You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


/*
This library will provide common mathematical and string functions in
SQL queries using the operating system libraries or provided
definitions.  It includes the following functions:

Math: acos, asin, atan, atn2, atan2, acosh, asinh, atanh, difference,
degrees, radians, cos, sin, tan, cot, cosh, sinh, tanh, coth, exp,
log, log10, power, sign, sqrt, square, ceil, floor, pi.

String: replicate, charindex, leftstr, rightstr, ltrim, rtrim, trim,
replace, reverse, proper, padl, padr, padc, strfilter.

Aggregate: stdev, variance, mode, median, lower_quartile,
upper_quartile.

The string functions ltrim, rtrim, trim, replace are included in
recent versions of SQLite and so by default do not build.

Compilation instructions:
 Compile this C source file into a dynamic library as follows:
 * Linux:
   gcc -fPIC -lm -shared extension-functions.c -o libsqlitefunctions.so
 * Mac OS X:
   gcc -fno-common -dynamiclib extension-functions.c -o libsqlitefunctions.dylib
 (You may need to add flags
  -I /opt/local/include/ -L/opt/local/lib -lsqlite3
  if your sqlite3 is installed from Mac ports, or
  -I /sw/include/ -L/sw/lib -lsqlite3
  if installed with Fink.)
 * Windows:
  1. Install MinGW (http://www.mingw.org/) and you will get the gcc
  (gnu compiler collection)
  2. add the path to your path variable (isn't done during the
   installation!)
  3. compile:
   gcc -shared -I "path" -o libsqlitefunctions.so extension-functions.c
   (path = path of sqlite3ext.h; i.e. C:\programs\sqlite)

Usage instructions for applications calling the sqlite3 API functions:
  In your application, call sqlite3_enable_load_extension(db,1) to
  allow loading external libraries.  Then load the library libsqlitefunctions
  using sqlite3_load_extension; the third argument should be 0.
  See http://www.sqlite.org/cvstrac/wiki?p=LoadableExtensions.
  Select statements may now use these functions, as in
  SELECT cos(radians(inclination)) FROM satsum WHERE satnum = 25544;

Usage instructions for the sqlite3 program:
  If the program is built so that loading extensions is permitted,
  the following will work:
   sqlite> SELECT load_extension('./libsqlitefunctions.so');
   sqlite> select cos(radians(45));
   0.707106781186548
  Note: Loading extensions is by default prohibited as a
  security measure; see "Security Considerations" in
  http://www.sqlite.org/cvstrac/wiki?p=LoadableExtensions.
  If the sqlite3 program and library are built this
  way, you cannot use these functions from the program, you
  must write your own program using the sqlite3 API, and call
  sqlite3_enable_load_extension as described above, or else
  rebuilt the sqlite3 program to allow loadable extensions.

Alterations:
The instructions are for Linux, Mac OS X, and Windows; users of other
OSes may need to modify this procedure.  In particular, if your math
library lacks one or more of the needed trig or log functions, comment
out the appropriate HAVE_ #define at the top of file.  If you do not
wish to make a loadable module, comment out the define for
COMPILE_SQLITE_EXTENSIONS_AS_LOADABLE_MODULE.  If you are using a
version of SQLite without the trim functions and replace, comment out
the HAVE_TRIM #define.

Liam Healy

History:
2010-01-06 Correct check for argc in squareFunc, and add Windows
compilation instructions.
2009-06-24 Correct check for argc in properFunc.
2008-09-14 Add check that memory was actually allocated after
sqlite3_malloc or sqlite3StrDup, call sqlite3_result_error_nomem if
not.  Thanks to <PRESIDIO_ANONYMIZED_PERSON>.
2008-06-13 Change to instructions to indicate use of the math library
and that program might work.
2007-10-01 Minor clarification to instructions.
2007-09-29 Compilation as loadable module is optional with
COMPILE_SQLITE_EXTENSIONS_AS_LOADABLE_MODULE.
2007-09-28 Use sqlite3_extension_init and macros
SQLITE_EXTENSION_INIT1, SQLITE_EXTENSION_INIT2, so that it works with
sqlite3_load_extension.  Thanks to <PRESIDIO_ANONYMIZED_PERSON> and Joe Wilson.
New instructions for Mac compilation.
2007-09-17 With help from Joe Wilson and Nuno Luca, made use of
external interfaces so that compilation is no longer dependent on
SQLite source code.  Merged source, header, and README into a single
file.  Added casts so that Mac will compile without warnings (unsigned
and signed char).
2007-09-05 Included some definitions from sqlite 3.3.13 so that this
will continue to work in newer versions of sqlite.  Completed
description of functions available.
2007-03-27 Revised description.
2007-03-23 Small cleanup and a bug fix on the code.  This was mainly
letting errno flag errors encountered in the math library and checking
the result, rather than pre-checking.  This fixes a bug in power that
would cause an error if any non-positive number was raised to any
power.
2007-02-07 posted by Mikey C to sqlite mailing list.
Original code 2006 June 05 by relicoder.

*/

//#include "config.h"

// #define COMPILE_SQLITE_EXTENSIONS_AS_LOADABLE_MODULE 1
#define HAVE_ACOSH 1
#define HAVE_ASINH 1
#define HAVE_ATANH 1
#define HAVE_SINH 1
#define HAVE_COSH 1
#define HAVE_TANH 1
#define HAVE_LOG10 1
#define HAVE_ISBLANK 1
#define SQLITE_SOUNDEX 1
#define HAVE_TRIM 1		/* LMH 2007-03-25 if sqlite has trim functions */

#define __STDC_FORMAT_MACROS

#ifdef COMPILE_SQLITE_EXTENSIONS_AS_LOADABLE_MODULE
#include "sqlite3ext.h"
SQLITE_EXTENSION_INIT1
#else
#include "sqlite3.h"
#endif

#include <ctype.h>
/* relicoder */
#include <math.h>
#include <string.h>
#include <stdio.h>
#include <errno.h>		/* LMH 2007-03-25 */

#include <stdlib.h>
#include <assert.h>

#ifndef _MAP_H_
#define _MAP_H_

#include <stdint.h>
#include <inttypes.h>

#include "sqlite-extension-func.hh"

/*
** Simple binary tree implementation to use in median, mode and quartile calculations
** Tree is not necessarily balanced. That would require something like red&black trees of AVL
*/

typedef int(*cmp_func)(const void *, const void *);
typedef void(*map_iterator)(void*, int64_t, void*);

typedef struct node{
  struct node *l;
  struct node *r;
  void* data;
  int64_t count;
} node;

typedef struct map{
  node *base;
  cmp_func cmp;
  short free;
} map;

/*
** creates a map given a comparison function
*/
map map_make(cmp_func cmp);

/*
** inserts the element e into map m
*/
void map_insert(map *m, void *e);

/*
** executes function iter over all elements in the map, in key increasing order
*/
void map_iterate(map *m, map_iterator iter, void* p);

/*
** frees all memory used by a map
*/
void map_destroy(map *m);

/*
** compares 2 integers
** to use with map_make
*/
int int_cmp(const void *a, const void *b);

/*
** compares 2 doubles
** to use with map_make
*/
int double_cmp(const void *a, const void *b);

#endif /* _MAP_H_ */

typedef uint8_t         u8;
typedef uint16_t        u16;
typedef int64_t         i64;

static char *sqlite3StrDup( const char *z ) {
    char *res = (char *) sqlite3_malloc(strlen(z) + 1 );
    return strcpy( res, z );
}

/*
** These are copied verbatim from fun.c so as to not have the names exported
*/

/* LMH from sqlite3 3.3.13 */
/*
** This table maps from the first byte of a UTF-8 character to the number
** of trailing bytes expected. A value '4' indicates that the table key
** is not a legal first byte for a UTF-8 character.
*/
static const u8 xtra_utf8_bytes[256]  = {
/* 0xxxxxxx */
0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,

/* 10wwwwww */
4, 4, 4, 4, 4, 4, 4, 4,     4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4,     4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4,     4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4,     4, 4, 4, 4, 4, 4, 4, 4,

/* 110yyyyy */
1, 1, 1, 1, 1, 1, 1, 1,     1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1,     1, 1, 1, 1, 1, 1, 1, 1,

/* 1110zzzz */
2, 2, 2, 2, 2, 2, 2, 2,     2, 2, 2, 2, 2, 2, 2, 2,

/* 11110yyy */
3, 3, 3, 3, 3, 3, 3, 3,     4, 4, 4, 4, 4, 4, 4, 4,
};


