From a1b0ff173520fc73a182e57b06b1d0228b343711 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Fri, 30 Jun 2023 18:35:43 +0000
Subject: [PATCH 01/17] Experiments with a new algorithm for converting
 ieee-754 binary64 numbers into decimal.

FossilOrigin-Name: e923405e448385085224f9289991b303d86b02763535ea77d6fcee98ba6fc1f2
---
 manifest        | 22 +++++++++--------
 manifest.uuid   |  2 +-
 src/func.c      | 22 +++++++++++++++++
 src/sqliteInt.h | 15 ++++++++++++
 src/util.c      | 63 +++++++++++++++++++++++++++++++++++++++++++++++++
 5 files changed, 113 insertions(+), 11 deletions(-)

diff --git a/manifest b/manifest
index 0b84625ebf..95d4799b5d 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Add\ssupport\sfor\ssqlite3_stmt_scanstatus_v2()\sprofiling\sof\sGROUP\sBY\sclauses\sthat\suse\sa\stemp\sb-tree,\sand\sfor\ssub-queries\simplemented\sas\sco-routines.
-D 2023-06-30T18:31:37.545
+C Experiments\swith\sa\snew\salgorithm\sfor\sconverting\sieee-754\sbinary64\snumbers\ninto\sdecimal.
+D 2023-06-30T18:35:43.344
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -590,7 +590,7 @@ F src/delete.c cd5f5cd06ed0b6a882ec1a8c2a0d73b3cecb28479ad19e9931c4706c5e2182be
 F src/expr.c 8d1656b65e26af3e34f78e947ac423f0d20c214ed25a67486e433bf16ca6b543
 F src/fault.c 460f3e55994363812d9d60844b2a6de88826e007
 F src/fkey.c a7fcbf7e66d14dbb73cf49f31489ebf66d0e6006c62b95246924a3bae9f37b36
-F src/func.c 6b4804738b4d869f40625958b476a8f964d3df65b626e72a530d76051863cf32
+F src/func.c 699e19ca0dc580a024eb343f3a3abfb646e5438e36d377023d485a3038d789d5
 F src/global.c bd0892ade7289f6e20bff44c07d06371f2ff9b53cea359e7854b9b72f65adc30
 F src/hash.c 9ee4269fb1d6632a6fecfb9479c93a1f29271bddbbaf215dd60420bcb80c7220
 F src/hash.h 3340ab6e1d13e725571d7cee6d3e3135f0779a7d8e76a9ce0a85971fa3953c51
@@ -642,7 +642,7 @@ F src/shell.c.in 2c02c819349de410d63fcc0217763dfe5a42dbe58f2d68046d4ea8a376d12c2
 F src/sqlite.h.in 3076d78836b6dac53b3ab0875fc8fd15bca8077aad4d33c85336e05af6aef8c7
 F src/sqlite3.rc 5121c9e10c3964d5755191c80dd1180c122fc3a8
 F src/sqlite3ext.h da473ce2b3d0ae407a6300c4a164589b9a6bfdbec9462688a8593ff16f3bb6e4
-F src/sqliteInt.h b677ba33397479f9a2fa1223fcd24b561cc8c77c7d073798f7b7118e15d69dbb
+F src/sqliteInt.h 6ef127217c54e4707b1ca500508340542ca3c2a5aa08ee7a00aaa4834e68992d
 F src/sqliteLimit.h 33b1c9baba578d34efe7dfdb43193b366111cdf41476b1e82699e14c11ee1fb6
 F src/status.c 160c445d7d28c984a0eae38c144f6419311ed3eace59b44ac6dafc20db4af749
 F src/table.c 0f141b58a16de7e2fbe81c308379e7279f4c6b50eb08efeec5892794a0ba30d1
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c 4264102045fdb36e9af3ff361e390a5f7a76342a2bd7069e55d8ad332026d6b5
+F src/util.c 447fd1d981bab37788397c24f980ce555438168f28badde1227441f6d67f1214
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -2041,9 +2041,11 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P f936f101406069b29218c89a36581b4497226fb61906782ea368f12d943c901c 4e8718dc35dbbaf75f17265a88d14acd9750dc75efbadf41377f9c97e732009c
-R 4da01a7efae23c104b98c2eba70ec2ef
-T +closed 4e8718dc35dbbaf75f17265a88d14acd9750dc75efbadf41377f9c97e732009c
-U dan
-Z 8ca5997f8884b68f398b8d0f077d59ae
+P 7afad1f759f7ceda873c6d869422fd56fe4399c2d24d47ad9bc3b84b06d830d1
+R b84c58ae5f50c9a21c1125fd73d7f10d
+T *branch * fp-to-decimal-refactor
+T *sym-fp-to-decimal-refactor *
+T -sym-trunk *
+U drh
+Z aad0befdc05a87e7f362b0543d2a6962
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index f482cd32b9..2a088950c5 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-7afad1f759f7ceda873c6d869422fd56fe4399c2d24d47ad9bc3b84b06d830d1
\ No newline at end of file
+e923405e448385085224f9289991b303d86b02763535ea77d6fcee98ba6fc1f2
\ No newline at end of file
diff --git a/src/func.c b/src/func.c
index b243591863..4cf930b208 100644
--- a/src/func.c
+++ b/src/func.c
@@ -2371,6 +2371,23 @@ static void signFunc(
   sqlite3_result_int(context, x<0.0 ? -1 : x>0.0 ? +1 : 0);
 }
 
+
+#if 1 /* Temporary prototyping logic */
+static void fpdecodeFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  double r = sqlite3_value_double(argv[0]);
+  FpDecode s;
+  char zBuf[50];
+  UNUSED_PARAMETER(argc);
+  sqlite3FpDecode(&s, r);
+  sqlite3_snprintf(sizeof(zBuf), zBuf, "%c%.*s/%d", s.sign, s.n, s.z, s.iDP);
+  sqlite3_result_text(context, zBuf, -1, SQLITE_TRANSIENT);
+}
+#endif /* Temporary prototyping logic */
+
 /*
 ** All of the FuncDef structures in the aBuiltinFunc[] array above
 ** to the global function hash table.  This occurs at start-time (as
@@ -2442,6 +2459,11 @@ void sqlite3RegisterBuiltinFunctions(void){
     FUNCTION(unicode,            1, 0, 0, unicodeFunc      ),
     FUNCTION(char,              -1, 0, 0, charFunc         ),
     FUNCTION(abs,                1, 0, 0, absFunc          ),
+
+#if 1  /* Temporary prototyping function */
+    FUNCTION(fpdecode,           1, 0, 0, fpdecodeFunc     ),
+#endif
+  
 #ifndef SQLITE_OMIT_FLOATING_POINT
     FUNCTION(round,              1, 0, 0, roundFunc        ),
     FUNCTION(round,              2, 0, 0, roundFunc        ),
diff --git a/src/sqliteInt.h b/src/sqliteInt.h
index d7a2d90fc2..b4705b5e26 100644
--- a/src/sqliteInt.h
+++ b/src/sqliteInt.h
@@ -1239,6 +1239,7 @@ typedef struct Schema Schema;
 typedef struct Expr Expr;
 typedef struct ExprList ExprList;
 typedef struct FKey FKey;
+typedef struct FpDecode FpDecode;
 typedef struct FuncDestructor FuncDestructor;
 typedef struct FuncDef FuncDef;
 typedef struct FuncDefHash FuncDefHash;
@@ -4597,6 +4598,20 @@ struct PrintfArguments {
   sqlite3_value **apArg;   /* The argument values */
 };
 
+/*
+** An instance of this object receives the decoding of a floating point
+** value into an approximate decimal representation.
+*/
+struct FpDecode {
+  char sign;           /* '+' or '-' */
+  char isNan;          /* True if not-a-number */
+  char isInf;          /* True if infinity */
+  int n;               /* Significant digits in the decode */
+  int iDP;             /* Location of the decimal point */
+  char z[24];          /* Significiant digits */
+};
+
+void sqlite3FpDecode(FpDecode*,double);
 char *sqlite3MPrintf(sqlite3*,const char*, ...);
 char *sqlite3VMPrintf(sqlite3*,const char*, va_list);
 #if defined(SQLITE_DEBUG) || defined(SQLITE_HAVE_OS_TRACE)
diff --git a/src/util.c b/src/util.c
index abd36eda87..29bc8524da 100644
--- a/src/util.c
+++ b/src/util.c
@@ -928,6 +928,69 @@ int sqlite3Atoi(const char *z){
   return x;
 }
 
+/*
+** Decode a floating-point value into an approximate decimal
+** representation.
+*/
+void sqlite3FpDecode(FpDecode *p, double r){
+  int i;
+  u64 v;
+  int e, exp = 0;
+  if( r<0.0 ){
+    p->sign = '-';
+    r = -r;
+  }else if( r==0.0 ){
+    p->sign = '+';
+    p->n = 1;
+    p->iDP = 1;
+    p->z[0] = '0';
+    return;
+  }else{
+    p->sign = '+';
+  }
+  memcpy(&v,&r,8);
+  e = v>>52;
+  if( e==0x7ff ){
+    if( v==0x7ff0000000000000L ){
+      p->isInf = 1;
+      p->isNan = 0;
+      p->z[0] = 'I';
+      p->z[1] = 'n';
+      p->z[2] = 'f';
+    }else{
+      p->isInf = 0;
+      p->isNan = 1;
+      p->z[0] = 'N';
+      p->z[1] = 'a';
+      p->z[2] = 'N';
+    }
+    p->n = 3;
+    p->iDP = 3;
+    return;
+  }
+  /* At this point, r is positive (non-zero) and is not Inf or NaN.
+  ** The strategy is to multiple or divide r by powers of 10 until
+  ** it is in between 1.0e+17 and 1.0e+19.  Then convert r into
+  ** an unsigned 64-bit integer v, and extract digits from v.
+  */
+  if( r>=1.0e+19 ){
+    while( r>=1.0e+119 ){ exp+=100; r /= 1.0e+100; }
+    while( r>=1.0e+29  ){ exp+=10;  r /= 1.0e+10;  }
+    while( r>=1.0e+19  ){ exp++;    r /= 10.0;     }
+  }else if( r<1.0e+17 ){
+    while( r<1.0e-97   ){ exp-=100; r *= 1.0e+100; }
+    while( r<1.0e+07   ){ exp-=10;  r *= 1.0e+10;  }
+    while( r<1.0e+17   ){ exp--;    r *= 10.0;     }
+  }
+  v = (u64)r;
+  i = sizeof(p->z);
+  while( v ){  p->z[i--] = (v%10) + '0'; v /= 10; }
+  p->n = sizeof(p->z) - i;
+  p->iDP = p->n + exp;
+  memmove(p->z, &p->z[i+1], p->n);
+  while( p->n>0 && p->z[p->n-1]=='0' ){ p->n--; }
+}
+
 /*
 ** Try to convert z into an unsigned 32-bit integer.  Return true on
 ** success and false if there is an error.

From 002330dc483ff706bcce8f0df2851dd6c656fc55 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Fri, 30 Jun 2023 19:41:57 +0000
Subject: [PATCH 02/17] Add decimal rounding to the sqlite3FpDecode() routine.

FossilOrigin-Name: 27871140caa833f0bc0962e44356993938e93dcf81c1074382b1560a3e1aeb61
---
 manifest        | 19 ++++++++-----------
 manifest.uuid   |  2 +-
 src/func.c      |  7 +++++--
 src/sqliteInt.h |  2 +-
 src/util.c      | 32 +++++++++++++++++++++++++++++---
 5 files changed, 44 insertions(+), 18 deletions(-)

diff --git a/manifest b/manifest
index 95d4799b5d..264c838ce7 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Experiments\swith\sa\snew\salgorithm\sfor\sconverting\sieee-754\sbinary64\snumbers\ninto\sdecimal.
-D 2023-06-30T18:35:43.344
+C Add\sdecimal\srounding\sto\sthe\ssqlite3FpDecode()\sroutine.
+D 2023-06-30T19:41:57.301
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -590,7 +590,7 @@ F src/delete.c cd5f5cd06ed0b6a882ec1a8c2a0d73b3cecb28479ad19e9931c4706c5e2182be
 F src/expr.c 8d1656b65e26af3e34f78e947ac423f0d20c214ed25a67486e433bf16ca6b543
 F src/fault.c 460f3e55994363812d9d60844b2a6de88826e007
 F src/fkey.c a7fcbf7e66d14dbb73cf49f31489ebf66d0e6006c62b95246924a3bae9f37b36
-F src/func.c 699e19ca0dc580a024eb343f3a3abfb646e5438e36d377023d485a3038d789d5
+F src/func.c a6917bd4d4d81ac2320664ea982f85e1a08e566162ef1c776e965fc974b26502
 F src/global.c bd0892ade7289f6e20bff44c07d06371f2ff9b53cea359e7854b9b72f65adc30
 F src/hash.c 9ee4269fb1d6632a6fecfb9479c93a1f29271bddbbaf215dd60420bcb80c7220
 F src/hash.h 3340ab6e1d13e725571d7cee6d3e3135f0779a7d8e76a9ce0a85971fa3953c51
@@ -642,7 +642,7 @@ F src/shell.c.in 2c02c819349de410d63fcc0217763dfe5a42dbe58f2d68046d4ea8a376d12c2
 F src/sqlite.h.in 3076d78836b6dac53b3ab0875fc8fd15bca8077aad4d33c85336e05af6aef8c7
 F src/sqlite3.rc 5121c9e10c3964d5755191c80dd1180c122fc3a8
 F src/sqlite3ext.h da473ce2b3d0ae407a6300c4a164589b9a6bfdbec9462688a8593ff16f3bb6e4
-F src/sqliteInt.h 6ef127217c54e4707b1ca500508340542ca3c2a5aa08ee7a00aaa4834e68992d
+F src/sqliteInt.h 333195d3a62c34af256216e229deb052d87d1068785467a590b56acba0b6c711
 F src/sqliteLimit.h 33b1c9baba578d34efe7dfdb43193b366111cdf41476b1e82699e14c11ee1fb6
 F src/status.c 160c445d7d28c984a0eae38c144f6419311ed3eace59b44ac6dafc20db4af749
 F src/table.c 0f141b58a16de7e2fbe81c308379e7279f4c6b50eb08efeec5892794a0ba30d1
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c 447fd1d981bab37788397c24f980ce555438168f28badde1227441f6d67f1214
+F src/util.c 4a7343a01de122783d6d84c508af15674990578703d5bf55294066978c943f35
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -2041,11 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P 7afad1f759f7ceda873c6d869422fd56fe4399c2d24d47ad9bc3b84b06d830d1
-R b84c58ae5f50c9a21c1125fd73d7f10d
-T *branch * fp-to-decimal-refactor
-T *sym-fp-to-decimal-refactor *
-T -sym-trunk *
+P e923405e448385085224f9289991b303d86b02763535ea77d6fcee98ba6fc1f2
+R 49ab12ffcc52cccbb997811489070376
 U drh
-Z aad0befdc05a87e7f362b0543d2a6962
+Z 1293fc1c53a0c963d9c920ddba4be394
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index 2a088950c5..0ff7f30242 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-e923405e448385085224f9289991b303d86b02763535ea77d6fcee98ba6fc1f2
\ No newline at end of file
+27871140caa833f0bc0962e44356993938e93dcf81c1074382b1560a3e1aeb61
\ No newline at end of file
diff --git a/src/func.c b/src/func.c
index 4cf930b208..e41af59b7b 100644
--- a/src/func.c
+++ b/src/func.c
@@ -2379,10 +2379,12 @@ static void fpdecodeFunc(
   sqlite3_value **argv
 ){
   double r = sqlite3_value_double(argv[0]);
+  int n = 15;
   FpDecode s;
   char zBuf[50];
-  UNUSED_PARAMETER(argc);
-  sqlite3FpDecode(&s, r);
+
+  if( argc>=2 ) n = sqlite3_value_int(argv[1]);
+  sqlite3FpDecode(&s, r, n);
   sqlite3_snprintf(sizeof(zBuf), zBuf, "%c%.*s/%d", s.sign, s.n, s.z, s.iDP);
   sqlite3_result_text(context, zBuf, -1, SQLITE_TRANSIENT);
 }
@@ -2462,6 +2464,7 @@ void sqlite3RegisterBuiltinFunctions(void){
 
 #if 1  /* Temporary prototyping function */
     FUNCTION(fpdecode,           1, 0, 0, fpdecodeFunc     ),
+    FUNCTION(fpdecode,           2, 0, 0, fpdecodeFunc     ),
 #endif
   
 #ifndef SQLITE_OMIT_FLOATING_POINT
diff --git a/src/sqliteInt.h b/src/sqliteInt.h
index b4705b5e26..96cac978c7 100644
--- a/src/sqliteInt.h
+++ b/src/sqliteInt.h
@@ -4611,7 +4611,7 @@ struct FpDecode {
   char z[24];          /* Significiant digits */
 };
 
-void sqlite3FpDecode(FpDecode*,double);
+void sqlite3FpDecode(FpDecode*,double,int);
 char *sqlite3MPrintf(sqlite3*,const char*, ...);
 char *sqlite3VMPrintf(sqlite3*,const char*, va_list);
 #if defined(SQLITE_DEBUG) || defined(SQLITE_HAVE_OS_TRACE)
diff --git a/src/util.c b/src/util.c
index 29bc8524da..73f834ebbb 100644
--- a/src/util.c
+++ b/src/util.c
@@ -931,8 +931,13 @@ int sqlite3Atoi(const char *z){
 /*
 ** Decode a floating-point value into an approximate decimal
 ** representation.
+**
+** Round the decimal representation to n significant digits if
+** n is positive.  Or round to -n signficant digits after the
+** decimal point if n is negative.  No rounding is performed if
+** n is zero.
 */
-void sqlite3FpDecode(FpDecode *p, double r){
+void sqlite3FpDecode(FpDecode *p, double r, int iRound){
   int i;
   u64 v;
   int e, exp = 0;
@@ -983,10 +988,31 @@ void sqlite3FpDecode(FpDecode *p, double r){
     while( r<1.0e+17   ){ exp--;    r *= 10.0;     }
   }
   v = (u64)r;
-  i = sizeof(p->z);
+  i = sizeof(p->z)-1;
   while( v ){  p->z[i--] = (v%10) + '0'; v /= 10; }
-  p->n = sizeof(p->z) - i;
+  p->n = sizeof(p->z) - 1 - i;
   p->iDP = p->n + exp;
+  if( iRound<0 ) iRound = p->iDP - iRound;
+  if( iRound>0 && iRound<p->n ){
+    char *z = &p->z[i+1];
+    p->n = iRound;
+    if( z[iRound]>='5' ){
+      int j = iRound-1;
+      while( 1 /*exit-by-break*/ ){
+        z[j]++;
+        if( z[j]<='9' ) break;
+        z[j] = '0';
+        if( j==0 ){
+          p->z[i--] = '1';
+          p->n++;
+          p->iDP++;
+          break;
+        }else{
+          j--;
+        }
+      }
+    }
+  }
   memmove(p->z, &p->z[i+1], p->n);
   while( p->n>0 && p->z[p->n-1]=='0' ){ p->n--; }
 }

From aebeabacffbcf6df4ebf0952022fd776fa18ae64 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Fri, 30 Jun 2023 23:18:44 +0000
Subject: [PATCH 03/17] Begin cutting over sqlite3FpDecode() into printf(). 
 The code in this check-in gets a lot right, but there are still some
 formatting discrepencies.

