Merge #44: Avoid nullptr for unused SQR* tables

acd145f Avoid nullptr for unused SQR* tables (Pieter Wuille)

Pull request description:

  Recent compilers complain about usage of nullptrs, seemingly being unable to infer they're unused. Fix this by replacing them with a pointer to another table of the same type.

  Fixes #42

Top commit has no ACKs.

Tree-SHA512: 4bfcf51273f4a852282b2c3eb23d29496ec01e3b8bf787d90df9960071958923ba35372e1d1695726187f0bc0d18ca0ea6c7113b51d580f467be081774a29856

Author: sipa

doc/gen_params.sage

@@ -175,15 +175,15 @@ def pick_modulus(bits, style):
     elif style == CLMUL:
         # Fast CLMUL reduction requires that bits + the highest
         #  set bit are less than 66.
-        moduli = filter(lambda x: bits+x[1] <= 66, moduli) + moduli
+        moduli = list(filter((lambda x: bits+x[1] <= 66), moduli)) + moduli
         multi_sqr = True
         need_trans = True
         if not moduli or moduli[0][2].change_ring(ZZ)(2) == 3 + 2**bits:
             # For modulus 3, CLMUL_TRI is obviously better.
             return None
     elif style == CLMUL_TRI:
-        moduli = filter(lambda x: bits+x[1] <= 66, moduli) + moduli
-        moduli = filter(lambda x: x[0] == 3, moduli)
+        moduli = list(filter(lambda x: bits+x[1] <= 66, moduli)) + moduli
+        moduli = list(filter(lambda x: x[0] == 3, moduli))
         multi_sqr = True
         need_trans = True
     else:
@@ -273,10 +273,13 @@ def print_result(bits, style):
         #  F(2) linear and can be computed by a simple bit-matrix.
         # Repeated squaring is especially useful in powering ladders such as
         #  for inversion.
-        sqr2 = "nullptr"
-        sqr4 = "nullptr"
-        sqr8 = "nullptr"
-        sqr16 = "nullptr"
+        # When certain repeated squaring tables are not in use, use the QRT
+        # table instead to make the C++ compiler happy (it always has the
+        # same type).
+        sqr2 = "&QRT_TABLE_%s" % table_id
+        sqr4 = "&QRT_TABLE_%s" % table_id
+        sqr8 = "&QRT_TABLE_%s" % table_id
+        sqr16 = "&QRT_TABLE_%s" % table_id
         if ((bits - 1) >= 4):
             if include_table:
                 print("constexpr %s SQR2_TABLE_%s({%s});" % (rtyp, table_id, ", ".join([fmt(x,typ) for x in sqr_table(f, bits, 2)])))

src/fields/clmul_1byte.cpp

@@ -24,23 +24,23 @@ namespace {
 typedef RecLinTrans<uint8_t, 2> StatTableTRI2;
 constexpr StatTableTRI2 SQR_TABLE_TRI2({0x1, 0x3});
 constexpr StatTableTRI2 QRT_TABLE_TRI2({0x2, 0});
-typedef FieldTri<uint8_t, 2, 1, StatTableTRI2, &SQR_TABLE_TRI2, nullptr, nullptr, nullptr, nullptr, &QRT_TABLE_TRI2, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri2;
+typedef FieldTri<uint8_t, 2, 1, StatTableTRI2, &SQR_TABLE_TRI2, &QRT_TABLE_TRI2, &QRT_TABLE_TRI2, &QRT_TABLE_TRI2, &QRT_TABLE_TRI2, &QRT_TABLE_TRI2, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri2;
 #endif
 
 #ifndef DISABLE_FIELD_3
 // 3 bit field
 typedef RecLinTrans<uint8_t, 3> StatTableTRI3;
 constexpr StatTableTRI3 SQR_TABLE_TRI3({0x1, 0x4, 0x6});
 constexpr StatTableTRI3 QRT_TABLE_TRI3({0, 0x4, 0x6});
-typedef FieldTri<uint8_t, 3, 1, StatTableTRI3, &SQR_TABLE_TRI3, nullptr, nullptr, nullptr, nullptr, &QRT_TABLE_TRI3, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri3;
+typedef FieldTri<uint8_t, 3, 1, StatTableTRI3, &SQR_TABLE_TRI3, &QRT_TABLE_TRI3, &QRT_TABLE_TRI3, &QRT_TABLE_TRI3, &QRT_TABLE_TRI3, &QRT_TABLE_TRI3, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri3;
 #endif
 
