+/// CountLeadingOnes_64 - This function performs the operation
+/// of counting the number of ones from the most significant bit to the first
+/// zero bit (64 bit edition.)
+/// Returns 64 if the word is all ones.
+inline unsigned CountLeadingOnes_64(uint64_t Value) {
+ return CountLeadingZeros_64(~Value);
+}
+
+/// CountTrailingZeros_32 - this function performs the platform optimal form of
+/// counting the number of zeros from the least significant bit to the first one
+/// bit. Ex. CountTrailingZeros_32(0xFF00FF00) == 8.
+/// Returns 32 if the word is zero.
+inline unsigned CountTrailingZeros_32(uint32_t Value) {
+#if __GNUC__ >= 4
+ return Value ? __builtin_ctz(Value) : 32;
+#else
+ static const unsigned Mod37BitPosition[] = {
+ 32, 0, 1, 26, 2, 23, 27, 0, 3, 16, 24, 30, 28, 11, 0, 13,
+ 4, 7, 17, 0, 25, 22, 31, 15, 29, 10, 12, 6, 0, 21, 14, 9,
+ 5, 20, 8, 19, 18
+ };
+ return Mod37BitPosition[(-Value & Value) % 37];
+#endif
+}
+
+/// CountTrailingOnes_32 - this function performs the operation of
+/// counting the number of ones from the least significant bit to the first zero
+/// bit. Ex. CountTrailingOnes_32(0x00FF00FF) == 8.
+/// Returns 32 if the word is all ones.
+inline unsigned CountTrailingOnes_32(uint32_t Value) {
+ return CountTrailingZeros_32(~Value);
+}
+
+/// CountTrailingZeros_64 - This function performs the platform optimal form
+/// of counting the number of zeros from the least significant bit to the first
+/// one bit (64 bit edition.)
+/// Returns 64 if the word is zero.
+inline unsigned CountTrailingZeros_64(uint64_t Value) {
+#if __GNUC__ >= 4
+ return Value ? __builtin_ctzll(Value) : 64;
+#else
+ static const unsigned Mod67Position[] = {
+ 64, 0, 1, 39, 2, 15, 40, 23, 3, 12, 16, 59, 41, 19, 24, 54,
+ 4, 64, 13, 10, 17, 62, 60, 28, 42, 30, 20, 51, 25, 44, 55,
+ 47, 5, 32, 65, 38, 14, 22, 11, 58, 18, 53, 63, 9, 61, 27,
+ 29, 50, 43, 46, 31, 37, 21, 57, 52, 8, 26, 49, 45, 36, 56,
+ 7, 48, 35, 6, 34, 33, 0
+ };
+ return Mod67Position[(-Value & Value) % 67];
+#endif
+}
+
+/// CountTrailingOnes_64 - This function performs the operation
+/// of counting the number of ones from the least significant bit to the first
+/// zero bit (64 bit edition.)
+/// Returns 64 if the word is all ones.
+inline unsigned CountTrailingOnes_64(uint64_t Value) {
+ return CountTrailingZeros_64(~Value);
+}
+
+/// CountPopulation_32 - this function counts the number of set bits in a value.
+/// Ex. CountPopulation(0xF000F000) = 8
+/// Returns 0 if the word is zero.
+inline unsigned CountPopulation_32(uint32_t Value) {
+#if __GNUC__ >= 4
+ return __builtin_popcount(Value);
+#else
+ uint32_t v = Value - ((Value >> 1) & 0x55555555);
+ v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
+ return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
+#endif
+}
+
+/// CountPopulation_64 - this function counts the number of set bits in a value,
+/// (64 bit edition.)
+inline unsigned CountPopulation_64(uint64_t Value) {
+#if __GNUC__ >= 4
+ return __builtin_popcountll(Value);
+#else
+ uint64_t v = Value - ((Value >> 1) & 0x5555555555555555ULL);
+ v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
+ v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
+ return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
+#endif
+}
+
+/// Log2_32 - This function returns the floor log base 2 of the specified value,
+/// -1 if the value is zero. (32 bit edition.)
+/// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
+inline unsigned Log2_32(uint32_t Value) {
+ return 31 - CountLeadingZeros_32(Value);
+}
+
+/// Log2_64 - This function returns the floor log base 2 of the specified value,
+/// -1 if the value is zero. (64 bit edition.)
+inline unsigned Log2_64(uint64_t Value) {
+ return 63 - CountLeadingZeros_64(Value);
+}
+
+/// Log2_32_Ceil - This function returns the ceil log base 2 of the specified
+/// value, 32 if the value is zero. (32 bit edition).
+/// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
+inline unsigned Log2_32_Ceil(uint32_t Value) {
+ return 32-CountLeadingZeros_32(Value-1);
+}
+
+/// Log2_64_Ceil - This function returns the ceil log base 2 of the specified
+/// value, 64 if the value is zero. (64 bit edition.)
+inline unsigned Log2_64_Ceil(uint64_t Value) {
+ return 64-CountLeadingZeros_64(Value-1);
+}
+
+/// GreatestCommonDivisor64 - Return the greatest common divisor of the two
+/// values using Euclid's algorithm.
+inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
+ while (B) {
+ uint64_t T = B;
+ B = A % B;
+ A = T;