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//===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
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// The LLVM Compiler Infrastructure
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// This file is distributed under the University of Illinois Open Source
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// License. See LICENSE.TXT for details.
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//===----------------------------------------------------------------------===//
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// This file contains some functions that are useful for math stuff.
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//===----------------------------------------------------------------------===//
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#ifndef LLVM_SUPPORT_MATHEXTRAS_H
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#define LLVM_SUPPORT_MATHEXTRAS_H
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#include "llvm/System/DataTypes.h"
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// NOTE: The following support functions use the _32/_64 extensions instead of
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// type overloading so that signed and unsigned integers can be used without
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/// Hi_32 - This function returns the high 32 bits of a 64 bit value.
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inline uint32_t Hi_32(uint64_t Value) {
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return static_cast<uint32_t>(Value >> 32);
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/// Lo_32 - This function returns the low 32 bits of a 64 bit value.
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inline uint32_t Lo_32(uint64_t Value) {
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return static_cast<uint32_t>(Value);
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/// isInt - Checks if an integer fits into the given bit width.
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inline bool isInt(int64_t x) {
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return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
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// Template specializations to get better code for common cases.
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inline bool isInt<8>(int64_t x) {
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return static_cast<int8_t>(x) == x;
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inline bool isInt<16>(int64_t x) {
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return static_cast<int16_t>(x) == x;
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inline bool isInt<32>(int64_t x) {
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return static_cast<int32_t>(x) == x;
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/// isUInt - Checks if an unsigned integer fits into the given bit width.
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inline bool isUInt(uint64_t x) {
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return N >= 64 || x < (UINT64_C(1)<<N);
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// Template specializations to get better code for common cases.
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inline bool isUInt<8>(uint64_t x) {
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return static_cast<uint8_t>(x) == x;
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inline bool isUInt<16>(uint64_t x) {
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return static_cast<uint16_t>(x) == x;
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inline bool isUInt<32>(uint64_t x) {
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return static_cast<uint32_t>(x) == x;
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/// isMask_32 - This function returns true if the argument is a sequence of ones
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/// starting at the least significant bit with the remainder zero (32 bit
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/// version). Ex. isMask_32(0x0000FFFFU) == true.
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inline bool isMask_32(uint32_t Value) {
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return Value && ((Value + 1) & Value) == 0;
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/// isMask_64 - This function returns true if the argument is a sequence of ones
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/// starting at the least significant bit with the remainder zero (64 bit
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inline bool isMask_64(uint64_t Value) {
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return Value && ((Value + 1) & Value) == 0;
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/// isShiftedMask_32 - This function returns true if the argument contains a
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/// sequence of ones with the remainder zero (32 bit version.)
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/// Ex. isShiftedMask_32(0x0000FF00U) == true.
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inline bool isShiftedMask_32(uint32_t Value) {
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return isMask_32((Value - 1) | Value);
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/// isShiftedMask_64 - This function returns true if the argument contains a
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/// sequence of ones with the remainder zero (64 bit version.)
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inline bool isShiftedMask_64(uint64_t Value) {
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return isMask_64((Value - 1) | Value);
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/// isPowerOf2_32 - This function returns true if the argument is a power of
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/// two > 0. Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
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inline bool isPowerOf2_32(uint32_t Value) {
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return Value && !(Value & (Value - 1));
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/// isPowerOf2_64 - This function returns true if the argument is a power of two
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/// > 0 (64 bit edition.)
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inline bool isPowerOf2_64(uint64_t Value) {
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return Value && !(Value & (Value - int64_t(1L)));
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/// ByteSwap_16 - This function returns a byte-swapped representation of the
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/// 16-bit argument, Value.
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inline uint16_t ByteSwap_16(uint16_t Value) {
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#if defined(_MSC_VER) && !defined(_DEBUG)
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// The DLL version of the runtime lacks these functions (bug!?), but in a
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// release build they're replaced with BSWAP instructions anyway.