FossilOrigin-Name: c134d423e79ba5d3343d7480229822a0c83210f67f12129e0237181f892f97a5
---
 manifest      |  14 ++--
 manifest.uuid |   2 +-
 src/printf.c  | 193 +++++++++++---------------------------------------
 src/util.c    |   4 ++
 4 files changed, 54 insertions(+), 159 deletions(-)

diff --git a/manifest b/manifest
index 264c838ce7..1f8f9a511b 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Add\sdecimal\srounding\sto\sthe\ssqlite3FpDecode()\sroutine.
-D 2023-06-30T19:41:57.301
+C Begin\scutting\sover\ssqlite3FpDecode()\sinto\sprintf().\s\sThe\scode\sin\sthis\ncheck-in\sgets\sa\slot\sright,\sbut\sthere\sare\sstill\ssome\sformatting\ndiscrepencies.
+D 2023-06-30T23:18:44.905
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -633,7 +633,7 @@ F src/pcache1.c 602acb23c471bb8d557a6f0083cc2be641d6cafcafa19e481eba7ef4c9ca0f00
 F src/pragma.c 37b8fb02d090262280c86e1e2654bf59d8dbfbfe8dc6733f2b968a11374c095a
 F src/pragma.h e690a356c18e98414d2e870ea791c1be1545a714ba623719deb63f7f226d8bb7
 F src/prepare.c d6c4354f8ea0dc06962fbabc4b68c4471a45276a2918c929be00f9f537f69eb1
-F src/printf.c a87473be34fa2acafa27692b8ae078275c7e23360956c93c07ff22f5d609cbd7
+F src/printf.c a3497bdf4e62b8bd56d4a9bb16f9da08ab86951612fcb252206f3f96a8f64557
 F src/random.c 606b00941a1d7dd09c381d3279a058d771f406c5213c9932bbd93d5587be4b9c
 F src/resolve.c 37953a5f36c60bea413c3c04efcd433b6177009f508ef2ace0494728912fe2e9
 F src/rowset.c 8432130e6c344b3401a8874c3cb49fefe6873fec593294de077afea2dce5ec97
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c 4a7343a01de122783d6d84c508af15674990578703d5bf55294066978c943f35
+F src/util.c f7efa26a9cae5efc0d01d008fe4bf0e5e1acc09c1a4a3f30d5097a8c67888d2f
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -2041,8 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P e923405e448385085224f9289991b303d86b02763535ea77d6fcee98ba6fc1f2
-R 49ab12ffcc52cccbb997811489070376
+P 27871140caa833f0bc0962e44356993938e93dcf81c1074382b1560a3e1aeb61
+R c28c8d21096bb9e27eacb6f123a9309b
 U drh
-Z 1293fc1c53a0c963d9c920ddba4be394
+Z 82b4e7c76d72d8b25d46a6dcbe6ae7dd
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index 0ff7f30242..96ea34cab0 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-27871140caa833f0bc0962e44356993938e93dcf81c1074382b1560a3e1aeb61
\ No newline at end of file
+c134d423e79ba5d3343d7480229822a0c83210f67f12129e0237181f892f97a5
\ No newline at end of file
diff --git a/src/printf.c b/src/printf.c
index 37033ee50a..e804117613 100644
--- a/src/printf.c
+++ b/src/printf.c
@@ -105,57 +105,6 @@ static const et_info fmtinfo[] = {
 **    %!S   Like %S but prefer the zName over the zAlias
 */
 
-/* Floating point constants used for rounding */
-static const double arRound[] = {
-  5.0e-01, 5.0e-02, 5.0e-03, 5.0e-04, 5.0e-05,
-  5.0e-06, 5.0e-07, 5.0e-08, 5.0e-09, 5.0e-10,
-};
-
-/*
-** If SQLITE_OMIT_FLOATING_POINT is defined, then none of the floating point
-** conversions will work.
-*/
-#ifndef SQLITE_OMIT_FLOATING_POINT
-/*
-** "*val" is a double such that 0.1 <= *val < 10.0
-** Return the ascii code for the leading digit of *val, then
-** multiply "*val" by 10.0 to renormalize.
-**
-** Example:
-**     input:     *val = 3.14159
-**     output:    *val = 1.4159    function return = '3'
-**
-** The counter *cnt is incremented each time.  After counter exceeds
-** 16 (the number of significant digits in a 64-bit float) '0' is
-** always returned.
-*/
-static char et_getdigit(LONGDOUBLE_TYPE *val, int *cnt){
-  int digit;
-  LONGDOUBLE_TYPE d;
-  if( (*cnt)<=0 ) return '0';
-  (*cnt)--;
-  digit = (int)*val;
-  d = digit;
-  digit += '0';
-  *val = (*val - d)*10.0;
-  return (char)digit;
-}
-#endif /* SQLITE_OMIT_FLOATING_POINT */
-
-#ifndef SQLITE_OMIT_FLOATING_POINT
-/*
-** "*val" is a u64.  *msd is a divisor used to extract the
-** most significant digit of *val.  Extract that most significant
-** digit and return it.
-*/
-static char et_getdigit_int(u64 *val, u64 *msd){
-  u64 x = (*val)/(*msd);
-  *val -= x*(*msd);
-  if( *msd>=10 ) *msd /= 10;
-  return '0' + (char)(x & 15);
-}
-#endif /* SQLITE_OMIT_FLOATING_POINT */
-
 /*
 ** Set the StrAccum object to an error mode.
 */
@@ -247,20 +196,16 @@ void sqlite3_str_vappendf(
   u8 bArgList;               /* True for SQLITE_PRINTF_SQLFUNC */
   char prefix;               /* Prefix character.  "+" or "-" or " " or '\0'. */
   sqlite_uint64 longvalue;   /* Value for integer types */
-  LONGDOUBLE_TYPE realvalue; /* Value for real types */
-  sqlite_uint64 msd;         /* Divisor to get most-significant-digit
-                             ** of longvalue */
+  double realvalue;          /* Value for real types */
   const et_info *infop;      /* Pointer to the appropriate info structure */
   char *zOut;                /* Rendering buffer */
   int nOut;                  /* Size of the rendering buffer */
   char *zExtra = 0;          /* Malloced memory used by some conversion */
-#ifndef SQLITE_OMIT_FLOATING_POINT
-  int  exp, e2;              /* exponent of real numbers */
-  int nsd;                   /* Number of significant digits returned */
-  double rounder;            /* Used for rounding floating point values */
+  int exp, e2;               /* exponent of real numbers */
+  int j;                     /* Number of significant digits returned */
   etByte flag_dp;            /* True if decimal point should be shown */
   etByte flag_rtz;           /* True if trailing zeros should be removed */
-#endif
+
   PrintfArguments *pArgList = 0; /* Arguments for SQLITE_PRINTF_SQLFUNC */
   char buf[etBUFSIZE];       /* Conversion buffer */
 
@@ -535,94 +480,51 @@ void sqlite3_str_vappendf(
         break;
       case etFLOAT:
       case etEXP:
-      case etGENERIC:
+      case etGENERIC: {
+        FpDecode s;
+
         if( bArgList ){
           realvalue = getDoubleArg(pArgList);
         }else{
           realvalue = va_arg(ap,double);
         }
-#ifdef SQLITE_OMIT_FLOATING_POINT
-        length = 0;
-#else
         if( precision<0 ) precision = 6;         /* Set default precision */
 #ifdef SQLITE_FP_PRECISION_LIMIT
         if( precision>SQLITE_FP_PRECISION_LIMIT ){
           precision = SQLITE_FP_PRECISION_LIMIT;
         }
 #endif
-        if( realvalue<0.0 ){
-          realvalue = -realvalue;
+        sqlite3FpDecode(&s, realvalue, xtype==etFLOAT ? -precision : precision);
+        if( s.isNan ){
+          if( flag_zeropad ){
+            bufpt = "null";
+            length = 4;
+          }else{
+            bufpt = "NaN";
+            length = 3;
+          }
+          break;
+        }
+        if( s.isInf ){
+          if( s.sign=='-' ){
+            bufpt = "-Inf";
+            length = 4;
+          }else{
+            bufpt = "Inf";
+            length = 3;
+          }
+          break;
+        }
+        if( flag_prefix ){
+          prefix = flag_prefix;
+        }else if( s.sign=='-' ){
           prefix = '-';
         }else{
-          prefix = flag_prefix;
+          prefix = 0;
         }
-        exp = 0;
-        if( xtype==etGENERIC && precision>0 ) precision--;
-        testcase( precision>0xfff );
-        if( realvalue<9.22e+18
-         && realvalue==(LONGDOUBLE_TYPE)(longvalue = (u64)realvalue)
-        ){
-          /* Number is a pure integer that can be represented as u64 */
-          for(msd=1; msd*10<=longvalue; msd *= 10, exp++){}
-          if( exp>precision && xtype!=etFLOAT ){
-            u64 rnd = msd/2;
-            int kk = precision;
-            while( kk-- > 0 ){  rnd /= 10; }
-            longvalue += rnd;
-          }
-        }else{
-          msd = 0;
-          longvalue = 0;  /* To prevent a compiler warning */
-          idx = precision & 0xfff;
-          rounder = arRound[idx%10];
-          while( idx>=10 ){ rounder *= 1.0e-10; idx -= 10; }
-          if( xtype==etFLOAT ){
-            double rx = (double)realvalue;
-            sqlite3_uint64 u;
-            int ex;
-            memcpy(&u, &rx, sizeof(u));
-            ex = -1023 + (int)((u>>52)&0x7ff);
-            if( precision+(ex/3) < 15 ) rounder += realvalue*3e-16;
-            realvalue += rounder;
-          }
-          if( sqlite3IsNaN((double)realvalue) ){
-            if( flag_zeropad ){
-              bufpt = "null";
-              length = 4;
-            }else{
-              bufpt = "NaN";
-              length = 3;
-            }
-            break;
-          }
 
-          /* Normalize realvalue to within 10.0 > realvalue >= 1.0 */
-          if( ALWAYS(realvalue>0.0) ){
-            LONGDOUBLE_TYPE scale = 1.0L;
-            while( realvalue>=1e100*scale && exp<=350){ scale*=1e100L;exp+=100;}
-            while( realvalue>=1e10*scale && exp<=350 ){ scale*=1e10L; exp+=10; }
-            while( realvalue>=10.0*scale && exp<=350 ){ scale*=10.0L; exp++; }
-            realvalue /= scale;
-            while( realvalue<1e-8 ){ realvalue *= 1e8L; exp-=8; }
-            while( realvalue<1.0 ){ realvalue *= 10.0L; exp--; }
-            if( exp>350 ){
-              if( flag_zeropad ){
-                realvalue = 9.0;
-                exp = 999;
-              }else{
-                bufpt = buf;
-                buf[0] = prefix;
-                memcpy(buf+(prefix!=0),"Inf",4);
-                length = 3+(prefix!=0);
-                break;
-              }
-            }
-            if( xtype!=etFLOAT ){
-              realvalue += rounder;
-              if( realvalue>=10.0 ){ realvalue *= 0.1; exp++; }
-            }
-          }
-        }
+        exp = s.iDP-1;
+        if( xtype==etGENERIC && precision>0 ) precision--;
 
         /*
         ** If the field type is etGENERIC, then convert to either etEXP
@@ -642,9 +544,8 @@ void sqlite3_str_vappendf(
         if( xtype==etEXP ){
           e2 = 0;
         }else{
-          e2 = exp;
+          e2 = s.iDP - 1;
         }
-        nsd = 16 + flag_altform2*10;
         bufpt = buf;
         {
           i64 szBufNeeded;           /* Size of a temporary buffer needed */
@@ -662,16 +563,12 @@ void sqlite3_str_vappendf(
           *(bufpt++) = prefix;
         }
         /* Digits prior to the decimal point */
+        j = 0;
         if( e2<0 ){
           *(bufpt++) = '0';
-        }else if( msd>0 ){
-          for(; e2>=0; e2--){
-            *(bufpt++) = et_getdigit_int(&longvalue,&msd);
-            if( cThousand && (e2%3)==0 && e2>1 ) *(bufpt++) = ',';
-          }
         }else{
           for(; e2>=0; e2--){
-            *(bufpt++) = et_getdigit(&realvalue,&nsd);
+            *(bufpt++) = s.z[j++];
             if( cThousand && (e2%3)==0 && e2>1 ) *(bufpt++) = ',';
           }
         }
@@ -681,19 +578,12 @@ void sqlite3_str_vappendf(
         }
         /* "0" digits after the decimal point but before the first
         ** significant digit of the number */
-        for(e2++; e2<0; precision--, e2++){
-          assert( precision>0 );
+        for(e2++; e2<0 && precision>0; precision--, e2++){
           *(bufpt++) = '0';
         }
         /* Significant digits after the decimal point */
-        if( msd>0 ){
-          while( (precision--)>0 ){
-            *(bufpt++) = et_getdigit_int(&longvalue,&msd);
-          }
-        }else{
-          while( (precision--)>0 ){
-            *(bufpt++) = et_getdigit(&realvalue,&nsd);
-          }
+        while( (precision--)>0 ){
+          *(bufpt++) = j<s.n ? s.z[j++] : '0';
         }
         /* Remove trailing zeros and the "." if no digits follow the "." */
         if( flag_rtz && flag_dp ){
@@ -709,6 +599,7 @@ void sqlite3_str_vappendf(
         }
         /* Add the "eNNN" suffix */
         if( xtype==etEXP ){
+          exp = s.iDP - 1;
           *(bufpt++) = aDigits[infop->charset];
           if( exp<0 ){
             *(bufpt++) = '-'; exp = -exp;
@@ -742,8 +633,8 @@ void sqlite3_str_vappendf(
           while( nPad-- ) bufpt[i++] = '0';
           length = width;
         }
-#endif /* !defined(SQLITE_OMIT_FLOATING_POINT) */
         break;
+      }
       case etSIZE:
         if( !bArgList ){
           *(va_arg(ap,int*)) = pAccum->nChar;
diff --git a/src/util.c b/src/util.c
index 73f834ebbb..cd4eec8d2d 100644
--- a/src/util.c
+++ b/src/util.c
@@ -949,6 +949,8 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound){
     p->n = 1;
     p->iDP = 1;
     p->z[0] = '0';
+    p->isNan = 0;
+    p->isInf = 0;
     return;
   }else{
     p->sign = '+';
@@ -973,6 +975,8 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound){
     p->iDP = 3;
     return;
   }
+  p->isNan = p->isInf = 0;
+
   /* At this point, r is positive (non-zero) and is not Inf or NaN.
   ** The strategy is to multiple or divide r by powers of 10 until
   ** it is in between 1.0e+17 and 1.0e+19.  Then convert r into

From 3f073f9ef83806332ac2a9f62a2c574bf891d048 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Fri, 30 Jun 2023 23:42:46 +0000
Subject: [PATCH 04/17] Fix an issue with the "+" attribute in printf().