 #ifndef DISABLE_FIELD_4
 // 4 bit field
 typedef RecLinTrans<uint8_t, 4> StatTableTRI4;
 constexpr StatTableTRI4 SQR_TABLE_TRI4({0x1, 0x4, 0x3, 0xc});
 constexpr StatTableTRI4 QRT_TABLE_TRI4({0x6, 0xa, 0x8, 0});
-typedef FieldTri<uint8_t, 4, 1, StatTableTRI4, &SQR_TABLE_TRI4, nullptr, nullptr, nullptr, nullptr, &QRT_TABLE_TRI4, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri4;
+typedef FieldTri<uint8_t, 4, 1, StatTableTRI4, &SQR_TABLE_TRI4, &QRT_TABLE_TRI4, &QRT_TABLE_TRI4, &QRT_TABLE_TRI4, &QRT_TABLE_TRI4, &QRT_TABLE_TRI4, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri4;
 #endif
 
 #ifndef DISABLE_FIELD_5
@@ -49,8 +49,8 @@ typedef RecLinTrans<uint8_t, 5> StatTable5;
 constexpr StatTable5 SQR_TABLE_5({0x1, 0x4, 0x10, 0xa, 0xd});
 constexpr StatTable5 SQR2_TABLE_5({0x1, 0x10, 0xd, 0xe, 0x1b});
 constexpr StatTable5 QRT_TABLE_5({0x14, 0x8, 0xa, 0, 0xe});
-typedef Field<uint8_t, 5, 5, StatTable5, &SQR_TABLE_5, &SQR2_TABLE_5, nullptr, nullptr, nullptr, &QRT_TABLE_5, IdTrans, &ID_TRANS, &ID_TRANS> Field5;
-typedef FieldTri<uint8_t, 5, 2, RecLinTrans<uint8_t, 5>, &SQR_TABLE_5, &SQR2_TABLE_5, nullptr, nullptr, nullptr, &QRT_TABLE_5, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri5;
+typedef Field<uint8_t, 5, 5, StatTable5, &SQR_TABLE_5, &SQR2_TABLE_5, &QRT_TABLE_5, &QRT_TABLE_5, &QRT_TABLE_5, &QRT_TABLE_5, IdTrans, &ID_TRANS, &ID_TRANS> Field5;
+typedef FieldTri<uint8_t, 5, 2, RecLinTrans<uint8_t, 5>, &SQR_TABLE_5, &SQR2_TABLE_5, &QRT_TABLE_5, &QRT_TABLE_5, &QRT_TABLE_5, &QRT_TABLE_5, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri5;
 #endif
 
 #ifndef DISABLE_FIELD_6
@@ -59,7 +59,7 @@ typedef RecLinTrans<uint8_t, 6> StatTableTRI6;
 constexpr StatTableTRI6 SQR_TABLE_TRI6({0x1, 0x4, 0x10, 0x3, 0xc, 0x30});
 constexpr StatTableTRI6 SQR2_TABLE_TRI6({0x1, 0x10, 0xc, 0x5, 0x13, 0x3c});
 constexpr StatTableTRI6 QRT_TABLE_TRI6({0x3a, 0x26, 0x24, 0x14, 0x20, 0});
-typedef FieldTri<uint8_t, 6, 1, StatTableTRI6, &SQR_TABLE_TRI6, &SQR2_TABLE_TRI6, nullptr, nullptr, nullptr, &QRT_TABLE_TRI6, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri6;
+typedef FieldTri<uint8_t, 6, 1, StatTableTRI6, &SQR_TABLE_TRI6, &SQR2_TABLE_TRI6, &QRT_TABLE_TRI6, &QRT_TABLE_TRI6, &QRT_TABLE_TRI6, &QRT_TABLE_TRI6, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri6;
 #endif
 
