-C Were\swe\sto\schoose\sto\sintegrate\sthe\scarray()\stable-valued\sfunction\sinto\sthe\namalgamation,\sthat\sintegration\smight\slook\ssomething\slike\sthis.
-D 2025-10-08T15:32:55.195
+C This\sis\show\sthe\spercentile()\sfamily\sof\sfunctions\smight\sbe\sintegrated\sinto\nthe\samalgamation,\sshould\swe\select\sto\sdo\ssuch\sa\sthing.
+D 2025-10-08T16:29:14.772
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U drh
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# Remove this line to create a well-formed Fossil manifest.
sqlite3_result_int(context, x<0.0 ? -1 : x>0.0 ? +1 : 0);
}
+/***********************************************************************
+** This section implements the percentile(Y,P) SQL function and similar.
+** Requirements:
+**
+** (1) The percentile(Y,P) function is an aggregate function taking
+** exactly two arguments.
+**
+** (2) If the P argument to percentile(Y,P) is not the same for every
+** row in the aggregate then an error is thrown. The word "same"
+** in the previous sentence means that the value differ by less
+** than 0.001.
+**
+** (3) If the P argument to percentile(Y,P) evaluates to anything other
+** than a number in the range of 0.0 to 100.0 inclusive then an
+** error is thrown.
+**
+** (4) If any Y argument to percentile(Y,P) evaluates to a value that
+** is not NULL and is not numeric then an error is thrown.
+**
+** (5) If any Y argument to percentile(Y,P) evaluates to plus or minus
+** infinity then an error is thrown. (SQLite always interprets NaN
+** values as NULL.)
+**
+** (6) Both Y and P in percentile(Y,P) can be arbitrary expressions,
+** including CASE WHEN expressions.
+**
+** (7) The percentile(Y,P) aggregate is able to handle inputs of at least
+** one million (1,000,000) rows.
+**
+** (8) If there are no non-NULL values for Y, then percentile(Y,P)
+** returns NULL.
+**
+** (9) If there is exactly one non-NULL value for Y, the percentile(Y,P)
+** returns the one Y value.
+**
+** (10) If there N non-NULL values of Y where N is two or more and
+** the Y values are ordered from least to greatest and a graph is
+** drawn from 0 to N-1 such that the height of the graph at J is
+** the J-th Y value and such that straight lines are drawn between
+** adjacent Y values, then the percentile(Y,P) function returns
+** the height of the graph at P*(N-1)/100.
+**
+** (11) The percentile(Y,P) function always returns either a floating
+** point number or NULL.
+**
+** (12) The percentile(Y,P) is implemented as a single C99 source-code
+** file that compiles into a shared-library or DLL that can be loaded
+** into SQLite using the sqlite3_load_extension() interface.
+**
+** (13) A separate median(Y) function is the equivalent percentile(Y,50).
+**
+** (14) A separate percentile_cont(Y,P) function is equivalent to
+** percentile(Y,P/100.0). In other words, the fraction value in
+** the second argument is in the range of 0 to 1 instead of 0 to 100.
+**
+** (15) A separate percentile_disc(Y,P) function is like
+** percentile_cont(Y,P) except that instead of returning the weighted
+** average of the nearest two input values, it returns the next lower
+** value. So the percentile_disc(Y,P) will always return a value
+** that was one of the inputs.
+**
+** (16) All of median(), percentile(Y,P), percentile_cont(Y,P) and
+** percentile_disc(Y,P) can be used as window functions.
+**
+** Differences from standard SQL:
+**
+** * The percentile_cont(X,P) function is equivalent to the following in
+** standard SQL:
+**
+** (percentile_cont(P) WITHIN GROUP (ORDER BY X))
+**
+** The SQLite syntax is much more compact. The standard SQL syntax
+** is also supported if SQLite is compiled with the
+** -DSQLITE_ENABLE_ORDERED_SET_AGGREGATES option.
+**
+** * No median(X) function exists in the SQL standard. App developers
+** are expected to write "percentile_cont(0.5)WITHIN GROUP(ORDER BY X)".
+**
+** * No percentile(Y,P) function exists in the SQL standard. Instead of
+** percential(Y,P), developers must write this:
+** "percentile_cont(P/100.0) WITHIN GROUP (ORDER BY Y)". Note that
+** the fraction parameter to percentile() goes from 0 to 100 whereas
+** the fraction parameter in SQL standard percentile_cont() goes from
+** 0 to 1.
+**
+** Implementation notes as of 2024-08-31:
+**
+** * The regular aggregate-function versions of these routines work
+** by accumulating all values in an array of doubles, then sorting
+** that array using quicksort before computing the answer. Thus
+** the runtime is O(NlogN) where N is the number of rows of input.