FossilOrigin-Name: bdfd1eb1d7b4c570a53d58789dac0bf55fdaf8eba515d5a0caf2e57e25b51952
---
 manifest      | 12 ++++++------
 manifest.uuid |  2 +-
 src/printf.c  |  2 +-
 3 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/manifest b/manifest
index 1f8f9a511b..2b00cbffa5 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Begin\scutting\sover\ssqlite3FpDecode()\sinto\sprintf().\s\sThe\scode\sin\sthis\ncheck-in\sgets\sa\slot\sright,\sbut\sthere\sare\sstill\ssome\sformatting\ndiscrepencies.
-D 2023-06-30T23:18:44.905
+C Fix\san\sissue\swith\sthe\s"+"\sattribute\sin\sprintf().
+D 2023-06-30T23:42:46.836
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -633,7 +633,7 @@ F src/pcache1.c 602acb23c471bb8d557a6f0083cc2be641d6cafcafa19e481eba7ef4c9ca0f00
 F src/pragma.c 37b8fb02d090262280c86e1e2654bf59d8dbfbfe8dc6733f2b968a11374c095a
 F src/pragma.h e690a356c18e98414d2e870ea791c1be1545a714ba623719deb63f7f226d8bb7
 F src/prepare.c d6c4354f8ea0dc06962fbabc4b68c4471a45276a2918c929be00f9f537f69eb1
-F src/printf.c a3497bdf4e62b8bd56d4a9bb16f9da08ab86951612fcb252206f3f96a8f64557
+F src/printf.c 890a111a37f300e171d9df601115774dc964c57b4b1ed7206da849d4861f0188
 F src/random.c 606b00941a1d7dd09c381d3279a058d771f406c5213c9932bbd93d5587be4b9c
 F src/resolve.c 37953a5f36c60bea413c3c04efcd433b6177009f508ef2ace0494728912fe2e9
 F src/rowset.c 8432130e6c344b3401a8874c3cb49fefe6873fec593294de077afea2dce5ec97
@@ -2041,8 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P 27871140caa833f0bc0962e44356993938e93dcf81c1074382b1560a3e1aeb61
-R c28c8d21096bb9e27eacb6f123a9309b
+P c134d423e79ba5d3343d7480229822a0c83210f67f12129e0237181f892f97a5
+R 8f07870f9b2d96881336f99b2799e75b
 U drh
-Z 82b4e7c76d72d8b25d46a6dcbe6ae7dd
+Z 159b2bbd6094de9112f8c4b9400c21f4
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index 96ea34cab0..c5dd949773 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-c134d423e79ba5d3343d7480229822a0c83210f67f12129e0237181f892f97a5
\ No newline at end of file
+bdfd1eb1d7b4c570a53d58789dac0bf55fdaf8eba515d5a0caf2e57e25b51952
\ No newline at end of file
diff --git a/src/printf.c b/src/printf.c
index e804117613..b71584af0c 100644
--- a/src/printf.c
+++ b/src/printf.c
@@ -516,7 +516,7 @@ void sqlite3_str_vappendf(
           break;
         }
         if( flag_prefix ){
-          prefix = flag_prefix;
+          prefix = s.sign;
         }else if( s.sign=='-' ){
           prefix = '-';
         }else{

From 42d042e602233be808084e78ccbaba1b497c69a3 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Sat, 1 Jul 2023 14:03:50 +0000
Subject: [PATCH 05/17] Progress towards fixing corner-case floating-point
 formatting issues.

FossilOrigin-Name: 1138b8d16edef16d2943d407e289d07d546a14e64c3efa3c94127631e06fafeb
---
 manifest      | 14 +++++++-------
 manifest.uuid |  2 +-
 src/printf.c  | 17 +++++++++++------
 src/util.c    | 12 ++++++++++--
 4 files changed, 29 insertions(+), 16 deletions(-)

diff --git a/manifest b/manifest
index 2b00cbffa5..253d40cde3 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Fix\san\sissue\swith\sthe\s"+"\sattribute\sin\sprintf().
-D 2023-06-30T23:42:46.836
+C Progress\stowards\sfixing\scorner-case\sfloating-point\sformatting\sissues.
+D 2023-07-01T14:03:50.030
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -633,7 +633,7 @@ F src/pcache1.c 602acb23c471bb8d557a6f0083cc2be641d6cafcafa19e481eba7ef4c9ca0f00
 F src/pragma.c 37b8fb02d090262280c86e1e2654bf59d8dbfbfe8dc6733f2b968a11374c095a
 F src/pragma.h e690a356c18e98414d2e870ea791c1be1545a714ba623719deb63f7f226d8bb7
 F src/prepare.c d6c4354f8ea0dc06962fbabc4b68c4471a45276a2918c929be00f9f537f69eb1
-F src/printf.c 890a111a37f300e171d9df601115774dc964c57b4b1ed7206da849d4861f0188
+F src/printf.c 1291f62b21bbad23d7f9557d5255a0749fb24b86d4bc293fe7210e5a2cdf51b4
 F src/random.c 606b00941a1d7dd09c381d3279a058d771f406c5213c9932bbd93d5587be4b9c
 F src/resolve.c 37953a5f36c60bea413c3c04efcd433b6177009f508ef2ace0494728912fe2e9
 F src/rowset.c 8432130e6c344b3401a8874c3cb49fefe6873fec593294de077afea2dce5ec97
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c f7efa26a9cae5efc0d01d008fe4bf0e5e1acc09c1a4a3f30d5097a8c67888d2f
+F src/util.c fc7991df98ed37aca761b40671f39b1359ed4accdcd60546ce58a6e9cb28d6c3
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -2041,8 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P c134d423e79ba5d3343d7480229822a0c83210f67f12129e0237181f892f97a5
-R 8f07870f9b2d96881336f99b2799e75b
+P bdfd1eb1d7b4c570a53d58789dac0bf55fdaf8eba515d5a0caf2e57e25b51952
+R fb72667e1d4a1498dbacfca13643a6ba
 U drh
-Z 159b2bbd6094de9112f8c4b9400c21f4
+Z 2c618a760c02dc2da550092622885ef7
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index c5dd949773..6095020f47 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-bdfd1eb1d7b4c570a53d58789dac0bf55fdaf8eba515d5a0caf2e57e25b51952
\ No newline at end of file
+1138b8d16edef16d2943d407e289d07d546a14e64c3efa3c94127631e06fafeb
\ No newline at end of file
diff --git a/src/printf.c b/src/printf.c
index b71584af0c..78f59757df 100644
--- a/src/printf.c
+++ b/src/printf.c
@@ -494,7 +494,11 @@ void sqlite3_str_vappendf(
           precision = SQLITE_FP_PRECISION_LIMIT;
         }
 #endif
-        sqlite3FpDecode(&s, realvalue, xtype==etFLOAT ? -precision : precision);
+        switch( xtype ){
+          case etFLOAT:    sqlite3FpDecode(&s, realvalue, -precision);  break;
+          case etGENERIC:  sqlite3FpDecode(&s, realvalue, precision);   break;
+          case etEXP:      sqlite3FpDecode(&s, realvalue, precision+1); break;
+        }
         if( s.isNan ){
           if( flag_zeropad ){
             bufpt = "null";
@@ -509,18 +513,19 @@ void sqlite3_str_vappendf(
           if( s.sign=='-' ){
             bufpt = "-Inf";
             length = 4;
+          }else if( flag_prefix=='+' ){
+            bufpt = "+Inf";
+            length = 4;
           }else{
             bufpt = "Inf";
             length = 3;
           }
           break;
         }
-        if( flag_prefix ){
-          prefix = s.sign;
-        }else if( s.sign=='-' ){
+        if( s.sign=='-' ){
           prefix = '-';
         }else{
-          prefix = 0;
+          prefix = flag_prefix;
         }
 
         exp = s.iDP-1;
@@ -568,7 +573,7 @@ void sqlite3_str_vappendf(
           *(bufpt++) = '0';
         }else{
           for(; e2>=0; e2--){
-            *(bufpt++) = s.z[j++];
+            *(bufpt++) = j<s.n ? s.z[j++] : '0';
             if( cThousand && (e2%3)==0 && e2>1 ) *(bufpt++) = ',';
           }
         }
diff --git a/src/util.c b/src/util.c
index cd4eec8d2d..a648dc2d11 100644
--- a/src/util.c
+++ b/src/util.c
@@ -957,7 +957,7 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound){
   }
   memcpy(&v,&r,8);
   e = v>>52;
-  if( e==0x7ff ){
+  if( (e&0x7ff)==0x7ff ){
     if( v==0x7ff0000000000000L ){
       p->isInf = 1;
       p->isNan = 0;
@@ -996,7 +996,15 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound){
   while( v ){  p->z[i--] = (v%10) + '0'; v /= 10; }
   p->n = sizeof(p->z) - 1 - i;
   p->iDP = p->n + exp;
-  if( iRound<0 ) iRound = p->iDP - iRound;
+  if( iRound<0 ){
+    iRound = p->iDP - iRound;
+    if( iRound==0 && p->z[i+1]>='5' ){
+      iRound = 1;
+      p->z[i--] = '0';
+      p->n++;
+      p->iDP++;
+    }
+  }
   if( iRound>0 && iRound<p->n ){
     char *z = &p->z[i+1];
     p->n = iRound;

From 9ee9444a0adbf8f04081447d70d570f17c1a6e6a Mon Sep 17 00:00:00 2001
From: drh <>
Date: Sat, 1 Jul 2023 15:23:24 +0000
Subject: [PATCH 06/17] Improved response to Infinity and NaN.  Remove the
 termporary fpdecode() function.

FossilOrigin-Name: 76ab8ae809a47a66688e2d50c20dc87ce946d82e9ffebb3adda55c451fad07fc
---
 manifest        | 18 ++++++++---------
 manifest.uuid   |  2 +-
 src/func.c      | 25 ------------------------
 src/printf.c    | 52 ++++++++++++++++++++++++++-----------------------
 src/sqliteInt.h |  3 +--
 src/util.c      | 22 ++++-----------------
 6 files changed, 43 insertions(+), 79 deletions(-)

diff --git a/manifest b/manifest
index 253d40cde3..c7e0fa72ac 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Progress\stowards\sfixing\scorner-case\sfloating-point\sformatting\sissues.
-D 2023-07-01T14:03:50.030
+C Improved\sresponse\sto\sInfinity\sand\sNaN.\s\sRemove\sthe\stermporary\sfpdecode()\nfunction.
+D 2023-07-01T15:23:24.956
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -590,7 +590,7 @@ F src/delete.c cd5f5cd06ed0b6a882ec1a8c2a0d73b3cecb28479ad19e9931c4706c5e2182be
 F src/expr.c 8d1656b65e26af3e34f78e947ac423f0d20c214ed25a67486e433bf16ca6b543
 F src/fault.c 460f3e55994363812d9d60844b2a6de88826e007
 F src/fkey.c a7fcbf7e66d14dbb73cf49f31489ebf66d0e6006c62b95246924a3bae9f37b36
-F src/func.c a6917bd4d4d81ac2320664ea982f85e1a08e566162ef1c776e965fc974b26502
+F src/func.c 6b4804738b4d869f40625958b476a8f964d3df65b626e72a530d76051863cf32
 F src/global.c bd0892ade7289f6e20bff44c07d06371f2ff9b53cea359e7854b9b72f65adc30
 F src/hash.c 9ee4269fb1d6632a6fecfb9479c93a1f29271bddbbaf215dd60420bcb80c7220
 F src/hash.h 3340ab6e1d13e725571d7cee6d3e3135f0779a7d8e76a9ce0a85971fa3953c51
@@ -633,7 +633,7 @@ F src/pcache1.c 602acb23c471bb8d557a6f0083cc2be641d6cafcafa19e481eba7ef4c9ca0f00
 F src/pragma.c 37b8fb02d090262280c86e1e2654bf59d8dbfbfe8dc6733f2b968a11374c095a
 F src/pragma.h e690a356c18e98414d2e870ea791c1be1545a714ba623719deb63f7f226d8bb7
 F src/prepare.c d6c4354f8ea0dc06962fbabc4b68c4471a45276a2918c929be00f9f537f69eb1
-F src/printf.c 1291f62b21bbad23d7f9557d5255a0749fb24b86d4bc293fe7210e5a2cdf51b4
+F src/printf.c 161c522372d34eccb6fbc75b62c40533559ce3f7816a95854dc17e1fa4b4c0d7
 F src/random.c 606b00941a1d7dd09c381d3279a058d771f406c5213c9932bbd93d5587be4b9c
 F src/resolve.c 37953a5f36c60bea413c3c04efcd433b6177009f508ef2ace0494728912fe2e9
 F src/rowset.c 8432130e6c344b3401a8874c3cb49fefe6873fec593294de077afea2dce5ec97
@@ -642,7 +642,7 @@ F src/shell.c.in 2c02c819349de410d63fcc0217763dfe5a42dbe58f2d68046d4ea8a376d12c2
 F src/sqlite.h.in 3076d78836b6dac53b3ab0875fc8fd15bca8077aad4d33c85336e05af6aef8c7
 F src/sqlite3.rc 5121c9e10c3964d5755191c80dd1180c122fc3a8
 F src/sqlite3ext.h da473ce2b3d0ae407a6300c4a164589b9a6bfdbec9462688a8593ff16f3bb6e4
-F src/sqliteInt.h 333195d3a62c34af256216e229deb052d87d1068785467a590b56acba0b6c711
+F src/sqliteInt.h 8c1922b2780624225223fd407f995b04392175d33dfcbbca37fe1f00e1abfd0a
 F src/sqliteLimit.h 33b1c9baba578d34efe7dfdb43193b366111cdf41476b1e82699e14c11ee1fb6
 F src/status.c 160c445d7d28c984a0eae38c144f6419311ed3eace59b44ac6dafc20db4af749
 F src/table.c 0f141b58a16de7e2fbe81c308379e7279f4c6b50eb08efeec5892794a0ba30d1
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c fc7991df98ed37aca761b40671f39b1359ed4accdcd60546ce58a6e9cb28d6c3
+F src/util.c 9cddb6a7b31656609e8585475c30e6148a442273b73bfbb3eaabd56e04f157dd
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -2041,8 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P bdfd1eb1d7b4c570a53d58789dac0bf55fdaf8eba515d5a0caf2e57e25b51952
-R fb72667e1d4a1498dbacfca13643a6ba
+P 1138b8d16edef16d2943d407e289d07d546a14e64c3efa3c94127631e06fafeb
+R 9f9cd9357c9913af2aa19cc840191091
 U drh
-Z 2c618a760c02dc2da550092622885ef7
+Z 1a305ec6bce26e8306c1bccf245f209e
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index 6095020f47..2f293ccf31 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-1138b8d16edef16d2943d407e289d07d546a14e64c3efa3c94127631e06fafeb
\ No newline at end of file
+76ab8ae809a47a66688e2d50c20dc87ce946d82e9ffebb3adda55c451fad07fc
\ No newline at end of file
diff --git a/src/func.c b/src/func.c
index e41af59b7b..b243591863 100644
--- a/src/func.c
+++ b/src/func.c
@@ -2371,25 +2371,6 @@ static void signFunc(
   sqlite3_result_int(context, x<0.0 ? -1 : x>0.0 ? +1 : 0);
 }
 