/*
** This table maps from the number of trailing bytes in a UTF-8 character
** to an integer constant that is effectively calculated for each character
** read by a naive implementation of a UTF-8 character reader. The code
** in the READ_UTF8 macro explains things best.
*/
static const int xtra_utf8_bits[] =  {
  0,
  12416,          /* (0xC0 << 6) + (0x80) */
  925824,         /* (0xE0 << 12) + (0x80 << 6) + (0x80) */
  63447168        /* (0xF0 << 18) + (0x80 << 12) + (0x80 << 6) + 0x80 */
};

/*
** If a UTF-8 character contains N bytes extra bytes (N bytes follow
** the initial byte so that the total character length is N+1) then
** masking the character with utf8_mask[N] must produce a non-zero
** result.  Otherwise, we have an (illegal) overlong encoding.
*/
static const unsigned long utf_mask[] = {
  0x00000000,
  0xffffff80,
  0xfffff800,
  0xffff0000,
};

/* LMH salvaged from sqlite3 3.3.13 source code src/utf.c */
#define READ_UTF8(zIn, c) { \
  int xtra;                                            \
  c = *(zIn)++;                                        \
  xtra = xtra_utf8_bytes[c];                           \
  switch( xtra ){                                      \
    case 4: c = (int)0xFFFD; break;                    \
    case 3: c = (c<<6) + *(zIn)++;                     \
    case 2: c = (c<<6) + *(zIn)++;                     \
    case 1: c = (c<<6) + *(zIn)++;                     \
    c -= xtra_utf8_bits[xtra];                         \
    if( (utf_mask[xtra]&c)==0                          \
        || (c&0xFFFFF800)==0xD800                      \
        || (c&0xFFFFFFFE)==0xFFFE ){  c = 0xFFFD; }    \
  }                                                    \
}

static int sqlite3ReadUtf8(const unsigned char *z){
  int c;
  READ_UTF8(z, c);
  return c;
}

#define SKIP_UTF8(zIn) {                               \
  zIn += (xtra_utf8_bytes[*(u8 *)zIn] + 1);            \
}

/*
** pZ is a UTF-8 encoded unicode string. If nByte is less than zero,
** return the number of unicode characters in pZ up to (but not including)
** the first 0x00 byte. If nByte is not less than zero, return the
** number of unicode characters in the first nByte of pZ (or up to
** the first 0x00, whichever comes first).
*/
static int sqlite3Utf8CharLen(const char *z, int nByte){
  int r = 0;
  const char *zTerm;
  if( nByte>=0 ){
    zTerm = &z[nByte];
  }else{
    zTerm = (const char *)(-1);
  }
  assert( z<=zTerm );
  while( *z!=0 && z<zTerm ){
    SKIP_UTF8(z);
    r++;
  }
  return r;
}

/*
** X is a pointer to the first byte of a UTF-8 character.  Increment
** X so that it points to the next character.  This only works right
** if X points to a well-formed UTF-8 string.
*/
#define sqliteNextChar(X)  while( (0xc0&*++(X))==0x80 ){}
#define sqliteCharVal(X)   sqlite3ReadUtf8(X)

/*
** This is a macro that facilitates writting wrappers for math.h functions
** it creates code for a function to use in SQlite that gets one numeric input
** and returns a floating point value.
**
** Could have been implemented using pointers to functions but this way it's inline
** and thus more efficient. Lower * ranking though...
**
** Parameters:
** name:      function name to de defined (eg: sinFunc)
** function:  function defined in math.h to wrap (eg: sin)
** domain:    boolean condition that CAN'T happen in terms of the input parameter rVal
**            (eg: rval<0 for sqrt)
*/
/* LMH 2007-03-25 Changed to use errno and remove domain; no pre-checking for errors. */
#define GEN_MATH_WRAP_DOUBLE_1(name, function) \
static void name(sqlite3_context *context, int argc, sqlite3_value **argv){\
  double rVal = 0.0, val;\
  assert( argc==1 );\
  switch( sqlite3_value_type(argv[0]) ){\
    case SQLITE_NULL: {\
      sqlite3_result_null(context);\
      break;\
    }\
    default: {\
      rVal = sqlite3_value_double(argv[0]);\
      errno = 0;\
      val = function(rVal);\
      if (errno == 0) {\
        sqlite3_result_double(context, val);\
      } else {\
        sqlite3_result_error(context, strerror(errno), errno);\
      }\
      break;\
    }\
  }\
}\


/*
** Example of GEN_MATH_WRAP_DOUBLE_1 usage
** this creates function sqrtFunc to wrap the math.h standard function sqrt(x)=x^0.5
*/
GEN_MATH_WRAP_DOUBLE_1(sqrtFunc, sqrt)

/* trignometric functions */
GEN_MATH_WRAP_DOUBLE_1(acosFunc, acos)
GEN_MATH_WRAP_DOUBLE_1(asinFunc, asin)
GEN_MATH_WRAP_DOUBLE_1(atanFunc, atan)

/*
** Many of systems don't have inverse hyperbolic trig functions so this will emulate
** them on those systems in terms of log and sqrt (formulas are too trivial to demand
** written proof here)
*/

#ifndef HAVE_ACOSH
static double acosh(double x){
  return log(x + sqrt(x*x - 1.0));
}
#endif

GEN_MATH_WRAP_DOUBLE_1(acoshFunc, acosh)

#ifndef HAVE_ASINH
static double asinh(double x){
  return log(x + sqrt(x*x + 1.0));
}
#endif

GEN_MATH_WRAP_DOUBLE_1(asinhFunc, asinh)

#ifndef HAVE_ATANH
static double atanh(double x){
  return (1.0/2.0)*log((1+x)/(1-x)) ;
}
#endif

GEN_MATH_WRAP_DOUBLE_1(atanhFunc, atanh)

/*
** math.h doesn't require cot (cotangent) so it's defined here
*/
static double cot(double x){
  return 1.0/tan(x);
}

GEN_MATH_WRAP_DOUBLE_1(sinFunc, sin)
GEN_MATH_WRAP_DOUBLE_1(cosFunc, cos)
GEN_MATH_WRAP_DOUBLE_1(tanFunc, tan)
GEN_MATH_WRAP_DOUBLE_1(cotFunc, cot)

static double coth(double x){
  return 1.0/tanh(x);
}

/*
** Many systems don't have hyperbolic trigonometric functions so this will emulate
** them on those systems directly from the definition in terms of exp
*/
#ifndef HAVE_SINH
static double sinh(double x){
  return (exp(x)-exp(-x))/2.0;
}
#endif

GEN_MATH_WRAP_DOUBLE_1(sinhFunc, sinh)

#ifndef HAVE_COSH
static double cosh(double x){
  return (exp(x)+exp(-x))/2.0;
}
#endif

GEN_MATH_WRAP_DOUBLE_1(coshFunc, cosh)

#ifndef HAVE_TANH
static double tanh(double x){
  return sinh(x)/cosh(x);
}
#endif

GEN_MATH_WRAP_DOUBLE_1(tanhFunc, tanh)

GEN_MATH_WRAP_DOUBLE_1(cothFunc, coth)

/*
** Some systems lack log in base 10. This will emulate it
*/

#ifndef HAVE_LOG10
static double log10(double x){
  static double l10 = -1.0;
  if( l10<0.0 ){
    l10 = log(10.0);
  }
  return log(x)/l10;
}
#endif

GEN_MATH_WRAP_DOUBLE_1(logFunc, log)
GEN_MATH_WRAP_DOUBLE_1(log10Func, log10)
GEN_MATH_WRAP_DOUBLE_1(expFunc, exp)

/*
** Fallback for systems where math.h doesn't define M_PI
*/
#undef M_PI
#ifndef M_PI
/*
** static double PI = acos(-1.0);
** #define M_PI (PI)
*/
#define M_PI 3.14159265358979323846
#endif

/* Convert Degrees into Radians */
static double deg2rad(double x){
  return x*M_PI/180.0;
}

/* Convert Radians into Degrees */
static double rad2deg(double x){
  return 180.0*x/M_PI;
}

GEN_MATH_WRAP_DOUBLE_1(rad2degFunc, rad2deg)
GEN_MATH_WRAP_DOUBLE_1(deg2radFunc, deg2rad)

/* constant function that returns the value of PI=3.1415... */
static void piFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  sqlite3_result_double(context, M_PI);
}

/*
** Implements the sqrt function, it has the peculiarity of returning an integer when the
** the argument is an integer.
** Since SQLite isn't strongly typed (almost untyped actually) this is a bit pedantic
*/
static void squareFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  i64 iVal = 0;
  double rVal = 0.0;
  assert( argc==1 );
  switch( sqlite3_value_type(argv[0]) ){
    case SQLITE_INTEGER: {
      iVal = sqlite3_value_int64(argv[0]);
      sqlite3_result_int64(context, iVal*iVal);
      break;
    }
    case SQLITE_NULL: {
      sqlite3_result_null(context);
      break;
    }
    default: {
      rVal = sqlite3_value_double(argv[0]);
      sqlite3_result_double(context, rVal*rVal);
      break;
    }
  }
}

