libdivide.h

// libdivide.h - Optimized integer division
// https://libdivide.com
//
// Copyright (C) 2010 - 2021 ridiculous_fish, <libdivide@ridiculousfish.com>
// Copyright (C) 2016 - 2021 Kim Walisch, <kim.walisch@gmail.com>
//
// libdivide is dual-licensed under the Boost or zlib licenses.
// You may use libdivide under the terms of either of these.
// See LICENSE.txt for more details.

#ifndef LIBDIVIDE_H
#define LIBDIVIDE_H

#define LIBDIVIDE_VERSION "5.0"
#define LIBDIVIDE_VERSION_MAJOR 5
#define LIBDIVIDE_VERSION_MINOR 0

#include <stdint.h>
#if !defined(__AVR__)
#include <stdio.h>
#include <stdlib.h>
#endif

#if defined(LIBDIVIDE_SSE2)
#include <emmintrin.h>
#endif
#if defined(LIBDIVIDE_AVX2) || defined(LIBDIVIDE_AVX512)
#include <immintrin.h>
#endif
#if defined(LIBDIVIDE_NEON)
#include <arm_neon.h>
#endif

#if defined(_MSC_VER)
#include <intrin.h>
#pragma warning(push)
// disable warning C4146: unary minus operator applied
// to unsigned type, result still unsigned
#pragma warning(disable : 4146)
// disable warning C4204: nonstandard extension used : non-constant aggregate
// initializer
//
// It's valid C99
#pragma warning(disable : 4204)
#define LIBDIVIDE_VC
#endif

#if !defined(__has_builtin)
#define __has_builtin(x) 0
#endif

#if defined(__SIZEOF_INT128__)
#define HAS_INT128_T
// clang-cl on Windows does not yet support 128-bit division
#if !(defined(__clang__) && defined(LIBDIVIDE_VC))
#define HAS_INT128_DIV
#endif
#endif

#if defined(__x86_64__) || defined(_M_X64)
#define LIBDIVIDE_X86_64
#endif

#if defined(__i386__)
#define LIBDIVIDE_i386
#endif

#if defined(__GNUC__) || defined(__clang__)
#define LIBDIVIDE_GCC_STYLE_ASM
#endif

#if defined(__cplusplus) || defined(LIBDIVIDE_VC)
#define LIBDIVIDE_FUNCTION __FUNCTION__
#else
#define LIBDIVIDE_FUNCTION __func__
#endif

// Set up forced inlining if possible.
// We need both the attribute and keyword to avoid "might not be inlineable" warnings.
#ifdef __has_attribute
#if __has_attribute(always_inline)
#define LIBDIVIDE_INLINE __attribute__((always_inline)) inline
#endif
#endif
#ifndef LIBDIVIDE_INLINE
#define LIBDIVIDE_INLINE inline
#endif

#if defined(__AVR__)
#define LIBDIVIDE_ERROR(msg)
#else
#define LIBDIVIDE_ERROR(msg)                                                                     \
    do {                                                                                         \
        fprintf(stderr, "libdivide.h:%d: %s(): Error: %s\n", __LINE__, LIBDIVIDE_FUNCTION, msg); \
        abort();                                                                                 \
    } while (0)
#endif

#if defined(LIBDIVIDE_ASSERTIONS_ON) && !defined(__AVR__)
#define LIBDIVIDE_ASSERT(x)                                                           \
    do {                                                                              \
        if (!(x)) {                                                                   \
            fprintf(stderr, "libdivide.h:%d: %s(): Assertion failed: %s\n", __LINE__, \
                LIBDIVIDE_FUNCTION, #x);                                              \
            abort();                                                                  \
        }                                                                             \
    } while (0)
#else
#define LIBDIVIDE_ASSERT(x)
#endif

#ifdef __cplusplus
namespace libdivide
{
#endif

// pack divider structs to prevent compilers from padding.
// This reduces memory usage by up to 43% when using a large
// array of libdivide dividers and improves performance
// by up to 10% because of reduced memory bandwidth.
#pragma pack(push, 1)

struct libdivide_u16_t
{
	uint16_t magic;
	uint8_t more;
};

struct libdivide_s16_t
{
	int16_t magic;
	uint8_t more;
};

struct libdivide_u32_t
{
	uint32_t magic;
	uint8_t more;
};

struct libdivide_s32_t
{
	int32_t magic;
	uint8_t more;
};

struct libdivide_u64_t
{
	uint64_t magic;
	uint8_t more;
};

struct libdivide_s64_t
{
	int64_t magic;
	uint8_t more;
};

struct libdivide_u16_branchfree_t
{
	uint16_t magic;
	uint8_t more;
};

struct libdivide_s16_branchfree_t
{
	int16_t magic;
	uint8_t more;
};

struct libdivide_u32_branchfree_t
{
	uint32_t magic;
	uint8_t more;
};

struct libdivide_s32_branchfree_t
{
	int32_t magic;
	uint8_t more;
};

struct libdivide_u64_branchfree_t
{
	uint64_t magic;
	uint8_t more;
};

struct libdivide_s64_branchfree_t
{
	int64_t magic;
	uint8_t more;
};

#pragma pack(pop)

// Explanation of the "more" field:
//
// * Bits 0-5 is the shift value (for shift path or mult path).
// * Bit 6 is the add indicator for mult path.
// * Bit 7 is set if the divisor is negative. We use bit 7 as the negative
//   divisor indicator so that we can efficiently use sign extension to
//   create a bitmask with all bits set to 1 (if the divisor is negative)
//   or 0 (if the divisor is positive).
//
// u32: [0-4] shift value
//      [5] ignored
//      [6] add indicator
//      magic number of 0 indicates shift path
//
// s32: [0-4] shift value
//      [5] ignored
//      [6] add indicator
//      [7] indicates negative divisor
//      magic number of 0 indicates shift path
//
// u64: [0-5] shift value
//      [6] add indicator
//      magic number of 0 indicates shift path
//
// s64: [0-5] shift value
//      [6] add indicator
//      [7] indicates negative divisor
//      magic number of 0 indicates shift path
//
// In s32 and s64 branchfree modes, the magic number is negated according to
// whether the divisor is negated. In branchfree strategy, it is not negated.

enum
{
	LIBDIVIDE_16_SHIFT_MASK = 0x1F,
	LIBDIVIDE_32_SHIFT_MASK = 0x1F,
	LIBDIVIDE_64_SHIFT_MASK = 0x3F,
	LIBDIVIDE_ADD_MARKER = 0x40,
	LIBDIVIDE_NEGATIVE_DIVISOR = 0x80
};

static LIBDIVIDE_INLINE struct libdivide_s16_t libdivide_s16_gen(int16_t d);
static LIBDIVIDE_INLINE struct libdivide_u16_t libdivide_u16_gen(uint16_t d);
static LIBDIVIDE_INLINE struct libdivide_s32_t libdivide_s32_gen(int32_t d);
static LIBDIVIDE_INLINE struct libdivide_u32_t libdivide_u32_gen(uint32_t d);
static LIBDIVIDE_INLINE struct libdivide_s64_t libdivide_s64_gen(int64_t d);
static LIBDIVIDE_INLINE struct libdivide_u64_t libdivide_u64_gen(uint64_t d);

static LIBDIVIDE_INLINE struct libdivide_s16_branchfree_t libdivide_s16_branchfree_gen(int16_t d);
static LIBDIVIDE_INLINE struct libdivide_u16_branchfree_t libdivide_u16_branchfree_gen(uint16_t d);
static LIBDIVIDE_INLINE struct libdivide_s32_branchfree_t libdivide_s32_branchfree_gen(int32_t d);
static LIBDIVIDE_INLINE struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t d);
static LIBDIVIDE_INLINE struct libdivide_s64_branchfree_t libdivide_s64_branchfree_gen(int64_t d);
static LIBDIVIDE_INLINE struct libdivide_u64_branchfree_t libdivide_u64_branchfree_gen(uint64_t d);

static LIBDIVIDE_INLINE int16_t libdivide_s16_do_raw(int16_t numer, int16_t magic, uint8_t more);
static LIBDIVIDE_INLINE int16_t libdivide_s16_do(
	int16_t numer, const struct libdivide_s16_t *denom);
static LIBDIVIDE_INLINE uint16_t libdivide_u16_do_raw(uint16_t numer, uint16_t magic, uint8_t more);
static LIBDIVIDE_INLINE uint16_t libdivide_u16_do(
	uint16_t numer, const struct libdivide_u16_t *denom);
static LIBDIVIDE_INLINE int32_t libdivide_s32_do(
	int32_t numer, const struct libdivide_s32_t *denom);
static LIBDIVIDE_INLINE uint32_t libdivide_u32_do(
	uint32_t numer, const struct libdivide_u32_t *denom);
static LIBDIVIDE_INLINE int64_t libdivide_s64_do(
	int64_t numer, const struct libdivide_s64_t *denom);
static LIBDIVIDE_INLINE uint64_t libdivide_u64_do(
	uint64_t numer, const struct libdivide_u64_t *denom);