-
-#if 1 /* Temporary prototyping logic */
-static void fpdecodeFunc(
-  sqlite3_context *context,
-  int argc,
-  sqlite3_value **argv
-){
-  double r = sqlite3_value_double(argv[0]);
-  int n = 15;
-  FpDecode s;
-  char zBuf[50];
-
-  if( argc>=2 ) n = sqlite3_value_int(argv[1]);
-  sqlite3FpDecode(&s, r, n);
-  sqlite3_snprintf(sizeof(zBuf), zBuf, "%c%.*s/%d", s.sign, s.n, s.z, s.iDP);
-  sqlite3_result_text(context, zBuf, -1, SQLITE_TRANSIENT);
-}
-#endif /* Temporary prototyping logic */
-
 /*
 ** All of the FuncDef structures in the aBuiltinFunc[] array above
 ** to the global function hash table.  This occurs at start-time (as
@@ -2461,12 +2442,6 @@ void sqlite3RegisterBuiltinFunctions(void){
     FUNCTION(unicode,            1, 0, 0, unicodeFunc      ),
     FUNCTION(char,              -1, 0, 0, charFunc         ),
     FUNCTION(abs,                1, 0, 0, absFunc          ),
-
-#if 1  /* Temporary prototyping function */
-    FUNCTION(fpdecode,           1, 0, 0, fpdecodeFunc     ),
-    FUNCTION(fpdecode,           2, 0, 0, fpdecodeFunc     ),
-#endif
-  
 #ifndef SQLITE_OMIT_FLOATING_POINT
     FUNCTION(round,              1, 0, 0, roundFunc        ),
     FUNCTION(round,              2, 0, 0, roundFunc        ),
diff --git a/src/printf.c b/src/printf.c
index 78f59757df..4de06c1162 100644
--- a/src/printf.c
+++ b/src/printf.c
@@ -482,6 +482,7 @@ void sqlite3_str_vappendf(
       case etEXP:
       case etGENERIC: {
         FpDecode s;
+        int iRound;
 
         if( bArgList ){
           realvalue = getDoubleArg(pArgList);
@@ -494,33 +495,36 @@ void sqlite3_str_vappendf(
           precision = SQLITE_FP_PRECISION_LIMIT;
         }
 #endif
-        switch( xtype ){
-          case etFLOAT:    sqlite3FpDecode(&s, realvalue, -precision);  break;
-          case etGENERIC:  sqlite3FpDecode(&s, realvalue, precision);   break;
-          case etEXP:      sqlite3FpDecode(&s, realvalue, precision+1); break;
+        if( xtype==etFLOAT ){
+          iRound = -precision;
+        }else if( xtype==etGENERIC ){
+          iRound = precision;
+        }else{
+          iRound = precision+1;
         }
-        if( s.isNan ){
-          if( flag_zeropad ){
-            bufpt = "null";
-            length = 4;
+        sqlite3FpDecode(&s, realvalue, iRound);
+        if( s.isSpecial ){
+          if( s.isSpecial==2 ){
+            bufpt = flag_zeropad ? "null" : "NaN";
+            length = sqlite3Strlen30(bufpt);
+            break;
+          }else if( flag_zeropad ){
+            s.z[0] = '9';
+            s.iDP = 1000;
+            s.n = 1;
           }else{
-            bufpt = "NaN";
-            length = 3;
+            memcpy(buf, "-Inf", 5);
+            bufpt = buf;
+            if( s.sign=='-' ){
+              /* no-op */
+            }else if( flag_prefix ){
+              buf[0] = flag_prefix;
+            }else{
+              bufpt++;
+            }
+            length = sqlite3Strlen30(bufpt);
+            break;
           }
-          break;
-        }
-        if( s.isInf ){
-          if( s.sign=='-' ){
-            bufpt = "-Inf";
-            length = 4;
-          }else if( flag_prefix=='+' ){
-            bufpt = "+Inf";
-            length = 4;
-          }else{
-            bufpt = "Inf";
-            length = 3;
-          }
-          break;
         }
         if( s.sign=='-' ){
           prefix = '-';
diff --git a/src/sqliteInt.h b/src/sqliteInt.h
index 96cac978c7..011a44bcb9 100644
--- a/src/sqliteInt.h
+++ b/src/sqliteInt.h
@@ -4604,8 +4604,7 @@ struct PrintfArguments {
 */
 struct FpDecode {
   char sign;           /* '+' or '-' */
-  char isNan;          /* True if not-a-number */
-  char isInf;          /* True if infinity */
+  char isSpecial;      /* 1: Infinity  2: NaN */
   int n;               /* Significant digits in the decode */
   int iDP;             /* Location of the decimal point */
   char z[24];          /* Significiant digits */
diff --git a/src/util.c b/src/util.c
index a648dc2d11..0950d8427a 100644
--- a/src/util.c
+++ b/src/util.c
@@ -941,6 +941,7 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound){
   int i;
   u64 v;
   int e, exp = 0;
+  p->isSpecial = 0;
   if( r<0.0 ){
     p->sign = '-';
     r = -r;
@@ -949,8 +950,6 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound){
     p->n = 1;
     p->iDP = 1;
     p->z[0] = '0';
-    p->isNan = 0;
-    p->isInf = 0;
     return;
   }else{
     p->sign = '+';
@@ -958,24 +957,11 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound){
   memcpy(&v,&r,8);
   e = v>>52;
   if( (e&0x7ff)==0x7ff ){
-    if( v==0x7ff0000000000000L ){
-      p->isInf = 1;
-      p->isNan = 0;
-      p->z[0] = 'I';
-      p->z[1] = 'n';
-      p->z[2] = 'f';
-    }else{
-      p->isInf = 0;
-      p->isNan = 1;
-      p->z[0] = 'N';
-      p->z[1] = 'a';
-      p->z[2] = 'N';
-    }
-    p->n = 3;
-    p->iDP = 3;
+    p->isSpecial = 1 + (v!=0x7ff0000000000000L);
+    p->n = 0;
+    p->iDP = 0;
     return;
   }
-  p->isNan = p->isInf = 0;
 
   /* At this point, r is positive (non-zero) and is not Inf or NaN.
   ** The strategy is to multiple or divide r by powers of 10 until

From 17c20bb15e5f51e12efd95fd3dc8806f939d8af8 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Sat, 1 Jul 2023 17:56:00 +0000
Subject: [PATCH 07/17] Improved rounding policy.

FossilOrigin-Name: 6f1122e942b8269552daaf13d647d200d8546ec25f36310d67037c6b58d09976
---
 manifest         | 20 ++++++++++----------
 manifest.uuid    |  2 +-
 src/func.c       |  2 +-
 src/printf.c     |  2 +-
 src/sqliteInt.h  |  2 +-
 src/util.c       |  7 ++++---
 test/round1.test |  4 ++--
 7 files changed, 20 insertions(+), 19 deletions(-)

diff --git a/manifest b/manifest
index c7e0fa72ac..5d34c0afa1 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Improved\sresponse\sto\sInfinity\sand\sNaN.\s\sRemove\sthe\stermporary\sfpdecode()\nfunction.
-D 2023-07-01T15:23:24.956
+C Improved\srounding\spolicy.
+D 2023-07-01T17:56:00.664
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -590,7 +590,7 @@ F src/delete.c cd5f5cd06ed0b6a882ec1a8c2a0d73b3cecb28479ad19e9931c4706c5e2182be
 F src/expr.c 8d1656b65e26af3e34f78e947ac423f0d20c214ed25a67486e433bf16ca6b543
 F src/fault.c 460f3e55994363812d9d60844b2a6de88826e007
 F src/fkey.c a7fcbf7e66d14dbb73cf49f31489ebf66d0e6006c62b95246924a3bae9f37b36
-F src/func.c 6b4804738b4d869f40625958b476a8f964d3df65b626e72a530d76051863cf32
+F src/func.c 02ad65dea00c07db33df86ad649a81a503ac7b8a259e89d00e7a81e16ae9d2d6
 F src/global.c bd0892ade7289f6e20bff44c07d06371f2ff9b53cea359e7854b9b72f65adc30
 F src/hash.c 9ee4269fb1d6632a6fecfb9479c93a1f29271bddbbaf215dd60420bcb80c7220
 F src/hash.h 3340ab6e1d13e725571d7cee6d3e3135f0779a7d8e76a9ce0a85971fa3953c51
@@ -633,7 +633,7 @@ F src/pcache1.c 602acb23c471bb8d557a6f0083cc2be641d6cafcafa19e481eba7ef4c9ca0f00
 F src/pragma.c 37b8fb02d090262280c86e1e2654bf59d8dbfbfe8dc6733f2b968a11374c095a
 F src/pragma.h e690a356c18e98414d2e870ea791c1be1545a714ba623719deb63f7f226d8bb7
 F src/prepare.c d6c4354f8ea0dc06962fbabc4b68c4471a45276a2918c929be00f9f537f69eb1
-F src/printf.c 161c522372d34eccb6fbc75b62c40533559ce3f7816a95854dc17e1fa4b4c0d7
+F src/printf.c 1d2d5ba8c2d6446b89ca4afeeb5e99f8c09ca8cfd6947e33493112771ea7532a
 F src/random.c 606b00941a1d7dd09c381d3279a058d771f406c5213c9932bbd93d5587be4b9c
 F src/resolve.c 37953a5f36c60bea413c3c04efcd433b6177009f508ef2ace0494728912fe2e9
 F src/rowset.c 8432130e6c344b3401a8874c3cb49fefe6873fec593294de077afea2dce5ec97
@@ -642,7 +642,7 @@ F src/shell.c.in 2c02c819349de410d63fcc0217763dfe5a42dbe58f2d68046d4ea8a376d12c2
 F src/sqlite.h.in 3076d78836b6dac53b3ab0875fc8fd15bca8077aad4d33c85336e05af6aef8c7
 F src/sqlite3.rc 5121c9e10c3964d5755191c80dd1180c122fc3a8
 F src/sqlite3ext.h da473ce2b3d0ae407a6300c4a164589b9a6bfdbec9462688a8593ff16f3bb6e4
-F src/sqliteInt.h 8c1922b2780624225223fd407f995b04392175d33dfcbbca37fe1f00e1abfd0a
+F src/sqliteInt.h 3d4125cc1c38777f307e7d374890f085d09f6e15298e09a4f74919744ec2ad62
 F src/sqliteLimit.h 33b1c9baba578d34efe7dfdb43193b366111cdf41476b1e82699e14c11ee1fb6
 F src/status.c 160c445d7d28c984a0eae38c144f6419311ed3eace59b44ac6dafc20db4af749
 F src/table.c 0f141b58a16de7e2fbe81c308379e7279f4c6b50eb08efeec5892794a0ba30d1
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c 9cddb6a7b31656609e8585475c30e6148a442273b73bfbb3eaabd56e04f157dd
+F src/util.c 87e6762b026cd733312838b0e9b9acb43d3a3c88c5e612e8077a7320c2bc1692
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -1399,7 +1399,7 @@ F test/returningfault.test ae4c4b5e8745813287a359d9ccdb9d5c883c2e68afb18fb076793
 F test/rollback.test 06680159bc6746d0f26276e339e3ae2f951c64812468308838e0a3362d911eaa
 F test/rollback2.test 3f3a4e20401825017df7e7671e9f31b6de5fae5620c2b9b49917f52f8c160a8f
 F test/rollbackfault.test 0e646aeab8840c399cfbfa43daab46fd609cf04a
-F test/round1.test 1bb32cf3fc505eed9e86b5e523d07e15d4428189665524587512fbcc85d114bb
+F test/round1.test 29c3c9039936ed024d672f003c4d35ee11c14c0acb75c5f7d6188ff16190cfd4
 F test/rowallock.test 3f88ec6819489d0b2341c7a7528ae17c053ab7cc
 F test/rowhash.test 0bc1d31415e4575d10cacf31e1a66b5cc0f8be81
 F test/rowid.test e29025be95baf6b32f0d5edef59a7633028325896a98f1caa8019559ca910350
@@ -2041,8 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P 1138b8d16edef16d2943d407e289d07d546a14e64c3efa3c94127631e06fafeb
-R 9f9cd9357c9913af2aa19cc840191091
+P 76ab8ae809a47a66688e2d50c20dc87ce946d82e9ffebb3adda55c451fad07fc
+R bac28918fe04cf4bb6c5ec2b0ffa1827
 U drh
-Z 1a305ec6bce26e8306c1bccf245f209e
+Z 6ffcf546adee0eb6c01fe1a8fc34f949
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index 2f293ccf31..f7aec02361 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-76ab8ae809a47a66688e2d50c20dc87ce946d82e9ffebb3adda55c451fad07fc
\ No newline at end of file
+6f1122e942b8269552daaf13d647d200d8546ec25f36310d67037c6b58d09976
\ No newline at end of file
diff --git a/src/func.c b/src/func.c
index b243591863..07ada2ef6e 100644
--- a/src/func.c
+++ b/src/func.c
@@ -461,7 +461,7 @@ static void roundFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
   }else if( n==0 ){ 
     r = (double)((sqlite_int64)(r+(r<0?-0.5:+0.5)));
   }else{
-    zBuf = sqlite3_mprintf("%.*f",n,r);
+    zBuf = sqlite3_mprintf("%!.*f",n,r);
     if( zBuf==0 ){
       sqlite3_result_error_nomem(context);
       return;
diff --git a/src/printf.c b/src/printf.c
index 4de06c1162..f00ad4cb2e 100644
--- a/src/printf.c
+++ b/src/printf.c
@@ -502,7 +502,7 @@ void sqlite3_str_vappendf(
         }else{
           iRound = precision+1;
         }
-        sqlite3FpDecode(&s, realvalue, iRound);
+        sqlite3FpDecode(&s, realvalue, iRound, flag_altform2 ? 26 : 16);
         if( s.isSpecial ){
           if( s.isSpecial==2 ){
             bufpt = flag_zeropad ? "null" : "NaN";
diff --git a/src/sqliteInt.h b/src/sqliteInt.h
index 011a44bcb9..5662ab4fd2 100644
--- a/src/sqliteInt.h
+++ b/src/sqliteInt.h
@@ -4610,7 +4610,7 @@ struct FpDecode {
   char z[24];          /* Significiant digits */
 };
 
-void sqlite3FpDecode(FpDecode*,double,int);
+void sqlite3FpDecode(FpDecode*,double,int,int);
 char *sqlite3MPrintf(sqlite3*,const char*, ...);
 char *sqlite3VMPrintf(sqlite3*,const char*, va_list);
 #if defined(SQLITE_DEBUG) || defined(SQLITE_HAVE_OS_TRACE)
diff --git a/src/util.c b/src/util.c
index 0950d8427a..41359ea2a2 100644
--- a/src/util.c
+++ b/src/util.c
@@ -937,7 +937,7 @@ int sqlite3Atoi(const char *z){
 ** decimal point if n is negative.  No rounding is performed if
 ** n is zero.
 */
-void sqlite3FpDecode(FpDecode *p, double r, int iRound){
+void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
   int i;
   u64 v;
   int e, exp = 0;
@@ -972,7 +972,7 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound){
     while( r>=1.0e+119 ){ exp+=100; r /= 1.0e+100; }
     while( r>=1.0e+29  ){ exp+=10;  r /= 1.0e+10;  }
     while( r>=1.0e+19  ){ exp++;    r /= 10.0;     }
-  }else if( r<1.0e+17 ){
+  }else{
     while( r<1.0e-97   ){ exp-=100; r *= 1.0e+100; }
     while( r<1.0e+07   ){ exp-=10;  r *= 1.0e+10;  }
     while( r<1.0e+17   ){ exp--;    r *= 10.0;     }
@@ -991,8 +991,9 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound){
       p->iDP++;
     }
   }
-  if( iRound>0 && iRound<p->n ){
+  if( iRound>0 && (iRound<p->n || p->n>mxRound) ){
     char *z = &p->z[i+1];
+    if( iRound>mxRound ) iRound = mxRound;
     p->n = iRound;
     if( z[iRound]>='5' ){
       int j = iRound-1;
diff --git a/test/round1.test b/test/round1.test
index 2244a399ab..2857593be8 100644
--- a/test/round1.test
+++ b/test/round1.test
@@ -34,8 +34,8 @@ for {set iTest 1} {$iTest<=50000} {incr iTest} {
    set r2 $x1.$x4
    set ans [string trimright $r2 0]
    if {[string match *. $ans]} {set ans ${ans}0}
-   do_test $iTest/$n/${r}5=>$ans {
-     set x [db one "SELECT round(${r}5,$n)"]
+   do_test $iTest/$n/${r}6=>$ans {
+     set x [db one "SELECT round(${r}6,$n)"]
    } $ans
 }
 

From 453be55b85d98ab55d7398cbebf81f413d1d7794 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Sat, 1 Jul 2023 18:33:26 +0000
Subject: [PATCH 08/17] Reinstate the fpdecode() SQL function for testing, but
 only when compiled with SQLITE_DEBUG.

FossilOrigin-Name: 07eab52e0801bb0e4743b304a06ad16e18cdf8eaa18c0faf8d47a1f5d8576ea0
---
 manifest      | 14 +++++++-------
 manifest.uuid |  2 +-
 src/func.c    | 34 ++++++++++++++++++++++++++++++++++
 src/printf.c  |  2 +-
 4 files changed, 43 insertions(+), 9 deletions(-)

diff --git a/manifest b/manifest
index 5d34c0afa1..d3e50a606b 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Improved\srounding\spolicy.
-D 2023-07-01T17:56:00.664
+C Reinstate\sthe\sfpdecode()\sSQL\sfunction\sfor\stesting,\sbut\sonly\swhen\scompiled\nwith\sSQLITE_DEBUG.
+D 2023-07-01T18:33:26.856
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -590,7 +590,7 @@ F src/delete.c cd5f5cd06ed0b6a882ec1a8c2a0d73b3cecb28479ad19e9931c4706c5e2182be
 F src/expr.c 8d1656b65e26af3e34f78e947ac423f0d20c214ed25a67486e433bf16ca6b543
 F src/fault.c 460f3e55994363812d9d60844b2a6de88826e007
 F src/fkey.c a7fcbf7e66d14dbb73cf49f31489ebf66d0e6006c62b95246924a3bae9f37b36
-F src/func.c 02ad65dea00c07db33df86ad649a81a503ac7b8a259e89d00e7a81e16ae9d2d6
+F src/func.c 6028c160f693bdd018b651b5468a0a8e790f4e01e200796916b2d10a5d3237aa
 F src/global.c bd0892ade7289f6e20bff44c07d06371f2ff9b53cea359e7854b9b72f65adc30
 F src/hash.c 9ee4269fb1d6632a6fecfb9479c93a1f29271bddbbaf215dd60420bcb80c7220
 F src/hash.h 3340ab6e1d13e725571d7cee6d3e3135f0779a7d8e76a9ce0a85971fa3953c51
@@ -633,7 +633,7 @@ F src/pcache1.c 602acb23c471bb8d557a6f0083cc2be641d6cafcafa19e481eba7ef4c9ca0f00
 F src/pragma.c 37b8fb02d090262280c86e1e2654bf59d8dbfbfe8dc6733f2b968a11374c095a
 F src/pragma.h e690a356c18e98414d2e870ea791c1be1545a714ba623719deb63f7f226d8bb7
 F src/prepare.c d6c4354f8ea0dc06962fbabc4b68c4471a45276a2918c929be00f9f537f69eb1
-F src/printf.c 1d2d5ba8c2d6446b89ca4afeeb5e99f8c09ca8cfd6947e33493112771ea7532a
+F src/printf.c 84b7b4b647f336934a5ab2e7f0c52555833cc0778d2d60e016cca52ee8c6cd8f
 F src/random.c 606b00941a1d7dd09c381d3279a058d771f406c5213c9932bbd93d5587be4b9c
 F src/resolve.c 37953a5f36c60bea413c3c04efcd433b6177009f508ef2ace0494728912fe2e9
 F src/rowset.c 8432130e6c344b3401a8874c3cb49fefe6873fec593294de077afea2dce5ec97
@@ -2041,8 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P 76ab8ae809a47a66688e2d50c20dc87ce946d82e9ffebb3adda55c451fad07fc
-R bac28918fe04cf4bb6c5ec2b0ffa1827
+P 6f1122e942b8269552daaf13d647d200d8546ec25f36310d67037c6b58d09976
+R eef1ed887e702bb26e5ed7046220e6a0
 U drh
-Z 6ffcf546adee0eb6c01fe1a8fc34f949
+Z 09a504821196951b22da7c1db783401d
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index f7aec02361..9eae2022f6 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-6f1122e942b8269552daaf13d647d200d8546ec25f36310d67037c6b58d09976
\ No newline at end of file
+07eab52e0801bb0e4743b304a06ad16e18cdf8eaa18c0faf8d47a1f5d8576ea0
\ No newline at end of file
diff --git a/src/func.c b/src/func.c
index 07ada2ef6e..c6a49de613 100644
--- a/src/func.c
+++ b/src/func.c
@@ -2371,6 +2371,37 @@ static void signFunc(
   sqlite3_result_int(context, x<0.0 ? -1 : x>0.0 ? +1 : 0);
 }
 
