/* ** 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