static LIBDIVIDE_INLINE int16_t libdivide_s16_branchfree_do(
	int16_t numer, const struct libdivide_s16_branchfree_t *denom);
static LIBDIVIDE_INLINE uint16_t libdivide_u16_branchfree_do(
	uint16_t numer, const struct libdivide_u16_branchfree_t *denom);
static LIBDIVIDE_INLINE int32_t libdivide_s32_branchfree_do(
	int32_t numer, const struct libdivide_s32_branchfree_t *denom);
static LIBDIVIDE_INLINE uint32_t libdivide_u32_branchfree_do(
	uint32_t numer, const struct libdivide_u32_branchfree_t *denom);
static LIBDIVIDE_INLINE int64_t libdivide_s64_branchfree_do(
	int64_t numer, const struct libdivide_s64_branchfree_t *denom);
static LIBDIVIDE_INLINE uint64_t libdivide_u64_branchfree_do(
	uint64_t numer, const struct libdivide_u64_branchfree_t *denom);

static LIBDIVIDE_INLINE int16_t libdivide_s16_recover(const struct libdivide_s16_t *denom);
static LIBDIVIDE_INLINE uint16_t libdivide_u16_recover(const struct libdivide_u16_t *denom);
static LIBDIVIDE_INLINE int32_t libdivide_s32_recover(const struct libdivide_s32_t *denom);
static LIBDIVIDE_INLINE uint32_t libdivide_u32_recover(const struct libdivide_u32_t *denom);
static LIBDIVIDE_INLINE int64_t libdivide_s64_recover(const struct libdivide_s64_t *denom);
static LIBDIVIDE_INLINE uint64_t libdivide_u64_recover(const struct libdivide_u64_t *denom);

static LIBDIVIDE_INLINE int16_t libdivide_s16_branchfree_recover(
	const struct libdivide_s16_branchfree_t *denom);
static LIBDIVIDE_INLINE uint16_t libdivide_u16_branchfree_recover(
	const struct libdivide_u16_branchfree_t *denom);
static LIBDIVIDE_INLINE int32_t libdivide_s32_branchfree_recover(
	const struct libdivide_s32_branchfree_t *denom);
static LIBDIVIDE_INLINE uint32_t libdivide_u32_branchfree_recover(
	const struct libdivide_u32_branchfree_t *denom);
static LIBDIVIDE_INLINE int64_t libdivide_s64_branchfree_recover(
	const struct libdivide_s64_branchfree_t *denom);
static LIBDIVIDE_INLINE uint64_t libdivide_u64_branchfree_recover(
	const struct libdivide_u64_branchfree_t *denom);

//////// Internal Utility Functions

static LIBDIVIDE_INLINE uint16_t libdivide_mullhi_u16(uint16_t x, uint16_t y)
{
	uint32_t xl = x, yl = y;
	uint32_t rl = xl * yl;
	return (uint16_t)(rl >> 16);
}

static LIBDIVIDE_INLINE int16_t libdivide_mullhi_s16(int16_t x, int16_t y)
{
	int32_t xl = x, yl = y;
	int32_t rl = xl * yl;
	// needs to be arithmetic shift
	return (int16_t)(rl >> 16);
}

static LIBDIVIDE_INLINE uint32_t libdivide_mullhi_u32(uint32_t x, uint32_t y)
{
	uint64_t xl = x, yl = y;
	uint64_t rl = xl * yl;
	return (uint32_t)(rl >> 32);
}

static LIBDIVIDE_INLINE int32_t libdivide_mullhi_s32(int32_t x, int32_t y)
{
	int64_t xl = x, yl = y;
	int64_t rl = xl * yl;
	// needs to be arithmetic shift
	return (int32_t)(rl >> 32);
}

static LIBDIVIDE_INLINE uint64_t libdivide_mullhi_u64(uint64_t x, uint64_t y)
{
#if defined(LIBDIVIDE_VC) && defined(LIBDIVIDE_X86_64)
	return __umulh(x, y);
#elif defined(HAS_INT128_T)
	__uint128_t xl = x, yl = y;
	__uint128_t rl = xl * yl;
	return (uint64_t)(rl >> 64);
#else
	// full 128 bits are x0 * y0 + (x0 * y1 << 32) + (x1 * y0 << 32) + (x1 * y1 << 64)
	uint32_t mask = 0xFFFFFFFF;
	uint32_t x0 = (uint32_t)(x & mask);
	uint32_t x1 = (uint32_t)(x >> 32);
	uint32_t y0 = (uint32_t)(y & mask);
	uint32_t y1 = (uint32_t)(y >> 32);
	uint32_t x0y0_hi = libdivide_mullhi_u32(x0, y0);
	uint64_t x0y1 = x0 * (uint64_t)y1;
	uint64_t x1y0 = x1 * (uint64_t)y0;
	uint64_t x1y1 = x1 * (uint64_t)y1;
	uint64_t temp = x1y0 + x0y0_hi;
	uint64_t temp_lo = temp & mask;
	uint64_t temp_hi = temp >> 32;

	return x1y1 + temp_hi + ((temp_lo + x0y1) >> 32);
#endif
}

static LIBDIVIDE_INLINE int64_t libdivide_mullhi_s64(int64_t x, int64_t y)
{
#if defined(LIBDIVIDE_VC) && defined(LIBDIVIDE_X86_64)
	return __mulh(x, y);
#elif defined(HAS_INT128_T)
	__int128_t xl = x, yl = y;
	__int128_t rl = xl * yl;
	return (int64_t)(rl >> 64);
#else
	// full 128 bits are x0 * y0 + (x0 * y1 << 32) + (x1 * y0 << 32) + (x1 * y1 << 64)
	uint32_t mask = 0xFFFFFFFF;
	uint32_t x0 = (uint32_t)(x & mask);
	uint32_t y0 = (uint32_t)(y & mask);
	int32_t x1 = (int32_t)(x >> 32);
	int32_t y1 = (int32_t)(y >> 32);
	uint32_t x0y0_hi = libdivide_mullhi_u32(x0, y0);
	int64_t t = x1 * (int64_t)y0 + x0y0_hi;
	int64_t w1 = x0 * (int64_t)y1 + (t & mask);

	return x1 * (int64_t)y1 + (t >> 32) + (w1 >> 32);
#endif
}

static LIBDIVIDE_INLINE int16_t libdivide_count_leading_zeros16(uint16_t val)
{
#if defined(__AVR__)
	// Fast way to count leading zeros
	// On the AVR 8-bit architecture __builtin_clz() works on a int16_t.
	return __builtin_clz(val);
#elif defined(__GNUC__) || __has_builtin(__builtin_clz)
	// Fast way to count leading zeros
	return __builtin_clz(val) - 16;
#elif defined(LIBDIVIDE_VC)
	unsigned long result;
	if (_BitScanReverse(&result, (unsigned long)val))
	{
		return (int16_t)(15 - result);
	}
	return 0;
#else
	if (val == 0) return 16;
	int16_t result = 4;
	uint16_t hi = 0xFU << 12;
	while ((val & hi) == 0)
	{
		hi >>= 4;
		result += 4;
	}
	while (val & hi)
	{
		result -= 1;
		hi <<= 1;
	}
	return result;
#endif
}

static LIBDIVIDE_INLINE int32_t libdivide_count_leading_zeros32(uint32_t val)
{
#if defined(__AVR__)
	// Fast way to count leading zeros
	return __builtin_clzl(val);
#elif defined(__GNUC__) || __has_builtin(__builtin_clz)
	// Fast way to count leading zeros
	return __builtin_clz(val);
#elif defined(LIBDIVIDE_VC)
	unsigned long result;
	if (_BitScanReverse(&result, val))
	{
		return 31 - result;
	}
	return 0;
#else
	if (val == 0) return 32;
	int32_t result = 8;
	uint32_t hi = 0xFFU << 24;
	while ((val & hi) == 0)
	{
		hi >>= 8;
		result += 8;
	}
	while (val & hi)
	{
		result -= 1;
		hi <<= 1;
	}
	return result;
#endif
}

static LIBDIVIDE_INLINE int32_t libdivide_count_leading_zeros64(uint64_t val)
{
#if defined(__GNUC__) || __has_builtin(__builtin_clzll)
	// Fast way to count leading zeros
	return __builtin_clzll(val);
#elif defined(LIBDIVIDE_VC) && defined(_WIN64)
	unsigned long result;
	if (_BitScanReverse64(&result, val))
	{
		return 63 - result;
	}
	return 0;
#else
	uint32_t hi = val >> 32;
	uint32_t lo = val & 0xFFFFFFFF;
	if (hi != 0) return libdivide_count_leading_zeros32(hi);
	return 32 + libdivide_count_leading_zeros32(lo);
#endif
}

// libdivide_32_div_16_to_16: divides a 32-bit uint {u1, u0} by a 16-bit
// uint {v}. The result must fit in 16 bits.
// Returns the quotient directly and the remainder in *r
static LIBDIVIDE_INLINE uint16_t libdivide_32_div_16_to_16(
	uint16_t u1, uint16_t u0, uint16_t v, uint16_t *r)
{
	uint32_t n = ((uint32_t)u1 << 16) | u0;
	uint16_t result = (uint16_t)(n / v);
	*r = (uint16_t)(n - result * (uint32_t)v);
	return result;
}

