Merge latest trunk changes with this branch.

FossilOrigin-Name: 5ee3c27e20d12a126fb773b428bb864102b949a5b26a8d5c523753dcedf4be10

1 files changed, 161 insertions, 21 deletions

diff --git a/ext/misc/ieee754.c b/ext/misc/ieee754.c
index a67c91878..cb274c3f7 100644
--- a/ext/misc/ieee754.c
+++ b/ext/misc/ieee754.c
@@ -26,10 +26,64 @@
 **
 ** Examples:
 **
-**     ieee754(2.0)       ->     'ieee754(2,0)'
-**     ieee754(45.25)     ->     'ieee754(181,-2)'
-**     ieee754(2, 0)      ->     2.0
-**     ieee754(181, -2)   ->     45.25
+**     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
@@ -51,8 +105,19 @@ static void ieee754func(
     int isNeg;
     char zResult[100];
     assert( sizeof(m)==sizeof(r) );
-    if( sqlite3_value_type(argv[0])!=SQLITE_FLOAT ) return;
-    r = sqlite3_value_double(argv[0]);
+    if( sqlite3_value_type(argv[0])==SQLITE_BLOB
+     && sqlite3_value_bytes(argv[0])==sizeof(r)
+    ){
+      const unsigned char *x = sqlite3_value_blob(argv[0]);
+      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;
@@ -66,17 +131,31 @@ static void ieee754func(
     }else{
       e = a>>52;
       m = a & ((((sqlite3_int64)1)<<52)-1);
-      m |= ((sqlite3_int64)1)<<52;
+      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;
     }
-    sqlite3_snprintf(sizeof(zResult), zResult, "ieee754(%lld,%d)",
-                     m, e-1075);
-    sqlite3_result_text(context, zResult, -1, SQLITE_TRANSIENT);
-  }else if( argc==2 ){
+    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;
@@ -86,7 +165,7 @@ static void ieee754func(
       isNeg = 1;
       m = -m;
       if( m<0 ) return;
-    }else if( m==0 && e>1000 && e<1000 ){
+    }else if( m==0 && e>-1000 && e<1000 ){
       sqlite3_result_double(context, 0.0);
       return;
     }
@@ -99,8 +178,13 @@ static void ieee754func(
       e--;
     }
     e += 1075;
-    if( e<0 ) e = m = 0;
-    if( e>0x7ff ) e = 0x7ff;
+    if( e<=0 ){
+      /* Subnormal */
+      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;
@@ -109,6 +193,49 @@ static void ieee754func(
   }
 }
 
+/*
+** Functions to convert between blobs and floats.
+*/
+static void ieee754func_from_blob(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  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]);
+    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
+){
+  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)];
+    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);
+  }
+}
+
 
 #ifdef _WIN32
 __declspec(dllexport)
@@ -118,16 +245,29 @@ int sqlite3_ieee_init(
   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 },
+
+  };
+  int i;
   int rc = SQLITE_OK;
   SQLITE_EXTENSION_INIT2(pApi);
   (void)pzErrMsg;  /* Unused parameter */
-  rc = sqlite3_create_function(db, "ieee754", 1, 
-                               SQLITE_UTF8|SQLITE_INNOCUOUS, 0,
-                               ieee754func, 0, 0);
-  if( rc==SQLITE_OK ){
-    rc = sqlite3_create_function(db, "ieee754", 2,
-                                 SQLITE_UTF8|SQLITE_INNOCUOUS, 0,
-                                 ieee754func, 0, 0);
+  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;
 }