 #ifndef DISABLE_FIELD_7
@@ -68,7 +68,7 @@ typedef RecLinTrans<uint8_t, 4, 3> StatTableTRI7;
 constexpr StatTableTRI7 SQR_TABLE_TRI7({0x1, 0x4, 0x10, 0x40, 0x6, 0x18, 0x60});
 constexpr StatTableTRI7 SQR2_TABLE_TRI7({0x1, 0x10, 0x6, 0x60, 0x14, 0x46, 0x78});
 constexpr StatTableTRI7 QRT_TABLE_TRI7({0, 0x14, 0x16, 0x72, 0x12, 0x40, 0x7a});
-typedef FieldTri<uint8_t, 7, 1, StatTableTRI7, &SQR_TABLE_TRI7, &SQR2_TABLE_TRI7, nullptr, nullptr, nullptr, &QRT_TABLE_TRI7, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri7;
+typedef FieldTri<uint8_t, 7, 1, StatTableTRI7, &SQR_TABLE_TRI7, &SQR2_TABLE_TRI7, &QRT_TABLE_TRI7, &QRT_TABLE_TRI7, &QRT_TABLE_TRI7, &QRT_TABLE_TRI7, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri7;
 #endif
 
 #ifndef DISABLE_FIELD_8
@@ -77,7 +77,7 @@ typedef RecLinTrans<uint8_t, 4, 4> StatTable8;
 constexpr StatTable8 SQR_TABLE_8({0x1, 0x4, 0x10, 0x40, 0x1b, 0x6c, 0xab, 0x9a});
 constexpr StatTable8 SQR2_TABLE_8({0x1, 0x10, 0x1b, 0xab, 0x5e, 0x97, 0xb3, 0xc5});
 constexpr StatTable8 QRT_TABLE_8({0xbc, 0x2a, 0x28, 0x86, 0x2c, 0xde, 0x8e, 0});
-typedef Field<uint8_t, 8, 27, StatTable8, &SQR_TABLE_8, &SQR2_TABLE_8, nullptr, nullptr, nullptr, &QRT_TABLE_8, IdTrans, &ID_TRANS, &ID_TRANS> Field8;
+typedef Field<uint8_t, 8, 27, StatTable8, &SQR_TABLE_8, &SQR2_TABLE_8, &QRT_TABLE_8, &QRT_TABLE_8, &QRT_TABLE_8, &QRT_TABLE_8, IdTrans, &ID_TRANS, &ID_TRANS> Field8;
 #endif
 }
 

src/fields/clmul_2bytes.cpp

@@ -26,7 +26,7 @@ constexpr StatTableTRI9 SQR_TABLE_TRI9({0x1, 0x4, 0x10, 0x40, 0x100, 0x6, 0x18,
 constexpr StatTableTRI9 SQR2_TABLE_TRI9({0x1, 0x10, 0x100, 0x18, 0x180, 0x14, 0x140, 0x1e, 0x1e0});
 constexpr StatTableTRI9 SQR4_TABLE_TRI9({0x1, 0x180, 0x1e0, 0x198, 0x1fe, 0x80, 0xa0, 0x88, 0xaa});
 constexpr StatTableTRI9 QRT_TABLE_TRI9({0, 0x4e, 0x4c, 0x1aa, 0x48, 0x22, 0x1a2, 0x100, 0x58});
-typedef FieldTri<uint16_t, 9, 1, StatTableTRI9, &SQR_TABLE_TRI9, &SQR2_TABLE_TRI9, &SQR4_TABLE_TRI9, nullptr, nullptr, &QRT_TABLE_TRI9, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri9;
+typedef FieldTri<uint16_t, 9, 1, StatTableTRI9, &SQR_TABLE_TRI9, &SQR2_TABLE_TRI9, &SQR4_TABLE_TRI9, &QRT_TABLE_TRI9, &QRT_TABLE_TRI9, &QRT_TABLE_TRI9, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri9;
 #endif
 