// libdivide_64_div_32_to_32: divides a 64-bit uint {u1, u0} by a 32-bit
// uint {v}. The result must fit in 32 bits.
// Returns the quotient directly and the remainder in *r
static LIBDIVIDE_INLINE uint32_t libdivide_64_div_32_to_32(
	uint32_t u1, uint32_t u0, uint32_t v, uint32_t *r)
{
#if (defined(LIBDIVIDE_i386) || defined(LIBDIVIDE_X86_64)) && defined(LIBDIVIDE_GCC_STYLE_ASM)
	uint32_t result;
	__asm__("divl %[v]" : "=a"(result), "=d"(*r) : [v] "r"(v), "a"(u0), "d"(u1));
	return result;
#else
	uint64_t n = ((uint64_t)u1 << 32) | u0;
	uint32_t result = (uint32_t)(n / v);
	*r = (uint32_t)(n - result * (uint64_t)v);
	return result;
#endif
}

// libdivide_128_div_64_to_64: divides a 128-bit uint {numhi, numlo} by a 64-bit uint {den}. The
// result must fit in 64 bits. Returns the quotient directly and the remainder in *r
static LIBDIVIDE_INLINE uint64_t libdivide_128_div_64_to_64(
	uint64_t numhi, uint64_t numlo, uint64_t den, uint64_t *r)
{
	// N.B. resist the temptation to use __uint128_t here.
	// In LLVM compiler-rt, it performs a 128/128 -> 128 division which is many times slower than
	// necessary. In gcc it's better but still slower than the divlu implementation, perhaps because
	// it's not LIBDIVIDE_INLINEd.
#if defined(LIBDIVIDE_X86_64) && defined(LIBDIVIDE_GCC_STYLE_ASM)
	uint64_t result;
	__asm__("divq %[v]" : "=a"(result), "=d"(*r) : [v] "r"(den), "a"(numlo), "d"(numhi));
	return result;
#else
	// We work in base 2**32.
	// A uint32 holds a single digit. A uint64 holds two digits.
	// Our numerator is conceptually [num3, num2, num1, num0].
	// Our denominator is [den1, den0].
	const uint64_t b = ((uint64_t)1 << 32);

	// The high and low digits of our computed quotient.
	uint32_t q1;
	uint32_t q0;

	// The normalization shift factor.
	int shift;

	// The high and low digits of our denominator (after normalizing).
	// Also the low 2 digits of our numerator (after normalizing).
	uint32_t den1;
	uint32_t den0;
	uint32_t num1;
	uint32_t num0;

	// A partial remainder.
	uint64_t rem;

	// The estimated quotient, and its corresponding remainder (unrelated to true remainder).
	uint64_t qhat;
	uint64_t rhat;

	// Variables used to correct the estimated quotient.
	uint64_t c1;
	uint64_t c2;

	// Check for overflow and divide by 0.
	if (numhi >= den)
	{
		if (r != NULL) *r = ~0ull;
		return ~0ull;
	}

	// Determine the normalization factor. We multiply den by this, so that its leading digit is at
	// least half b. In binary this means just shifting left by the number of leading zeros, so that
	// there's a 1 in the MSB.
	// We also shift numer by the same amount. This cannot overflow because numhi < den.
	// The expression (-shift & 63) is the same as (64 - shift), except it avoids the UB of shifting
	// by 64. The funny bitwise 'and' ensures that numlo does not get shifted into numhi if shift is
	// 0. clang 11 has an x86 codegen bug here: see LLVM bug 50118. The sequence below avoids it.
	shift = libdivide_count_leading_zeros64(den);
	den <<= shift;
	numhi <<= shift;
	numhi |= (numlo >> (-shift & 63)) & (-(int64_t)shift >> 63);
	numlo <<= shift;

	// Extract the low digits of the numerator and both digits of the denominator.
	num1 = (uint32_t)(numlo >> 32);
	num0 = (uint32_t)(numlo & 0xFFFFFFFFu);
	den1 = (uint32_t)(den >> 32);
	den0 = (uint32_t)(den & 0xFFFFFFFFu);

	// We wish to compute q1 = [n3 n2 n1] / [d1 d0].
	// Estimate q1 as [n3 n2] / [d1], and then correct it.
	// Note while qhat may be 2 digits, q1 is always 1 digit.
	qhat = numhi / den1;
	rhat = numhi % den1;
	c1 = qhat * den0;
	c2 = rhat * b + num1;
	if (c1 > c2) qhat -= (c1 - c2 > den) ? 2 : 1;
	q1 = (uint32_t)qhat;

	// Compute the true (partial) remainder.
	rem = numhi * b + num1 - q1 * den;

	// We wish to compute q0 = [rem1 rem0 n0] / [d1 d0].
	// Estimate q0 as [rem1 rem0] / [d1] and correct it.
	qhat = rem / den1;
	rhat = rem % den1;
	c1 = qhat * den0;
	c2 = rhat * b + num0;
	if (c1 > c2) qhat -= (c1 - c2 > den) ? 2 : 1;
	q0 = (uint32_t)qhat;

	// Return remainder if requested.
	if (r != NULL) *r = (rem * b + num0 - q0 * den) >> shift;
	return ((uint64_t)q1 << 32) | q0;
#endif
}

// Bitshift a u128 in place, left (signed_shift > 0) or right (signed_shift < 0)
static LIBDIVIDE_INLINE void libdivide_u128_shift(
	uint64_t *u1, uint64_t *u0, int32_t signed_shift)
{
	if (signed_shift > 0)
	{
		uint32_t shift = signed_shift;
		*u1 <<= shift;
		*u1 |= *u0 >> (64 - shift);
		*u0 <<= shift;
	}
	else if (signed_shift < 0)
	{
		uint32_t shift = -signed_shift;
		*u0 >>= shift;
		*u0 |= *u1 << (64 - shift);
		*u1 >>= shift;
	}
}

// Computes a 128 / 128 -> 64 bit division, with a 128 bit remainder.
static LIBDIVIDE_INLINE uint64_t libdivide_128_div_128_to_64(
	uint64_t u_hi, uint64_t u_lo, uint64_t v_hi, uint64_t v_lo, uint64_t *r_hi, uint64_t *r_lo)
{
#if defined(HAS_INT128_T) && defined(HAS_INT128_DIV)
	__uint128_t ufull = u_hi;
	__uint128_t vfull = v_hi;
	ufull = (ufull << 64) | u_lo;
	vfull = (vfull << 64) | v_lo;
	uint64_t res = (uint64_t)(ufull / vfull);
	__uint128_t remainder = ufull - (vfull * res);
	*r_lo = (uint64_t)remainder;
	*r_hi = (uint64_t)(remainder >> 64);
	return res;
#else
	// Adapted from "Unsigned Doubleword Division" in Hacker's Delight
	// We want to compute u / v
	typedef struct
	{
		uint64_t hi;
		uint64_t lo;
	} u128_t;
	u128_t u = {u_hi, u_lo};
	u128_t v = {v_hi, v_lo};

	if (v.hi == 0)
	{
		// divisor v is a 64 bit value, so we just need one 128/64 division
		// Note that we are simpler than Hacker's Delight here, because we know
		// the quotient fits in 64 bits whereas Hacker's Delight demands a full
		// 128 bit quotient
		*r_hi = 0;
		return libdivide_128_div_64_to_64(u.hi, u.lo, v.lo, r_lo);
	}
	// Here v >= 2**64
	// We know that v.hi != 0, so count leading zeros is OK
	// We have 0 <= n <= 63
	uint32_t n = libdivide_count_leading_zeros64(v.hi);

	// Normalize the divisor so its MSB is 1
	u128_t v1t = v;
	libdivide_u128_shift(&v1t.hi, &v1t.lo, n);
	uint64_t v1 = v1t.hi;  // i.e. v1 = v1t >> 64

	// To ensure no overflow
	u128_t u1 = u;
	libdivide_u128_shift(&u1.hi, &u1.lo, -1);

	// Get quotient from divide unsigned insn.
	uint64_t rem_ignored;
	uint64_t q1 = libdivide_128_div_64_to_64(u1.hi, u1.lo, v1, &rem_ignored);

	// Undo normalization and division of u by 2.
	u128_t q0 = {0, q1};
	libdivide_u128_shift(&q0.hi, &q0.lo, n);
	libdivide_u128_shift(&q0.hi, &q0.lo, -63);

	// Make q0 correct or too small by 1
	// Equivalent to `if (q0 != 0) q0 = q0 - 1;`
	if (q0.hi != 0 || q0.lo != 0)
	{
		q0.hi -= (q0.lo == 0);  // borrow
		q0.lo -= 1;
	}

	// Now q0 is correct.
	// Compute q0 * v as q0v
	// = (q0.hi << 64 + q0.lo) * (v.hi << 64 + v.lo)
	// = (q0.hi * v.hi << 128) + (q0.hi * v.lo << 64) +
	//   (q0.lo * v.hi <<  64) + q0.lo * v.lo)
	// Each term is 128 bit
	// High half of full product (upper 128 bits!) are dropped
	u128_t q0v = {0, 0};
	q0v.hi = q0.hi * v.lo + q0.lo * v.hi + libdivide_mullhi_u64(q0.lo, v.lo);
	q0v.lo = q0.lo * v.lo;

