Implement normalization and simplify power table

include/fmt/format-inl.h

@@ -294,35 +294,28 @@ const uint64_t basic_data<T>::POWERS_OF_10_64[] = {
 // These are generated by support/compute-powers.py.
 template <typename T>
 const uint64_t basic_data<T>::POW10_SIGNIFICANDS[] = {
-  0xfa8fd5a0081c0288ull, 0xbaaee17fa23ebf76ull, 0x8b16fb203055ac76ull,
-  0xcf42894a5dce35eaull, 0x9a6bb0aa55653b2dull, 0xe61acf033d1a45dfull,
-  0xab70fe17c79ac6caull, 0xff77b1fcbebcdc4full, 0xbe5691ef416bd60cull,
-  0x8dd01fad907ffc3cull, 0xd3515c2831559a83ull, 0x9d71ac8fada6c9b5ull,
-  0xea9c227723ee8bcbull, 0xaecc49914078536dull, 0x823c12795db6ce57ull,
-  0xc21094364dfb5637ull, 0x9096ea6f3848984full, 0xd77485cb25823ac7ull,
-  0xa086cfcd97bf97f4ull, 0xef340a98172aace5ull, 0xb23867fb2a35b28eull,
-  0x84c8d4dfd2c63f3bull, 0xc5dd44271ad3cdbaull, 0x936b9fcebb25c996ull,
-  0xdbac6c247d62a584ull, 0xa3ab66580d5fdaf6ull, 0xf3e2f893dec3f126ull,
-  0xb5b5ada8aaff80b8ull, 0x87625f056c7c4a8bull, 0xc9bcff6034c13053ull,
-  0x964e858c91ba2655ull, 0xdff9772470297ebdull, 0xa6dfbd9fb8e5b88full,
-  0xf8a95fcf88747d94ull, 0xb94470938fa89bcfull, 0x8a08f0f8bf0f156bull,
-  0xcdb02555653131b6ull, 0x993fe2c6d07b7facull, 0xe45c10c42a2b3b06ull,
-  0xaa242499697392d3ull, 0xfd87b5f28300ca0eull, 0xbce5086492111aebull,
-  0x8cbccc096f5088ccull, 0xd1b71758e219652cull, 0x9c40000000000000ull,
-  0xe8d4a51000000000ull, 0xad78ebc5ac620000ull, 0x813f3978f8940984ull,
-  0xc097ce7bc90715b3ull, 0x8f7e32ce7bea5c70ull, 0xd5d238a4abe98068ull,
-  0x9f4f2726179a2245ull, 0xed63a231d4c4fb27ull, 0xb0de65388cc8ada8ull,
-  0x83c7088e1aab65dbull, 0xc45d1df942711d9aull, 0x924d692ca61be758ull,
-  0xda01ee641a708deaull, 0xa26da3999aef774aull, 0xf209787bb47d6b85ull,
-  0xb454e4a179dd1877ull, 0x865b86925b9bc5c2ull, 0xc83553c5c8965d3dull,
-  0x952ab45cfa97a0b3ull, 0xde469fbd99a05fe3ull, 0xa59bc234db398c25ull,
-  0xf6c69a72a3989f5cull, 0xb7dcbf5354e9beceull, 0x88fcf317f22241e2ull,
-  0xcc20ce9bd35c78a5ull, 0x98165af37b2153dfull, 0xe2a0b5dc971f303aull,
-  0xa8d9d1535ce3b396ull, 0xfb9b7cd9a4a7443cull, 0xbb764c4ca7a44410ull,