/*
** Wraps the pow math.h function
** When both the base and the exponent are integers the result should be integer
** (see sqrt just before this). Here the result is always double
*/
/* LMH 2007-03-25 Changed to use errno; no pre-checking for errors.  Also removes
  but that was present in the pre-checking that called sqlite3_result_error on
  a non-positive first argument, which is not always an error. */
static void powerFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  double r1 = 0.0;
  double r2 = 0.0;
  double val;

  assert( argc==2 );

  if( sqlite3_value_type(argv[0]) == SQLITE_NULL || sqlite3_value_type(argv[1]) == SQLITE_NULL ){
    sqlite3_result_null(context);
  }else{
    r1 = sqlite3_value_double(argv[0]);
    r2 = sqlite3_value_double(argv[1]);
    errno = 0;
    val = pow(r1,r2);
    if (errno == 0) {
      sqlite3_result_double(context, val);
    } else {
      sqlite3_result_error(context, strerror(errno), errno);
    }
  }
}

/*
** atan2 wrapper
*/
static void atn2Func(sqlite3_context *context, int argc, sqlite3_value **argv){
  double r1 = 0.0;
  double r2 = 0.0;

  assert( argc==2 );

  if( sqlite3_value_type(argv[0]) == SQLITE_NULL || sqlite3_value_type(argv[1]) == SQLITE_NULL ){
    sqlite3_result_null(context);
  }else{
    r1 = sqlite3_value_double(argv[0]);
    r2 = sqlite3_value_double(argv[1]);
    sqlite3_result_double(context, atan2(r1,r2));
  }
}

/*
** Implementation of the sign() function
** return one of 3 possibilities +1,0 or -1 when the argument is respectively
** positive, 0 or negative.
** When the argument is NULL the result is also NULL (completly conventional)
*/
static void signFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  double rVal=0.0;
  i64 iVal=0;
  assert( argc==1 );
  switch( sqlite3_value_type(argv[0]) ){
    case SQLITE_INTEGER: {
      iVal = sqlite3_value_int64(argv[0]);
      iVal = ( iVal > 0) ? 1: ( iVal < 0 ) ? -1: 0;
      sqlite3_result_int64(context, iVal);
      break;
    }
    case SQLITE_NULL: {
      sqlite3_result_null(context);
      break;
    }
    default: {
 /* 2nd change below. Line for abs was: if( rVal<0 ) rVal = rVal * -1.0;  */

      rVal = sqlite3_value_double(argv[0]);
      rVal = ( rVal > 0) ? 1: ( rVal < 0 ) ? -1: 0;
      sqlite3_result_double(context, rVal);
      break;
    }
  }
}


/*
** smallest integer value not less than argument
*/
static void ceilFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  double rVal=0.0;
  assert( argc==1 );
  switch( sqlite3_value_type(argv[0]) ){
    case SQLITE_INTEGER: {
      i64 iVal = sqlite3_value_int64(argv[0]);
      sqlite3_result_int64(context, iVal);
      break;
    }
    case SQLITE_NULL: {
      sqlite3_result_null(context);
      break;
    }
    default: {
      rVal = sqlite3_value_double(argv[0]);
      sqlite3_result_int64(context, (i64) ceil(rVal));
      break;
    }
  }
}

/*
** largest integer value not greater than argument
*/
static void floorFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  double rVal=0.0;
  assert( argc==1 );
  switch( sqlite3_value_type(argv[0]) ){
    case SQLITE_INTEGER: {
      i64 iVal = sqlite3_value_int64(argv[0]);
      sqlite3_result_int64(context, iVal);
      break;
    }
    case SQLITE_NULL: {
      sqlite3_result_null(context);
      break;
    }
    default: {
      rVal = sqlite3_value_double(argv[0]);
      sqlite3_result_int64(context, (i64) floor(rVal));
      break;
    }
  }
}

/*
** Given a string (s) in the first argument and an integer (n) in the second returns the
** string that constains s contatenated n times
*/
static void replicateFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  unsigned char *z;        /* input string */
  unsigned char *zo;       /* result string */
  i64 iCount;              /* times to repeat */
  i64 nLen;                /* length of the input string (no multibyte considerations) */
  i64 nTLen;               /* length of the result string (no multibyte considerations) */
  i64 i=0;

  if( argc!=2 || SQLITE_NULL==sqlite3_value_type(argv[0]) )
    return;

  iCount = sqlite3_value_int64(argv[1]);

  if( iCount<0 ){
    sqlite3_result_error(context, "domain error", -1);
  }else{

    nLen  = sqlite3_value_bytes(argv[0]);
    nTLen = nLen*iCount;
    z= (unsigned char *) sqlite3_malloc(nTLen + 1);
    zo= (unsigned char *) sqlite3_malloc(nLen + 1);
    if (!z || !zo){
      sqlite3_result_error_nomem(context);
      if (z) sqlite3_free(z);
      if (zo) sqlite3_free(zo);
      return;
    }
    strcpy((char*)zo, (char*)sqlite3_value_text(argv[0]));

    for(i=0; i<iCount; ++i){
      strcpy((char*)(z+i*nLen), (char*)zo);
    }

    sqlite3_result_text(context, (char*)z, -1, SQLITE_TRANSIENT);
    sqlite3_free(z);
    sqlite3_free(zo);
  }
}

/*
** Some systems (win32 among others) don't have an isblank function, this will emulate it.
** This function is not UFT-8 safe since it only analyses a byte character.
*/
#ifndef HAVE_ISBLANK
int isblank(char c){
  return( ' '==c || '\t'==c );
}
#endif

static void properFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  const unsigned char *z;     /* input string */
  unsigned char *zo;          /* output string */
  unsigned char *zt;          /* iterator */
  char r;
  int c=1;

  assert( argc==1);
  if( SQLITE_NULL==sqlite3_value_type(argv[0]) ){
    sqlite3_result_null(context);
    return;
  }

  z = sqlite3_value_text(argv[0]);
  zo = (unsigned char *)sqlite3StrDup((char *) z);
  if (!zo) {
    sqlite3_result_error_nomem(context);
    return;
  }
  zt = zo;

  while( (r = *(z++))!=0 ){
    if( isblank(r) ){
      c=1;
    }else{
      if( c==1 ){
        r = toupper(r);
      }else{
        r = tolower(r);
      }
      c=0;
    }
    *(zt++) = r;
  }
  *zt = '\0';

  sqlite3_result_text(context, (char*)zo, -1, SQLITE_TRANSIENT);
  sqlite3_free(zo);
}

/*
** given an input string (s) and an integer (n) adds spaces at the begining of  s
** until it has a length of n characters.
** When s has a length >=n it's a NOP
** padl(NULL) = NULL
*/
static void padlFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  i64 ilen;          /* length to pad to */
  i64 zl;            /* length of the input string (UTF-8 chars) */
  int i = 0;
  const char *zi;    /* input string */
  char *zo;          /* output string */
  char *zt;

  assert( argc==2 );

  if( sqlite3_value_type(argv[0]) == SQLITE_NULL ){
    sqlite3_result_null(context);
  }else{
    zi = (char *)sqlite3_value_text(argv[0]);
    ilen = sqlite3_value_int64(argv[1]);
    /* check domain */
    if(ilen<0){
      sqlite3_result_error(context, "domain error", -1);
      return;
    }
    zl = sqlite3Utf8CharLen(zi, -1);
    if( zl>=ilen ){
      /* string is longer than the requested pad length, return the same string (dup it) */
      zo = sqlite3StrDup(zi);
      if (!zo){
        sqlite3_result_error_nomem(context);
        return;
      }
      sqlite3_result_text(context, zo, -1, SQLITE_TRANSIENT);
    }else{
      zo = (char *) sqlite3_malloc(strlen(zi) + ilen - zl + 1);
      if (!zo){
        sqlite3_result_error_nomem(context);
        return;
      }
      zt = zo;
      for(i=1; i+zl<=ilen; ++i){
        *(zt++)=' ';
      }
      /* no need to take UTF-8 into consideration here */
      strcpy(zt,zi);
    }
    sqlite3_result_text(context, zo, -1, SQLITE_TRANSIENT);
    sqlite3_free(zo);
  }
}