	// Compute u - q0v as u_q0v
	// This is the remainder
	u128_t u_q0v = u;
	u_q0v.hi -= q0v.hi + (u.lo < q0v.lo);  // second term is borrow
	u_q0v.lo -= q0v.lo;

	// Check if u_q0v >= v
	// This checks if our remainder is larger than the divisor
	if ((u_q0v.hi > v.hi) || (u_q0v.hi == v.hi && u_q0v.lo >= v.lo))
	{
		// Increment q0
		q0.lo += 1;
		q0.hi += (q0.lo == 0);  // carry

		// Subtract v from remainder
		u_q0v.hi -= v.hi + (u_q0v.lo < v.lo);
		u_q0v.lo -= v.lo;
	}

	*r_hi = u_q0v.hi;
	*r_lo = u_q0v.lo;

	LIBDIVIDE_ASSERT(q0.hi == 0);
	return q0.lo;
#endif
}

////////// UINT16

static LIBDIVIDE_INLINE struct libdivide_u16_t libdivide_internal_u16_gen(
	uint16_t d, int branchfree)
{
	if (d == 0)
	{
		LIBDIVIDE_ERROR("divider must be != 0");
	}

	struct libdivide_u16_t result;
	uint8_t floor_log_2_d = (uint8_t)(15 - libdivide_count_leading_zeros16(d));

	// Power of 2
	if ((d & (d - 1)) == 0)
	{
		// We need to subtract 1 from the shift value in case of an unsigned
		// branchfree divider because there is a hardcoded right shift by 1
		// in its division algorithm. Because of this we also need to add back
		// 1 in its recovery algorithm.
		result.magic = 0;
		result.more = (uint8_t)(floor_log_2_d - (branchfree != 0));
	}
	else
	{
		uint8_t more;
		uint16_t rem, proposed_m;
		proposed_m = libdivide_32_div_16_to_16((uint16_t)1 << floor_log_2_d, 0, d, &rem);

		LIBDIVIDE_ASSERT(rem > 0 && rem < d);
		const uint16_t e = d - rem;

		// This power works if e < 2**floor_log_2_d.
		if (!branchfree && (e < ((uint16_t)1 << floor_log_2_d)))
		{
			// This power works
			more = floor_log_2_d;
		}
		else
		{
			// We have to use the general 17-bit algorithm.  We need to compute
			// (2**power) / d. However, we already have (2**(power-1))/d and
			// its remainder.  By doubling both, and then correcting the
			// remainder, we can compute the larger division.
			// don't care about overflow here - in fact, we expect it
			proposed_m += proposed_m;
			const uint16_t twice_rem = rem + rem;
			if (twice_rem >= d || twice_rem < rem) proposed_m += 1;
			more = floor_log_2_d | LIBDIVIDE_ADD_MARKER;
		}
		result.magic = 1 + proposed_m;
		result.more = more;
		// result.more's shift should in general be ceil_log_2_d. But if we
		// used the smaller power, we subtract one from the shift because we're
		// using the smaller power. If we're using the larger power, we
		// subtract one from the shift because it's taken care of by the add
		// indicator. So floor_log_2_d happens to be correct in both cases.
	}
	return result;
}

struct libdivide_u16_t libdivide_u16_gen(uint16_t d)
{
	return libdivide_internal_u16_gen(d, 0);
}

struct libdivide_u16_branchfree_t libdivide_u16_branchfree_gen(uint16_t d)
{
	if (d == 1)
	{
		LIBDIVIDE_ERROR("branchfree divider must be != 1");
	}
	struct libdivide_u16_t tmp = libdivide_internal_u16_gen(d, 1);
	struct libdivide_u16_branchfree_t ret =
	{
		tmp.magic, (uint8_t)(tmp.more & LIBDIVIDE_16_SHIFT_MASK)
	};
	return ret;
}

// The original libdivide_u16_do takes a const pointer. However, this cannot be used
// with a compile time constant libdivide_u16_t: it will generate a warning about
// taking the address of a temporary. Hence this overload.
uint16_t libdivide_u16_do_raw(uint16_t numer, uint16_t magic, uint8_t more)
{
	if (!magic)
	{
		return numer >> more;
	}
	else
	{
		uint16_t q = libdivide_mullhi_u16(magic, numer);
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			uint16_t t = ((numer - q) >> 1) + q;
			return t >> (more & LIBDIVIDE_16_SHIFT_MASK);
		}
		else
		{
			// All upper bits are 0,
			// don't need to mask them off.
			return q >> more;
		}
	}
}

uint16_t libdivide_u16_do(uint16_t numer, const struct libdivide_u16_t *denom)
{
	return libdivide_u16_do_raw(numer, denom->magic, denom->more);
}

uint16_t libdivide_u16_branchfree_do(
	uint16_t numer, const struct libdivide_u16_branchfree_t *denom)
{
	uint16_t q = libdivide_mullhi_u16(denom->magic, numer);
	uint16_t t = ((numer - q) >> 1) + q;
	return t >> denom->more;
}

uint16_t libdivide_u16_recover(const struct libdivide_u16_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_16_SHIFT_MASK;

	if (!denom->magic)
	{
		return (uint16_t)1 << shift;
	}
	else if (!(more & LIBDIVIDE_ADD_MARKER))
	{
		// We compute q = n/d = n*m / 2^(16 + shift)
		// Therefore we have d = 2^(16 + shift) / m
		// We need to ceil it.
		// We know d is not a power of 2, so m is not a power of 2,
		// so we can just add 1 to the floor
		uint16_t hi_dividend = (uint16_t)1 << shift;
		uint16_t rem_ignored;
		return 1 + libdivide_32_div_16_to_16(hi_dividend, 0, denom->magic, &rem_ignored);
	}
	else
	{
		// Here we wish to compute d = 2^(16+shift+1)/(m+2^16).
		// Notice (m + 2^16) is a 17 bit number. Use 32 bit division for now
		// Also note that shift may be as high as 15, so shift + 1 will
		// overflow. So we have to compute it as 2^(16+shift)/(m+2^16), and
		// then double the quotient and remainder.
		uint32_t half_n = (uint32_t)1 << (16 + shift);
		uint32_t d = ((uint32_t)1 << 16) | denom->magic;
		// Note that the quotient is guaranteed <= 16 bits, but the remainder
		// may need 17!
		uint16_t half_q = (uint16_t)(half_n / d);
		uint32_t rem = half_n % d;
		// We computed 2^(16+shift)/(m+2^16)
		// Need to double it, and then add 1 to the quotient if doubling th
		// remainder would increase the quotient.
		// Note that rem<<1 cannot overflow, since rem < d and d is 17 bits
		uint16_t full_q = half_q + half_q + ((rem << 1) >= d);

		// We rounded down in gen (hence +1)
		return full_q + 1;
	}
}

uint16_t libdivide_u16_branchfree_recover(const struct libdivide_u16_branchfree_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_16_SHIFT_MASK;

	if (!denom->magic)
	{
		return (uint16_t)1 << (shift + 1);
	}
	else
	{
		// Here we wish to compute d = 2^(16+shift+1)/(m+2^16).
		// Notice (m + 2^16) is a 17 bit number. Use 32 bit division for now
		// Also note that shift may be as high as 15, so shift + 1 will
		// overflow. So we have to compute it as 2^(16+shift)/(m+2^16), and
		// then double the quotient and remainder.
		uint32_t half_n = (uint32_t)1 << (16 + shift);
		uint32_t d = ((uint32_t)1 << 16) | denom->magic;
		// Note that the quotient is guaranteed <= 16 bits, but the remainder
		// may need 17!
		uint16_t half_q = (uint16_t)(half_n / d);
		uint32_t rem = half_n % d;
		// We computed 2^(16+shift)/(m+2^16)
		// Need to double it, and then add 1 to the quotient if doubling th
		// remainder would increase the quotient.
		// Note that rem<<1 cannot overflow, since rem < d and d is 33 bits
		uint16_t full_q = half_q + half_q + ((rem << 1) >= d);

		// We rounded down in gen (hence +1)
		return full_q + 1;
	}
}

////////// UINT32

static LIBDIVIDE_INLINE struct libdivide_u32_t libdivide_internal_u32_gen(
	uint32_t d, int branchfree)
{
	if (d == 0)
	{
		LIBDIVIDE_ERROR("divider must be != 0");
	}

	struct libdivide_u32_t result;
	uint32_t floor_log_2_d = 31 - libdivide_count_leading_zeros32(d);

	// Power of 2
	if ((d & (d - 1)) == 0)
	{
		// We need to subtract 1 from the shift value in case of an unsigned
		// branchfree divider because there is a hardcoded right shift by 1
		// in its division algorithm. Because of this we also need to add back
		// 1 in its recovery algorithm.
		result.magic = 0;
		result.more = (uint8_t)(floor_log_2_d - (branchfree != 0));
	}
	else
	{
		uint8_t more;
		uint32_t rem, proposed_m;
		proposed_m = libdivide_64_div_32_to_32((uint32_t)1 << floor_log_2_d, 0, d, &rem);