+#ifdef SQLITE_DEBUG
+/*
+** Implementation of fpdecode(x,y,z) function.
+**
+** x is a real number that is to be decoded.  y is the precision.
+** z is the maximum real precision.
+*/
+static void fpdecodeFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  FpDecode s;
+  double x;
+  int y, z;
+  char zBuf[100];
+  UNUSED_PARAMETER(argc);
+  assert( argc==3 );
+  x = sqlite3_value_double(argv[0]);
+  y = sqlite3_value_int(argv[1]);
+  z = sqlite3_value_int(argv[2]);
+  sqlite3FpDecode(&s, x, y, z);
+  if( s.isSpecial==2 ){
+    sqlite3_snprintf(sizeof(zBuf), zBuf, "NaN");
+  }else{
+    sqlite3_snprintf(sizeof(zBuf), zBuf, "%c%.*s/%d", s.sign, s.n, s.z, s.iDP);
+  }
+  sqlite3_result_text(context, zBuf, -1, SQLITE_TRANSIENT);
+}
+#endif /* SQLITE_DEBUG */
+
 /*
 ** All of the FuncDef structures in the aBuiltinFunc[] array above
 ** to the global function hash table.  This occurs at start-time (as
@@ -2442,6 +2473,9 @@ void sqlite3RegisterBuiltinFunctions(void){
     FUNCTION(unicode,            1, 0, 0, unicodeFunc      ),
     FUNCTION(char,              -1, 0, 0, charFunc         ),
     FUNCTION(abs,                1, 0, 0, absFunc          ),
+#ifdef SQLITE_DEBUG
+    FUNCTION(fpdecode,           3, 0, 0, fpdecodeFunc     ),
+#endif
 #ifndef SQLITE_OMIT_FLOATING_POINT
     FUNCTION(round,              1, 0, 0, roundFunc        ),
     FUNCTION(round,              2, 0, 0, roundFunc        ),
diff --git a/src/printf.c b/src/printf.c
index f00ad4cb2e..3fb1a322a0 100644
--- a/src/printf.c
+++ b/src/printf.c
@@ -202,7 +202,6 @@ void sqlite3_str_vappendf(
   int nOut;                  /* Size of the rendering buffer */
   char *zExtra = 0;          /* Malloced memory used by some conversion */
   int exp, e2;               /* exponent of real numbers */
-  int j;                     /* Number of significant digits returned */
   etByte flag_dp;            /* True if decimal point should be shown */
   etByte flag_rtz;           /* True if trailing zeros should be removed */
 
@@ -483,6 +482,7 @@ void sqlite3_str_vappendf(
       case etGENERIC: {
         FpDecode s;
         int iRound;
+        int j;
 
         if( bArgList ){
           realvalue = getDoubleArg(pArgList);

From fecdff43545a50c14634ed087682635d1405f440 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Sat, 1 Jul 2023 20:21:27 +0000
Subject: [PATCH 09/17] This check-in adds the use of "long double" to
 sqlite3FpDecode() which when run on x86 using a compiler that translates
 "long double" into binary80, causes all legacy tests to pass.  But on a
 system where "long double" is just an alias for "double", some of the tests
 are still failing.

FossilOrigin-Name: ce06982f880339cf46704e95c907249827c3e44af2b9420005200ca8abd3f371
---
 manifest      | 12 ++++++------
 manifest.uuid |  2 +-
 src/util.c    | 24 +++++++++++++-----------
 3 files changed, 20 insertions(+), 18 deletions(-)

diff --git a/manifest b/manifest
index d3e50a606b..60a8a88fd4 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Reinstate\sthe\sfpdecode()\sSQL\sfunction\sfor\stesting,\sbut\sonly\swhen\scompiled\nwith\sSQLITE_DEBUG.
-D 2023-07-01T18:33:26.856
+C This\scheck-in\sadds\sthe\suse\sof\s"long\sdouble"\sto\ssqlite3FpDecode()\swhich\swhen\nrun\son\sx86\susing\sa\scompiler\sthat\stranslates\s"long\sdouble"\sinto\sbinary80,\ncauses\sall\slegacy\stests\sto\spass.\s\sBut\son\sa\ssystem\swhere\s"long\sdouble"\sis\sjust\nan\salias\sfor\s"double",\ssome\sof\sthe\stests\sare\sstill\sfailing.
+D 2023-07-01T20:21:27.087
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c 87e6762b026cd733312838b0e9b9acb43d3a3c88c5e612e8077a7320c2bc1692
+F src/util.c d68692390be083744bd0dfafc797472b0d304743040220e18b93bc9bad8c8d6e
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -2041,8 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P 6f1122e942b8269552daaf13d647d200d8546ec25f36310d67037c6b58d09976
-R eef1ed887e702bb26e5ed7046220e6a0
+P 07eab52e0801bb0e4743b304a06ad16e18cdf8eaa18c0faf8d47a1f5d8576ea0
+R c4051b06b266c29a490b4cec354913fc
 U drh
-Z 09a504821196951b22da7c1db783401d
+Z 95eef79511e3e10371b4b76031a5a06d
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index 9eae2022f6..d2f8b9d453 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-07eab52e0801bb0e4743b304a06ad16e18cdf8eaa18c0faf8d47a1f5d8576ea0
\ No newline at end of file
+ce06982f880339cf46704e95c907249827c3e44af2b9420005200ca8abd3f371
\ No newline at end of file
diff --git a/src/util.c b/src/util.c
index 41359ea2a2..a560f26133 100644
--- a/src/util.c
+++ b/src/util.c
@@ -937,15 +937,16 @@ int sqlite3Atoi(const char *z){
 ** decimal point if n is negative.  No rounding is performed if
 ** n is zero.
 */
-void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
+void sqlite3FpDecode(FpDecode *p, double rr, int iRound, int mxRound){
   int i;
   u64 v;
   int e, exp = 0;
+  long double r;
   p->isSpecial = 0;
-  if( r<0.0 ){
+  if( rr<0.0 ){
     p->sign = '-';
-    r = -r;
-  }else if( r==0.0 ){
+    rr = -rr;
+  }else if( rr==0.0 ){
     p->sign = '+';
     p->n = 1;
     p->iDP = 1;
@@ -954,7 +955,7 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
   }else{
     p->sign = '+';
   }
-  memcpy(&v,&r,8);
+  memcpy(&v,&rr,8);
   e = v>>52;
   if( (e&0x7ff)==0x7ff ){
     p->isSpecial = 1 + (v!=0x7ff0000000000000L);
@@ -962,6 +963,7 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
     p->iDP = 0;
     return;
   }
+  r = rr;
 
   /* At this point, r is positive (non-zero) and is not Inf or NaN.
   ** The strategy is to multiple or divide r by powers of 10 until
@@ -969,13 +971,13 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
   ** an unsigned 64-bit integer v, and extract digits from v.
   */
   if( r>=1.0e+19 ){
-    while( r>=1.0e+119 ){ exp+=100; r /= 1.0e+100; }
-    while( r>=1.0e+29  ){ exp+=10;  r /= 1.0e+10;  }
-    while( r>=1.0e+19  ){ exp++;    r /= 10.0;     }
+    while( r>=1.0e+119L ){ exp+=100; r *= 1.0e-100L; }
+    while( r>=1.0e+29L  ){ exp+=10;  r *= 1.0e-10L;  }
+    while( r>=1.0e+19L  ){ exp++;    r *= 1.0e-1L;   }
   }else{
-    while( r<1.0e-97   ){ exp-=100; r *= 1.0e+100; }
-    while( r<1.0e+07   ){ exp-=10;  r *= 1.0e+10;  }
-    while( r<1.0e+17   ){ exp--;    r *= 10.0;     }
+    while( r<1.0e-97L   ){ exp-=100; r *= 1.0e+100L; }
+    while( r<1.0e+07L   ){ exp-=10;  r *= 1.0e+10L;  }
+    while( r<1.0e+17L   ){ exp--;    r *= 1.0e+1L;   }
   }
   v = (u64)r;
   i = sizeof(p->z)-1;

From c27bda0b7911186d1e11c8ffcd55818cfa211009 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Mon, 3 Jul 2023 00:40:37 +0000
Subject: [PATCH 10/17] An idea for improving accuracy of fp-to-decimal
 conversion for systems that do not have "long double".  Does not quite work. 
 Retained only for documentation purposes.

FossilOrigin-Name: 702243333843219f8904ee0fd12283080d6c6b3fc1ffb36c534cdefb3563c00d
---
 manifest      | 15 +++++++-----
 manifest.uuid |  2 +-
 src/util.c    | 64 ++++++++++++++++++++++++++++++++++++---------------
 3 files changed, 55 insertions(+), 26 deletions(-)

diff --git a/manifest b/manifest
index 60a8a88fd4..f969dca2f8 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C This\scheck-in\sadds\sthe\suse\sof\s"long\sdouble"\sto\ssqlite3FpDecode()\swhich\swhen\nrun\son\sx86\susing\sa\scompiler\sthat\stranslates\s"long\sdouble"\sinto\sbinary80,\ncauses\sall\slegacy\stests\sto\spass.\s\sBut\son\sa\ssystem\swhere\s"long\sdouble"\sis\sjust\nan\salias\sfor\s"double",\ssome\sof\sthe\stests\sare\sstill\sfailing.
-D 2023-07-01T20:21:27.087
+C An\sidea\sfor\simproving\saccuracy\sof\sfp-to-decimal\sconversion\sfor\ssystems\sthat\ndo\snot\shave\s"long\sdouble".\s\sDoes\snot\squite\swork.\s\sRetained\sonly\sfor\ndocumentation\spurposes.
+D 2023-07-03T00:40:37.359
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c d68692390be083744bd0dfafc797472b0d304743040220e18b93bc9bad8c8d6e
+F src/util.c 12741de9969af5134488b7c89a97ecc22144f93f62c6255f797abb9b3121608a
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -2041,8 +2041,11 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P 07eab52e0801bb0e4743b304a06ad16e18cdf8eaa18c0faf8d47a1f5d8576ea0
-R c4051b06b266c29a490b4cec354913fc
+P ce06982f880339cf46704e95c907249827c3e44af2b9420005200ca8abd3f371
+R ae7783ab51788007ac81a8600cb6b0a8
+T *branch * fp-to-decimal-branch1
+T *sym-fp-to-decimal-branch1 *
+T -sym-fp-to-decimal-refactor *
 U drh
-Z 95eef79511e3e10371b4b76031a5a06d
+Z 0f216e6dd96bccb8187eb2a64c983082
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index d2f8b9d453..d8fd936394 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-ce06982f880339cf46704e95c907249827c3e44af2b9420005200ca8abd3f371
\ No newline at end of file
+702243333843219f8904ee0fd12283080d6c6b3fc1ffb36c534cdefb3563c00d
\ No newline at end of file
diff --git a/src/util.c b/src/util.c
index a560f26133..9bc37c4f9a 100644
--- a/src/util.c
+++ b/src/util.c
@@ -937,16 +937,18 @@ int sqlite3Atoi(const char *z){
 ** decimal point if n is negative.  No rounding is performed if
 ** n is zero.
 */
-void sqlite3FpDecode(FpDecode *p, double rr, int iRound, int mxRound){
+void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
   int i;
   u64 v;
   int e, exp = 0;
-  long double r;
   p->isSpecial = 0;
-  if( rr<0.0 ){
+
+  /* Convert negative numbers to positive.  Deal with Infinity, 0.0, and
+  ** NaN. */
+  if( r<0.0 ){
     p->sign = '-';
-    rr = -rr;
-  }else if( rr==0.0 ){
+    r = -r;
+  }else if( r==0.0 ){
     p->sign = '+';
     p->n = 1;
     p->iDP = 1;
@@ -955,7 +957,7 @@ void sqlite3FpDecode(FpDecode *p, double rr, int iRound, int mxRound){
   }else{
     p->sign = '+';
   }
-  memcpy(&v,&rr,8);
+  memcpy(&v,&r,8);
   e = v>>52;
   if( (e&0x7ff)==0x7ff ){
     p->isSpecial = 1 + (v!=0x7ff0000000000000L);
@@ -963,23 +965,47 @@ void sqlite3FpDecode(FpDecode *p, double rr, int iRound, int mxRound){
     p->iDP = 0;
     return;
   }
-  r = rr;
 
-  /* At this point, r is positive (non-zero) and is not Inf or NaN.
-  ** The strategy is to multiple or divide r by powers of 10 until
-  ** it is in between 1.0e+17 and 1.0e+19.  Then convert r into
-  ** an unsigned 64-bit integer v, and extract digits from v.
+  /* Multiply r by powers of ten until it lands somewhere in between
+  ** 1.0e+19 and 1.0e+17.
   */
-  if( r>=1.0e+19 ){
-    while( r>=1.0e+119L ){ exp+=100; r *= 1.0e-100L; }
-    while( r>=1.0e+29L  ){ exp+=10;  r *= 1.0e-10L;  }
-    while( r>=1.0e+19L  ){ exp++;    r *= 1.0e-1L;   }
+  if( sizeof(long double)>8
+   || (v & 0x0000000000ffffffLL)==0
+   || (v & 0xffffffffff000000LL)==0
+  ){
+    long double rr = r;
+    if( rr>=1.0e+19 ){
+      while( rr>=1.0e+119L ){ exp+=100; rr *= 1.0e-100L; }
+      while( rr>=1.0e+29L  ){ exp+=10;  rr *= 1.0e-10L;  }
+      while( rr>=1.0e+19L  ){ exp++;    rr *= 1.0e-1L;   }
+    }else{
+      while( rr<1.0e-97L   ){ exp-=100; rr *= 1.0e+100L; }
+      while( rr<1.0e+07L   ){ exp-=10;  rr *= 1.0e+10L;  }
+      while( rr<1.0e+17L   ){ exp--;    rr *= 1.0e+1L;   }
+    }
+    v = (u64)rr;
   }else{
-    while( r<1.0e-97L   ){ exp-=100; r *= 1.0e+100L; }
-    while( r<1.0e+07L   ){ exp-=10;  r *= 1.0e+10L;  }
-    while( r<1.0e+17L   ){ exp--;    r *= 1.0e+1L;   }
+    double r2, r3;
+    v &= 0xffffffffff000000LL;
+    memcpy(&r2, &v, 8);
+    assert( r2<r );
+    assert( r2>0.0 );
+    r3 = r - r2;
+    assert( r3>0.0 );
+    if( r2>=1.0e+19 ){
+      while( r2>=1.0e+119L ){ exp+=100; r2 *= 1.0e-100; r3 *= 1.0e-100; }
+      while( r2>=1.0e+29L  ){ exp+=10;  r2 *= 1.0e-10;  r3 *= 1.0e-10;  }
+      while( r2>=1.0e+19L  ){ exp++;    r2 *= 1.0e-1;   r3 *= 1.0e-1;   }
+    }else{
+      while( r2<1.0e-97L   ){ exp-=100; r2 *= 1.0e+100; r3 *= 1.0e+100; }
+      while( r2<1.0e+07L   ){ exp-=10;  r2 *= 1.0e+10;  r3 *= 1.0e+10;  }
+      while( r2<1.0e+17L   ){ exp--;    r2 *= 1.0e+1;   r3 *= 1.0e+1;   }
+    }
+    v = (u64)(r2+r3);
   }
-  v = (u64)r;
+
+
+  /* Extract significant digits. */
   i = sizeof(p->z)-1;
   while( v ){  p->z[i--] = (v%10) + '0'; v /= 10; }
   p->n = sizeof(p->z) - 1 - i;

From c8885d42fe4799a265c69f4a6bbd4cdb3cf4daea Mon Sep 17 00:00:00 2001
From: drh <>
Date: Mon, 3 Jul 2023 09:07:23 +0000
Subject: [PATCH 11/17] Replace the dodgy error estimating logic in the
 previous check-in with full-up Dekker double-double multiplication, and this
 idea works much better. There are still a few inaccuracies, but it is much
 closer.