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return _byteswap_ushort(Value);
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uint16_t Hi = Value << 8;
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uint16_t Lo = Value >> 8;
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/// ByteSwap_32 - This function returns a byte-swapped representation of the
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/// 32-bit argument, Value.
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inline uint32_t ByteSwap_32(uint32_t Value) {
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#if defined(__llvm__) || \
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(__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3)) && !defined(__ICC)
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return __builtin_bswap32(Value);
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#elif defined(_MSC_VER) && !defined(_DEBUG)
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return _byteswap_ulong(Value);
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uint32_t Byte0 = Value & 0x000000FF;
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uint32_t Byte1 = Value & 0x0000FF00;
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uint32_t Byte2 = Value & 0x00FF0000;
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uint32_t Byte3 = Value & 0xFF000000;
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return (Byte0 << 24) | (Byte1 << 8) | (Byte2 >> 8) | (Byte3 >> 24);
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/// ByteSwap_64 - This function returns a byte-swapped representation of the
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/// 64-bit argument, Value.
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inline uint64_t ByteSwap_64(uint64_t Value) {
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#if defined(__llvm__) || \
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(__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3)) && !defined(__ICC)
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return __builtin_bswap64(Value);
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#elif defined(_MSC_VER) && !defined(_DEBUG)
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return _byteswap_uint64(Value);
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uint64_t Hi = ByteSwap_32(uint32_t(Value));
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uint32_t Lo = ByteSwap_32(uint32_t(Value >> 32));
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return (Hi << 32) | Lo;
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/// CountLeadingZeros_32 - this function performs the platform optimal form of
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/// counting the number of zeros from the most significant bit to the first one
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/// bit. Ex. CountLeadingZeros_32(0x00F000FF) == 8.
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/// Returns 32 if the word is zero.
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inline unsigned CountLeadingZeros_32(uint32_t Value) {
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unsigned Count; // result
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// PowerPC is defined for __builtin_clz(0)
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#if !defined(__ppc__) && !defined(__ppc64__)
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if (!Value) return 32;
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Count = __builtin_clz(Value);
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if (!Value) return 32;
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// bisection method for count leading zeros
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for (unsigned Shift = 32 >> 1; Shift; Shift >>= 1) {
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uint32_t Tmp = Value >> Shift;
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/// CountLeadingOnes_32 - this function performs the operation of
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/// counting the number of ones from the most significant bit to the first zero
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/// bit. Ex. CountLeadingOnes_32(0xFF0FFF00) == 8.
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/// Returns 32 if the word is all ones.
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inline unsigned CountLeadingOnes_32(uint32_t Value) {
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return CountLeadingZeros_32(~Value);
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/// CountLeadingZeros_64 - This function performs the platform optimal form
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/// of counting the number of zeros from the most significant bit to the first
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/// one bit (64 bit edition.)
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/// Returns 64 if the word is zero.
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inline unsigned CountLeadingZeros_64(uint64_t Value) {
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unsigned Count; // result
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// PowerPC is defined for __builtin_clzll(0)
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#if !defined(__ppc__) && !defined(__ppc64__)
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if (!Value) return 64;
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Count = __builtin_clzll(Value);
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if (sizeof(long) == sizeof(int64_t)) {
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if (!Value) return 64;
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// bisection method for count leading zeros
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for (unsigned Shift = 64 >> 1; Shift; Shift >>= 1) {
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uint64_t Tmp = Value >> Shift;
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uint32_t Hi = Hi_32(Value);
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// if some bits in hi portion
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// leading zeros in hi portion plus all bits in lo portion
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Count = CountLeadingZeros_32(Hi);
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uint32_t Lo = Lo_32(Value);
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// same as 32 bit value
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Count = CountLeadingZeros_32(Lo)+32;
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/// CountLeadingOnes_64 - This function performs the operation
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/// of counting the number of ones from the most significant bit to the first
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/// zero bit (64 bit edition.)