-  0x8bab8eefb6409c1aull, 0xd01fef10a657842cull, 0x9b10a4e5e9913129ull,
-  0xe7109bfba19c0c9dull, 0xac2820d9623bf429ull, 0x80444b5e7aa7cf85ull,
-  0xbf21e44003acdd2dull, 0x8e679c2f5e44ff8full, 0xd433179d9c8cb841ull,
-  0x9e19db92b4e31ba9ull, 0xeb96bf6ebadf77d9ull, 0xaf87023b9bf0ee6bull
+  0xfa8fd5a0081c0288, 0xbaaee17fa23ebf76, 0x8b16fb203055ac76, 0xcf42894a5dce35ea,
+  0x9a6bb0aa55653b2d, 0xe61acf033d1a45df, 0xab70fe17c79ac6ca, 0xff77b1fcbebcdc4f,
+  0xbe5691ef416bd60c, 0x8dd01fad907ffc3c, 0xd3515c2831559a83, 0x9d71ac8fada6c9b5,
+  0xea9c227723ee8bcb, 0xaecc49914078536d, 0x823c12795db6ce57, 0xc21094364dfb5637,
+  0x9096ea6f3848984f, 0xd77485cb25823ac7, 0xa086cfcd97bf97f4, 0xef340a98172aace5,
+  0xb23867fb2a35b28e, 0x84c8d4dfd2c63f3b, 0xc5dd44271ad3cdba, 0x936b9fcebb25c996,
+  0xdbac6c247d62a584, 0xa3ab66580d5fdaf6, 0xf3e2f893dec3f126, 0xb5b5ada8aaff80b8,
+  0x87625f056c7c4a8b, 0xc9bcff6034c13053, 0x964e858c91ba2655, 0xdff9772470297ebd,
+  0xa6dfbd9fb8e5b88f, 0xf8a95fcf88747d94, 0xb94470938fa89bcf, 0x8a08f0f8bf0f156b,
+  0xcdb02555653131b6, 0x993fe2c6d07b7fac, 0xe45c10c42a2b3b06, 0xaa242499697392d3,
+  0xfd87b5f28300ca0e, 0xbce5086492111aeb, 0x8cbccc096f5088cc, 0xd1b71758e219652c,
+  0x9c40000000000000, 0xe8d4a51000000000, 0xad78ebc5ac620000, 0x813f3978f8940984,
+  0xc097ce7bc90715b3, 0x8f7e32ce7bea5c70, 0xd5d238a4abe98068, 0x9f4f2726179a2245,
+  0xed63a231d4c4fb27, 0xb0de65388cc8ada8, 0x83c7088e1aab65db, 0xc45d1df942711d9a,
+  0x924d692ca61be758, 0xda01ee641a708dea, 0xa26da3999aef774a, 0xf209787bb47d6b85,
+  0xb454e4a179dd1877, 0x865b86925b9bc5c2, 0xc83553c5c8965d3d, 0x952ab45cfa97a0b3,
+  0xde469fbd99a05fe3, 0xa59bc234db398c25, 0xf6c69a72a3989f5c, 0xb7dcbf5354e9bece,
+  0x88fcf317f22241e2, 0xcc20ce9bd35c78a5, 0x98165af37b2153df, 0xe2a0b5dc971f303a,
+  0xa8d9d1535ce3b396, 0xfb9b7cd9a4a7443c, 0xbb764c4ca7a44410, 0x8bab8eefb6409c1a,
+  0xd01fef10a657842c, 0x9b10a4e5e9913129, 0xe7109bfba19c0c9d, 0xac2820d9623bf429,
+  0x80444b5e7aa7cf85, 0xbf21e44003acdd2d, 0x8e679c2f5e44ff8f, 0xd433179d9c8cb841,
+  0x9e19db92b4e31ba9, 0xeb96bf6ebadf77d9, 0xaf87023b9bf0ee6b
 };
 