/*
** given an input string (s) and an integer (n) appends spaces at the end of  s
** until it has a length of n characters.
** When s has a length >=n it's a NOP
** padl(NULL) = NULL
*/
static void padrFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  i64 ilen;          /* length to pad to */
  i64 zl;            /* length of the input string (UTF-8 chars) */
  i64 zll;           /* length of the input string (bytes) */
  int i = 0;
  const char *zi;    /* input string */
  char *zo;          /* output string */
  char *zt;

  assert( argc==2 );

  if( sqlite3_value_type(argv[0]) == SQLITE_NULL ){
    sqlite3_result_null(context);
  }else{
    zi = (char *)sqlite3_value_text(argv[0]);
    ilen = sqlite3_value_int64(argv[1]);
    /* check domain */
    if(ilen<0){
      sqlite3_result_error(context, "domain error", -1);
      return;
    }
    zl = sqlite3Utf8CharLen(zi, -1);
    if( zl>=ilen ){
      /* string is longer than the requested pad length, return the same string (dup it) */
      zo = sqlite3StrDup(zi);
      if (!zo){
        sqlite3_result_error_nomem(context);
        return;
      }
      sqlite3_result_text(context, zo, -1, SQLITE_TRANSIENT);
    }else{
      zll = strlen(zi);
      zo = (char *) sqlite3_malloc(zll + ilen - zl + 1);
      if (!zo){
        sqlite3_result_error_nomem(context);
        return;
      }
      zt = strcpy(zo,zi)+zll;
      for(i=1; i+zl<=ilen; ++i){
        *(zt++) = ' ';
      }
      *zt = '\0';
    }
    sqlite3_result_text(context, zo, -1, SQLITE_TRANSIENT);
    sqlite3_free(zo);
  }
}

/*
** given an input string (s) and an integer (n) appends spaces at the end of  s
** and adds spaces at the begining of s until it has a length of n characters.
** Tries to add has many characters at the left as at the right.
** When s has a length >=n it's a NOP
** padl(NULL) = NULL
*/
static void padcFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  i64 ilen;           /* length to pad to */
  i64 zl;             /* length of the input string (UTF-8 chars) */
  i64 zll;            /* length of the input string (bytes) */
  int i = 0;
  const char *zi;     /* input string */
  char *zo;           /* output string */
  char *zt;

  assert( argc==2 );

  if( sqlite3_value_type(argv[0]) == SQLITE_NULL ){
    sqlite3_result_null(context);
  }else{
    zi = (char *)sqlite3_value_text(argv[0]);
    ilen = sqlite3_value_int64(argv[1]);
    /* check domain */
    if(ilen<0){
      sqlite3_result_error(context, "domain error", -1);
      return;
    }
    zl = sqlite3Utf8CharLen(zi, -1);
    if( zl>=ilen ){
      /* string is longer than the requested pad length, return the same string (dup it) */
      zo = sqlite3StrDup(zi);
      if (!zo){
        sqlite3_result_error_nomem(context);
        return;
      }
      sqlite3_result_text(context, zo, -1, SQLITE_TRANSIENT);
    }else{
      zll = strlen(zi);
      zo = (char *) sqlite3_malloc(zll + ilen - zl + 1);
      if (!zo){
        sqlite3_result_error_nomem(context);
        return;
      }
      zt = zo;
      for(i=1; 2*i+zl<=ilen; ++i){
        *(zt++) = ' ';
      }
      strcpy(zt, zi);
      zt+=zll;
      for(; i+zl<=ilen; ++i){
        *(zt++) = ' ';
      }
      *zt = '\0';
    }
    sqlite3_result_text(context, zo, -1, SQLITE_TRANSIENT);
    sqlite3_free(zo);
  }
}

/*
** given 2 string (s1,s2) returns the string s1 with the characters NOT in s2 removed
** assumes strings are UTF-8 encoded
*/
static void strfilterFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  const char *zi1;        /* first parameter string (searched string) */
  const char *zi2;        /* second parameter string (vcontains valid characters) */
  const char *z1;
  const char *z21;
  const char *z22;
  char *zo;               /* output string */
  char *zot;
  int c1 = 0;
  int c2 = 0;

  assert( argc==2 );

  if( sqlite3_value_type(argv[0]) == SQLITE_NULL || sqlite3_value_type(argv[1]) == SQLITE_NULL ){
    sqlite3_result_null(context);
  }else{
    zi1 = (char *)sqlite3_value_text(argv[0]);
    zi2 = (char *)sqlite3_value_text(argv[1]);
    /*
    ** maybe I could allocate less, but that would imply 2 passes, rather waste
    ** (possibly) some memory
    */
    zo = (char *) sqlite3_malloc(strlen(zi1) + 1);
    if (!zo){
      sqlite3_result_error_nomem(context);
      return;
    }
    zot = zo;
    z1 = zi1;
    while( (c1=sqliteCharVal((unsigned char *)z1))!=0 ){
      z21=zi2;
      while( (c2=sqliteCharVal((unsigned char *)z21))!=0 && c2!=c1 ){
        sqliteNextChar(z21);
      }
      if( c2!=0){
        z22=z21;
        sqliteNextChar(z22);
        strncpy(zot, z21, z22-z21);
        zot+=z22-z21;
      }
      sqliteNextChar(z1);
    }
    *zot = '\0';

    sqlite3_result_text(context, zo, -1, SQLITE_TRANSIENT);
    sqlite3_free(zo);
  }
}

/*
** Given a string z1, retutns the (0 based) index of it's first occurence
** in z2 after the first s characters.
** Returns -1 when there isn't a match.
** updates p to point to the character where the match occured.
** This is an auxiliary function.
*/
static int _substr(const char* z1, const char* z2, int s, const char** p){
  int c = 0;
  int rVal=-1;
  const char* zt1;
  const char* zt2;
  int c1,c2;

  if( '\0'==*z1 ){
    return -1;
  }

  while( (sqliteCharVal((unsigned char *)z2) != 0) && (c++)<s){
    sqliteNextChar(z2);
  }

  c = 0;
  while( (sqliteCharVal((unsigned char *)z2)) != 0 ){
    zt1 = z1;
    zt2 = z2;

    do{
      c1 = sqliteCharVal((unsigned char *)zt1);
      c2 = sqliteCharVal((unsigned char *)zt2);
      if (c1 == 0) {
          break;
      }
      if (c2 == 0) {
          break;
      }
      sqliteNextChar(zt1);
      sqliteNextChar(zt2);
    }while( c1 == c2 && c1 != 0 && c2 != 0 );

    if( c1 == 0 ){
      rVal = c;
      break;
    }

    sqliteNextChar(z2);
    ++c;
  }
  if(p){
    *p=z2;
  }
  return rVal >=0 ? rVal+s : rVal;
}

/*
** given 2 input strings (s1,s2) and an integer (n) searches from the nth character
** for the string s1. Returns the position where the match occured.
** Characters are counted from 1.
** 0 is returned when no match occurs.
*/

static void charindexFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  const u8 *z1;          /* s1 string */
  u8 *z2;                /* s2 string */
  int s=0;
  int rVal=0;

  assert( argc==3 ||argc==2);

  if( SQLITE_NULL==sqlite3_value_type(argv[0]) || SQLITE_NULL==sqlite3_value_type(argv[1])){
    sqlite3_result_null(context);
    return;
  }

  z1 = sqlite3_value_text(argv[0]);
  if( z1==0 ) return;
  z2 = (u8*) sqlite3_value_text(argv[1]);
  if(argc==3){
    s = sqlite3_value_int(argv[2])-1;
    if(s<0){
      s=0;
    }
  }else{
    s = 0;
  }

  rVal = _substr((char *)z1,(char *)z2,s,NULL);
  sqlite3_result_int(context, rVal+1);
}

/*
** given a string (s) and an integer (n) returns the n leftmost (UTF-8) characters
** if the string has a length<=n or is NULL this function is NOP
*/
static void leftFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  int c=0;
  int cc=0;
  int l=0;
  const unsigned char *z;       /* input string */
  const unsigned char *zt;
  unsigned char *rz;            /* output string */

  assert( argc==2);

  if( SQLITE_NULL==sqlite3_value_type(argv[0]) || SQLITE_NULL==sqlite3_value_type(argv[1])){
    sqlite3_result_null(context);
    return;
  }

  z  = sqlite3_value_text(argv[0]);
  l  = sqlite3_value_int(argv[1]);
  zt = z;

  while( sqliteCharVal(zt) && c++<l)
    sqliteNextChar(zt);

  cc=zt-z;

  rz = (unsigned char *) sqlite3_malloc(zt - z + 1);
  if (!rz){
    sqlite3_result_error_nomem(context);
    return;
  }
  strncpy((char*) rz, (char*) z, zt-z);
  *(rz+cc) = '\0';
  sqlite3_result_text(context, (char*)rz, -1, SQLITE_TRANSIENT);
  sqlite3_free(rz);
}