		LIBDIVIDE_ASSERT(rem > 0 && rem < d);
		const uint32_t e = d - rem;

		// This power works if e < 2**floor_log_2_d.
		if (!branchfree && (e < ((uint32_t)1 << floor_log_2_d)))
		{
			// This power works
			more = (uint8_t)floor_log_2_d;
		}
		else
		{
			// We have to use the general 33-bit algorithm.  We need to compute
			// (2**power) / d. However, we already have (2**(power-1))/d and
			// its remainder.  By doubling both, and then correcting the
			// remainder, we can compute the larger division.
			// don't care about overflow here - in fact, we expect it
			proposed_m += proposed_m;
			const uint32_t twice_rem = rem + rem;
			if (twice_rem >= d || twice_rem < rem) proposed_m += 1;
			more = (uint8_t)(floor_log_2_d | LIBDIVIDE_ADD_MARKER);
		}
		result.magic = 1 + proposed_m;
		result.more = more;
		// result.more's shift should in general be ceil_log_2_d. But if we
		// used the smaller power, we subtract one from the shift because we're
		// using the smaller power. If we're using the larger power, we
		// subtract one from the shift because it's taken care of by the add
		// indicator. So floor_log_2_d happens to be correct in both cases.
	}
	return result;
}

struct libdivide_u32_t libdivide_u32_gen(uint32_t d)
{
	return libdivide_internal_u32_gen(d, 0);
}

struct libdivide_u32_branchfree_t libdivide_u32_branchfree_gen(uint32_t d)
{
	if (d == 1)
	{
		LIBDIVIDE_ERROR("branchfree divider must be != 1");
	}
	struct libdivide_u32_t tmp = libdivide_internal_u32_gen(d, 1);
	struct libdivide_u32_branchfree_t ret =
	{
		tmp.magic, (uint8_t)(tmp.more & LIBDIVIDE_32_SHIFT_MASK)
	};
	return ret;
}

uint32_t libdivide_u32_do(uint32_t numer, const struct libdivide_u32_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		return numer >> more;
	}
	else
	{
		uint32_t q = libdivide_mullhi_u32(denom->magic, numer);
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			uint32_t t = ((numer - q) >> 1) + q;
			return t >> (more & LIBDIVIDE_32_SHIFT_MASK);
		}
		else
		{
			// All upper bits are 0,
			// don't need to mask them off.
			return q >> more;
		}
	}
}

uint32_t libdivide_u32_branchfree_do(
	uint32_t numer, const struct libdivide_u32_branchfree_t *denom)
{
	uint32_t q = libdivide_mullhi_u32(denom->magic, numer);
	uint32_t t = ((numer - q) >> 1) + q;
	return t >> denom->more;
}

uint32_t libdivide_u32_recover(const struct libdivide_u32_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;

	if (!denom->magic)
	{
		return (uint32_t)1 << shift;
	}
	else if (!(more & LIBDIVIDE_ADD_MARKER))
	{
		// We compute q = n/d = n*m / 2^(32 + shift)
		// Therefore we have d = 2^(32 + shift) / m
		// We need to ceil it.
		// We know d is not a power of 2, so m is not a power of 2,
		// so we can just add 1 to the floor
		uint32_t hi_dividend = (uint32_t)1 << shift;
		uint32_t rem_ignored;
		return 1 + libdivide_64_div_32_to_32(hi_dividend, 0, denom->magic, &rem_ignored);
	}
	else
	{
		// Here we wish to compute d = 2^(32+shift+1)/(m+2^32).
		// Notice (m + 2^32) is a 33 bit number. Use 64 bit division for now
		// Also note that shift may be as high as 31, so shift + 1 will
		// overflow. So we have to compute it as 2^(32+shift)/(m+2^32), and
		// then double the quotient and remainder.
		uint64_t half_n = (uint64_t)1 << (32 + shift);
		uint64_t d = ((uint64_t)1 << 32) | denom->magic;
		// Note that the quotient is guaranteed <= 32 bits, but the remainder
		// may need 33!
		uint32_t half_q = (uint32_t)(half_n / d);
		uint64_t rem = half_n % d;
		// We computed 2^(32+shift)/(m+2^32)
		// Need to double it, and then add 1 to the quotient if doubling th
		// remainder would increase the quotient.
		// Note that rem<<1 cannot overflow, since rem < d and d is 33 bits
		uint32_t full_q = half_q + half_q + ((rem << 1) >= d);

		// We rounded down in gen (hence +1)
		return full_q + 1;
	}
}

uint32_t libdivide_u32_branchfree_recover(const struct libdivide_u32_branchfree_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;

	if (!denom->magic)
	{
		return (uint32_t)1 << (shift + 1);
	}
	else
	{
		// Here we wish to compute d = 2^(32+shift+1)/(m+2^32).
		// Notice (m + 2^32) is a 33 bit number. Use 64 bit division for now
		// Also note that shift may be as high as 31, so shift + 1 will
		// overflow. So we have to compute it as 2^(32+shift)/(m+2^32), and
		// then double the quotient and remainder.
		uint64_t half_n = (uint64_t)1 << (32 + shift);
		uint64_t d = ((uint64_t)1 << 32) | denom->magic;
		// Note that the quotient is guaranteed <= 32 bits, but the remainder
		// may need 33!
		uint32_t half_q = (uint32_t)(half_n / d);
		uint64_t rem = half_n % d;
		// We computed 2^(32+shift)/(m+2^32)
		// Need to double it, and then add 1 to the quotient if doubling th
		// remainder would increase the quotient.
		// Note that rem<<1 cannot overflow, since rem < d and d is 33 bits
		uint32_t full_q = half_q + half_q + ((rem << 1) >= d);

		// We rounded down in gen (hence +1)
		return full_q + 1;
	}
}

/////////// UINT64

static LIBDIVIDE_INLINE struct libdivide_u64_t libdivide_internal_u64_gen(
	uint64_t d, int branchfree)
{
	if (d == 0)
	{
		LIBDIVIDE_ERROR("divider must be != 0");
	}

	struct libdivide_u64_t result;
	uint32_t floor_log_2_d = 63 - libdivide_count_leading_zeros64(d);

	// Power of 2
	if ((d & (d - 1)) == 0)
	{
		// We need to subtract 1 from the shift value in case of an unsigned
		// branchfree divider because there is a hardcoded right shift by 1
		// in its division algorithm. Because of this we also need to add back
		// 1 in its recovery algorithm.
		result.magic = 0;
		result.more = (uint8_t)(floor_log_2_d - (branchfree != 0));
	}
	else
	{
		uint64_t proposed_m, rem;
		uint8_t more;
		// (1 << (64 + floor_log_2_d)) / d
		proposed_m = libdivide_128_div_64_to_64((uint64_t)1 << floor_log_2_d, 0, d, &rem);

		LIBDIVIDE_ASSERT(rem > 0 && rem < d);
		const uint64_t e = d - rem;

		// This power works if e < 2**floor_log_2_d.
		if (!branchfree && e < ((uint64_t)1 << floor_log_2_d))
		{
			// This power works
			more = (uint8_t)floor_log_2_d;
		}
		else
		{
			// We have to use the general 65-bit algorithm.  We need to compute
			// (2**power) / d. However, we already have (2**(power-1))/d and
			// its remainder. By doubling both, and then correcting the
			// remainder, we can compute the larger division.
			// don't care about overflow here - in fact, we expect it
			proposed_m += proposed_m;
			const uint64_t twice_rem = rem + rem;
			if (twice_rem >= d || twice_rem < rem) proposed_m += 1;
			more = (uint8_t)(floor_log_2_d | LIBDIVIDE_ADD_MARKER);
		}
		result.magic = 1 + proposed_m;
		result.more = more;
		// result.more's shift should in general be ceil_log_2_d. But if we
		// used the smaller power, we subtract one from the shift because we're
		// using the smaller power. If we're using the larger power, we
		// subtract one from the shift because it's taken care of by the add
		// indicator. So floor_log_2_d happens to be correct in both cases,
		// which is why we do it outside of the if statement.
	}
	return result;
}

struct libdivide_u64_t libdivide_u64_gen(uint64_t d)
{
	return libdivide_internal_u64_gen(d, 0);
}

struct libdivide_u64_branchfree_t libdivide_u64_branchfree_gen(uint64_t d)
{
	if (d == 1)
	{
		LIBDIVIDE_ERROR("branchfree divider must be != 1");
	}
	struct libdivide_u64_t tmp = libdivide_internal_u64_gen(d, 1);
	struct libdivide_u64_branchfree_t ret =
	{
		tmp.magic, (uint8_t)(tmp.more & LIBDIVIDE_64_SHIFT_MASK)
	};
	return ret;
}