+**
+** * For the window-function versions of these routines, the array of
+** inputs is sorted as soon as the first value is computed. Thereafter,
+** the array is kept in sorted order using an insert-sort. This
+** results in O(N*K) performance where K is the size of the window.
+** One can imagine alternative implementations that give O(N*logN*logK)
+** performance, but they require more complex logic and data structures.
+** The developers have elected to keep the asymptotically slower
+** algorithm for now, for simplicity, under the theory that window
+** functions are seldom used and when they are, the window size K is
+** often small. The developers might revisit that decision later,
+** should the need arise.
+*/
+
+/* The following object is the group context for a single percentile()
+** aggregate. Remember all input Y values until the very end.
+** Those values are accumulated in the Percentile.a[] array.
+*/
+typedef struct Percentile Percentile;
+struct Percentile {
+ unsigned nAlloc; /* Number of slots allocated for a[] */
+ unsigned nUsed; /* Number of slots actually used in a[] */
+ char bSorted; /* True if a[] is already in sorted order */
+ char bKeepSorted; /* True if advantageous to keep a[] sorted */
+ char bPctValid; /* True if rPct is valid */
+ double rPct; /* Fraction. 0.0 to 1.0 */
+ double *a; /* Array of Y values */
+};
+
+/*
+** Return TRUE if the input floating-point number is an infinity.
+*/
+static int percentIsInfinity(double r){
+ sqlite3_uint64 u;
+ assert( sizeof(u)==sizeof(r) );
+ memcpy(&u, &r, sizeof(u));
+ return ((u>>52)&0x7ff)==0x7ff;
+}
+
+/*
+** Return TRUE if two doubles differ by 0.001 or less.
+*/
+static int percentSameValue(double a, double b){
+ a -= b;
+ return a>=-0.001 && a<=0.001;
+}
+
+/*
+** Search p (which must have p->bSorted) looking for an entry with
+** value y. Return the index of that entry.
+**
+** If bExact is true, return -1 if the entry is not found.
+**
+** If bExact is false, return the index at which a new entry with
+** value y should be insert in order to keep the values in sorted
+** order. The smallest return value in this case will be 0, and
+** the largest return value will be p->nUsed.
+*/
+static int percentBinarySearch(Percentile *p, double y, int bExact){
+ int iFirst = 0; /* First element of search range */
+ int iLast = p->nUsed - 1; /* Last element of search range */
+ while( iLast>=iFirst ){
+ int iMid = (iFirst+iLast)/2;
+ double x = p->a[iMid];
+ if( x<y ){
+ iFirst = iMid + 1;
+ }else if( x>y ){
+ iLast = iMid - 1;
+ }else{
+ return iMid;
+ }
+ }
+ if( bExact ) return -1;
+ return iFirst;
+}
+
+/*
+** Generate an error for a percentile function.
+**
+** The error format string must have exactly one occurrence of "%%s()"
+** (with two '%' characters). That substring will be replaced by the name
+** of the function.
+*/
+static void percentError(sqlite3_context *pCtx, const char *zFormat, ...){
+ char *zMsg1;
+ char *zMsg2;
+ va_list ap;
+
+ va_start(ap, zFormat);
+ zMsg1 = sqlite3_vmprintf(zFormat, ap);
+ va_end(ap);
+ zMsg2 = zMsg1 ? sqlite3_mprintf(zMsg1, sqlite3VdbeFuncName(pCtx)) : 0;
+ sqlite3_result_error(pCtx, zMsg2, -1);
+ sqlite3_free(zMsg1);
+ sqlite3_free(zMsg2);
+}
+
+/*
+** The "step" function for percentile(Y,P) is called once for each
+** input row.
+*/
+static void percentStep(sqlite3_context *pCtx, int argc, sqlite3_value **argv){
+ Percentile *p;
+ double rPct;
+ int eType;
+ double y;
+ assert( argc==2 || argc==1 );
+
+ if( argc==1 ){
+ /* Requirement 13: median(Y) is the same as percentile(Y,50). */
+ rPct = 0.5;
+ }else{
+ /* P must be a number between 0 and 100 for percentile() or between
+ ** 0.0 and 1.0 for percentile_cont() and percentile_disc().
+ **
+ ** The user-data is an integer which is 10 times the upper bound.
