Enhancements to the DECIMAL extension:

(1) If the argument to decimal(X) is a floating point value (or an 8-byte blob),
the floating point value is expanded into its exact decimal representation.
(2) Function decimal_sci(X) works the same except it returns the result in
scientific notation.
(3) New function decimal_pow2(N) returns the full decimal expansion of the N-th
integer power of 2.

FossilOrigin-Name: 8baf8c10aecb261751f2b154356ab224b79d07230929ec9f123791278e601bba

1 files changed, 214 insertions, 67 deletions

diff --git a/ext/misc/decimal.c b/ext/misc/decimal.c
index 865f3ce24..6c080c200 100644
--- a/ext/misc/decimal.c
+++ b/ext/misc/decimal.c
@@ -292,22 +292,6 @@ static void decimal_result_sci(sqlite3_context *pCtx, Decimal *p){
 }
 
 /*
-** SQL Function:   decimal(X)
-**
-** Convert input X into decimal and then back into text
-*/
-static void decimalFunc(
-  sqlite3_context *context,
-  int argc,
-  sqlite3_value **argv
-){
-  Decimal *p = decimal_new(context, argv[0], 0, 0);
-  UNUSED_PARAMETER(argc);
-  decimal_result(context, p);
-  decimal_free(p);
-}
-
-/*
 ** Compare to Decimal objects.  Return negative, 0, or positive if the
 ** first object is less than, equal to, or greater than the second.
 **
@@ -399,7 +383,7 @@ static void decimal_expand(Decimal *p, int nDigit, int nFrac){
 }
 
 /*
-** Add the value pB into pA.
+** Add the value pB into pA.   A := A + B.
 **
 ** Both pA and pB might become denormalized by this routine.
 */
@@ -469,6 +453,200 @@ static void decimal_add(Decimal *pA, Decimal *pB){
 }
 
 /*
+** 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 = decimal_new(0, 0, 3, (unsigned char*)"1.0");
+  if( pA==0 || pA->oom ) goto pow2_fault;
+  if( N==0 ) return pA;
+  if( N>0 ){
+    pX = decimal_new(0, 0, 3, (unsigned char*)"2.0");
+  }else{
+    N = -N;
+    pX = decimal_new(0, 0, 3, (unsigned char*)"0.5");
+  }
+  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 = decimal_new(0, 0, (int)strlen(zNum), (unsigned char*)zNum);
+  pX = decimalPow2(e);
+  decimalMul(pA, pX);
+  decimal_free(pX);
+  return pA;
+}
+
+/*
+** SQL Function:   decimal(X)
+**
+** Convert input X into decimal and then back into text.
+**
+** If X is originally a float, then a full decoding of that floating
+** point value is done.  Or if X is an 8-byte blob, it is interpreted
+** as a float and similarly expanded.
+*/
+static void decimalFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  Decimal *p = 0;
+  UNUSED_PARAMETER(argc);
+  switch( sqlite3_value_type(argv[0]) ){
+    case SQLITE_TEXT:
+    case SQLITE_INTEGER: {
+      p = decimal_new(context, argv[0], 0, 0);
+      break;
+    }
+
+    case SQLITE_FLOAT: {
+      p = decimalFromDouble(sqlite3_value_double(argv[0]));
+      break;
+    }
+
+    case SQLITE_BLOB: {
+      const unsigned char *x;
+      unsigned int i;
+      sqlite3_uint64 v = 0;
+      double r;
+
+      if( sqlite3_value_bytes(argv[0])!=sizeof(r) ) break;
+      x = sqlite3_value_blob(argv[0]);
+      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;
+    }
+  }
+  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(
@@ -592,11 +770,6 @@ static void decimalSumFinalize(sqlite3_context *context){
 ** SQL Function:   decimal_mul(X, Y)
 **
 ** Return the product of X and Y.
-**
-** 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 decimalMulFunc(
   sqlite3_context *context,
@@ -605,67 +778,39 @@ static void decimalMulFunc(
 ){
   Decimal *pA = decimal_new(context, argv[0], 0, 0);
   Decimal *pB = decimal_new(context, argv[1], 0, 0);
-  signed char *acc = 0;
-  int i, j, k;
-  int minFrac;
   UNUSED_PARAMETER(argc);
   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 ){
-    sqlite3_result_error_nomem(context);
+  decimalMul(pA, pB);
+  if( pA->oom ){
     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--;
-  }
   decimal_result(context, pA);
 
 mul_end:
-  sqlite3_free(acc);
   decimal_free(pA);
   decimal_free(pB);
 }
 
 /*
-** SQL Function:   decimal_sci(X)
+** SQL Function:   decimal_pow2(N)
 **
-** Convert decimal number X into scientific notation ("+N.NNNe+NN").
+** Return the N-th power of 2.  N must be an integer.
 */
-static void decimalSciFunc(
+static void decimalPow2Func(
   sqlite3_context *context,
   int argc,
   sqlite3_value **argv
 ){
-  Decimal *pA = decimal_new(context, argv[0], 0, 0);
   UNUSED_PARAMETER(argc);
-  decimal_result_sci(context, pA);
-  decimal_free(pA);
+  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
@@ -680,14 +825,16 @@ int sqlite3_decimal_init(
   static const struct {
     const char *zFuncName;
     int nArg;
+    int iArg;
     void (*xFunc)(sqlite3_context*,int,sqlite3_value**);
   } aFunc[] = {
-    { "decimal",       1,   decimalFunc        },
-    { "decimal_cmp",   2,   decimalCmpFunc     },
-    { "decimal_add",   2,   decimalAddFunc     },
-    { "decimal_sub",   2,   decimalSubFunc     },
-    { "decimal_mul",   2,   decimalMulFunc     },
-    { "decimal_sci",   1,   decimalSciFunc     },
+    { "decimal",       1, 0,  decimalFunc        },
+    { "decimal_cmp",   2, 0,  decimalCmpFunc     },
+    { "decimal_add",   2, 0,  decimalAddFunc     },
+    { "decimal_sub",   2, 0,  decimalSubFunc     },
+    { "decimal_mul",   2, 0,  decimalMulFunc     },
+    { "decimal_sci",   1, 1,  decimalFunc        },
+    { "decimal_pow2",  1, 0,  decimalPow2Func    },
   };
   unsigned int i;
   (void)pzErrMsg;  /* Unused parameter */
@@ -697,7 +844,7 @@ int sqlite3_decimal_init(
   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,
-                   0, aFunc[i].xFunc, 0, 0);
+                   aFunc[i].iArg ? db : 0, aFunc[i].xFunc, 0, 0);
   }
   if( rc==SQLITE_OK ){
     rc = sqlite3_create_window_function(db, "decimal_sum", 1,