 #ifndef DISABLE_FIELD_10
@@ -36,8 +36,8 @@ constexpr StatTable10 SQR_TABLE_10({0x1, 0x4, 0x10, 0x40, 0x100, 0x9, 0x24, 0x90
 constexpr StatTable10 SQR2_TABLE_10({0x1, 0x10, 0x100, 0x24, 0x240, 0x41, 0x19, 0x190, 0x136, 0x344});
 constexpr StatTable10 SQR4_TABLE_10({0x1, 0x240, 0x136, 0x141, 0x35d, 0x18, 0x265, 0x2e6, 0x227, 0x36b});
 constexpr StatTable10 QRT_TABLE_10({0xec, 0x86, 0x84, 0x30e, 0x80, 0x3c2, 0x306, 0, 0x90, 0x296});
-typedef Field<uint16_t, 10, 9, StatTable10, &SQR_TABLE_10, &SQR2_TABLE_10, &SQR4_TABLE_10, nullptr, nullptr, &QRT_TABLE_10, IdTrans, &ID_TRANS, &ID_TRANS> Field10;
-typedef FieldTri<uint16_t, 10, 3, RecLinTrans<uint16_t, 5, 5>, &SQR_TABLE_10, &SQR2_TABLE_10, &SQR4_TABLE_10, nullptr, nullptr, &QRT_TABLE_10, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri10;
+typedef Field<uint16_t, 10, 9, StatTable10, &SQR_TABLE_10, &SQR2_TABLE_10, &SQR4_TABLE_10, &QRT_TABLE_10, &QRT_TABLE_10, &QRT_TABLE_10, IdTrans, &ID_TRANS, &ID_TRANS> Field10;
+typedef FieldTri<uint16_t, 10, 3, RecLinTrans<uint16_t, 5, 5>, &SQR_TABLE_10, &SQR2_TABLE_10, &SQR4_TABLE_10, &QRT_TABLE_10, &QRT_TABLE_10, &QRT_TABLE_10, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri10;
 #endif
 
 #ifndef DISABLE_FIELD_11
@@ -48,7 +48,7 @@ constexpr StatTable11 SQR2_TABLE_11({0x1, 0x10, 0x100, 0xa, 0xa0, 0x205, 0x44, 0
 constexpr StatTable11 SQR4_TABLE_11({0x1, 0xa0, 0x428, 0x1a, 0x645, 0x3a9, 0x144, 0x2d5, 0x9e, 0x4e7, 0x649});
 constexpr StatTable11 QRT_TABLE_11({0x734, 0x48, 0x4a, 0x1de, 0x4e, 0x35e, 0x1d6, 0x200, 0x5e, 0, 0x37e});
 typedef Field<uint16_t, 11, 5, StatTable11, &SQR_TABLE_11, &SQR2_TABLE_11, &SQR4_TABLE_11, nullptr, nullptr, &QRT_TABLE_11, IdTrans, &ID_TRANS, &ID_TRANS> Field11;
-typedef FieldTri<uint16_t, 11, 2, RecLinTrans<uint16_t, 6, 5>, &SQR_TABLE_11, &SQR2_TABLE_11, &SQR4_TABLE_11, nullptr, nullptr, &QRT_TABLE_11, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri11;
+typedef FieldTri<uint16_t, 11, 2, RecLinTrans<uint16_t, 6, 5>, &SQR_TABLE_11, &SQR2_TABLE_11, &SQR4_TABLE_11, &QRT_TABLE_11, &QRT_TABLE_11, &QRT_TABLE_11, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri11;
 #endif
 
