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