uint64_t libdivide_u64_do(uint64_t numer, const struct libdivide_u64_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		return numer >> more;
	}
	else
	{
		uint64_t q = libdivide_mullhi_u64(denom->magic, numer);
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			uint64_t t = ((numer - q) >> 1) + q;
			return t >> (more & LIBDIVIDE_64_SHIFT_MASK);
		}
		else
		{
			// All upper bits are 0,
			// don't need to mask them off.
			return q >> more;
		}
	}
}

uint64_t libdivide_u64_branchfree_do(
	uint64_t numer, const struct libdivide_u64_branchfree_t *denom)
{
	uint64_t q = libdivide_mullhi_u64(denom->magic, numer);
	uint64_t t = ((numer - q) >> 1) + q;
	return t >> denom->more;
}

uint64_t libdivide_u64_recover(const struct libdivide_u64_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;

	if (!denom->magic)
	{
		return (uint64_t)1 << shift;
	}
	else if (!(more & LIBDIVIDE_ADD_MARKER))
	{
		// We compute q = n/d = n*m / 2^(64 + shift)
		// Therefore we have d = 2^(64 + shift) / m
		// We need to ceil it.
		// We know d is not a power of 2, so m is not a power of 2,
		// so we can just add 1 to the floor
		uint64_t hi_dividend = (uint64_t)1 << shift;
		uint64_t rem_ignored;
		return 1 + libdivide_128_div_64_to_64(hi_dividend, 0, denom->magic, &rem_ignored);
	}
	else
	{
		// Here we wish to compute d = 2^(64+shift+1)/(m+2^64).
		// Notice (m + 2^64) is a 65 bit number. This gets hairy. See
		// libdivide_u32_recover for more on what we do here.
		// TODO: do something better than 128 bit math

		// Full n is a (potentially) 129 bit value
		// half_n is a 128 bit value
		// Compute the hi half of half_n. Low half is 0.
		uint64_t half_n_hi = (uint64_t)1 << shift, half_n_lo = 0;
		// d is a 65 bit value. The high bit is always set to 1.
		const uint64_t d_hi = 1, d_lo = denom->magic;
		// Note that the quotient is guaranteed <= 64 bits,
		// but the remainder may need 65!
		uint64_t r_hi, r_lo;
		uint64_t half_q =
			libdivide_128_div_128_to_64(half_n_hi, half_n_lo, d_hi, d_lo, &r_hi, &r_lo);
		// We computed 2^(64+shift)/(m+2^64)
		// Double the remainder ('dr') and check if that is larger than d
		// Note that d is a 65 bit value, so r1 is small and so r1 + r1
		// cannot overflow
		uint64_t dr_lo = r_lo + r_lo;
		uint64_t dr_hi = r_hi + r_hi + (dr_lo < r_lo);  // last term is carry
		int dr_exceeds_d = (dr_hi > d_hi) || (dr_hi == d_hi && dr_lo >= d_lo);
		uint64_t full_q = half_q + half_q + (dr_exceeds_d ? 1 : 0);
		return full_q + 1;
	}
}

uint64_t libdivide_u64_branchfree_recover(const struct libdivide_u64_branchfree_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;

	if (!denom->magic)
	{
		return (uint64_t)1 << (shift + 1);
	}
	else
	{
		// Here we wish to compute d = 2^(64+shift+1)/(m+2^64).
		// Notice (m + 2^64) is a 65 bit number. This gets hairy. See
		// libdivide_u32_recover for more on what we do here.
		// TODO: do something better than 128 bit math

		// Full n is a (potentially) 129 bit value
		// half_n is a 128 bit value
		// Compute the hi half of half_n. Low half is 0.
		uint64_t half_n_hi = (uint64_t)1 << shift, half_n_lo = 0;
		// d is a 65 bit value. The high bit is always set to 1.
		const uint64_t d_hi = 1, d_lo = denom->magic;
		// Note that the quotient is guaranteed <= 64 bits,
		// but the remainder may need 65!
		uint64_t r_hi, r_lo;
		uint64_t half_q =
			libdivide_128_div_128_to_64(half_n_hi, half_n_lo, d_hi, d_lo, &r_hi, &r_lo);
		// We computed 2^(64+shift)/(m+2^64)
		// Double the remainder ('dr') and check if that is larger than d
		// Note that d is a 65 bit value, so r1 is small and so r1 + r1
		// cannot overflow
		uint64_t dr_lo = r_lo + r_lo;
		uint64_t dr_hi = r_hi + r_hi + (dr_lo < r_lo);  // last term is carry
		int dr_exceeds_d = (dr_hi > d_hi) || (dr_hi == d_hi && dr_lo >= d_lo);
		uint64_t full_q = half_q + half_q + (dr_exceeds_d ? 1 : 0);
		return full_q + 1;
	}
}

/////////// SINT16

static LIBDIVIDE_INLINE struct libdivide_s16_t libdivide_internal_s16_gen(
	int16_t d, int branchfree)
{
	if (d == 0)
	{
		LIBDIVIDE_ERROR("divider must be != 0");
	}

	struct libdivide_s16_t result;

	// If d is a power of 2, or negative a power of 2, we have to use a shift.
	// This is especially important because the magic algorithm fails for -1.
	// To check if d is a power of 2 or its inverse, it suffices to check
	// whether its absolute value has exactly one bit set. This works even for
	// INT_MIN, because abs(INT_MIN) == INT_MIN, and INT_MIN has one bit set
	// and is a power of 2.
	uint16_t ud = (uint16_t)d;
	uint16_t absD = (d < 0) ? -ud : ud;
	uint16_t floor_log_2_d = 15 - libdivide_count_leading_zeros16(absD);
	// check if exactly one bit is set,
	// don't care if absD is 0 since that's divide by zero
	if ((absD & (absD - 1)) == 0)
	{
		// Branchfree and normal paths are exactly the same
		result.magic = 0;
		result.more = (uint8_t)(floor_log_2_d | (d < 0 ? LIBDIVIDE_NEGATIVE_DIVISOR : 0));
	}
	else
	{
		LIBDIVIDE_ASSERT(floor_log_2_d >= 1);

		uint8_t more;
		// the dividend here is 2**(floor_log_2_d + 31), so the low 16 bit word
		// is 0 and the high word is floor_log_2_d - 1
		uint16_t rem, proposed_m;
		proposed_m = libdivide_32_div_16_to_16((uint16_t)1 << (floor_log_2_d - 1), 0, absD, &rem);
		const uint16_t e = absD - rem;

		// We are going to start with a power of floor_log_2_d - 1.
		// This works if works if e < 2**floor_log_2_d.
		if (!branchfree && e < ((uint16_t)1 << floor_log_2_d))
		{
			// This power works
			more = (uint8_t)(floor_log_2_d - 1);
		}
		else
		{
			// We need to go one higher. This should not make proposed_m
			// overflow, but it will make it negative when interpreted as an
			// int16_t.
			proposed_m += proposed_m;
			const uint16_t twice_rem = rem + rem;
			if (twice_rem >= absD || twice_rem < rem) proposed_m += 1;
			more = (uint8_t)(floor_log_2_d | LIBDIVIDE_ADD_MARKER);
		}

		proposed_m += 1;
		int16_t magic = (int16_t)proposed_m;

		// Mark if we are negative. Note we only negate the magic number in the
		// branchfull case.
		if (d < 0)
		{
			more |= LIBDIVIDE_NEGATIVE_DIVISOR;
			if (!branchfree)
			{
				magic = -magic;
			}
		}

		result.more = more;
		result.magic = magic;
	}
	return result;
}

struct libdivide_s16_t libdivide_s16_gen(int16_t d)
{
	return libdivide_internal_s16_gen(d, 0);
}

struct libdivide_s16_branchfree_t libdivide_s16_branchfree_gen(int16_t d)
{
	struct libdivide_s16_t tmp = libdivide_internal_s16_gen(d, 1);
	struct libdivide_s16_branchfree_t result = {tmp.magic, tmp.more};
	return result;
}

// The original libdivide_s16_do takes a const pointer. However, this cannot be used
// with a compile time constant libdivide_s16_t: it will generate a warning about
// taking the address of a temporary. Hence this overload.
int16_t libdivide_s16_do_raw(int16_t numer, int16_t magic, uint8_t more)
{
	uint8_t shift = more & LIBDIVIDE_16_SHIFT_MASK;

	if (!magic)
	{
		uint16_t sign = (int8_t)more >> 7;
		uint16_t mask = ((uint16_t)1 << shift) - 1;
		uint16_t uq = numer + ((numer >> 15) & mask);
		int16_t q = (int16_t)uq;
		q >>= shift;
		q = (q ^ sign) - sign;
		return q;
	}
	else
	{
		uint16_t uq = (uint16_t)libdivide_mullhi_s16(magic, numer);
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift and then sign extend
			int16_t sign = (int8_t)more >> 7;
			// q += (more < 0 ? -numer : numer)
			// cast required to avoid UB
			uq += ((uint16_t)numer ^ sign) - sign;
		}
		int16_t q = (int16_t)uq;
		q >>= shift;
		q += (q < 0);
		return q;
	}
}

int16_t libdivide_s16_do(int16_t numer, const struct libdivide_s16_t *denom)
{
	return libdivide_s16_do_raw(numer, denom->magic, denom->more);
}

int16_t libdivide_s16_branchfree_do(int16_t numer, const struct libdivide_s16_branchfree_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_16_SHIFT_MASK;
	// must be arithmetic shift and then sign extend
	int16_t sign = (int8_t)more >> 7;
	int16_t magic = denom->magic;
	int16_t q = libdivide_mullhi_s16(magic, numer);
	q += numer;

