From 18657a960e125336f704ea058e25c27bd3900dcb Mon Sep 17 00:00:00 2001 From: Daniel Baumann Date: Sun, 5 May 2024 19:28:19 +0200 Subject: Adding upstream version 3.40.1. Signed-off-by: Daniel Baumann --- ext/misc/ieee754.c | 293 +++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 293 insertions(+) create mode 100644 ext/misc/ieee754.c (limited to 'ext/misc/ieee754.c') diff --git a/ext/misc/ieee754.c b/ext/misc/ieee754.c new file mode 100644 index 0000000..ff5d2d3 --- /dev/null +++ b/ext/misc/ieee754.c @@ -0,0 +1,293 @@ +/* +** 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 +#include + +/* 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>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>= 8; + } + sqlite3_result_blob(context, a, sizeof(r), SQLITE_TRANSIENT); + } +} + + +#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 }, + + }; + unsigned int i; + int rc = SQLITE_OK; + SQLITE_EXTENSION_INIT2(pApi); + (void)pzErrMsg; /* Unused parameter */ + for(i=0; i