/*
** 2013-05-28
**
** 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.
**
******************************************************************************
**
** This file contains code to implement the percentile(Y,P) SQL function
** as described below:
**
** (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.
*/
#include "sqlite3ext.h"
SQLITE_EXTENSION_INIT1
#include <assert.h>
#include <string.h>
#include <stdlib.h>
/* The following object is the session context for a single percentile()
** function. We have to 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[] */
double rPct; /* 1.0 more than the value for P */
double *a; /* Array of Y values */
};
/*
** Return TRUE if the input floating-point number is an infinity.
*/
static int isInfinity(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 sameValue(double a, double b){
a -= b;
return a>=-0.001 && a<=0.001;
}
/*
** 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 );
/* Requirement 3: P must be a number between 0 and 100 */
eType = sqlite3_value_numeric_type(argv[1]);
rPct = sqlite3_value_double(argv[1]);
if( (eType!=SQLITE_INTEGER && eType!=SQLITE_FLOAT) ||
((rPct = sqlite3_value_double(argv[1]))<0.0 || rPct>100.0) ){
sqlite3_result_error(pCtx, "2nd argument to percentile() is not "
"a number between 0.0 and 100.0", -1);
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->rPct==0.0 ){
p->rPct = rPct+1.0;
}else if( !sameValue(p->rPct,rPct+1.0) ){
sqlite3_result_error(pCtx, "2nd argument to percentile() is not the "
"same for all input rows", -1);
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 ){
sqlite3_result_error(pCtx, "1st argument to percentile() is not "
"numeric", -1);
return;
}
/* Throw an error if the Y value is infinity or NaN */
y = sqlite3_value_double(argv[0]);
if( isInfinity(y) ){
sqlite3_result_error(pCtx, "Inf input to percentile()", -1);
return;
}
/* Allocate and store the Y */
if( p->nUsed>=p->nAlloc ){
unsigned n = p->nAlloc*2 + 250;
double *a = sqlite3_realloc(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;
}
p->a[p->nUsed++] = y;
}
/*
** Compare to doubles for sorting using qsort()
*/
static int doubleCmp(const void *pA, const void *pB){
double a = *(double*)pA;
double b = *(double*)pB;
if( a==b ) return 0;
if( a<b ) return -1;
return +1;
}
/*
** Called to compute the final output of percentile() and to clean
** up all allocated memory.
*/
static void percentFinal(sqlite3_context *pCtx){
Percentile *p;
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 ){
qsort(p->a, p->nUsed, sizeof(double), doubleCmp);
ix = (p->rPct-1.0)*(p->nUsed-1)*0.01;
i1 = (unsigned)ix;
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);
}
sqlite3_free(p->a);
memset(p, 0, sizeof(*p));
}
#ifdef _WIN32
__declspec(dllexport)
#endif
int sqlite3_percentile_init(
sqlite3 *db,
char **pzErrMsg,
const sqlite3_api_routines *pApi
){
int rc = SQLITE_OK;
SQLITE_EXTENSION_INIT2(pApi);
(void)pzErrMsg; /* Unused parameter */
rc = sqlite3_create_function(db, "percentile", 2, SQLITE_UTF8, 0,
0, percentStep, percentFinal);
return rc;
}