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libsql/libsql-sqlite3/ext/misc/decimal.c
ad hoc bf899d0b9a
restructure repository
2023-10-16 13:58:16 +02:00

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/*
** 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;
}
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