/*
** 2013-04-17
**
** 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 SQLite extension implements functions for the exact display
** and input of IEEE754 Binary64 floating-point numbers.
**
** ieee754(X)
** ieee754(Y,Z)
**
** In the first form, the value X should be a floating-point number.
** The function will return a string of the form 'ieee754(Y,Z)' where
** Y and Z are integers such that X==Y*pow(2,Z).
**
** In the second form, Y and Z are integers which are the mantissa and
** base-2 exponent of a new floating point number. The function returns
** a floating-point value equal to Y*pow(2,Z).
**
** Examples:
**
** ieee754(2.0) -> 'ieee754(2,0)'
** ieee754(45.25) -> 'ieee754(181,-2)'
** ieee754(2, 0) -> 2.0
** ieee754(181, -2) -> 45.25
**
** Two additional functions break apart the one-argument ieee754()
** result into separate integer values:
**
** ieee754_mantissa(45.25) -> 181
** ieee754_exponent(45.25) -> -2
**
** These functions convert binary64 numbers into blobs and back again.
**
** ieee754_from_blob(x'3ff0000000000000') -> 1.0
** ieee754_to_blob(1.0) -> x'3ff0000000000000'
**
** In all single-argument functions, if the argument is an 8-byte blob
** then that blob is interpreted as a big-endian binary64 value.
**
**
** EXACT DECIMAL REPRESENTATION OF BINARY64 VALUES
** -----------------------------------------------
**
** This extension in combination with the separate 'decimal' extension
** can be used to compute the exact decimal representation of binary64
** values. To begin, first compute a table of exponent values:
**
** CREATE TABLE pow2(x INTEGER PRIMARY KEY, v TEXT);
** WITH RECURSIVE c(x,v) AS (
** VALUES(0,'1')
** UNION ALL
** SELECT x+1, decimal_mul(v,'2') FROM c WHERE x+1<=971
** ) INSERT INTO pow2(x,v) SELECT x, v FROM c;
** WITH RECURSIVE c(x,v) AS (
** VALUES(-1,'0.5')
** UNION ALL
** SELECT x-1, decimal_mul(v,'0.5') FROM c WHERE x-1>=-1075
** ) INSERT INTO pow2(x,v) SELECT x, v FROM c;
**
** Then, to compute the exact decimal representation of a floating
** point value (the value 47.49 is used in the example) do:
**
** WITH c(n) AS (VALUES(47.49))
** ---------------^^^^^---- Replace with whatever you want
** SELECT decimal_mul(ieee754_mantissa(c.n),pow2.v)
** FROM pow2, c WHERE pow2.x=ieee754_exponent(c.n);
**
** Here is a query to show various boundry values for the binary64
** number format:
**
** WITH c(name,bin) AS (VALUES
** ('minimum positive value', x'0000000000000001'),
** ('maximum subnormal value', x'000fffffffffffff'),
** ('mininum positive nornal value', x'0010000000000000'),
** ('maximum value', x'7fefffffffffffff'))
** SELECT c.name, decimal_mul(ieee754_mantissa(c.bin),pow2.v)
** FROM pow2, c WHERE pow2.x=ieee754_exponent(c.bin);
**
*/
#include "sqlite3ext.h"
SQLITE_EXTENSION_INIT1
#include <assert.h>
#include <string.h>
/* Mark a function parameter as unused, to suppress nuisance compiler
** warnings. */
#ifndef UNUSED_PARAMETER
# define UNUSED_PARAMETER(X) (void)(X)
#endif
/*
** Implementation of the ieee754() function
*/
static void ieee754func(
sqlite3_context *context,
int argc,
sqlite3_value **argv
){
if( argc==1 ){
sqlite3_int64 m, a;
double r;
int e;
int isNeg;
char zResult[100];
assert( sizeof(m)==sizeof(r) );
if( sqlite3_value_type(argv[0])==SQLITE_BLOB
&& sqlite3_value_bytes(argv[0])==sizeof(r)
){
const unsigned char *x = sqlite3_value_blob(argv[0]);
unsigned int i;
sqlite3_uint64 v = 0;
for(i=0; i<sizeof(r); i++){
v = (v<<8) | x[i];
}
memcpy(&r, &v, sizeof(r));
}else{
r = sqlite3_value_double(argv[0]);
}
if( r<0.0 ){
isNeg = 1;
r = -r;
}else{
isNeg = 0;
}
memcpy(&a,&r,sizeof(a));
if( a==0 ){
e = 0;
m = 0;
}else{
e = a>>52;
m = a & ((((sqlite3_int64)1)<<52)-1);
if( e==0 ){
m <<= 1;
}else{
m |= ((sqlite3_int64)1)<<52;
}
while( e<1075 && m>0 && (m&1)==0 ){
m >>= 1;
e++;
}
if( isNeg ) m = -m;
}
switch( *(int*)sqlite3_user_data(context) ){
case 0:
sqlite3_snprintf(sizeof(zResult), zResult, "ieee754(%lld,%d)",
m, e-1075);
sqlite3_result_text(context, zResult, -1, SQLITE_TRANSIENT);
break;
case 1:
sqlite3_result_int64(context, m);
break;
case 2:
sqlite3_result_int(context, e-1075);
break;
}
}else{
sqlite3_int64 m, e, a;
double r;
int isNeg = 0;
m = sqlite3_value_int64(argv[0]);
e = sqlite3_value_int64(argv[1]);
/* Limit the range of e. Ticket 22dea1cfdb9151e4 2021-03-02 */
if( e>10000 ){
e = 10000;
}else if( e<-10000 ){
e = -10000;
}
if( m<0 ){
isNeg = 1;
m = -m;
if( m<0 ) return;
}else if( m==0 && e>-1000 && e<1000 ){
sqlite3_result_double(context, 0.0);
return;
}
while( (m>>32)&0xffe00000 ){
m >>= 1;
e++;
}
while( m!=0 && ((m>>32)&0xfff00000)==0 ){
m <<= 1;
e--;
}
e += 1075;
if( e<=0 ){
/* Subnormal */
if( 1-e >= 64 ){
m = 0;
}else{
m >>= 1-e;
}
e = 0;
}else if( e>0x7ff ){
e = 0x7ff;
}
a = m & ((((sqlite3_int64)1)<<52)-1);
a |= e<<52;
if( isNeg ) a |= ((sqlite3_uint64)1)<<63;
memcpy(&r, &a, sizeof(r));
sqlite3_result_double(context, r);