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/// Returns 64 if the word is all ones.
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inline unsigned CountLeadingOnes_64(uint64_t Value) {
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return CountLeadingZeros_64(~Value);
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/// CountTrailingZeros_32 - this function performs the platform optimal form of
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/// counting the number of zeros from the least significant bit to the first one
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/// bit. Ex. CountTrailingZeros_32(0xFF00FF00) == 8.
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/// Returns 32 if the word is zero.
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inline unsigned CountTrailingZeros_32(uint32_t Value) {
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return Value ? __builtin_ctz(Value) : 32;
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static const unsigned Mod37BitPosition[] = {
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32, 0, 1, 26, 2, 23, 27, 0, 3, 16, 24, 30, 28, 11, 0, 13,
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4, 7, 17, 0, 25, 22, 31, 15, 29, 10, 12, 6, 0, 21, 14, 9,
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return Mod37BitPosition[(-Value & Value) % 37];
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/// CountTrailingOnes_32 - this function performs the operation of
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/// counting the number of ones from the least significant bit to the first zero
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/// bit. Ex. CountTrailingOnes_32(0x00FF00FF) == 8.
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/// Returns 32 if the word is all ones.
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inline unsigned CountTrailingOnes_32(uint32_t Value) {
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return CountTrailingZeros_32(~Value);
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/// CountTrailingZeros_64 - This function performs the platform optimal form
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/// of counting the number of zeros from the least significant bit to the first
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/// one bit (64 bit edition.)
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/// Returns 64 if the word is zero.
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inline unsigned CountTrailingZeros_64(uint64_t Value) {
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return Value ? __builtin_ctzll(Value) : 64;
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static const unsigned Mod67Position[] = {
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64, 0, 1, 39, 2, 15, 40, 23, 3, 12, 16, 59, 41, 19, 24, 54,
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4, 64, 13, 10, 17, 62, 60, 28, 42, 30, 20, 51, 25, 44, 55,
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47, 5, 32, 65, 38, 14, 22, 11, 58, 18, 53, 63, 9, 61, 27,
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29, 50, 43, 46, 31, 37, 21, 57, 52, 8, 26, 49, 45, 36, 56,
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7, 48, 35, 6, 34, 33, 0
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return Mod67Position[(-Value & Value) % 67];
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/// CountTrailingOnes_64 - This function performs the operation
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/// of counting the number of ones from the least significant bit to the first
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/// zero bit (64 bit edition.)
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/// Returns 64 if the word is all ones.
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inline unsigned CountTrailingOnes_64(uint64_t Value) {
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return CountTrailingZeros_64(~Value);
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/// CountPopulation_32 - this function counts the number of set bits in a value.
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/// Ex. CountPopulation(0xF000F000) = 8
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/// Returns 0 if the word is zero.
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inline unsigned CountPopulation_32(uint32_t Value) {
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return __builtin_popcount(Value);
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uint32_t v = Value - ((Value >> 1) & 0x55555555);
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v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
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return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
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/// CountPopulation_64 - this function counts the number of set bits in a value,
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/// (64 bit edition.)
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inline unsigned CountPopulation_64(uint64_t Value) {
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return __builtin_popcountll(Value);
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uint64_t v = Value - ((Value >> 1) & 0x5555555555555555ULL);
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v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
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v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
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return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
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/// Log2_32 - This function returns the floor log base 2 of the specified value,
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/// -1 if the value is zero. (32 bit edition.)
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/// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
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inline unsigned Log2_32(uint32_t Value) {
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return 31 - CountLeadingZeros_32(Value);
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/// Log2_64 - This function returns the floor log base 2 of the specified value,
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/// -1 if the value is zero. (64 bit edition.)