	// If q is non-negative, we have nothing to do
	// If q is negative, we want to add either (2**shift)-1 if d is a power of
	// 2, or (2**shift) if it is not a power of 2
	uint16_t is_power_of_2 = (magic == 0);
	uint16_t q_sign = (uint16_t)(q >> 15);
	q += q_sign & (((uint16_t)1 << shift) - is_power_of_2);

	// Now arithmetic right shift
	q >>= shift;
	// Negate if needed
	q = (q ^ sign) - sign;

	return q;
}

int16_t libdivide_s16_recover(const struct libdivide_s16_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_16_SHIFT_MASK;
	if (!denom->magic)
	{
		uint16_t absD = (uint16_t)1 << shift;
		if (more & LIBDIVIDE_NEGATIVE_DIVISOR)
		{
			absD = -absD;
		}
		return (int16_t)absD;
	}
	else
	{
		// Unsigned math is much easier
		// We negate the magic number only in the branchfull case, and we don't
		// know which case we're in. However we have enough information to
		// determine the correct sign of the magic number. The divisor was
		// negative if LIBDIVIDE_NEGATIVE_DIVISOR is set. If ADD_MARKER is set,
		// the magic number's sign is opposite that of the divisor.
		// We want to compute the positive magic number.
		int negative_divisor = (more & LIBDIVIDE_NEGATIVE_DIVISOR);
		int magic_was_negated = (more & LIBDIVIDE_ADD_MARKER) ? denom->magic > 0 : denom->magic < 0;

		// Handle the power of 2 case (including branchfree)
		if (denom->magic == 0)
		{
			int16_t result = (uint16_t)1 << shift;
			return negative_divisor ? -result : result;
		}

		uint16_t d = (uint16_t)(magic_was_negated ? -denom->magic : denom->magic);
		uint32_t n = (uint32_t)1 << (16 + shift);  // this shift cannot exceed 30
		uint16_t q = (uint16_t)(n / d);
		int16_t result = (int16_t)q;
		result += 1;
		return negative_divisor ? -result : result;
	}
}

int16_t libdivide_s16_branchfree_recover(const struct libdivide_s16_branchfree_t *denom)
{
	return libdivide_s16_recover((const struct libdivide_s16_t *)denom);
}

/////////// SINT32

static LIBDIVIDE_INLINE struct libdivide_s32_t libdivide_internal_s32_gen(
	int32_t d, int branchfree)
{
	if (d == 0)
	{
		LIBDIVIDE_ERROR("divider must be != 0");
	}

	struct libdivide_s32_t result;

	// If d is a power of 2, or negative a power of 2, we have to use a shift.
	// This is especially important because the magic algorithm fails for -1.
	// To check if d is a power of 2 or its inverse, it suffices to check
	// whether its absolute value has exactly one bit set. This works even for
	// INT_MIN, because abs(INT_MIN) == INT_MIN, and INT_MIN has one bit set
	// and is a power of 2.
	uint32_t ud = (uint32_t)d;
	uint32_t absD = (d < 0) ? -ud : ud;
	uint32_t floor_log_2_d = 31 - libdivide_count_leading_zeros32(absD);
	// check if exactly one bit is set,
	// don't care if absD is 0 since that's divide by zero
	if ((absD & (absD - 1)) == 0)
	{
		// Branchfree and normal paths are exactly the same
		result.magic = 0;
		result.more = (uint8_t)(floor_log_2_d | (d < 0 ? LIBDIVIDE_NEGATIVE_DIVISOR : 0));
	}
	else
	{
		LIBDIVIDE_ASSERT(floor_log_2_d >= 1);

		uint8_t more;
		// the dividend here is 2**(floor_log_2_d + 31), so the low 32 bit word
		// is 0 and the high word is floor_log_2_d - 1
		uint32_t rem, proposed_m;
		proposed_m = libdivide_64_div_32_to_32((uint32_t)1 << (floor_log_2_d - 1), 0, absD, &rem);
		const uint32_t e = absD - rem;

		// We are going to start with a power of floor_log_2_d - 1.
		// This works if works if e < 2**floor_log_2_d.
		if (!branchfree && e < ((uint32_t)1 << floor_log_2_d))
		{
			// This power works
			more = (uint8_t)(floor_log_2_d - 1);
		}
		else
		{
			// We need to go one higher. This should not make proposed_m
			// overflow, but it will make it negative when interpreted as an
			// int32_t.
			proposed_m += proposed_m;
			const uint32_t twice_rem = rem + rem;
			if (twice_rem >= absD || twice_rem < rem) proposed_m += 1;
			more = (uint8_t)(floor_log_2_d | LIBDIVIDE_ADD_MARKER);
		}

		proposed_m += 1;
		int32_t magic = (int32_t)proposed_m;

		// Mark if we are negative. Note we only negate the magic number in the
		// branchfull case.
		if (d < 0)
		{
			more |= LIBDIVIDE_NEGATIVE_DIVISOR;
			if (!branchfree)
			{
				magic = -magic;
			}
		}

		result.more = more;
		result.magic = magic;
	}
	return result;
}

struct libdivide_s32_t libdivide_s32_gen(int32_t d)
{
	return libdivide_internal_s32_gen(d, 0);
}

struct libdivide_s32_branchfree_t libdivide_s32_branchfree_gen(int32_t d)
{
	struct libdivide_s32_t tmp = libdivide_internal_s32_gen(d, 1);
	struct libdivide_s32_branchfree_t result = {tmp.magic, tmp.more};
	return result;
}

int32_t libdivide_s32_do(int32_t numer, const struct libdivide_s32_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;

	if (!denom->magic)
	{
		uint32_t sign = (int8_t)more >> 7;
		uint32_t mask = ((uint32_t)1 << shift) - 1;
		uint32_t uq = numer + ((numer >> 31) & mask);
		int32_t q = (int32_t)uq;
		q >>= shift;
		q = (q ^ sign) - sign;
		return q;
	}
	else
	{
		uint32_t uq = (uint32_t)libdivide_mullhi_s32(denom->magic, numer);
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift and then sign extend
			int32_t sign = (int8_t)more >> 7;
			// q += (more < 0 ? -numer : numer)
			// cast required to avoid UB
			uq += ((uint32_t)numer ^ sign) - sign;
		}
		int32_t q = (int32_t)uq;
		q >>= shift;
		q += (q < 0);
		return q;
	}
}

int32_t libdivide_s32_branchfree_do(int32_t numer, const struct libdivide_s32_branchfree_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
	// must be arithmetic shift and then sign extend
	int32_t sign = (int8_t)more >> 7;
	int32_t magic = denom->magic;
	int32_t q = libdivide_mullhi_s32(magic, numer);
	q += numer;

	// If q is non-negative, we have nothing to do
	// If q is negative, we want to add either (2**shift)-1 if d is a power of
	// 2, or (2**shift) if it is not a power of 2
	uint32_t is_power_of_2 = (magic == 0);
	uint32_t q_sign = (uint32_t)(q >> 31);
	q += q_sign & (((uint32_t)1 << shift) - is_power_of_2);

	// Now arithmetic right shift
	q >>= shift;
	// Negate if needed
	q = (q ^ sign) - sign;

	return q;
}

int32_t libdivide_s32_recover(const struct libdivide_s32_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
	if (!denom->magic)
	{
		uint32_t absD = (uint32_t)1 << shift;
		if (more & LIBDIVIDE_NEGATIVE_DIVISOR)
		{
			absD = -absD;
		}
		return (int32_t)absD;
	}
	else
	{
		// Unsigned math is much easier
		// We negate the magic number only in the branchfull case, and we don't
		// know which case we're in. However we have enough information to
		// determine the correct sign of the magic number. The divisor was
		// negative if LIBDIVIDE_NEGATIVE_DIVISOR is set. If ADD_MARKER is set,
		// the magic number's sign is opposite that of the divisor.
		// We want to compute the positive magic number.
		int negative_divisor = (more & LIBDIVIDE_NEGATIVE_DIVISOR);
		int magic_was_negated = (more & LIBDIVIDE_ADD_MARKER) ? denom->magic > 0 : denom->magic < 0;

		// Handle the power of 2 case (including branchfree)
		if (denom->magic == 0)
		{
			int32_t result = (uint32_t)1 << shift;
			return negative_divisor ? -result : result;
		}

		uint32_t d = (uint32_t)(magic_was_negated ? -denom->magic : denom->magic);
		uint64_t n = (uint64_t)1 << (32 + shift);  // this shift cannot exceed 30
		uint32_t q = (uint32_t)(n / d);
		int32_t result = (int32_t)q;
		result += 1;
		return negative_divisor ? -result : result;
	}
}

int32_t libdivide_s32_branchfree_recover(const struct libdivide_s32_branchfree_t *denom)
{
	return libdivide_s32_recover((const struct libdivide_s32_t *)denom);
}