 // Binary exponents of pow(10, k), for k = -348, -340, ..., 340, corresponding

include/fmt/format.h

@@ -258,7 +258,17 @@ inline dummy_int isnan(...) { return dummy_int(); }
 inline dummy_int _isnan(...) { return dummy_int(); }
 
 // A handmade floating-point number f * pow(2, e).
-struct fp {
+class fp {
+ private:
+  // All sizes are in bits.
+  static constexpr int char_size = std::numeric_limits<unsigned char>::digits;
+  // Subtract 1 to account for an implicit most significant bit in the
+  // normalized form.
+  static constexpr int double_significand_size =
+    std::numeric_limits<double>::digits - 1;
+  static constexpr uint64_t implicit_bit = 1ull << double_significand_size;
+
+ public:
   uint64_t f;
   int e;
 
@@ -270,24 +280,36 @@ struct fp {
   explicit fp(Double d) {
     // Assume double is in the format [sign][exponent][significand].
     typedef std::numeric_limits<Double> limits;
-    const int double_size =
-      sizeof(Double) * std::numeric_limits<unsigned char>::digits;
-    // Subtract 1 to account for an implicit most significant bit in the
-    // normalized form.
-    const int significand_size = limits::digits - 1;
-    const int exponent_size = double_size - significand_size - 1;  // -1 for sign
-    const uint64_t implicit_bit = 1ull << significand_size;
+    const int double_size = sizeof(Double) * char_size;
+    const int exponent_size =
+      double_size - double_significand_size - 1;  // -1 for sign
     const uint64_t significand_mask = implicit_bit - 1;
     const uint64_t exponent_mask = (~0ull >> 1) & ~significand_mask;
     const int exponent_bias = (1 << exponent_size) - limits::max_exponent - 1;
     auto u = bit_cast<uint64_t>(d);
-    auto biased_e = (u & exponent_mask) >> significand_size;
+    auto biased_e = (u & exponent_mask) >> double_significand_size;
     f = u & significand_mask;
     if (biased_e != 0)
       f += implicit_bit;
     else
       biased_e = 1;  // Subnormals use biased exponent 1 (min exponent).
-    e = biased_e - exponent_bias - significand_size;
+    e = biased_e - exponent_bias - double_significand_size;
+  }
+
+  // Normalizes the value converted from double and multiplied by (1 << SHIFT).
+  template <int SHIFT = 0>
+  void normalize() {
+    // Handle subnormals.
+    auto shifted_implicit_bit = implicit_bit << SHIFT;
+    while ((f & shifted_implicit_bit) == 0) {
+      f <<= 1;
+      --e;
+    }
+    auto fp_significand_size = sizeof(f) * char_size;
+    // Subtract 1 to account for hidden bit.
+    auto offset = fp_significand_size - double_significand_size - SHIFT - 1;
+    f <<= offset;
+    e -= offset;
   }
 };
 

support/compute-powers.py

@@ -39,9 +39,9 @@ for i, exp in enumerate(range(min_exponent, max_exponent + 1, step)):
 
 print('Significands:', end='')
 for i, fp in enumerate(powers):
-    if i % 3 == 0:
+    if i % 4 == 0:
         print(end='\n ')
-    print(' {:0<#16x}ull'.format(fp.f, ), end=',')
+    print(' {:0<#16x}'.format(fp.f, ), end=',')
 
 print('\n\nExponents:', end='')
 for i, fp in enumerate(powers):

test/util-test.cc

@@ -881,17 +881,40 @@ TEST(UtilTest, ParseNonnegativeInt) {
         fmt::format_error, "number is too big");
 }
 
-TEST(UtilTest, FPSubtract) {
-  auto r = fp(123, 1) - fp(102, 1);
-  EXPECT_EQ(r.f, 21u);
-  EXPECT_EQ(r.e, 1);
+template <bool is_iec559>
+void test_construct_from_double() {
+  fmt::print("warning: double is not IEC559, skipping FP tests\n");
 }
 
-TEST(UtilTest, FPMultiply) {
-  auto r = fp(123ULL << 32, 4) * fp(56ULL << 32, 7);
-  EXPECT_EQ(r.f, 123u * 56u);
-  EXPECT_EQ(r.e, 4 + 7 + 64);
-  r = fp(123ULL << 32, 4) * fp(567ULL << 31, 8);
-  EXPECT_EQ(r.f, (123 * 567 + 1u) / 2);
-  EXPECT_EQ(r.e, 4 + 8 + 64);
+template <>
+void test_construct_from_double<true>() {
+  auto v = fp(1.23);
+  EXPECT_EQ(v.f, 0x13ae147ae147aeu);
+  EXPECT_EQ(v.e, -52);
+}
+
+TEST(FPTest, ConstructFromDouble) {
+  test_construct_from_double<std::numeric_limits<double>::is_iec559>();
+}
+
+TEST(FPTest, Normalize) {
+  auto v = fp(0xbeef, 42);
+  v.normalize();
+  EXPECT_EQ(0xbeef000000000000, v.f);
+  EXPECT_EQ(-6, v.e);
+}
+
+TEST(FPTest, Subtract) {
+  auto v = fp(123, 1) - fp(102, 1);
+  EXPECT_EQ(v.f, 21u);
+  EXPECT_EQ(v.e, 1);
+}
+
+TEST(FPTest, Multiply) {
+  auto v = fp(123ULL << 32, 4) * fp(56ULL << 32, 7);
+  EXPECT_EQ(v.f, 123u * 56u);
+  EXPECT_EQ(v.e, 4 + 7 + 64);
+  v = fp(123ULL << 32, 4) * fp(567ULL << 31, 8);
+  EXPECT_EQ(v.f, (123 * 567 + 1u) / 2);
+  EXPECT_EQ(v.e, 4 + 8 + 64);
 }