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inline unsigned Log2_64(uint64_t Value) {
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return 63 - CountLeadingZeros_64(Value);
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/// Log2_32_Ceil - This function returns the ceil log base 2 of the specified
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/// value, 32 if the value is zero. (32 bit edition).
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/// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
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inline unsigned Log2_32_Ceil(uint32_t Value) {
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return 32-CountLeadingZeros_32(Value-1);
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/// Log2_64_Ceil - This function returns the ceil log base 2 of the specified
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/// value, 64 if the value is zero. (64 bit edition.)
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inline unsigned Log2_64_Ceil(uint64_t Value) {
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return 64-CountLeadingZeros_64(Value-1);
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/// GreatestCommonDivisor64 - Return the greatest common divisor of the two
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/// values using Euclid's algorithm.
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inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
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/// BitsToDouble - This function takes a 64-bit integer and returns the bit
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/// equivalent double.
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inline double BitsToDouble(uint64_t Bits) {
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/// BitsToFloat - This function takes a 32-bit integer and returns the bit
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/// equivalent float.
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inline float BitsToFloat(uint32_t Bits) {
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/// DoubleToBits - This function takes a double and returns the bit
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/// equivalent 64-bit integer. Note that copying doubles around
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/// changes the bits of NaNs on some hosts, notably x86, so this
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/// routine cannot be used if these bits are needed.
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inline uint64_t DoubleToBits(double Double) {
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/// FloatToBits - This function takes a float and returns the bit
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/// equivalent 32-bit integer. Note that copying floats around
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/// changes the bits of NaNs on some hosts, notably x86, so this
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/// routine cannot be used if these bits are needed.
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inline uint32_t FloatToBits(float Float) {
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/// Platform-independent wrappers for the C99 isnan() function.
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/// Platform-independent wrappers for the C99 isinf() function.
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/// MinAlign - A and B are either alignments or offsets. Return the minimum
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/// alignment that may be assumed after adding the two together.
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static inline uint64_t MinAlign(uint64_t A, uint64_t B) {
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// The largest power of 2 that divides both A and B.
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return (A | B) & -(A | B);
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/// NextPowerOf2 - Returns the next power of two (in 64-bits)
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/// that is strictly greater than A. Returns zero on overflow.
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static inline uint64_t NextPowerOf2(uint64_t A) {
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/// RoundUpToAlignment - Returns the next integer (mod 2**64) that is
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/// greater than or equal to \arg Value and is a multiple of \arg
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/// Align. Align must be non-zero.
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/// RoundUpToAlignment(5, 8) = 8
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/// RoundUpToAlignment(17, 8) = 24
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/// RoundUpToAlignment(~0LL, 8) = 0
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inline uint64_t RoundUpToAlignment(uint64_t Value, uint64_t Align) {
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return ((Value + Align - 1) / Align) * Align;
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/// OffsetToAlignment - Return the offset to the next integer (mod 2**64) that
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/// is greater than or equal to \arg Value and is a multiple of \arg
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/// Align. Align must be non-zero.
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inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
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return RoundUpToAlignment(Value, Align) - Value;
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/// abs64 - absolute value of a 64-bit int. Not all environments support
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/// "abs" on whatever their name for the 64-bit int type is. The absolute
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/// value of the largest negative number is undefined, as with "abs".
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inline int64_t abs64(int64_t x) {
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return (x < 0) ? -x : x;
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/// SignExtend32 - Sign extend B-bit number x to 32-bit int.
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/// Usage int32_t r = SignExtend32<5>(x);
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template <unsigned B> inline int32_t SignExtend32(uint32_t x) {
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return int32_t(x << (32 - B)) >> (32 - B);
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/// SignExtend64 - Sign extend B-bit number x to 64-bit int.
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/// Usage int64_t r = SignExtend64<5>(x);
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template <unsigned B> inline int64_t SignExtend64(uint64_t x) {
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return int64_t(x << (64 - B)) >> (64 - B);
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} // End llvm namespace