FossilOrigin-Name: 4fa6938dac2d3d813a37664053db31451a2a065f78dd212488f5f7f8d583ddc5
---
 manifest        | 17 +++++------
 manifest.uuid   |  2 +-
 src/util.c      | 77 +++++++++++++++++++++++++++++++++++++------------
 test/atof1.test |  6 ++--
 4 files changed, 69 insertions(+), 33 deletions(-)

diff --git a/manifest b/manifest
index f969dca2f8..a420e218ba 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C An\sidea\sfor\simproving\saccuracy\sof\sfp-to-decimal\sconversion\sfor\ssystems\sthat\ndo\snot\shave\s"long\sdouble".\s\sDoes\snot\squite\swork.\s\sRetained\sonly\sfor\ndocumentation\spurposes.
-D 2023-07-03T00:40:37.359
+C Replace\sthe\sdodgy\serror\sestimating\slogic\sin\sthe\sprevious\scheck-in\swith\nfull-up\sDekker\sdouble-double\smultiplication,\sand\sthis\sidea\sworks\smuch\sbetter.\nThere\sare\sstill\sa\sfew\sinaccuracies,\sbut\sit\sis\smuch\scloser.
+D 2023-07-03T09:07:23.117
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c 12741de9969af5134488b7c89a97ecc22144f93f62c6255f797abb9b3121608a
+F src/util.c 1feadae2da54a59ab7ec82d4b94ed22f94bb5d4df25e41e73c05c8f3c1328607
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -775,7 +775,7 @@ F test/async2.test c0a9bd20816d7d6a2ceca7b8c03d3d69c28ffb8b
 F test/async3.test d73a062002376d7edc1fe3edff493edbec1fc2f7
 F test/async4.test 1787e3952128aa10238bf39945126de7ca23685a
 F test/async5.test 383ab533fdb9f7ad228cc99ee66e1acb34cc0dc0
-F test/atof1.test 1f24a6f16e44892848298bd8e488159d4a60cf47be003d32747a136103c9bbac
+F test/atof1.test b4dbc37187649e23ba92e06e0d2c076304516967b5a8b0af50f8e4f2323e654c
 F test/atomic.test 065a453dde33c77ff586d91ccaa6ed419829d492dbb1a5694b8a09f3f9d7d061
 F test/atomic2.test b6863b4aa552543874f80b42fb3063f1c8c2e3d8e56b6562f00a3cc347b5c1da
 F test/atrc.c c388fac43dbba05c804432a7135ae688b32e8f25818e9994ffba4b64cf60c27c
@@ -2041,11 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P ce06982f880339cf46704e95c907249827c3e44af2b9420005200ca8abd3f371
-R ae7783ab51788007ac81a8600cb6b0a8
-T *branch * fp-to-decimal-branch1
-T *sym-fp-to-decimal-branch1 *
-T -sym-fp-to-decimal-refactor *
+P 702243333843219f8904ee0fd12283080d6c6b3fc1ffb36c534cdefb3563c00d
+R 0bc2956a2833c937de8e3462962e6784
 U drh
-Z 0f216e6dd96bccb8187eb2a64c983082
+Z 2f85ae3f7bbd29aeb71b560da07ddd48
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index d8fd936394..8bb5c10510 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-702243333843219f8904ee0fd12283080d6c6b3fc1ffb36c534cdefb3563c00d
\ No newline at end of file
+4fa6938dac2d3d813a37664053db31451a2a065f78dd212488f5f7f8d583ddc5
\ No newline at end of file
diff --git a/src/util.c b/src/util.c
index 9bc37c4f9a..b7d6bd58e8 100644
--- a/src/util.c
+++ b/src/util.c
@@ -928,6 +928,31 @@ int sqlite3Atoi(const char *z){
   return x;
 }
 
+/* Double-Double multiplication.  *(z,zz) = (x,xx) * (y,yy)
+**
+** Reference:
+**   T. J. Dekker, "A Floating-Point Technique for Extending the
+**   Available Precision".  1971-07-26.
+*/
+static void mul2(
+  double x,  double xx,
+  double y,  double yy,
+  double *z, double *zz
+){
+  double hx, tx, hy, ty, p, q, c, cc;
+  p = 67108865.0 * x;
+  hx = x - p + p; tx = x - hx;
+  p = 67108865.0 * y;
+  hy = y - p + p; ty = y - hy;
+  p = hx*hy;
+  q = hx*ty + tx*hy;
+  c = p+q;
+  cc = p - c + q + tx*ty;
+  cc = x*yy + xx*y + cc;
+  *z = c + cc;
+  *zz = c - *z + cc;
+}
+
 /*
 ** Decode a floating-point value into an approximate decimal
 ** representation.
@@ -969,10 +994,7 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
   /* Multiply r by powers of ten until it lands somewhere in between
   ** 1.0e+19 and 1.0e+17.
   */
-  if( sizeof(long double)>8
-   || (v & 0x0000000000ffffffLL)==0
-   || (v & 0xffffffffff000000LL)==0
-  ){
+  if( sizeof(long double)>8 && 0 ){
     long double rr = r;
     if( rr>=1.0e+19 ){
       while( rr>=1.0e+119L ){ exp+=100; rr *= 1.0e-100L; }
@@ -985,23 +1007,40 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
     }
     v = (u64)rr;
   }else{
-    double r2, r3;
-    v &= 0xffffffffff000000LL;
-    memcpy(&r2, &v, 8);
-    assert( r2<r );
-    assert( r2>0.0 );
-    r3 = r - r2;
-    assert( r3>0.0 );
-    if( r2>=1.0e+19 ){
-      while( r2>=1.0e+119L ){ exp+=100; r2 *= 1.0e-100; r3 *= 1.0e-100; }
-      while( r2>=1.0e+29L  ){ exp+=10;  r2 *= 1.0e-10;  r3 *= 1.0e-10;  }
-      while( r2>=1.0e+19L  ){ exp++;    r2 *= 1.0e-1;   r3 *= 1.0e-1;   }
+    double rr = 0.0;
+    if( r>=1.0e+19 ){
+      while( r>=1.0e+119 ){
+        if( r>=1.0e+300 ){
+          exp += 300;
+          r *= 1.0e-300;
+          break;
+        }
+        exp += 100;
+        mul2(r, rr, 1.0e-100, -1.99918998026028836196e-117, &r, &rr);
+      }
+      while( r>=1.0e+29 ){
+        exp += 10;
+        mul2(r,rr, 1.0e-10, -3.6432197315497741579e-27, &r, &rr);
+      }
+      while( r>=1.0e+19 ){
+        exp += 1;
+        mul2(r,rr, 1.0e-01, -5.5511151231257827021e-18, &r, &rr);
+      }
     }else{
-      while( r2<1.0e-97L   ){ exp-=100; r2 *= 1.0e+100; r3 *= 1.0e+100; }
-      while( r2<1.0e+07L   ){ exp-=10;  r2 *= 1.0e+10;  r3 *= 1.0e+10;  }
-      while( r2<1.0e+17L   ){ exp--;    r2 *= 1.0e+1;   r3 *= 1.0e+1;   }
+      while( r<1.0e-98  ){
+        exp -= 100;
+        mul2(r, rr, 1.0e+100, -1.5902891109759918046, &r, &rr);
+      }
+      while( r<1.0e+08  ){
+        exp -= 10;
+        mul2(r, rr, 1.0e+10, 0.0, &r, &rr);
+      }
+      while( r<1.0e+18  ){
+        exp -= 1;
+        mul2(r, rr, 1.0e+01, 0.0, &r, &rr);
+      }
     }
-    v = (u64)(r2+r3);
+    v = (u64)(r)+(u64)(rr);
   }
 
 
diff --git a/test/atof1.test b/test/atof1.test
index 5959c5d5b9..ecfbdd33ee 100644
--- a/test/atof1.test
+++ b/test/atof1.test
@@ -51,10 +51,10 @@ for {set i 1} {$i<20000} {incr i} {
     set y [db eval {SELECT $x=CAST(quote($x) AS real)}]
     if {!$y} {
       db eval {SELECT real2hex($x) a, real2hex(CAST(quote($x) AS real)) b} {}
-      puts "\nIN:    $a $xf"
-      puts [format {QUOTE: %16s %s} {} [db eval {SELECT quote($x)}]]
+      puts "\n!IN:    $a $xf"
+      puts [format {!QUOTE: %16s %s} {} [db eval {SELECT quote($x)}]]
       db eval {SELECT CAST(quote($x) AS real) c} {}
-      puts "OUT:   $b [format %.32e $c]"
+      puts "!OUT:   $b [format %.32e $c]"
     }
     set y
   } {1}

From 37b188fbca861daa26f649bfaa4c42771ff315d7 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Mon, 3 Jul 2023 10:00:38 +0000
Subject: [PATCH 12/17] Fix one constant in the normalization logic.  Improved
 error output from atof1.test.

FossilOrigin-Name: d3c48807100a358a70fdd799c8935eba1b765ace2e1ddea4475fd673006cb6da
---
 manifest        | 14 +++++++-------
 manifest.uuid   |  2 +-
 src/util.c      |  2 +-
 test/atof1.test |  8 +++++++-
 4 files changed, 16 insertions(+), 10 deletions(-)

diff --git a/manifest b/manifest
index a420e218ba..5ae086cfa2 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Replace\sthe\sdodgy\serror\sestimating\slogic\sin\sthe\sprevious\scheck-in\swith\nfull-up\sDekker\sdouble-double\smultiplication,\sand\sthis\sidea\sworks\smuch\sbetter.\nThere\sare\sstill\sa\sfew\sinaccuracies,\sbut\sit\sis\smuch\scloser.
-D 2023-07-03T09:07:23.117
+C Fix\sone\sconstant\sin\sthe\snormalization\slogic.\s\sImproved\serror\soutput\nfrom\satof1.test.
+D 2023-07-03T10:00:38.019
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c 1feadae2da54a59ab7ec82d4b94ed22f94bb5d4df25e41e73c05c8f3c1328607
+F src/util.c eae1eeaf2de968bc32d81274b6209a6685d8f68f8a44fb80bc77602860feede8
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -775,7 +775,7 @@ F test/async2.test c0a9bd20816d7d6a2ceca7b8c03d3d69c28ffb8b
 F test/async3.test d73a062002376d7edc1fe3edff493edbec1fc2f7
 F test/async4.test 1787e3952128aa10238bf39945126de7ca23685a
 F test/async5.test 383ab533fdb9f7ad228cc99ee66e1acb34cc0dc0
-F test/atof1.test b4dbc37187649e23ba92e06e0d2c076304516967b5a8b0af50f8e4f2323e654c
+F test/atof1.test 191ce0d7b0d527aafeafe659c31e2433e430324b5ebce3fb066178b4d9035767
 F test/atomic.test 065a453dde33c77ff586d91ccaa6ed419829d492dbb1a5694b8a09f3f9d7d061
 F test/atomic2.test b6863b4aa552543874f80b42fb3063f1c8c2e3d8e56b6562f00a3cc347b5c1da
 F test/atrc.c c388fac43dbba05c804432a7135ae688b32e8f25818e9994ffba4b64cf60c27c
@@ -2041,8 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P 702243333843219f8904ee0fd12283080d6c6b3fc1ffb36c534cdefb3563c00d
-R 0bc2956a2833c937de8e3462962e6784
+P 4fa6938dac2d3d813a37664053db31451a2a065f78dd212488f5f7f8d583ddc5
+R df6eb47114802d2c438e907f9bdbb126
 U drh
-Z 2f85ae3f7bbd29aeb71b560da07ddd48
+Z 7f5799444e9a2cb0ee3bb904fd4adcc7
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index 8bb5c10510..a69b8691ba 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-4fa6938dac2d3d813a37664053db31451a2a065f78dd212488f5f7f8d583ddc5
\ No newline at end of file
+d3c48807100a358a70fdd799c8935eba1b765ace2e1ddea4475fd673006cb6da
\ No newline at end of file
diff --git a/src/util.c b/src/util.c
index b7d6bd58e8..40662f021c 100644
--- a/src/util.c
+++ b/src/util.c
@@ -1027,7 +1027,7 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
         mul2(r,rr, 1.0e-01, -5.5511151231257827021e-18, &r, &rr);
       }
     }else{
-      while( r<1.0e-98  ){
+      while( r<1.0e-82  ){
         exp -= 100;
         mul2(r, rr, 1.0e+100, -1.5902891109759918046, &r, &rr);
       }
diff --git a/test/atof1.test b/test/atof1.test
index ecfbdd33ee..9386fb0589 100644
--- a/test/atof1.test
+++ b/test/atof1.test
@@ -51,7 +51,13 @@ for {set i 1} {$i<20000} {incr i} {
     set y [db eval {SELECT $x=CAST(quote($x) AS real)}]
     if {!$y} {
       db eval {SELECT real2hex($x) a, real2hex(CAST(quote($x) AS real)) b} {}
-      puts "\n!IN:    $a $xf"
+      puts ""
+      if {$x<0} {
+        puts "[format {!SCALE: %17s 1 23456789 123456789 123456789} {}]"
+      } else {
+        puts "[format {!SCALE: %16s 1 23456789 123456789 123456789} {}]"
+      }
+      puts "!IN:    $a $xf"
       puts [format {!QUOTE: %16s %s} {} [db eval {SELECT quote($x)}]]
       db eval {SELECT CAST(quote($x) AS real) c} {}
       puts "!OUT:   $b [format %.32e $c]"

From 5270d7424d2e9f47c450fe85753c0768e2f41b3b Mon Sep 17 00:00:00 2001
From: drh <>
Date: Mon, 3 Jul 2023 10:18:02 +0000
Subject: [PATCH 13/17] Faster Dekker multiplication that removes the
 restriction on input magnitude.

FossilOrigin-Name: 2994caf5884be07c889519c78fbac4ddcf267fcfe6a3265ecb6390bcd574532e
---
 manifest      | 12 ++++++------
 manifest.uuid |  2 +-
 src/util.c    | 18 +++++++++---------
 3 files changed, 16 insertions(+), 16 deletions(-)

diff --git a/manifest b/manifest
index 5ae086cfa2..593e1f7fd9 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Fix\sone\sconstant\sin\sthe\snormalization\slogic.\s\sImproved\serror\soutput\nfrom\satof1.test.
-D 2023-07-03T10:00:38.019
+C Faster\sDekker\smultiplication\sthat\sremoves\sthe\srestriction\son\sinput\smagnitude.
+D 2023-07-03T10:18:02.499
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c eae1eeaf2de968bc32d81274b6209a6685d8f68f8a44fb80bc77602860feede8
+F src/util.c e920f80d429285da398e33852e47b1731fd474d4fc8fd38ea16e74f7f15c100c
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -2041,8 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P 4fa6938dac2d3d813a37664053db31451a2a065f78dd212488f5f7f8d583ddc5
-R df6eb47114802d2c438e907f9bdbb126
+P d3c48807100a358a70fdd799c8935eba1b765ace2e1ddea4475fd673006cb6da
+R 46c57ca0802519e59042da4b712e623e
 U drh
-Z 7f5799444e9a2cb0ee3bb904fd4adcc7
+Z 937d038b18f0b1ea37450ce437120a68
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index a69b8691ba..1fa06bc7fa 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-d3c48807100a358a70fdd799c8935eba1b765ace2e1ddea4475fd673006cb6da
\ No newline at end of file
+2994caf5884be07c889519c78fbac4ddcf267fcfe6a3265ecb6390bcd574532e
\ No newline at end of file
diff --git a/src/util.c b/src/util.c
index 40662f021c..7456599bc9 100644
--- a/src/util.c
+++ b/src/util.c
@@ -940,10 +940,15 @@ static void mul2(
   double *z, double *zz
 ){
   double hx, tx, hy, ty, p, q, c, cc;
-  p = 67108865.0 * x;
-  hx = x - p + p; tx = x - hx;
-  p = 67108865.0 * y;
-  hy = y - p + p; ty = y - hy;
+  u64 m;
+  memcpy(&m, &x, 8);
+  m &= 0xfffffffffc000000L;
+  memcpy(&hx, &m, 8);
+  tx = x - hx;
+  memcpy(&m, &y, 8);
+  m &= 0xfffffffffc000000L;
+  memcpy(&hy, &m, 8);
+  ty = y - hy;
   p = hx*hy;
   q = hx*ty + tx*hy;
   c = p+q;
@@ -1010,11 +1015,6 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
     double rr = 0.0;
     if( r>=1.0e+19 ){
       while( r>=1.0e+119 ){
-        if( r>=1.0e+300 ){
-          exp += 300;
-          r *= 1.0e-300;
-          break;
-        }
         exp += 100;
         mul2(r, rr, 1.0e-100, -1.99918998026028836196e-117, &r, &rr);
       }

From bc2b65832e97ec400a50116b525fde8fb1bd9580 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Mon, 3 Jul 2023 10:35:29 +0000
Subject: [PATCH 14/17] Squeeze as many bits as we can out of normalization.