/*
** given a string (s) and an integer (n) returns the n rightmost (UTF-8) characters
** if the string has a length<=n or is NULL this function is NOP
*/
static void rightFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  int l=0;
  int c=0;
  int cc=0;
  const char *z;
  const char *zt;
  const char *ze;
  char *rz;

  assert( argc==2);

  if( SQLITE_NULL == sqlite3_value_type(argv[0]) || SQLITE_NULL == sqlite3_value_type(argv[1])){
    sqlite3_result_null(context);
    return;
  }

  z  = (char *)sqlite3_value_text(argv[0]);
  l  = sqlite3_value_int(argv[1]);
  zt = z;

  while( sqliteCharVal((unsigned char *)zt)!=0){
    sqliteNextChar(zt);
    ++c;
  }

  ze = zt;
  zt = z;

  cc=c-l;
  if(cc<0)
    cc=0;

  while( cc-- > 0 ){
    sqliteNextChar(zt);
  }

  rz = (char *) sqlite3_malloc(ze - zt + 1);
  if (!rz){
    sqlite3_result_error_nomem(context);
    return;
  }
  strcpy((char*) rz, (char*) (zt));
  sqlite3_result_text(context, (char*)rz, -1, SQLITE_TRANSIENT);
  sqlite3_free(rz);
}

#ifndef HAVE_TRIM
/*
** removes the whitespaces at the begining of a string.
*/
const char* ltrim(const char* s){
  while( *s==' ' )
    ++s;
  return s;
}

/*
** removes the whitespaces at the end of a string.
** !mutates the input string!
*/
void rtrim(char* s){
  char* ss = s+strlen(s)-1;
  while( ss>=s && *ss==' ' )
    --ss;
  *(ss+1)='\0';
}

/*
**  Removes the whitespace at the begining of a string
*/
static void ltrimFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  const char *z;

  assert( argc==1);

  if( SQLITE_NULL==sqlite3_value_type(argv[0]) ){
    sqlite3_result_null(context);
    return;
  }
  z = sqlite3_value_text(argv[0]);
  sqlite3_result_text(context, ltrim(z), -1, SQLITE_TRANSIENT);
}

/*
**  Removes the whitespace at the end of a string
*/
static void rtrimFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  const char *z;
  char *rz;
  /* try not to change data in argv */

  assert( argc==1);

  if( SQLITE_NULL==sqlite3_value_type(argv[0]) ){
    sqlite3_result_null(context);
    return;
  }
  z = sqlite3_value_text(argv[0]);
  rz = sqlite3StrDup(z);
  rtrim(rz);
  sqlite3_result_text(context, rz, -1, SQLITE_TRANSIENT);
  sqlite3_free(rz);
}

/*
**  Removes the whitespace at the begining and end of a string
*/
static void trimFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  const char *z;
  char *rz;
  /* try not to change data in argv */

  assert( argc==1);

  if( SQLITE_NULL==sqlite3_value_type(argv[0]) ){
    sqlite3_result_null(context);
    return;
  }
  z = sqlite3_value_text(argv[0]);
  rz = sqlite3StrDup(z);
  rtrim(rz);
  sqlite3_result_text(context, ltrim(rz), -1, SQLITE_TRANSIENT);
  sqlite3_free(rz);
}
#endif

/*
** given a pointer to a string s1, the length of that string (l1), a new string (s2)
** and it's length (l2) appends s2 to s1.
** All lengths in bytes.
** This is just an auxiliary function
*/
// static void _append(char **s1, int l1, const char *s2, int l2){
//   *s1 = realloc(*s1, (l1+l2+1)*sizeof(char));
//   strncpy((*s1)+l1, s2, l2);
//   *(*(s1)+l1+l2) = '\0';
// }

#ifndef HAVE_TRIM

/*
** given strings s, s1 and s2 replaces occurrences of s1 in s by s2
*/
static void replaceFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  const char *z1;     /* string s (first parameter) */
  const char *z2;     /* string s1 (second parameter) string to look for */
  const char *z3;     /* string s2 (third parameter) string to replace occurrences of s1 with */
  int lz1;
  int lz2;
  int lz3;
  int lzo=0;
  char *zo=0;
  int ret=0;
  const char *zt1;
  const char *zt2;

  assert( 3==argc );

  if( SQLITE_NULL==sqlite3_value_type(argv[0]) ){
    sqlite3_result_null(context);
    return;
  }

  z1 = sqlite3_value_text(argv[0]);
  z2 = sqlite3_value_text(argv[1]);
  z3 = sqlite3_value_text(argv[2]);
  /* handle possible null values */
  if( 0==z2 ){
    z2="";
  }
  if( 0==z3 ){
    z3="";
  }

  lz1 = strlen(z1);
  lz2 = strlen(z2);
  lz3 = strlen(z3);

#if 0
  /* special case when z2 is empty (or null) nothing will be changed */
  if( 0==lz2 ){
    sqlite3_result_text(context, z1, -1, SQLITE_TRANSIENT);
    return;
  }
#endif

  zt1=z1;
  zt2=z1;

  while(1){
    ret=_substr(z2,zt1 , 0, &zt2);

    if( ret<0 )
      break;

    _append(&zo, lzo, zt1, zt2-zt1);
    lzo+=zt2-zt1;
    _append(&zo, lzo, z3, lz3);
    lzo+=lz3;

    zt1=zt2+lz2;
  }
  _append(&zo, lzo, zt1, lz1-(zt1-z1));
  sqlite3_result_text(context, zo, -1, SQLITE_TRANSIENT);
  sqlite3_free(zo);
}
#endif

/*
** given a string returns the same string but with the characters in reverse order
*/
static void reverseFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  const char *z;
  const char *zt;
  char *rz;
  char *rzt;
  int l = 0;
  int i = 0;

  assert( 1==argc );

  if( SQLITE_NULL==sqlite3_value_type(argv[0]) ){
    sqlite3_result_null(context);
    return;
  }
  z = (char *)sqlite3_value_text(argv[0]);
  l = strlen(z);
  rz = (char *) sqlite3_malloc(l + 1);
  if (!rz){
    sqlite3_result_error_nomem(context);
    return;
  }
  rzt = rz+l;
  *(rzt--) = '\0';

  zt=z;
  while( sqliteCharVal((unsigned char *)zt)!=0 ){
    z=zt;
    sqliteNextChar(zt);
    for(i=1; zt-i>=z; ++i){
      *(rzt--)=*(zt-i);
    }
  }

  sqlite3_result_text(context, rz, -1, SQLITE_TRANSIENT);
  sqlite3_free(rz);
}

/*
** An instance of the following structure holds the context of a
** stdev() or variance() aggregate computation.
** implementaion of http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Algorithm_II
** less prone to rounding errors
*/
typedef struct StdevCtx StdevCtx;
struct StdevCtx {
  double rM;
  double rS;
  i64 cnt;          /* number of elements */
};

/*
** An instance of the following structure holds the context of a
** mode() or median() aggregate computation.
** Depends on structures defined in map.c (see map & map)
** These aggregate functions only work for integers and floats although
** they could be made to work for strings. This is usually considered meaningless.
** Only usuall order (for median), no use of collation functions (would this even make sense?)
*/
typedef struct ModeCtx ModeCtx;
struct ModeCtx {
  i64 riM;            /* integer value found so far */
  double rdM;         /* double value found so far */
  i64 cnt;            /* number of elements so far */
  double pcnt;        /* number of elements smaller than a percentile */
  i64 mcnt;           /* maximum number of occurrences (for mode) */
  i64 mn;             /* number of occurrences (for mode and percentiles) */
  i64 is_double;      /* whether the computation is being done for doubles (>0) or integers (=0) */
  map* m;             /* map structure used for the computation */
  int done;           /* whether the answer has been found */
};

/*
** called for each value received during a calculation of stdev or variance
*/
static void varianceStep(sqlite3_context *context, int argc, sqlite3_value **argv){
  StdevCtx *p;

  double delta;
  double x;

  assert( argc==1 );
  p = (StdevCtx *) sqlite3_aggregate_context(context, sizeof(*p));
  /* only consider non-null values */
  if( SQLITE_NULL != sqlite3_value_numeric_type(argv[0]) ){
    p->cnt++;
    x = sqlite3_value_double(argv[0]);
    delta = (x-p->rM);
    p->rM += delta/p->cnt;
    p->rS += delta*(x-p->rM);
  }
}