+ */
+ double mxFrac = (SQLITE_PTR_TO_INT(sqlite3_user_data(pCtx))&2)? 100.0 : 1.0;
+ eType = sqlite3_value_numeric_type(argv[1]);
+ rPct = sqlite3_value_double(argv[1])/mxFrac;
+ if( (eType!=SQLITE_INTEGER && eType!=SQLITE_FLOAT)
+ || rPct<0.0 || rPct>1.0
+ ){
+ percentError(pCtx, "the fraction argument to %%s()"
+ " is not between 0.0 and %.1f",
+ (double)mxFrac);
+ return;
+ }
+ }
+
+ /* Allocate the session context. */
+ p = (Percentile*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+ if( p==0 ) return;
+
+ /* Remember the P value. Throw an error if the P value is different
+ ** from any prior row, per Requirement (2). */
+ if( !p->bPctValid ){
+ p->rPct = rPct;
+ p->bPctValid = 1;
+ }else if( !percentSameValue(p->rPct,rPct) ){
+ percentError(pCtx, "the fraction argument to %%s()"
+ " is not the same for all input rows");
+ return;
+ }
+
+ /* Ignore rows for which Y is NULL */
+ eType = sqlite3_value_type(argv[0]);
+ if( eType==SQLITE_NULL ) return;
+
+ /* If not NULL, then Y must be numeric. Otherwise throw an error.
+ ** Requirement 4 */
+ if( eType!=SQLITE_INTEGER && eType!=SQLITE_FLOAT ){
+ percentError(pCtx, "input to %%s() is not numeric");
+ return;
+ }
+
+ /* Throw an error if the Y value is infinity or NaN */
+ y = sqlite3_value_double(argv[0]);
+ if( percentIsInfinity(y) ){
+ percentError(pCtx, "Inf input to %%s()");
+ return;
+ }
+
+ /* Allocate and store the Y */
+ if( p->nUsed>=p->nAlloc ){
+ unsigned n = p->nAlloc*2 + 250;
+ double *a = sqlite3_realloc64(p->a, sizeof(double)*n);
+ if( a==0 ){
+ sqlite3_free(p->a);
+ memset(p, 0, sizeof(*p));
+ sqlite3_result_error_nomem(pCtx);
+ return;
+ }
+ p->nAlloc = n;
+ p->a = a;
+ }
+ if( p->nUsed==0 ){
+ p->a[p->nUsed++] = y;
+ p->bSorted = 1;
+ }else if( !p->bSorted || y>=p->a[p->nUsed-1] ){
+ p->a[p->nUsed++] = y;
+ }else if( p->bKeepSorted ){
+ int i;
+ i = percentBinarySearch(p, y, 0);
+ if( i<(int)p->nUsed ){
+ memmove(&p->a[i+1], &p->a[i], (p->nUsed-i)*sizeof(p->a[0]));
+ }
+ p->a[i] = y;
+ p->nUsed++;
+ }else{
+ p->a[p->nUsed++] = y;
+ p->bSorted = 0;
+ }
+}
+
+/*
+** Interchange two doubles.
+*/
+#define SWAP_DOUBLE(X,Y) {double ttt=(X);(X)=(Y);(Y)=ttt;}
+
+/*
+** Sort an array of doubles.
+**
+** Algorithm: quicksort
+**
+** This is implemented separately rather than using the qsort() routine
+** from the standard library because:
+**
+** (1) To avoid a dependency on qsort()
+** (2) To avoid the function call to the comparison routine for each
+** comparison.
+*/
+static void percentSort(double *a, unsigned int n){
+ int iLt; /* Entries before a[iLt] are less than rPivot */
+ int iGt; /* Entries at or after a[iGt] are greater than rPivot */
+ int i; /* Loop counter */
+ double rPivot; /* The pivot value */
+
+ assert( n>=2 );
+ if( a[0]>a[n-1] ){
+ SWAP_DOUBLE(a[0],a[n-1])
+ }
+ if( n==2 ) return;
+ iGt = n-1;
+ i = n/2;
+ if( a[0]>a[i] ){
+ SWAP_DOUBLE(a[0],a[i])
+ }else if( a[i]>a[iGt] ){
+ SWAP_DOUBLE(a[i],a[iGt])
+ }
+ if( n==3 ) return;
+ rPivot = a[i];
+ iLt = i = 1;
+ do{
+ if( a[i]<rPivot ){
+ if( i>iLt ) SWAP_DOUBLE(a[i],a[iLt])
+ iLt++;
+ i++;
+ }else if( a[i]>rPivot ){
+ do{
+ iGt--;
+ }while( iGt>i && a[iGt]>rPivot );
+ SWAP_DOUBLE(a[i],a[iGt])
+ }else{
+ i++;
+ }
+ }while( i<iGt );
+ if( iLt>=2 ) percentSort(a, iLt);
+ if( n-iGt>=2 ) percentSort(a+iGt, n-iGt);
+
+/* Uncomment for testing */
+#if 0
+ for(i=0; i<n-1; i++){
+ assert( a[i]<=a[i+1] );
+ }
+#endif
+}
+
+
+/*
+** The "inverse" function for percentile(Y,P) is called to remove a
+** row that was previously inserted by "step".
