integer power of 2.
+*/
+static Decimal *decimalPow2(int N){
+  Decimal *pA = 0;      /* The result to be returned */
+  Decimal *pX = 0;      /* Multiplier */
+  if( N<-20000 || N>20000 ) goto pow2_fault;
+  pA = decimalNewFromText("1.0", 3);
+  if( pA==0 || pA->oom ) goto pow2_fault;
+  if( N==0 ) return pA;
+  if( N>0 ){
+    pX = decimalNewFromText("2.0", 3);
+  }else{
+    N = -N;
+    pX = decimalNewFromText("0.5", 3);
+  }
+  if( pX==0 || pX->oom ) goto pow2_fault;
+  while( 1 /* Exit by break */ ){
+    if( N & 1 ){
+      decimalMul(pA, pX);
+      if( pA->oom ) goto pow2_fault;
+    }
+    N >>= 1;
+    if( N==0 ) break;
+    decimalMul(pX, pX);
+  }
+  decimal_free(pX);
+  return pA;
+
+pow2_fault:
+  decimal_free(pA);
+  decimal_free(pX);
+  return 0;
+}
+
+/*
+** Use an IEEE754 binary64 ("double") to generate a new Decimal object.
+*/
+static Decimal *decimalFromDouble(double r){
+  sqlite3_int64 m, a;
+  int e;
+  int isNeg;
+  Decimal *pA;
+  Decimal *pX;
+  char zNum[100];
+  if( r<0.0 ){
+    isNeg = 1;
+    r = -r;
+  }else{
+    isNeg = 0;
+  }
+  memcpy(&a,&r,sizeof(a));
+  if( a==0 ){
+    e = 0;
+    m = 0;
+  }else{
+    e = a>>52;
+    m = a & ((((sqlite3_int64)1)<<52)-1);
+    if( e==0 ){
+      m <<= 1;
+    }else{
+      m |= ((sqlite3_int64)1)<<52;
+    }
+    while( e<1075 && m>0 && (m&1)==0 ){
+      m >>= 1;
+      e++;
+    }
+    if( isNeg ) m = -m;
+    e = e - 1075;
+    if( e>971 ){
+      return 0;  /* A NaN or an Infinity */
+    }
+  }
+
+  /* At this point m is the integer significand and e is the exponent */
+  sqlite3_snprintf(sizeof(zNum), zNum, "%lld", m);
+  pA = decimalNewFromText(zNum, (int)strlen(zNum));
+  pX = decimalPow2(e);
+  decimalMul(pA, pX);
+  decimal_free(pX);
+  return pA;
+}
+
+/*
+** SQL Function:   decimal(X)
+** OR:             decimal_exp(X)
+**
+** Convert input X into decimal and then back into text.
+**
+** If X is originally a float, then a full decimal expansion of that floating
+** point value is done.  Or if X is an 8-byte blob, it is interpreted
+** as a float and similarly expanded.
+**
+** The decimal_exp(X) function returns the result in exponential notation.
+** decimal(X) returns a complete decimal, without the e+NNN at the end.
+*/
+static void decimalFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  Decimal *p =  decimal_new(context, argv[0], 0);
+  UNUSED_PARAMETER(argc);
+  if( p ){
+    if( sqlite3_user_data(context)!=0 ){
+      decimal_result_sci(context, p);
+    }else{
+      decimal_result(context, p);
+    }
+    decimal_free(p);
+  }
+}
+
+/*
+** Compare text in decimal order.
+*/
+static int decimalCollFunc(
+  void *notUsed,
+  int nKey1, const void *pKey1,
+  int nKey2, const void *pKey2
+){
+  const unsigned char *zA = (const unsigned char*)pKey1;
+  const unsigned char *zB = (const unsigned char*)pKey2;
+  Decimal *pA = decimalNewFromText((const char*)zA, nKey1);
+  Decimal *pB = decimalNewFromText((const char*)zB, nKey2);
+  int rc;
+  UNUSED_PARAMETER(notUsed);
+  if( pA==0 || pB==0 ){
+    rc = 0;
+  }else{
+    rc = decimal_cmp(pA, pB);
+  }
+  decimal_free(pA);
+  decimal_free(pB);
+  return rc;
+}
+
+
+/*
+** SQL Function:   decimal_add(X, Y)
+**                 decimal_sub(X, Y)
+**
+** Return the sum or difference of X and Y.
+*/
+static void decimalAddFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  Decimal *pA = decimal_new(context, argv[0], 1);
+  Decimal *pB = decimal_new(context, argv[1], 1);
+  UNUSED_PARAMETER(argc);
+  decimal_add(pA, pB);
+  decimal_result(context, pA);
+  decimal_free(pA);
+  decimal_free(pB);
+}
+static void decimalSubFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  Decimal *pA = decimal_new(context, argv[0], 1);
+  Decimal *pB = decimal_new(context, argv[1], 1);
+  UNUSED_PARAMETER(argc);
+  if( pB ){
+    pB->sign = !pB->sign;
+    decimal_add(pA, pB);
+    decimal_result(context, pA);
+  }
+  decimal_free(pA);
+  decimal_free(pB);
+}
+
+/* Aggregate funcion:   decimal_sum(X)
+**
+** Works like sum() except that it uses decimal arithmetic for unlimited
+** precision.