FossilOrigin-Name: 25d1ad6df1ed460c2cc9f32e8a5106e121ae502044f83abf431c1d5b3879eb56
---
 manifest      | 12 ++++++------
 manifest.uuid |  2 +-
 src/util.c    | 14 +++++++-------
 3 files changed, 14 insertions(+), 14 deletions(-)

diff --git a/manifest b/manifest
index 593e1f7fd9..b7a2f9af88 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Faster\sDekker\smultiplication\sthat\sremoves\sthe\srestriction\son\sinput\smagnitude.
-D 2023-07-03T10:18:02.499
+C Squeeze\sas\smany\sbits\sas\swe\scan\sout\sof\snormalization.
+D 2023-07-03T10:35:29.478
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c e920f80d429285da398e33852e47b1731fd474d4fc8fd38ea16e74f7f15c100c
+F src/util.c 78be1d552e7038265bb944ef26c9ef94514bd061da19323a0321dde2874f0907
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -2041,8 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P d3c48807100a358a70fdd799c8935eba1b765ace2e1ddea4475fd673006cb6da
-R 46c57ca0802519e59042da4b712e623e
+P 2994caf5884be07c889519c78fbac4ddcf267fcfe6a3265ecb6390bcd574532e
+R 50ea777199102a639989a65cb4bb5a5a
 U drh
-Z 937d038b18f0b1ea37450ce437120a68
+Z 91cee9d1957f1c63a4a3d422340e91a7
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index 1fa06bc7fa..a5a0d7abae 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-2994caf5884be07c889519c78fbac4ddcf267fcfe6a3265ecb6390bcd574532e
\ No newline at end of file
+25d1ad6df1ed460c2cc9f32e8a5106e121ae502044f83abf431c1d5b3879eb56
\ No newline at end of file
diff --git a/src/util.c b/src/util.c
index 7456599bc9..6e740ef6ae 100644
--- a/src/util.c
+++ b/src/util.c
@@ -1013,29 +1013,29 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
     v = (u64)rr;
   }else{
     double rr = 0.0;
-    if( r>=1.0e+19 ){
-      while( r>=1.0e+119 ){
+    if( r>1.84e+19 ){
+      while( r>1.84e+119 ){
         exp += 100;
         mul2(r, rr, 1.0e-100, -1.99918998026028836196e-117, &r, &rr);
       }
-      while( r>=1.0e+29 ){
+      while( r>1.84e+29 ){
         exp += 10;
         mul2(r,rr, 1.0e-10, -3.6432197315497741579e-27, &r, &rr);
       }
-      while( r>=1.0e+19 ){
+      while( r>1.84e+19 ){
         exp += 1;
         mul2(r,rr, 1.0e-01, -5.5511151231257827021e-18, &r, &rr);
       }
     }else{
-      while( r<1.0e-82  ){
+      while( r<1.84e-82  ){
         exp -= 100;
         mul2(r, rr, 1.0e+100, -1.5902891109759918046, &r, &rr);
       }
-      while( r<1.0e+08  ){
+      while( r<1.84e+08  ){
         exp -= 10;
         mul2(r, rr, 1.0e+10, 0.0, &r, &rr);
       }
-      while( r<1.0e+18  ){
+      while( r<1.84e+18  ){
         exp -= 1;
         mul2(r, rr, 1.0e+01, 0.0, &r, &rr);
       }

From 841e596ad02b1b99e6c9578e9ecc5b0b56277948 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Mon, 3 Jul 2023 11:39:38 +0000
Subject: [PATCH 15/17] Final clean-up of the idea of using Dekker
 double-precision floating computations to improve accuracy.

FossilOrigin-Name: 40285d631072b79aba39cc20d4b217bdf0069f29ac9902cb97dec28d3e4cde11
---
 manifest      | 12 ++++++------
 manifest.uuid |  2 +-
 src/util.c    | 15 ++++++++++++---
 3 files changed, 19 insertions(+), 10 deletions(-)

diff --git a/manifest b/manifest
index b7a2f9af88..7130835d4e 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Squeeze\sas\smany\sbits\sas\swe\scan\sout\sof\snormalization.
-D 2023-07-03T10:35:29.478
+C Final\sclean-up\sof\sthe\sidea\sof\susing\sDekker\sdouble-precision\sfloating\ncomputations\sto\simprove\saccuracy.
+D 2023-07-03T11:39:38.542
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c 78be1d552e7038265bb944ef26c9ef94514bd061da19323a0321dde2874f0907
+F src/util.c 44855f67ac96b546b77b6c2ad128d1e28a56c495038cdda3cae25b8407442f3c
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -2041,8 +2041,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P 2994caf5884be07c889519c78fbac4ddcf267fcfe6a3265ecb6390bcd574532e
-R 50ea777199102a639989a65cb4bb5a5a
+P 25d1ad6df1ed460c2cc9f32e8a5106e121ae502044f83abf431c1d5b3879eb56
+R 8a559af6860b1623fc9d9f5fb9393b11
 U drh
-Z 91cee9d1957f1c63a4a3d422340e91a7
+Z 48672189b786297b4026c7966b4eccaa
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index a5a0d7abae..7757e469cd 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-25d1ad6df1ed460c2cc9f32e8a5106e121ae502044f83abf431c1d5b3879eb56
\ No newline at end of file
+40285d631072b79aba39cc20d4b217bdf0069f29ac9902cb97dec28d3e4cde11
\ No newline at end of file
diff --git a/src/util.c b/src/util.c
index 6e740ef6ae..cf4745bd0b 100644
--- a/src/util.c
+++ b/src/util.c
@@ -999,8 +999,8 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
   /* Multiply r by powers of ten until it lands somewhere in between
   ** 1.0e+19 and 1.0e+17.
   */
-  if( sizeof(long double)>8 && 0 ){
-    long double rr = r;
+  if( sizeof(LONGDOUBLE_TYPE)>8 ){
+    LONGDOUBLE_TYPE rr = r;
     if( rr>=1.0e+19 ){
       while( rr>=1.0e+119L ){ exp+=100; rr *= 1.0e-100L; }
       while( rr>=1.0e+29L  ){ exp+=10;  rr *= 1.0e-10L;  }
@@ -1012,6 +1012,15 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
     }
     v = (u64)rr;
   }else{
+    /* If high-precision floating point is not available using "long double",
+    ** then use Dekker-style double-double computation to increase the
+    ** precision.
+    **
+    ** The error terms on constants like 1.0e+100 computed using the
+    ** decimal extension, for example as follows:
+    **
+    **   SELECT decimal_sci(decimal_sub('1.0e+100',decimal(1.0e+100)));
+    */
     double rr = 0.0;
     if( r>1.84e+19 ){
       while( r>1.84e+119 ){
@@ -1029,7 +1038,7 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
     }else{
       while( r<1.84e-82  ){
         exp -= 100;
-        mul2(r, rr, 1.0e+100, -1.5902891109759918046, &r, &rr);
+        mul2(r, rr, 1.0e+100, -1.5902891109759918046e+83, &r, &rr);
       }
       while( r<1.84e+08  ){
         exp -= 10;

From 0478d1d88a523d3d8e5c8d5acd7eb9649937ec65 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Mon, 3 Jul 2023 12:58:18 +0000
Subject: [PATCH 16/17] New test cases for floating-point conversions.

FossilOrigin-Name: 9435ed76cd9bb1be02768b3853a2323834f67bda75d3e3f76f6aa7bd0bade3d7
---
 manifest          | 16 ++++++-------
 manifest.uuid     |  2 +-
 src/test1.c       | 61 +++++++++++++++++++++++++++++++++++++++++++++++
 src/util.c        | 14 +++++------
 test/fpconv1.test | 44 ++++++++++++++++++++++++++++++++++
 5 files changed, 121 insertions(+), 16 deletions(-)
 create mode 100644 test/fpconv1.test

diff --git a/manifest b/manifest
index fd10ee4899..0c46f90368 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C Use\sDekker\sdouble-precision\sfloating\spoint\sto\sdo\sthe\svalue\snormalization\nstep\sin\ssqlite3FpDecode()\sfor\ssystems\son\swhich\s"long\sdouble"\sis\s8\sbytes\sor\nless.
-D 2023-07-03T11:44:15.056
+C New\stest\scases\sfor\sfloating-point\sconversions.
+D 2023-07-03T12:58:18.851
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -647,7 +647,7 @@ F src/sqliteLimit.h 33b1c9baba578d34efe7dfdb43193b366111cdf41476b1e82699e14c11ee
 F src/status.c 160c445d7d28c984a0eae38c144f6419311ed3eace59b44ac6dafc20db4af749
 F src/table.c 0f141b58a16de7e2fbe81c308379e7279f4c6b50eb08efeec5892794a0ba30d1
 F src/tclsqlite.c ecbc3c99c0d0c3ed122a913f143026c26d38d57f33e06bb71185dd5c1efe37cd
-F src/test1.c 64b8462099618a6243f63ba701eea8913046cd7377a7a77a7e3a0ada42219275
+F src/test1.c ac81daaee5135d210f926e7d1501d6065d396decac57af94083e677cf7e175bd
 F src/test2.c 827446e259a3b7ab949da1542953edda7b5117982576d3e6f1c24a0dd20a5cef
 F src/test3.c e5178558c41ff53236ae0271e9acb3d6885a94981d2eb939536ee6474598840e
 F src/test4.c 4533b76419e7feb41b40582554663ed3cd77aaa54e135cf76b3205098cd6e664
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c 44855f67ac96b546b77b6c2ad128d1e28a56c495038cdda3cae25b8407442f3c
+F src/util.c 97f9a7a1a22db23984ca3ced12ed666327c17beeaf8481c3325a0c74369060dc
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -1014,6 +1014,7 @@ F test/fkey8.test 51deda7f1a1448bca95875e4a6e1a3a75b4bd7215e924e845bd60de60e4d84
 F test/fkey_malloc.test 594a7ea1fbab553c036c70813cd8bd9407d63749
 F test/fordelete.test ba98f14446b310f9c9d935b97ec748753d0144a28b356ba30d1f4f6958fdde5c
 F test/format4.test eeae341953db8b6bda7f549044797c3278a6cc345d11ada81471671b654f8ef4
+F test/fpconv1.test d5d8aa0c427533006c112fb1957cdd1ea68c1d0709470dabb9ca02c2e4c06ad8
 F test/fts-9fd058691.test 78b887e30ae6816df0e1fed6259de4b5a64ad33c
 F test/fts3.test 672a040ea57036fb4b6fdc09027c18d7d24ab654
 F test/fts3_common.tcl dffad248f9ce090800e272017d2898005c28ee6314fc1dd5550643a02666907a
@@ -2041,9 +2042,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P ce06982f880339cf46704e95c907249827c3e44af2b9420005200ca8abd3f371 40285d631072b79aba39cc20d4b217bdf0069f29ac9902cb97dec28d3e4cde11
-R 8a559af6860b1623fc9d9f5fb9393b11
-T +closed 40285d631072b79aba39cc20d4b217bdf0069f29ac9902cb97dec28d3e4cde11
+P 51f492b440728151ce64168d5436ba87ca60d84b89408e47c593fa731355afe4
+R 610c019b12f01dbb4053eb803e9a81bd
 U drh
-Z 98f04f31ed955532d376706d5d138150
+Z 391291e9df52bc2766a8acd3f9c94d15
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index b3071eda1b..f201e504af 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-51f492b440728151ce64168d5436ba87ca60d84b89408e47c593fa731355afe4
\ No newline at end of file
+9435ed76cd9bb1be02768b3853a2323834f67bda75d3e3f76f6aa7bd0bade3d7
\ No newline at end of file
diff --git a/src/test1.c b/src/test1.c
index c77aff2ed2..013adcbcb0 100644
--- a/src/test1.c
+++ b/src/test1.c
@@ -991,6 +991,46 @@ static void intrealFunction(
   sqlite3_test_control(SQLITE_TESTCTRL_RESULT_INTREAL, context);
 }
 
+/*
+** SQL function:  strtod(X)
+**
+** Use the C-library strtod() function to convert string X into a double.
+** Used for comparing the accuracy of SQLite's internal text-to-float conversion
+** routines against the C-library.
+*/
+static void shellStrtod(
+  sqlite3_context *pCtx,
+  int nVal,
+  sqlite3_value **apVal
+){
+  char *z = (char*)sqlite3_value_text(apVal[0]);
+  UNUSED_PARAMETER(nVal);
+  if( z==0 ) return;
+  sqlite3_result_double(pCtx, strtod(z,0));
+}
+
+/*
+** SQL function:  dtostr(X)
+**
+** Use the C-library printf() function to convert real value X into a string.
+** Used for comparing the accuracy of SQLite's internal float-to-text conversion
+** routines against the C-library.
+*/
+static void shellDtostr(
+  sqlite3_context *pCtx,
+  int nVal,
+  sqlite3_value **apVal
+){
+  double r = sqlite3_value_double(apVal[0]);
+  int n = nVal>=2 ? sqlite3_value_int(apVal[1]) : 26;
+  char z[400];
+  if( n<1 ) n = 1;
+  if( n>350 ) n = 350;
+  sprintf(z, "%#+.*e", n, r);
+  sqlite3_result_text(pCtx, z, -1, SQLITE_TRANSIENT);
+}
+
+
 /*
 ** Usage:  sqlite3_create_function DB
 **
@@ -1063,6 +1103,27 @@ static int SQLITE_TCLAPI test_create_function(
           0, intrealFunction, 0, 0);
   }
 
+  /* Functions strtod() and dtostr() work as in the shell.  These routines
+  ** use the standard C library to convert between floating point and
+  ** text.  This is used to compare SQLite's internal conversion routines
+  ** against the standard library conversion routines.
+  **
+  ** Both routines copy/pasted from the shell.c.in implementation
+  ** on 2023-07-03.
+  */
+  if( rc==SQLITE_OK ){
+    rc = sqlite3_create_function(db, "strtod", 1, SQLITE_UTF8, 0,
+                                 shellStrtod, 0, 0);
+  }
+  if( rc==SQLITE_OK ){
+    rc = sqlite3_create_function(db, "dtostr", 1, SQLITE_UTF8, 0,
+                                 shellDtostr, 0, 0);
+  }
+  if( rc==SQLITE_OK ){
+    rc = sqlite3_create_function(db, "dtostr", 2, SQLITE_UTF8, 0,
+                                 shellDtostr, 0, 0);
+  }
+
 #ifndef SQLITE_OMIT_UTF16
   /* Use the sqlite3_create_function16() API here. Mainly for fun, but also 
   ** because it is not tested anywhere else. */
diff --git a/src/util.c b/src/util.c
index cf4745bd0b..7642a29bca 100644
--- a/src/util.c
+++ b/src/util.c
@@ -934,7 +934,7 @@ int sqlite3Atoi(const char *z){
 **   T. J. Dekker, "A Floating-Point Technique for Extending the
 **   Available Precision".  1971-07-26.
 */
-static void mul2(
+static void dekkerMul2(
   double x,  double xx,
   double y,  double yy,
   double *z, double *zz
@@ -1025,28 +1025,28 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
     if( r>1.84e+19 ){
       while( r>1.84e+119 ){
         exp += 100;
-        mul2(r, rr, 1.0e-100, -1.99918998026028836196e-117, &r, &rr);
+        dekkerMul2(r, rr, 1.0e-100, -1.99918998026028836196e-117, &r, &rr);
       }
       while( r>1.84e+29 ){
         exp += 10;
-        mul2(r,rr, 1.0e-10, -3.6432197315497741579e-27, &r, &rr);
+        dekkerMul2(r,rr, 1.0e-10, -3.6432197315497741579e-27, &r, &rr);
       }
       while( r>1.84e+19 ){
         exp += 1;
-        mul2(r,rr, 1.0e-01, -5.5511151231257827021e-18, &r, &rr);
+        dekkerMul2(r,rr, 1.0e-01, -5.5511151231257827021e-18, &r, &rr);
       }
     }else{
       while( r<1.84e-82  ){
         exp -= 100;
-        mul2(r, rr, 1.0e+100, -1.5902891109759918046e+83, &r, &rr);
+        dekkerMul2(r, rr, 1.0e+100, -1.5902891109759918046e+83, &r, &rr);
       }
       while( r<1.84e+08  ){
         exp -= 10;
-        mul2(r, rr, 1.0e+10, 0.0, &r, &rr);
+        dekkerMul2(r, rr, 1.0e+10, 0.0, &r, &rr);
       }
       while( r<1.84e+18  ){
         exp -= 1;
-        mul2(r, rr, 1.0e+01, 0.0, &r, &rr);
+        dekkerMul2(r, rr, 1.0e+01, 0.0, &r, &rr);
       }
     }
     v = (u64)(r)+(u64)(rr);
diff --git a/test/fpconv1.test b/test/fpconv1.test
new file mode 100644
index 0000000000..195fdf9904
--- /dev/null
+++ b/test/fpconv1.test
@@ -0,0 +1,44 @@
+# 2023-07-03
+#
+# 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 file contains a test that attempts to verify the claim that the
+# floatpoint-to-text conversion routines built into SQLite maintain at
+# least 15 significant digits of accuracy.
+#
+
+set testdir [file dirname $argv0]
+source $testdir/tester.tcl
+
+if {[catch {load_static_extension db decimal} error]} {
+  puts "Skipping decimal tests, hit load error: $error"
+  finish_test; return
+}
+
+sqlite3_create_function db
+do_execsql_test fpconv1-1.0 {
+  WITH RECURSIVE
+       /* Number of random floating-point values to try.
+       ** On a circa 2016 x64 linux box, this test runs at
+       ** about 80000 cases per second  -------------------vvvvvv */
+    c(x) AS (VALUES(1) UNION ALL SELECT x+1 FROM c WHERE x<100000),
+    fp(y) AS MATERIALIZED (
+       SELECT CAST( format('%+d.%019d0e%+03d',
+                           random()%10,abs(random()),random()%200) AS real)
+        FROM c
+    )
+  SELECT y FROM fp
+   WHERE -log10(abs(decimal_sub(dtostr(y,24),format('%!.24e',y))/y))<15.0;
+                     /* Number of digits of accuracy required -------^^^^ */
+} {}
+#  ^---- Expect a empty set as the result.  The output is all tested numbers
+#        that fail to preserve at least 15 significant digits of accuracy.
+
+finish_test

From 1b3c6e727e11417a687fc09193828f5142a1b195 Mon Sep 17 00:00:00 2001
From: drh <>
Date: Mon, 3 Jul 2023 14:56:49 +0000
Subject: [PATCH 17/17] Whether or not to use the long-double floating point
 conversion technique is now a test-control setting.