+*/
+static void percentInverse(sqlite3_context *pCtx,int argc,sqlite3_value **argv){
+ Percentile *p;
+ int eType;
+ double y;
+ int i;
+ assert( argc==2 || argc==1 );
+
+ /* Allocate the session context. */
+ p = (Percentile*)sqlite3_aggregate_context(pCtx, sizeof(*p));
+ assert( p!=0 );
+
+ /* Ignore rows for which Y is NULL */
+ eType = sqlite3_value_type(argv[0]);
+ if( eType==SQLITE_NULL ) return;
+
+ /* If not NULL, then Y must be numeric. Otherwise throw an error.
+ ** Requirement 4 */
+ if( eType!=SQLITE_INTEGER && eType!=SQLITE_FLOAT ){
+ return;
+ }
+
+ /* Ignore the Y value if it is infinity or NaN */
+ y = sqlite3_value_double(argv[0]);
+ if( percentIsInfinity(y) ){
+ return;
+ }
+ if( p->bSorted==0 ){
+ assert( p->nUsed>1 );
+ percentSort(p->a, p->nUsed);
+ p->bSorted = 1;
+ }
+ p->bKeepSorted = 1;
+
+ /* Find and remove the row */
+ i = percentBinarySearch(p, y, 1);
+ if( i>=0 ){
+ p->nUsed--;
+ if( i<(int)p->nUsed ){
+ memmove(&p->a[i], &p->a[i+1], (p->nUsed - i)*sizeof(p->a[0]));
+ }
+ }
+}
+
+/*
+** Compute the final output of percentile(). Clean up all allocated
+** memory if and only if bIsFinal is true.
+*/
+static void percentCompute(sqlite3_context *pCtx, int bIsFinal){
+ Percentile *p;
+ int settings = SQLITE_PTR_TO_INT(sqlite3_user_data(pCtx))&1; /* Discrete? */
+ unsigned i1, i2;
+ double v1, v2;
+ double ix, vx;
+ p = (Percentile*)sqlite3_aggregate_context(pCtx, 0);
+ if( p==0 ) return;
+ if( p->a==0 ) return;
+ if( p->nUsed ){
+ if( p->bSorted==0 ){
+ assert( p->nUsed>1 );
+ percentSort(p->a, p->nUsed);
+ p->bSorted = 1;
+ }
+ ix = p->rPct*(p->nUsed-1);
+ i1 = (unsigned)ix;
+ if( settings & 1 ){
+ vx = p->a[i1];
+ }else{
+ i2 = ix==(double)i1 || i1==p->nUsed-1 ? i1 : i1+1;
+ v1 = p->a[i1];
+ v2 = p->a[i2];
+ vx = v1 + (v2-v1)*(ix-i1);
+ }
+ sqlite3_result_double(pCtx, vx);
+ }
+ if( bIsFinal ){
+ sqlite3_free(p->a);
+ memset(p, 0, sizeof(*p));
+ }else{
+ p->bKeepSorted = 1;
+ }
+}
+static void percentFinal(sqlite3_context *pCtx){
+ percentCompute(pCtx, 1);
+}
+static void percentValue(sqlite3_context *pCtx){
+ percentCompute(pCtx, 0);
+}
+/****** End of percentile family of functions ******/
+
+
#ifdef SQLITE_DEBUG
/*
** Implementation of fpdecode(x,y,z) function.
groupConcatFinalize, groupConcatValue, groupConcatInverse, 0),
WAGGREGATE(string_agg, 2, 0, 0, groupConcatStep,
groupConcatFinalize, groupConcatValue, groupConcatInverse, 0),
+
+ WAGGREGATE(median, 1, 0,0, percentStep,
+ percentFinal, percentValue, percentInverse,
+ SQLITE_INNOCUOUS|SQLITE_SELFORDER1),
+ WAGGREGATE(percentile, 2, 0x2,0, percentStep,
+ percentFinal, percentValue, percentInverse,
+ SQLITE_INNOCUOUS|SQLITE_SELFORDER1),
+ WAGGREGATE(percentile_cont, 2, 0,0, percentStep,
+ percentFinal, percentValue, percentInverse,
+ SQLITE_INNOCUOUS|SQLITE_SELFORDER1),
+ WAGGREGATE(percentile_disc, 2, 0x1,0, percentStep,
+ percentFinal, percentValue, percentInverse,
+ SQLITE_INNOCUOUS|SQLITE_SELFORDER1),
LIKEFUNC(glob, 2, &globInfo, SQLITE_FUNC_LIKE|SQLITE_FUNC_CASE),
#ifdef SQLITE_CASE_SENSITIVE_LIKE
INLINE_FUNC(coalesce, -4, INLINEFUNC_coalesce, 0 ),
INLINE_FUNC(iif, -4, INLINEFUNC_iif, 0 ),
INLINE_FUNC(if, -4, INLINEFUNC_iif, 0 ),
+
};
#ifndef SQLITE_OMIT_ALTERTABLE
sqlite3AlterFunctions();
projects / thirdparty / sqlite.git / commitdiff