+*/
+static void decimalSumStep(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  Decimal *p;
+  Decimal *pArg;
+  UNUSED_PARAMETER(argc);
+  p = sqlite3_aggregate_context(context, sizeof(*p));
+  if( p==0 ) return;
+  if( !p->isInit ){
+    p->isInit = 1;
+    p->a = sqlite3_malloc(2);
+    if( p->a==0 ){
+      p->oom = 1;
+    }else{
+      p->a[0] = 0;
+    }
+    p->nDigit = 1;
+    p->nFrac = 0;
+  }
+  if( sqlite3_value_type(argv[0])==SQLITE_NULL ) return;
+  pArg = decimal_new(context, argv[0], 1);
+  decimal_add(p, pArg);
+  decimal_free(pArg);
+}
+static void decimalSumInverse(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  Decimal *p;
+  Decimal *pArg;
+  UNUSED_PARAMETER(argc);
+  p = sqlite3_aggregate_context(context, sizeof(*p));
+  if( p==0 ) return;
+  if( sqlite3_value_type(argv[0])==SQLITE_NULL ) return;
+  pArg = decimal_new(context, argv[0], 1);
+  if( pArg ) pArg->sign = !pArg->sign;
+  decimal_add(p, pArg);
+  decimal_free(pArg);
+}
+static void decimalSumValue(sqlite3_context *context){
+  Decimal *p = sqlite3_aggregate_context(context, 0);
+  if( p==0 ) return;
+  decimal_result(context, p);
+}
+static void decimalSumFinalize(sqlite3_context *context){
+  Decimal *p = sqlite3_aggregate_context(context, 0);
+  if( p==0 ) return;
+  decimal_result(context, p);
+  decimal_clear(p);
+}
+
+/*
+** SQL Function:   decimal_mul(X, Y)
+**
+** Return the product of X and Y.
+*/
+static void decimalMulFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  Decimal *pA = decimal_new(context, argv[0], 1);
+  Decimal *pB = decimal_new(context, argv[1], 1);
+  UNUSED_PARAMETER(argc);
+  if( pA==0 || pA->oom || pA->isNull
+   || pB==0 || pB->oom || pB->isNull 
+  ){
+    goto mul_end;
+  }
+  decimalMul(pA, pB);
+  if( pA->oom ){
+    goto mul_end;
+  }
+  decimal_result(context, pA);
+
+mul_end:
+  decimal_free(pA);
+  decimal_free(pB);
+}
+
+/*
+** SQL Function:   decimal_pow2(N)
+**
+** Return the N-th power of 2.  N must be an integer.
+*/
+static void decimalPow2Func(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  UNUSED_PARAMETER(argc);
+  if( sqlite3_value_type(argv[0])==SQLITE_INTEGER ){
+    Decimal *pA = decimalPow2(sqlite3_value_int(argv[0]));
+    decimal_result_sci(context, pA);
+    decimal_free(pA);
+  }
+}
+
+#ifdef _WIN32
+__declspec(dllexport)
+#endif
+int sqlite3_decimal_init(
+  sqlite3 *db, 
+  char **pzErrMsg, 
+  const sqlite3_api_routines *pApi
+){
+  int rc = SQLITE_OK;
+  static const struct {
+    const char *zFuncName;
+    int nArg;
+    int iArg;
+    void (*xFunc)(sqlite3_context*,int,sqlite3_value**);
+  } aFunc[] = {
+    { "decimal",       1, 0,  decimalFunc        },
+    { "decimal_exp",   1, 1,  decimalFunc        },
+    { "decimal_cmp",   2, 0,  decimalCmpFunc     },
+    { "decimal_add",   2, 0,  decimalAddFunc     },
+    { "decimal_sub",   2, 0,  decimalSubFunc     },
+    { "decimal_mul",   2, 0,  decimalMulFunc     },
+    { "decimal_pow2",  1, 0,  decimalPow2Func    },
+  };
+  unsigned int i;
+  (void)pzErrMsg;  /* Unused parameter */
+
+  SQLITE_EXTENSION_INIT2(pApi);
+
+  for(i=0; i<(int)(sizeof(aFunc)/sizeof(aFunc[0])) && rc==SQLITE_OK; i++){
+    rc = sqlite3_create_function(db, aFunc[i].zFuncName, aFunc[i].nArg,
+                   SQLITE_UTF8|SQLITE_INNOCUOUS|SQLITE_DETERMINISTIC,
+                   aFunc[i].iArg ? db : 0, aFunc[i].xFunc, 0, 0);
+  }
+  if( rc==SQLITE_OK ){
+    rc = sqlite3_create_window_function(db, "decimal_sum", 1,
+                   SQLITE_UTF8|SQLITE_INNOCUOUS|SQLITE_DETERMINISTIC, 0,
+                   decimalSumStep, decimalSumFinalize,
+                   decimalSumValue, decimalSumInverse, 0);
+  }
+  if( rc==SQLITE_OK ){
+    rc = sqlite3_create_collation(db, "decimal", SQLITE_UTF8,
+                                  0, decimalCollFunc);
+  }
+  return rc;
+}