/*
** called for each value received during a calculation of mode of median
*/
static void modeStep(sqlite3_context *context, int argc, sqlite3_value **argv){
  ModeCtx *p;
  i64 xi=0;
  double xd=0.0;
  i64 *iptr;
  double *dptr;
  int type;

  assert( argc==1 );
  type = sqlite3_value_numeric_type(argv[0]);

  if( type == SQLITE_NULL)
    return;

  p = (ModeCtx *) sqlite3_aggregate_context(context, sizeof(*p));

  if( 0==(p->m) ){
    p->m = (map *) calloc(1, sizeof(map));
    if( type==SQLITE_INTEGER ){
      /* map will be used for integers */
      *(p->m) = map_make(int_cmp);
      p->is_double = 0;
    }else{
      p->is_double = 1;
      /* map will be used for doubles */
      *(p->m) = map_make(double_cmp);
    }
  }

  ++(p->cnt);

  if( 0==p->is_double ){
    xi = sqlite3_value_int64(argv[0]);
    iptr = (i64*)calloc(1,sizeof(i64));
    *iptr = xi;
    map_insert(p->m, iptr);
  }else{
    xd = sqlite3_value_double(argv[0]);
    dptr = (double*)calloc(1,sizeof(double));
    *dptr = xd;
    map_insert(p->m, dptr);
  }
}

/*
**  Auxiliary function that iterates all elements in a map and finds the mode
**  (most frequent value)
*/
static void modeIterate(void* e, i64 c, void* pp){
  i64 ei;
  double ed;
  ModeCtx *p = (ModeCtx*)pp;

  if( 0==p->is_double ){
    ei = *(int*)(e);

	if( p->mcnt==c ){
      ++p->mn;
    }else if( p->mcnt<c ){
      p->riM = ei;
      p->mcnt = c;
	  p->mn=1;
    }
  }else{
    ed = *(double*)(e);

	if( p->mcnt==c ){
      ++p->mn;
    }else if(p->mcnt<c){
      p->rdM = ed;
      p->mcnt = c;
	  p->mn=1;
    }
  }
}

/*
**  Auxiliary function that iterates all elements in a map and finds the median
**  (the value such that the number of elements smaller is equal the number of
**  elements larger)
*/
static void medianIterate(void* e, i64 c, void* pp){
  i64 ei;
  double ed;
  double iL;
  double iR;
  int il;
  int ir;
  ModeCtx *p = (ModeCtx*)pp;

  if(p->done>0)
    return;

  iL = p->pcnt;
  iR = p->cnt - p->pcnt;
  il = p->mcnt + c;
  ir = p->cnt - p->mcnt;

  if( il >= iL ){
    if( ir >= iR ){
    ++p->mn;
      if( 0==p->is_double ){
        ei = *(int*)(e);
        p->riM += ei;
      }else{
        ed = *(double*)(e);
        p->rdM += ed;
      }
    }else{
      p->done=1;
    }
  }
  p->mcnt+=c;
}

/*
** Returns the mode value
*/
static void modeFinalize(sqlite3_context *context){
  ModeCtx *p;
  p = (ModeCtx *) sqlite3_aggregate_context(context, 0);
  if( p && p->m ){
    map_iterate(p->m, modeIterate, p);
    map_destroy(p->m);
    free(p->m);

    if( 1==p->mn ){
      if( 0==p->is_double )
        sqlite3_result_int64(context, p->riM);
      else
        sqlite3_result_double(context, p->rdM);
    }
  }
}

/*
** auxiliary function for percentiles
*/
static void _medianFinalize(sqlite3_context *context){
  ModeCtx *p;
  p = (ModeCtx*) sqlite3_aggregate_context(context, 0);
  if( p && p->m ){
    p->done=0;
    map_iterate(p->m, medianIterate, p);
    map_destroy(p->m);
    free(p->m);

    if( 0==p->is_double )
      if( 1==p->mn )
      	sqlite3_result_int64(context, p->riM);
      else
      	sqlite3_result_double(context, p->riM*1.0/p->mn);
    else
      sqlite3_result_double(context, p->rdM/p->mn);
  }
}

/*
** Returns the median value
*/
static void medianFinalize(sqlite3_context *context){
  ModeCtx *p;
  p = (ModeCtx*) sqlite3_aggregate_context(context, 0);
  if( p!=0 ){
    p->pcnt = (p->cnt)/2.0;
    _medianFinalize(context);
  }
}

/*
** Returns the lower_quartile value
*/
static void lower_quartileFinalize(sqlite3_context *context){
  ModeCtx *p;
  p = (ModeCtx*) sqlite3_aggregate_context(context, 0);
  if( p!=0 ){
    p->pcnt = (p->cnt)/4.0;
    _medianFinalize(context);
  }
}

/*
** Returns the upper_quartile value
*/
static void upper_quartileFinalize(sqlite3_context *context){
  ModeCtx *p;
  p = (ModeCtx*) sqlite3_aggregate_context(context, 0);
  if( p!=0 ){
    p->pcnt = (p->cnt)*3/4.0;
    _medianFinalize(context);
  }
}

/*
** Returns the stdev value
*/
static void stdevFinalize(sqlite3_context *context){
  StdevCtx *p;
  p = (StdevCtx *) sqlite3_aggregate_context(context, 0);
  if( p && p->cnt>1 ){
    sqlite3_result_double(context, sqrt(p->rS/(p->cnt-1)));
  }else{
    sqlite3_result_double(context, 0.0);
  }
}

/*
** Returns the variance value
*/
static void varianceFinalize(sqlite3_context *context){
  StdevCtx *p;
  p = (StdevCtx *) sqlite3_aggregate_context(context, 0);
  if( p && p->cnt>1 ){
    sqlite3_result_double(context, p->rS/(p->cnt-1));
  }else{
    sqlite3_result_double(context, 0.0);
  }
}

#ifdef SQLITE_SOUNDEX

/* relicoder factored code */
/*
** Calculates the soundex value of a string
*/

static void soundex(const u8 *zIn, char *zResult){
  int i, j;
  static const unsigned char iCode[] = {
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 1, 2, 3, 0, 1, 2, 0, 0, 2, 2, 4, 5, 5, 0,
    1, 2, 6, 2, 3, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0,
    0, 0, 1, 2, 3, 0, 1, 2, 0, 0, 2, 2, 4, 5, 5, 0,
    1, 2, 6, 2, 3, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0,
  };

  for(i=0; zIn[i] && !isalpha(zIn[i]); i++){}
  if( zIn[i] ){
    zResult[0] = toupper(zIn[i]);
    for(j=1; j<4 && zIn[i]; i++){
      int code = iCode[zIn[i]&0x7f];
      if( code>0 ){
        zResult[j++] = code + '0';
      }
    }
    while( j<4 ){
      zResult[j++] = '0';
    }
    zResult[j] = 0;
  }else{
    strcpy(zResult, "?000");
  }
}

/*
** computes the number of different characters between the soundex value fo 2 strings
*/
static void differenceFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  char zResult1[8];
  char zResult2[8];
  char *zR1 = zResult1;
  char *zR2 = zResult2;
  int rVal = 0;
  int i = 0;
  const u8 *zIn1;
  const u8 *zIn2;

  assert( argc==2 );

  if( sqlite3_value_type(argv[0])==SQLITE_NULL || sqlite3_value_type(argv[1])==SQLITE_NULL ){
    sqlite3_result_null(context);
    return;
  }

  zIn1 = (u8*)sqlite3_value_text(argv[0]);
  zIn2 = (u8*)sqlite3_value_text(argv[1]);

  soundex(zIn1, zR1);
  soundex(zIn2, zR2);

  for(i=0; i<4; ++i){
    if( sqliteCharVal((unsigned char *)zR1)==sqliteCharVal((unsigned char *)zR2) )
      ++rVal;
    sqliteNextChar(zR1);
    sqliteNextChar(zR2);
  }
  sqlite3_result_int(context, rVal);
}
#endif