 #ifndef DISABLE_FIELD_12
@@ -58,8 +58,8 @@ constexpr StatTable12 SQR_TABLE_12({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x9, 0x2
 constexpr StatTable12 SQR2_TABLE_12({0x1, 0x10, 0x100, 0x9, 0x90, 0x900, 0x41, 0x410, 0x124, 0x249, 0x482, 0x804});
 constexpr StatTable12 SQR4_TABLE_12({0x1, 0x90, 0x124, 0x8, 0x480, 0x920, 0x40, 0x412, 0x924, 0x200, 0x82, 0x904});
 constexpr StatTable12 QRT_TABLE_12({0x48, 0xc10, 0xc12, 0x208, 0xc16, 0xd82, 0x200, 0x110, 0xc06, 0, 0xda2, 0x5a4});
-typedef Field<uint16_t, 12, 9, StatTable12, &SQR_TABLE_12, &SQR2_TABLE_12, &SQR4_TABLE_12, nullptr, nullptr, &QRT_TABLE_12, IdTrans, &ID_TRANS, &ID_TRANS> Field12;
-typedef FieldTri<uint16_t, 12, 3, RecLinTrans<uint16_t, 6, 6>, &SQR_TABLE_12, &SQR2_TABLE_12, &SQR4_TABLE_12, nullptr, nullptr, &QRT_TABLE_12, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri12;
+typedef Field<uint16_t, 12, 9, StatTable12, &SQR_TABLE_12, &SQR2_TABLE_12, &SQR4_TABLE_12, &QRT_TABLE_12, &QRT_TABLE_12, &QRT_TABLE_12, IdTrans, &ID_TRANS, &ID_TRANS> Field12;
+typedef FieldTri<uint16_t, 12, 3, RecLinTrans<uint16_t, 6, 6>, &SQR_TABLE_12, &SQR2_TABLE_12, &SQR4_TABLE_12, &QRT_TABLE_12, &QRT_TABLE_12, &QRT_TABLE_12, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri12;
 #endif
 
 #ifndef DISABLE_FIELD_13
@@ -69,7 +69,7 @@ constexpr StatTable13 SQR_TABLE_13({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000,
 constexpr StatTable13 SQR2_TABLE_13({0x1, 0x10, 0x100, 0x1000, 0xd8, 0xd80, 0x185a, 0x514, 0x1176, 0x17b8, 0x1b75, 0x17ff, 0x1f05});
 constexpr StatTable13 SQR4_TABLE_13({0x1, 0xd8, 0x1176, 0x1f05, 0xd96, 0x18e8, 0x68, 0xbdb, 0x1a61, 0x1af2, 0x1a37, 0x3b9, 0x1440});
 constexpr StatTable13 QRT_TABLE_13({0xcfc, 0x1500, 0x1502, 0x382, 0x1506, 0x149c, 0x38a, 0x118, 0x1516, 0, 0x14bc, 0x100e, 0x3ca});
-typedef Field<uint16_t, 13, 27, StatTable13, &SQR_TABLE_13, &SQR2_TABLE_13, &SQR4_TABLE_13, nullptr, nullptr, &QRT_TABLE_13, IdTrans, &ID_TRANS, &ID_TRANS> Field13;
+typedef Field<uint16_t, 13, 27, StatTable13, &SQR_TABLE_13, &SQR2_TABLE_13, &SQR4_TABLE_13, &QRT_TABLE_13, &QRT_TABLE_13, &QRT_TABLE_13, IdTrans, &ID_TRANS, &ID_TRANS> Field13;
 #endif
 
 #ifndef DISABLE_FIELD_14
@@ -79,8 +79,8 @@ constexpr StatTable14 SQR_TABLE_14({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000,
 constexpr StatTable14 SQR2_TABLE_14({0x1, 0x10, 0x100, 0x1000, 0x84, 0x840, 0x442, 0x401, 0x31, 0x310, 0x3100, 0x118c, 0x1844, 0x486});
 constexpr StatTable14 SQR4_TABLE_14({0x1, 0x84, 0x31, 0x1844, 0x501, 0x15ce, 0x3552, 0x3101, 0x8c5, 0x3a5, 0x1cf3, 0xd74, 0xc8a, 0x3411});
 constexpr StatTable14 QRT_TABLE_14({0x13f2, 0x206, 0x204, 0x3e06, 0x200, 0x1266, 0x3e0e, 0x114, 0x210, 0, 0x1246, 0x2848, 0x3e4e, 0x2258});
-typedef Field<uint16_t, 14, 33, StatTable14, &SQR_TABLE_14, &SQR2_TABLE_14, &SQR4_TABLE_14, nullptr, nullptr, &QRT_TABLE_14, IdTrans, &ID_TRANS, &ID_TRANS> Field14;
-typedef FieldTri<uint16_t, 14, 5, RecLinTrans<uint16_t, 5, 5, 4>, &SQR_TABLE_14, &SQR2_TABLE_14, &SQR4_TABLE_14, nullptr, nullptr, &QRT_TABLE_14, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri14;
+typedef Field<uint16_t, 14, 33, StatTable14, &SQR_TABLE_14, &SQR2_TABLE_14, &SQR4_TABLE_14, &QRT_TABLE_14, &QRT_TABLE_14, &QRT_TABLE_14, IdTrans, &ID_TRANS, &ID_TRANS> Field14;
+typedef FieldTri<uint16_t, 14, 5, RecLinTrans<uint16_t, 5, 5, 4>, &SQR_TABLE_14, &SQR2_TABLE_14, &SQR4_TABLE_14, &QRT_TABLE_14, &QRT_TABLE_14, &QRT_TABLE_14, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri14;
 #endif
 