}
}
/*
** Functions to convert between blobs and floats.
*/
static void ieee754func_from_blob(
sqlite3_context *context,
int argc,
sqlite3_value **argv
){
UNUSED_PARAMETER(argc);
if( sqlite3_value_type(argv[0])==SQLITE_BLOB
&& sqlite3_value_bytes(argv[0])==sizeof(double)
){
double r;
const unsigned char *x = sqlite3_value_blob(argv[0]);
unsigned int i;
sqlite3_uint64 v = 0;
for(i=0; i<sizeof(r); i++){
v = (v<<8) | x[i];
}
memcpy(&r, &v, sizeof(r));
sqlite3_result_double(context, r);
}
}
static void ieee754func_to_blob(
sqlite3_context *context,
int argc,
sqlite3_value **argv
){
UNUSED_PARAMETER(argc);
if( sqlite3_value_type(argv[0])==SQLITE_FLOAT
|| sqlite3_value_type(argv[0])==SQLITE_INTEGER
){
double r = sqlite3_value_double(argv[0]);
sqlite3_uint64 v;
unsigned char a[sizeof(r)];
unsigned int i;
memcpy(&v, &r, sizeof(r));
for(i=1; i<=sizeof(r); i++){
a[sizeof(r)-i] = v&0xff;
v >>= 8;
}
sqlite3_result_blob(context, a, sizeof(r), SQLITE_TRANSIENT);
}
}
/*
** SQL Function: ieee754_inc(r,N)
**
** Move the floating point value r by N quantums and return the new
** values.
**
** Behind the scenes: this routine merely casts r into a 64-bit unsigned
** integer, adds N, then casts the value back into float.
**
** Example: To find the smallest positive number:
**
** SELECT ieee754_inc(0.0,+1);
*/
static void ieee754inc(
sqlite3_context *context,
int argc,
sqlite3_value **argv
){
double r;
sqlite3_int64 N;
sqlite3_uint64 m1, m2;
double r2;
UNUSED_PARAMETER(argc);
r = sqlite3_value_double(argv[0]);
N = sqlite3_value_int64(argv[1]);
memcpy(&m1, &r, 8);
m2 = m1 + N;
memcpy(&r2, &m2, 8);
sqlite3_result_double(context, r2);
}
#ifdef _WIN32
__declspec(dllexport)
#endif
int sqlite3_ieee_init(
sqlite3 *db,
char **pzErrMsg,
const sqlite3_api_routines *pApi
){
static const struct {
char *zFName;
int nArg;
int iAux;
void (*xFunc)(sqlite3_context*,int,sqlite3_value**);
} aFunc[] = {
{ "ieee754", 1, 0, ieee754func },
{ "ieee754", 2, 0, ieee754func },
{ "ieee754_mantissa", 1, 1, ieee754func },
{ "ieee754_exponent", 1, 2, ieee754func },
{ "ieee754_to_blob", 1, 0, ieee754func_to_blob },
{ "ieee754_from_blob", 1, 0, ieee754func_from_blob },
{ "ieee754_inc", 2, 0, ieee754inc },
};
unsigned int i;
int rc = SQLITE_OK;
SQLITE_EXTENSION_INIT2(pApi);
(void)pzErrMsg; /* Unused parameter */
for(i=0; i<sizeof(aFunc)/sizeof(aFunc[0]) && rc==SQLITE_OK; i++){
rc = sqlite3_create_function(db, aFunc[i].zFName, aFunc[i].nArg,
SQLITE_UTF8|SQLITE_INNOCUOUS,
(void*)&aFunc[i].iAux,
aFunc[i].xFunc, 0, 0);
}
return rc;
}