/*
** This function registered all of the above C functions as SQL
** functions.  This should be the only routine in this file with
** external linkage.
*/
int common_extension_functions(struct FuncDef **basic_funcs,
                               struct FuncDefAgg **agg_funcs) {
  static struct FuncDef aFuncs[] = {
    /* math.h */
    { "acos",               1, SQLITE_UTF8,    0, acosFunc,
      help_text("acos")
          .sql_function()
          .with_summary("Returns the arccosine of a number, in radians")
          .with_parameter({"num", "A cosine value that is between -1 and 1"})
          .with_tags({"math"})
          .with_example({
              "To get the arccosine of 0.2",
              "SELECT acos(0.2)"
          })},
    { "asin",               1, SQLITE_UTF8,    0, asinFunc,
      help_text("asin")
          .sql_function()
          .with_summary("Returns the arcsine of a number, in radians")
          .with_parameter({"num", "A sine value that is between -1 and 1"})
          .with_tags({"math"})
          .with_example({
              "To get the arcsine of 0.2",
              "SELECT asin(0.2)"
          })},
    { "atan",               1, SQLITE_UTF8,    0, atanFunc,
      help_text("atan")
          .sql_function()
          .with_summary("Returns the arctangent of a number, in radians")
          .with_parameter({"num", "The number"})
          .with_tags({"math"})
          .with_example({
              "To get the arctangent of 0.2",
              "SELECT atan(0.2)"
          })},
    { "atn2",               2, SQLITE_UTF8,    0, atn2Func,
      help_text("atn2")
          .sql_function()
          .with_summary("Returns the angle in the plane between the positive X axis and the ray from (0, 0) to the point (x, y)")
          .with_parameter({"y", "The y coordinate of the point"})
          .with_parameter({"x", "The x coordinate of the point"})
          .with_tags({"math"})
          .with_example({
              "To get the angle, in degrees, for the point at (5, 5)",
              "SELECT degrees(atn2(5, 5))"
          })},
    /* XXX alias */
    { "atan2",              2, SQLITE_UTF8,    0, atn2Func,
      help_text("atan2")
          .sql_function()
          .with_summary("Returns the angle in the plane between the positive X axis and the ray from (0, 0) to the point (x, y)")
          .with_parameter({"y", "The y coordinate of the point"})
          .with_parameter({"x", "The x coordinate of the point"})
          .with_tags({"math"})
          .with_example({
              "To get the angle, in degrees, for the point at (5, 5)",
              "SELECT degrees(atan2(5, 5))"
          })},
    { "acosh",              1, SQLITE_UTF8,    0, acoshFunc,
      help_text("acosh")
          .sql_function()
          .with_summary("Returns the hyperbolic arccosine of a number")
          .with_parameter({"num", "A number that is one or more"})
          .with_tags({"math"})
          .with_example({
              "To get the hyperbolic arccosine of 1.2",
              "SELECT acosh(1.2)"
          })},
    { "asinh",              1, SQLITE_UTF8,    0, asinhFunc,
      help_text("asinh")
          .sql_function()
          .with_summary("Returns the hyperbolic arcsine of a number")
          .with_parameter({"num", "The number"})
          .with_tags({"math"})
          .with_example({
              "To get the hyperbolic arcsine of 0.2",
              "SELECT asinh(0.2)"
          })},
    { "atanh",              1, SQLITE_UTF8,    0, atanhFunc,
      help_text("atanh")
          .sql_function()
          .with_summary("Returns the hyperbolic arctangent of a number")
          .with_parameter({"num", "The number"})
          .with_tags({"math"})
          .with_example({
              "To get the hyperbolic arctangent of 0.2",
              "SELECT atanh(0.2)"
          })},

    { "difference",         2, SQLITE_UTF8,    0, differenceFunc},
    { "degrees",            1, SQLITE_UTF8,    0, rad2degFunc,
      help_text("degrees")
          .sql_function()
          .with_summary("Converts radians to degrees")
          .with_parameter({"radians", "The radians value to convert to degrees"})
          .with_tags({"math"})
          .with_example({
              "To convert PI to degrees",
              "SELECT degrees(pi())"
          })},
    { "radians",            1, SQLITE_UTF8,    0, deg2radFunc,
      help_text("radians")
          .sql_function()
          .with_summary("Converts degrees to radians")
          .with_parameter({"degrees", "The degrees value to convert to radians"})
          .with_tags({"math"})
          .with_example({
              "To convert 180 degrees to radians",
              "SELECT radians(180)"
          })},

    { "cos",                1, SQLITE_UTF8,    0, cosFunc  },
    { "sin",                1, SQLITE_UTF8,    0, sinFunc },
    { "tan",                1, SQLITE_UTF8,    0, tanFunc },
    { "cot",                1, SQLITE_UTF8,    0, cotFunc },
    { "cosh",               1, SQLITE_UTF8,    0, coshFunc  },
    { "sinh",               1, SQLITE_UTF8,    0, sinhFunc },
    { "tanh",               1, SQLITE_UTF8,    0, tanhFunc },
    { "coth",               1, SQLITE_UTF8,    0, cothFunc },

    { "exp",                1, SQLITE_UTF8,    0, expFunc,
      help_text("exp")
          .sql_function()
          .with_summary("Returns the value of e raised to the power of x")
          .with_parameter({"x", "The exponent"})
          .with_tags({"math"})
          .with_example({
              "To raise e to 2",
              "SELECT exp(2)"
          })},
    { "log",                1, SQLITE_UTF8,    0, logFunc,
      help_text("log")
          .sql_function()
          .with_summary("Returns the natural logarithm of x")
          .with_parameter({"x", "The number"})
          .with_tags({"math"})
          .with_example({
              "To get the natual logarithm of 8",
              "SELECT log(8)"
          })},
    { "log10",              1, SQLITE_UTF8,    0, log10Func,
      help_text("log10")
          .sql_function()
          .with_summary("Returns the base-10 logarithm of X")
          .with_parameter({"x", "The number"})
          .with_tags({"math"})
          .with_example({
              "To get the logarithm of 100",
              "SELECT log10(100)"
          })},
    { "power",              2, SQLITE_UTF8,    0, powerFunc,
      help_text("power")
          .sql_function()
          .with_summary("Returns the base to the given exponent")
          .with_parameter({"base", "The base number"})
          .with_parameter({"exp", "The exponent"})
          .with_tags({"math"})
          .with_example({
              "To raise two to the power of three",
              "SELECT power(2, 3)"
          })},
    { "sign",               1, SQLITE_UTF8,    0, signFunc,
      help_text("sign")
          .sql_function()
          .with_summary("Returns the sign of the given number as -1, 0, or 1")
          .with_parameter({"num", "The number"})
          .with_tags({"math"})
          .with_example({
              "To get the sign of 10",
              "SELECT sign(10)"
          })
          .with_example({
              "To get the sign of 0",
              "SELECT sign(0)"
          })
          .with_example({
              "To get the sign of -10",
              "SELECT sign(-10)"
          })},
    { "sqrt",               1, SQLITE_UTF8,    0, sqrtFunc },
    { "square",             1, SQLITE_UTF8,    0, squareFunc,
      help_text("square")
          .sql_function()
          .with_summary("Returns the square of the argument")
          .with_parameter({"num", "The number to square"})
          .with_tags({"math"})
          .with_example({
              "To get the square of two",
              "SELECT square(2)"
          })},

    { "ceil",               1, SQLITE_UTF8,    0, ceilFunc,
      help_text("ceil")
          .sql_function()
          .with_summary("Returns the smallest integer that is not less than the argument")
          .with_parameter({"num", "The number to raise to the ceiling"})
          .with_tags({"math"})
          .with_example({
              "To get the ceiling of 1.23",
              "SELECT ceil(1.23)"
          })},
    { "floor",              1, SQLITE_UTF8,    0, floorFunc,
      help_text("floor")
          .sql_function()
          .with_summary("Returns the largest integer that is not greater than the argument")
          .with_parameter({"num", "The number to lower to the floor"})
          .with_tags({"math"})
          .with_example({
              "To get the floor of 1.23",
              "SELECT floor(1.23)"
          })},

    { "pi",                 0, SQLITE_UTF8,    1, piFunc,
      help_text("pi")
          .sql_function()
          .with_summary("Returns the value of PI")
          .with_tags({"math"})
          .with_example({
              "To get the value of PI",
              "SELECT pi()"
          })},