 #ifndef DISABLE_FIELD_15
@@ -90,7 +90,7 @@ constexpr StatTableTRI15 SQR_TABLE_TRI15({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x
 constexpr StatTableTRI15 SQR2_TABLE_TRI15({0x1, 0x10, 0x100, 0x1000, 0x6, 0x60, 0x600, 0x6000, 0x14, 0x140, 0x1400, 0x4006, 0x78, 0x780, 0x7800});
 constexpr StatTableTRI15 SQR4_TABLE_TRI15({0x1, 0x6, 0x14, 0x78, 0x110, 0x660, 0x1540, 0x7f80, 0x106, 0x614, 0x1478, 0x7910, 0x1666, 0x7554, 0x3ffe});
 constexpr StatTableTRI15 QRT_TABLE_TRI15({0, 0x114, 0x116, 0x428, 0x112, 0x137a, 0x420, 0x6d62, 0x102, 0x73a, 0x135a, 0x6460, 0x460, 0x4000, 0x6de2});
-typedef FieldTri<uint16_t, 15, 1, StatTableTRI15, &SQR_TABLE_TRI15, &SQR2_TABLE_TRI15, &SQR4_TABLE_TRI15, nullptr, nullptr, &QRT_TABLE_TRI15, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri15;
+typedef FieldTri<uint16_t, 15, 1, StatTableTRI15, &SQR_TABLE_TRI15, &SQR2_TABLE_TRI15, &SQR4_TABLE_TRI15, &QRT_TABLE_TRI15, &QRT_TABLE_TRI15, &QRT_TABLE_TRI15, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri15;
 #endif
 
 #ifndef DISABLE_FIELD_16
@@ -100,7 +100,7 @@ constexpr StatTable16 SQR_TABLE_16({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000,
 constexpr StatTable16 SQR2_TABLE_16({0x1, 0x10, 0x100, 0x1000, 0x2b, 0x2b0, 0x2b00, 0xb056, 0x445, 0x4450, 0x45ac, 0x5a6c, 0xa647, 0x657e, 0x571a, 0x7127});
 constexpr StatTable16 SQR4_TABLE_16({0x1, 0x2b, 0x445, 0xa647, 0x12a1, 0xf69d, 0x7f07, 0x9825, 0x6fad, 0x399d, 0xb515, 0xd7d1, 0x3fb4, 0x4b06, 0xe4df, 0x93c7});
 constexpr StatTable16 QRT_TABLE_16({0x732, 0x72b8, 0x72ba, 0x7e96, 0x72be, 0x78b2, 0x7e9e, 0x8cba, 0x72ae, 0xfa24, 0x7892, 0x5892, 0x7ede, 0xbec6, 0x8c3a, 0});
-typedef Field<uint16_t, 16, 43, StatTable16, &SQR_TABLE_16, &SQR2_TABLE_16, &SQR4_TABLE_16, nullptr, nullptr, &QRT_TABLE_16, IdTrans, &ID_TRANS, &ID_TRANS> Field16;
+typedef Field<uint16_t, 16, 43, StatTable16, &SQR_TABLE_16, &SQR2_TABLE_16, &SQR4_TABLE_16, &QRT_TABLE_16, &QRT_TABLE_16, &QRT_TABLE_16, IdTrans, &ID_TRANS, &ID_TRANS> Field16;
 #endif
 }