FossilOrigin-Name: 02ae6caff1f7925c696ad263fe78b1036364d24b6373e1baec10d53aafb14a12
---
 manifest        | 24 ++++++++++++------------
 manifest.uuid   |  2 +-
 src/global.c    |  1 +
 src/main.c      | 12 ++++++++++++
 src/shell.c.in  |  9 +++++++++
 src/sqlite.h.in |  3 ++-
 src/sqliteInt.h |  1 +
 src/test1.c     | 25 +++++++++++++++++++++++++
 src/util.c      |  6 +++---
 9 files changed, 66 insertions(+), 17 deletions(-)

diff --git a/manifest b/manifest
index 0c46f90368..7cabc9b86f 100644
--- a/manifest
+++ b/manifest
@@ -1,5 +1,5 @@
-C New\stest\scases\sfor\sfloating-point\sconversions.
-D 2023-07-03T12:58:18.851
+C Whether\sor\snot\sto\suse\sthe\slong-double\sfloating\spoint\sconversion\stechnique\nis\snow\sa\stest-control\ssetting.
+D 2023-07-03T14:56:49.741
 F .fossil-settings/empty-dirs dbb81e8fc0401ac46a1491ab34a7f2c7c0452f2f06b54ebb845d024ca8283ef1
 F .fossil-settings/ignore-glob 35175cdfcf539b2318cb04a9901442804be81cd677d8b889fcc9149c21f239ea
 F LICENSE.md df5091916dbb40e6e9686186587125e1b2ff51f022cc334e886c19a0e9982724
@@ -591,7 +591,7 @@ F src/expr.c 8d1656b65e26af3e34f78e947ac423f0d20c214ed25a67486e433bf16ca6b543
 F src/fault.c 460f3e55994363812d9d60844b2a6de88826e007
 F src/fkey.c a7fcbf7e66d14dbb73cf49f31489ebf66d0e6006c62b95246924a3bae9f37b36
 F src/func.c 6028c160f693bdd018b651b5468a0a8e790f4e01e200796916b2d10a5d3237aa
-F src/global.c bd0892ade7289f6e20bff44c07d06371f2ff9b53cea359e7854b9b72f65adc30
+F src/global.c a16553245e315ee0cda8f9b0bf744efef9dc99f86e9d77f58975ea58824ded92
 F src/hash.c 9ee4269fb1d6632a6fecfb9479c93a1f29271bddbbaf215dd60420bcb80c7220
 F src/hash.h 3340ab6e1d13e725571d7cee6d3e3135f0779a7d8e76a9ce0a85971fa3953c51
 F src/hwtime.h f9c2dfb84dce7acf95ce6d289e46f5f9d3d1afd328e53da8f8e9008e3b3caae6
@@ -600,7 +600,7 @@ F src/insert.c 3f0a94082d978bbdd33c38fefea15346c6c6bffb70bc645a71dc0f1f87dd3276
 F src/json.c 14c474fb1249a46eb44e878e2361f36abfe686b134039b0d1883d93d61505b4a
 F src/legacy.c d7874bc885906868cd51e6c2156698f2754f02d9eee1bae2d687323c3ca8e5aa
 F src/loadext.c 176d6b2cb18a6ad73b133db17f6fc351c4d9a2d510deebdb76c22bde9cfd1465
-F src/main.c 5fd4b65d61ae6155f36756ed508a39b38b49355b031188961e8d923f43f4bc49
+F src/main.c 7bc04e53851c813454b73083e21f84fd8a6d3d32eaa242bb4974eda870e28fef
 F src/malloc.c 47b82c5daad557d9b963e3873e99c22570fb470719082c6658bf64e3012f7d23
 F src/mem0.c 6a55ebe57c46ca1a7d98da93aaa07f99f1059645
 F src/mem1.c 3bb59158c38e05f6270e761a9f435bf19827a264c13d1631c58b84bdc96d73b2
@@ -638,16 +638,16 @@ F src/random.c 606b00941a1d7dd09c381d3279a058d771f406c5213c9932bbd93d5587be4b9c
 F src/resolve.c 37953a5f36c60bea413c3c04efcd433b6177009f508ef2ace0494728912fe2e9
 F src/rowset.c 8432130e6c344b3401a8874c3cb49fefe6873fec593294de077afea2dce5ec97
 F src/select.c 3ab1186290a311a8ceed1286c0e286209f7fe97b2d02c7593258004ce295dd88
-F src/shell.c.in 2c02c819349de410d63fcc0217763dfe5a42dbe58f2d68046d4ea8a376d12c26
-F src/sqlite.h.in 3076d78836b6dac53b3ab0875fc8fd15bca8077aad4d33c85336e05af6aef8c7
+F src/shell.c.in e01d7e1d8a6b158320c97c955e1b14763289b82a73e3a155fa8efe0d546f0567
+F src/sqlite.h.in f999ef3642f381d69679b2516b430dbcb6c5a2a951b7f5e43dc4751b474a5774
 F src/sqlite3.rc 5121c9e10c3964d5755191c80dd1180c122fc3a8
 F src/sqlite3ext.h da473ce2b3d0ae407a6300c4a164589b9a6bfdbec9462688a8593ff16f3bb6e4
-F src/sqliteInt.h 3d4125cc1c38777f307e7d374890f085d09f6e15298e09a4f74919744ec2ad62
+F src/sqliteInt.h f6c5470b7db42318a3de1115757e94b76570ad7697ac547823e01f1166756f1d
 F src/sqliteLimit.h 33b1c9baba578d34efe7dfdb43193b366111cdf41476b1e82699e14c11ee1fb6
 F src/status.c 160c445d7d28c984a0eae38c144f6419311ed3eace59b44ac6dafc20db4af749
 F src/table.c 0f141b58a16de7e2fbe81c308379e7279f4c6b50eb08efeec5892794a0ba30d1
 F src/tclsqlite.c ecbc3c99c0d0c3ed122a913f143026c26d38d57f33e06bb71185dd5c1efe37cd
-F src/test1.c ac81daaee5135d210f926e7d1501d6065d396decac57af94083e677cf7e175bd
+F src/test1.c 86099cc02f22069d75b04ae9c105acde0edbce9033d5ac37262bad2e461e6000
 F src/test2.c 827446e259a3b7ab949da1542953edda7b5117982576d3e6f1c24a0dd20a5cef
 F src/test3.c e5178558c41ff53236ae0271e9acb3d6885a94981d2eb939536ee6474598840e
 F src/test4.c 4533b76419e7feb41b40582554663ed3cd77aaa54e135cf76b3205098cd6e664
@@ -705,7 +705,7 @@ F src/trigger.c ad6ab9452715fa9a8075442e15196022275b414b9141b566af8cdb7a1605f2b0
 F src/update.c 0aa36561167a7c40d01163238c297297962f31a15a8d742216b3c37cdf25f731
 F src/upsert.c 5303dc6c518fa7d4b280ec65170f465c7a70b7ac2b22491598f6d0b4875b3145
 F src/utf.c ee39565f0843775cc2c81135751ddd93eceb91a673ea2c57f61c76f288b041a0
-F src/util.c 97f9a7a1a22db23984ca3ced12ed666327c17beeaf8481c3325a0c74369060dc
+F src/util.c 452f1e5e4a85b7869daf15d9b6468ac754836467004fa04c3419f2bd628eb6ad
 F src/vacuum.c 604fcdaebe76f3497c855afcbf91b8fa5046b32de3045bab89cc008d68e40104
 F src/vdbe.c 74282a947234513872a83b0bab1b8c644ece64b3e27b053ef17677c8ff9c81e0
 F src/vdbe.h 41485521f68e9437fdb7ec4a90f9d86ab294e9bb8281e33b235915e29122cfc0
@@ -2042,8 +2042,8 @@ F vsixtest/vsixtest.tcl 6a9a6ab600c25a91a7acc6293828957a386a8a93
 F vsixtest/vsixtest.vcxproj.data 2ed517e100c66dc455b492e1a33350c1b20fbcdc
 F vsixtest/vsixtest.vcxproj.filters 37e51ffedcdb064aad6ff33b6148725226cd608e
 F vsixtest/vsixtest_TemporaryKey.pfx e5b1b036facdb453873e7084e1cae9102ccc67a0
-P 51f492b440728151ce64168d5436ba87ca60d84b89408e47c593fa731355afe4
-R 610c019b12f01dbb4053eb803e9a81bd
+P 9435ed76cd9bb1be02768b3853a2323834f67bda75d3e3f76f6aa7bd0bade3d7
+R c19a4cd19e732c53bd925a8fc2b0f976
 U drh
-Z 391291e9df52bc2766a8acd3f9c94d15
+Z ccc178a785227b10fda86cb46a381790
 # Remove this line to create a well-formed Fossil manifest.
diff --git a/manifest.uuid b/manifest.uuid
index f201e504af..64fd4d3539 100644
--- a/manifest.uuid
+++ b/manifest.uuid
@@ -1 +1 @@
-9435ed76cd9bb1be02768b3853a2323834f67bda75d3e3f76f6aa7bd0bade3d7
\ No newline at end of file
+02ae6caff1f7925c696ad263fe78b1036364d24b6373e1baec10d53aafb14a12
\ No newline at end of file
diff --git a/src/global.c b/src/global.c
index fcba7d7fa2..dc765522ec 100644
--- a/src/global.c
+++ b/src/global.c
@@ -243,6 +243,7 @@ SQLITE_WSD struct Sqlite3Config sqlite3Config = {
    SQLITE_ALLOW_COVERING_INDEX_SCAN,   /* bUseCis */
    0,                         /* bSmallMalloc */
    1,                         /* bExtraSchemaChecks */
+   sizeof(long double)>8,     /* bUseLongDouble */
    0x7ffffffe,                /* mxStrlen */
    0,                         /* neverCorrupt */
    SQLITE_DEFAULT_LOOKASIDE,  /* szLookaside, nLookaside */
diff --git a/src/main.c b/src/main.c
index 7e3fab8861..19f65dac6f 100644
--- a/src/main.c
+++ b/src/main.c
@@ -4470,6 +4470,18 @@ int sqlite3_test_control(int op, ...){
       break;
     }
 
+    /* sqlite3_test_control(SQLITE_TESTCTRL_USELONGDOUBLE, int X);
+    **
+    ** Enable long double usage if X>0.  Disable if X==0.  No-op if X<0.
+    ** Return the status of long double usage afterwards.
+    */
+    case SQLITE_TESTCTRL_USELONGDOUBLE: {
+      int b = va_arg(ap, int);
+      if( b>=0 ) sqlite3Config.bUseLongDouble = b>0;
+      rc = sqlite3Config.bUseLongDouble!=0;
+      break;
+    }
+
 
 #if defined(SQLITE_DEBUG) && !defined(SQLITE_OMIT_WSD)
     /* sqlite3_test_control(SQLITE_TESTCTRL_TUNE, id, *piValue)
diff --git a/src/shell.c.in b/src/shell.c.in
index 2b0884e1c0..295d405cbd 100644
--- a/src/shell.c.in
+++ b/src/shell.c.in
@@ -10876,6 +10876,7 @@ static int do_meta_command(char *zLine, ShellState *p){
     {"seek_count",         SQLITE_TESTCTRL_SEEK_COUNT,  0, ""               },
     {"sorter_mmap",        SQLITE_TESTCTRL_SORTER_MMAP, 0, "NMAX"           },
     {"tune",               SQLITE_TESTCTRL_TUNE,        1, "ID VALUE"       },
+    {"uselongdouble",      SQLITE_TESTCTRL_USELONGDOUBLE,0,"BOOLEAN"        },
     };
     int testctrl = -1;
     int iCtrl = -1;
@@ -10997,6 +10998,14 @@ static int do_meta_command(char *zLine, ShellState *p){
           }
           break;
 
+        /* sqlite3_test_control(int, int) */
+        case SQLITE_TESTCTRL_USELONGDOUBLE: {
+          int opt = nArg==3 ? booleanValue(azArg[2]) : -1;
+          rc2 = sqlite3_test_control(testctrl, opt);
+          isOk = 1;
+          break;
+        }
+
         /* sqlite3_test_control(sqlite3*) */
         case SQLITE_TESTCTRL_INTERNAL_FUNCTIONS:
           rc2 = sqlite3_test_control(testctrl, p->db);
diff --git a/src/sqlite.h.in b/src/sqlite.h.in
index c5a50c01be..59d9986c52 100644
--- a/src/sqlite.h.in
+++ b/src/sqlite.h.in
@@ -8176,7 +8176,8 @@ int sqlite3_test_control(int op, ...);
 #define SQLITE_TESTCTRL_TRACEFLAGS              31
 #define SQLITE_TESTCTRL_TUNE                    32
 #define SQLITE_TESTCTRL_LOGEST                  33
-#define SQLITE_TESTCTRL_LAST                    33  /* Largest TESTCTRL */
+#define SQLITE_TESTCTRL_USELONGDOUBLE           34
+#define SQLITE_TESTCTRL_LAST                    34  /* Largest TESTCTRL */
 
 /*
 ** CAPI3REF: SQL Keyword Checking
diff --git a/src/sqliteInt.h b/src/sqliteInt.h
index 5662ab4fd2..8eae8d166a 100644
--- a/src/sqliteInt.h
+++ b/src/sqliteInt.h
@@ -4090,6 +4090,7 @@ struct Sqlite3Config {
   u8 bUseCis;                       /* Use covering indices for full-scans */
   u8 bSmallMalloc;                  /* Avoid large memory allocations if true */
   u8 bExtraSchemaChecks;            /* Verify type,name,tbl_name in schema */
+  u8 bUseLongDouble;                /* Make use of long double */
   int mxStrlen;                     /* Maximum string length */
   int neverCorrupt;                 /* Database is always well-formed */
   int szLookaside;                  /* Default lookaside buffer size */
diff --git a/src/test1.c b/src/test1.c
index 013adcbcb0..acae44c8ac 100644
--- a/src/test1.c
+++ b/src/test1.c
@@ -7098,6 +7098,30 @@ static int SQLITE_TCLAPI extra_schema_checks(
   return TCL_OK;
 }
 
+/*
+** tclcmd:  use_long_double INT
+**
+** Enable or disable the use of long double.   Enable if the argument is
+** positive.  Disable if the argument is zero.  No-op if the argument is
+** negative.
+**
+** Return the new setting.
+*/
+static int SQLITE_TCLAPI use_long_double(
+  ClientData clientData, /* Pointer to sqlite3_enable_XXX function */
+  Tcl_Interp *interp,    /* The TCL interpreter that invoked this command */
+  int objc,              /* Number of arguments */
+  Tcl_Obj *CONST objv[]  /* Command arguments */
+){
+  int i = -1;
+  if( objc==2 ){
+    if( Tcl_GetBooleanFromObj(interp,objv[1],&i) ) return TCL_ERROR;
+  }
+  i = sqlite3_test_control(SQLITE_TESTCTRL_USELONGDOUBLE, i);
+  Tcl_SetObjResult(interp, Tcl_NewIntObj(i));
+  return TCL_OK;
+}
+
 /*
 ** tclcmd:  database_may_be_corrupt
 **
@@ -8986,6 +9010,7 @@ int Sqlitetest1_Init(Tcl_Interp *interp){
      { "reset_prng_state",              reset_prng_state,   0 },
      { "prng_seed",                     prng_seed,          0 },
      { "extra_schema_checks",           extra_schema_checks,    0},
+     { "use_long_double",               use_long_double,        0},
      { "database_never_corrupt",        database_never_corrupt, 0},
      { "database_may_be_corrupt",       database_may_be_corrupt, 0},
      { "optimization_control",          optimization_control,0},
diff --git a/src/util.c b/src/util.c
index 7642a29bca..dbf31d30f3 100644
--- a/src/util.c
+++ b/src/util.c
@@ -999,7 +999,7 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
   /* Multiply r by powers of ten until it lands somewhere in between
   ** 1.0e+19 and 1.0e+17.
   */
-  if( sizeof(LONGDOUBLE_TYPE)>8 ){
+  if( sqlite3Config.bUseLongDouble ){
     LONGDOUBLE_TYPE rr = r;
     if( rr>=1.0e+19 ){
       while( rr>=1.0e+119L ){ exp+=100; rr *= 1.0e-100L; }
@@ -1049,7 +1049,7 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
         dekkerMul2(r, rr, 1.0e+01, 0.0, &r, &rr);
       }
     }
-    v = (u64)(r)+(u64)(rr);
+    v = rr<0.0 ? (u64)r-(u64)(-rr) : (u64)r+(u64)rr;
   }
 
 
@@ -1089,7 +1089,7 @@ void sqlite3FpDecode(FpDecode *p, double r, int iRound, int mxRound){
     }
   }
   memmove(p->z, &p->z[i+1], p->n);
-  while( p->n>0 && p->z[p->n-1]=='0' ){ p->n--; }
+  while( ALWAYS(p->n>0) && p->z[p->n-1]=='0' ){ p->n--; }
 }
 
 /*