    /* string */
    { "replicate",          2, SQLITE_UTF8,    0, replicateFunc,
      help_text("replicate")
          .sql_function()
          .with_summary("Returns the given string concatenated N times.")
          .with_parameter({"str", "The string to replicate."})
          .with_parameter({"N", "The number of times to replicate the string."})
          .with_tags({"string"})
          .with_example({
              "To repeat the string 'abc' three times",
              "SELECT replicate('abc', 3)"
          })
    },
    { "charindex",          2, SQLITE_UTF8,    0, charindexFunc },
    { "charindex",          3, SQLITE_UTF8,    0, charindexFunc,
      help_text("charindex")
          .sql_function()
          .with_summary("Finds the first occurrence of the needle within the haystack and returns the number of prior characters plus 1, or 0 if Y is nowhere found within X")
          .with_parameter({"needle", "The string to look for in the haystack"})
          .with_parameter({"haystack", "The string to search within"})
          .with_parameter(help_text("start", "The one-based index within the haystack to start the search")
                              .optional())
          .with_tags({"string"})
          .with_example({
              "To search for the string 'abc' within 'abcabc' and starting at position 2",
              "SELECT charindex('abc', 'abcabc', 2)"
          })
          .with_example({
              "To search for the string 'abc' within 'abcdef' and starting at position 2",
              "SELECT charindex('abc', 'abcdef', 2)"
          })},
    { "leftstr",            2, SQLITE_UTF8,    0, leftFunc,
      help_text("leftstr")
          .sql_function()
          .with_summary("Returns the N leftmost (UTF-8) characters in the given string.")
          .with_parameter({"str", "The string to return subset."})
          .with_parameter({"N", "The number of characters from the left side of the string to return."})
          .with_tags({"string"})
          .with_example({
              "To get the first character of the string 'abc'",
              "SELECT leftstr('abc', 1)"
          })
          .with_example({
              "To get the first ten characters of a string, regardless of size",
              "SELECT leftstr('abc', 10)"
          })
    },
    { "rightstr",           2, SQLITE_UTF8,    0, rightFunc,
      help_text("rightstr")
          .sql_function()
          .with_summary("Returns the N rightmost (UTF-8) characters in the given string.")
          .with_parameter({"str", "The string to return subset."})
          .with_parameter({"N", "The number of characters from the right side of the string to return."})
          .with_tags({"string"})
          .with_example({
              "To get the last character of the string 'abc'",
              "SELECT rightstr('abc', 1)"
          })
          .with_example({
              "To get the last ten characters of a string, regardless of size",
              "SELECT rightstr('abc', 10)"
          })
    },
#ifndef HAVE_TRIM
    { "ltrim",              1, SQLITE_UTF8,    0, ltrimFunc },
    { "rtrim",              1, SQLITE_UTF8,    0, rtrimFunc },
    { "trim",               1, SQLITE_UTF8,    0, trimFunc },
    { "replace",            3, SQLITE_UTF8,    0, replaceFunc },
#endif
    { "reverse",            1, SQLITE_UTF8,    0, reverseFunc,
      help_text("reverse")
          .sql_function()
          .with_summary("Returns the reverse of the given string.")
          .with_parameter({"str", "The string to reverse."})
          .with_tags({"string"})
          .with_example({
              "To reverse the string 'abc'",
              "SELECT reverse('abc')"
          })
    },
    { "proper",             1, SQLITE_UTF8,    0, properFunc,
      help_text("proper")
          .sql_function()
          .with_summary("Capitalize the first character of words in the given string")
          .with_parameter({"str", "The string to capitalize."})
          .with_tags({"string"})
          .with_example({
              "To capitalize the words in the string 'hello, world!'",
              "SELECT proper('hello, world!')"
          })},
    { "padl",               2, SQLITE_UTF8,    0, padlFunc,
      help_text("padl")
          .sql_function()
          .with_summary("Pad the given string with leading spaces until it reaches the desired length")
          .with_parameter({"str", "The string to pad"})
          .with_parameter({"len", "The minimum desired length of the output string"})
          .with_tags({"string"})
          .with_example({
              "To pad the string 'abc' to a length of six characters",
              "SELECT padl('abc', 6)"
          })
          .with_example({
              "To pad the string 'abcdef' to a length of four characters",
              "SELECT padl('abcdef', 4)"
          })},
    { "padr",               2, SQLITE_UTF8,    0, padrFunc,
        help_text("padr")
        .sql_function()
        .with_summary("Pad the given string with trailing spaces until it reaches the desired length")
        .with_parameter({"str", "The string to pad"})
        .with_parameter({"len", "The minimum desired length of the output string"})
        .with_tags({"string"})
        .with_example({
            "To pad the string 'abc' to a length of six characters",
            "SELECT padr('abc', 6) || 'def'"
        })
        .with_example({
            "To pad the string 'abcdef' to a length of four characters",
            "SELECT padr('abcdef', 4) || 'ghi'"
        })},
    { "padc",               2, SQLITE_UTF8,    0, padcFunc,
      help_text("padc")
          .sql_function()
          .with_summary("Pad the given string with enough spaces to make it centered within the given length")
          .with_parameter({"str", "The string to pad"})
          .with_parameter({"len", "The minimum desired length of the output string"})
          .with_tags({"string"})
          .with_example({
              "To pad the string 'abc' to a length of six characters",
              "SELECT padc('abc', 6) || 'def'"
          })
          .with_example({
              "To pad the string 'abcdef' to a length of eight characters",
              "SELECT padc('abcdef', 8) || 'ghi'"
          })},
    { "strfilter",          2, SQLITE_UTF8,    0, strfilterFunc,
      help_text("strfilter")
          .sql_function()
          .with_summary("Returns the source string with only the characters given in the second parameter")
          .with_parameter({"source", "The string to filter"})
          .with_parameter({"include", "The characters to include in the result"})
          .with_tags({"string"})
          .with_example({
              "To get the 'b', 'c', and 'd' characters from the string 'abcabc'",
              "SELECT strfilter('abcabc', 'bcd')"
          })},

    { NULL }
  };

  /* Aggregate functions */
  static struct FuncDefAgg aAggs[] = {
    { "stdev",            1, 0, varianceStep, stdevFinalize  },
    { "stddev",           1, 0, varianceStep, stdevFinalize  },
    { "variance",         1, 0, varianceStep, varianceFinalize  },
    { "mode",             1, 0, modeStep,     modeFinalize  },
    { "median",           1, 0, modeStep,     medianFinalize  },
    { "lower_quartile",   1, 0, modeStep,     lower_quartileFinalize  },
    { "upper_quartile",   1, 0, modeStep,     upper_quartileFinalize  },

    { NULL }
  };

  *basic_funcs = aFuncs;
  *agg_funcs = aAggs;

  return SQLITE_OK;
}

#ifdef COMPILE_SQLITE_EXTENSIONS_AS_LOADABLE_MODULE
int sqlite3_extension_init(
    sqlite3 *db, char **pzErrMsg, const sqlite3_api_routines *pApi){
  SQLITE_EXTENSION_INIT2(pApi);
  RegisterExtensionFunctions(db);
  return 0;
}
#endif /* COMPILE_SQLITE_EXTENSIONS_AS_LOADABLE_MODULE */

map map_make(cmp_func cmp){
  map r;
  r.cmp=cmp;
  r.base = 0;
  r.free = 0;

  return r;
}

void* xcalloc(size_t nmemb, size_t size, const char* s){
  void* ret = calloc(nmemb, size);
  return ret;
}

static void xfree(void* p){
  free(p);
}

void node_insert(node** n, cmp_func cmp, void *e){
  int c;
  node* nn;
  if(*n==0){
    nn = (node*)xcalloc(1,sizeof(node), "for node");
    nn->data = e;
    nn->count = 1;
    *n=nn;
  }else{
    c=cmp((*n)->data,e);
    if(0==c){
      ++((*n)->count);
      xfree(e);
    }else if(c>0){
      /* put it right here */
      node_insert(&((*n)->l), cmp, e);
    }else{
      node_insert(&((*n)->r), cmp, e);
    }
  }
}

void map_insert(map *m, void *e){
  node_insert(&(m->base), m->cmp, e);
}

void node_iterate(node *n, map_iterator iter, void* p){
  if(n){
    if(n->l)
      node_iterate(n->l, iter, p);
    iter(n->data, n->count, p);
    if(n->r)
      node_iterate(n->r, iter, p);
  }
}

void map_iterate(map *m, map_iterator iter, void* p){
  node_iterate(m->base, iter, p);
}

void node_destroy(node *n){
  if(0!=n){
    xfree(n->data);
    if(n->l)
      node_destroy(n->l);
    if(n->r)
      node_destroy(n->r);

    xfree(n);
  }
}

void map_destroy(map *m){
  node_destroy(m->base);
}

int int_cmp(const void *a, const void *b){
  int64_t aa = *(int64_t *)(a);
  int64_t bb = *(int64_t *)(b);
  /* printf("cmp %d <=> %d\n",aa,bb); */
  if(aa==bb)
    return 0;
  else if(aa<bb)
    return -1;
  else
    return 1;
}

int double_cmp(const void *a, const void *b){
  double aa = *(double *)(a);
  double bb = *(double *)(b);
  /* printf("cmp %d <=> %d\n",aa,bb); */
  if(aa==bb)
    return 0;
  else if(aa<bb)
    return -1;
  else
    return 1;
}

void print_elem(void *e, int64_t c, void* p){
  int ee = *(int*)(e);
  printf("%d => %" PRId64 "\n", ee,c);
}