///////////// SINT64

static LIBDIVIDE_INLINE struct libdivide_s64_t libdivide_internal_s64_gen(
	int64_t d, int branchfree)
{
	if (d == 0)
	{
		LIBDIVIDE_ERROR("divider must be != 0");
	}

	struct libdivide_s64_t result;

	// If d is a power of 2, or negative a power of 2, we have to use a shift.
	// This is especially important because the magic algorithm fails for -1.
	// To check if d is a power of 2 or its inverse, it suffices to check
	// whether its absolute value has exactly one bit set.  This works even for
	// INT_MIN, because abs(INT_MIN) == INT_MIN, and INT_MIN has one bit set
	// and is a power of 2.
	uint64_t ud = (uint64_t)d;
	uint64_t absD = (d < 0) ? -ud : ud;
	uint32_t floor_log_2_d = 63 - libdivide_count_leading_zeros64(absD);
	// check if exactly one bit is set,
	// don't care if absD is 0 since that's divide by zero
	if ((absD & (absD - 1)) == 0)
	{
		// Branchfree and non-branchfree cases are the same
		result.magic = 0;
		result.more = (uint8_t)(floor_log_2_d | (d < 0 ? LIBDIVIDE_NEGATIVE_DIVISOR : 0));
	}
	else
	{
		// the dividend here is 2**(floor_log_2_d + 63), so the low 64 bit word
		// is 0 and the high word is floor_log_2_d - 1
		uint8_t more;
		uint64_t rem, proposed_m;
		proposed_m = libdivide_128_div_64_to_64((uint64_t)1 << (floor_log_2_d - 1), 0, absD, &rem);
		const uint64_t e = absD - rem;

		// We are going to start with a power of floor_log_2_d - 1.
		// This works if works if e < 2**floor_log_2_d.
		if (!branchfree && e < ((uint64_t)1 << floor_log_2_d))
		{
			// This power works
			more = (uint8_t)(floor_log_2_d - 1);
		}
		else
		{
			// We need to go one higher. This should not make proposed_m
			// overflow, but it will make it negative when interpreted as an
			// int32_t.
			proposed_m += proposed_m;
			const uint64_t twice_rem = rem + rem;
			if (twice_rem >= absD || twice_rem < rem) proposed_m += 1;
			// note that we only set the LIBDIVIDE_NEGATIVE_DIVISOR bit if we
			// also set ADD_MARKER this is an annoying optimization that
			// enables algorithm #4 to avoid the mask. However we always set it
			// in the branchfree case
			more = (uint8_t)(floor_log_2_d | LIBDIVIDE_ADD_MARKER);
		}
		proposed_m += 1;
		int64_t magic = (int64_t)proposed_m;

		// Mark if we are negative
		if (d < 0)
		{
			more |= LIBDIVIDE_NEGATIVE_DIVISOR;
			if (!branchfree)
			{
				magic = -magic;
			}
		}

		result.more = more;
		result.magic = magic;
	}
	return result;
}

struct libdivide_s64_t libdivide_s64_gen(int64_t d)
{
	return libdivide_internal_s64_gen(d, 0);
}

struct libdivide_s64_branchfree_t libdivide_s64_branchfree_gen(int64_t d)
{
	struct libdivide_s64_t tmp = libdivide_internal_s64_gen(d, 1);
	struct libdivide_s64_branchfree_t ret = {tmp.magic, tmp.more};
	return ret;
}

int64_t libdivide_s64_do(int64_t numer, const struct libdivide_s64_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;

	if (!denom->magic)    // shift path
	{
		uint64_t mask = ((uint64_t)1 << shift) - 1;
		uint64_t uq = numer + ((numer >> 63) & mask);
		int64_t q = (int64_t)uq;
		q >>= shift;
		// must be arithmetic shift and then sign-extend
		int64_t sign = (int8_t)more >> 7;
		q = (q ^ sign) - sign;
		return q;
	}
	else
	{
		uint64_t uq = (uint64_t)libdivide_mullhi_s64(denom->magic, numer);
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift and then sign extend
			int64_t sign = (int8_t)more >> 7;
			// q += (more < 0 ? -numer : numer)
			// cast required to avoid UB
			uq += ((uint64_t)numer ^ sign) - sign;
		}
		int64_t q = (int64_t)uq;
		q >>= shift;
		q += (q < 0);
		return q;
	}
}

int64_t libdivide_s64_branchfree_do(int64_t numer, const struct libdivide_s64_branchfree_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
	// must be arithmetic shift and then sign extend
	int64_t sign = (int8_t)more >> 7;
	int64_t magic = denom->magic;
	int64_t q = libdivide_mullhi_s64(magic, numer);
	q += numer;

	// If q is non-negative, we have nothing to do.
	// If q is negative, we want to add either (2**shift)-1 if d is a power of
	// 2, or (2**shift) if it is not a power of 2.
	uint64_t is_power_of_2 = (magic == 0);
	uint64_t q_sign = (uint64_t)(q >> 63);
	q += q_sign & (((uint64_t)1 << shift) - is_power_of_2);

	// Arithmetic right shift
	q >>= shift;
	// Negate if needed
	q = (q ^ sign) - sign;

	return q;
}

int64_t libdivide_s64_recover(const struct libdivide_s64_t *denom)
{
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
	if (denom->magic == 0)    // shift path
	{
		uint64_t absD = (uint64_t)1 << shift;
		if (more & LIBDIVIDE_NEGATIVE_DIVISOR)
		{
			absD = -absD;
		}
		return (int64_t)absD;
	}
	else
	{
		// Unsigned math is much easier
		int negative_divisor = (more & LIBDIVIDE_NEGATIVE_DIVISOR);
		int magic_was_negated = (more & LIBDIVIDE_ADD_MARKER) ? denom->magic > 0 : denom->magic < 0;

		uint64_t d = (uint64_t)(magic_was_negated ? -denom->magic : denom->magic);
		uint64_t n_hi = (uint64_t)1 << shift, n_lo = 0;
		uint64_t rem_ignored;
		uint64_t q = libdivide_128_div_64_to_64(n_hi, n_lo, d, &rem_ignored);
		int64_t result = (int64_t)(q + 1);
		if (negative_divisor)
		{
			result = -result;
		}
		return result;
	}
}

int64_t libdivide_s64_branchfree_recover(const struct libdivide_s64_branchfree_t *denom)
{
	return libdivide_s64_recover((const struct libdivide_s64_t *)denom);
}

// Simplest possible vector type division: treat the vector type as an array
// of underlying native type.
//
// Use a union to read a vector via pointer-to-integer, without violating strict
// aliasing.
#define SIMPLE_VECTOR_DIVISION(IntT, VecT, Algo)                          \
    const size_t count = sizeof(VecT) / sizeof(IntT);                     \
    union type_pun_vec {                                                  \
        VecT vec;                                                         \
        IntT arr[sizeof(VecT) / sizeof(IntT)];                            \
    };                                                                    \
    union type_pun_vec result;                                            \
    union type_pun_vec input;                                             \
    input.vec = numers;                                                   \
    for (size_t loop = 0; loop < count; ++loop) {                         \
        result.arr[loop] = libdivide_##Algo##_do(input.arr[loop], denom); \
    }                                                                     \
    return result.vec;

#if defined(LIBDIVIDE_NEON)

static LIBDIVIDE_INLINE uint16x8_t libdivide_u16_do_vec128(
	uint16x8_t numers, const struct libdivide_u16_t *denom);
static LIBDIVIDE_INLINE int16x8_t libdivide_s16_do_vec128(
	int16x8_t numers, const struct libdivide_s16_t *denom);
static LIBDIVIDE_INLINE uint32x4_t libdivide_u32_do_vec128(
	uint32x4_t numers, const struct libdivide_u32_t *denom);
static LIBDIVIDE_INLINE int32x4_t libdivide_s32_do_vec128(
	int32x4_t numers, const struct libdivide_s32_t *denom);
static LIBDIVIDE_INLINE uint64x2_t libdivide_u64_do_vec128(
	uint64x2_t numers, const struct libdivide_u64_t *denom);
static LIBDIVIDE_INLINE int64x2_t libdivide_s64_do_vec128(
	int64x2_t numers, const struct libdivide_s64_t *denom);

static LIBDIVIDE_INLINE uint16x8_t libdivide_u16_branchfree_do_vec128(
	uint16x8_t numers, const struct libdivide_u16_branchfree_t *denom);
static LIBDIVIDE_INLINE int16x8_t libdivide_s16_branchfree_do_vec128(
	int16x8_t numers, const struct libdivide_s16_branchfree_t *denom);
static LIBDIVIDE_INLINE uint32x4_t libdivide_u32_branchfree_do_vec128(
	uint32x4_t numers, const struct libdivide_u32_branchfree_t *denom);
static LIBDIVIDE_INLINE int32x4_t libdivide_s32_branchfree_do_vec128(
	int32x4_t numers, const struct libdivide_s32_branchfree_t *denom);
static LIBDIVIDE_INLINE uint64x2_t libdivide_u64_branchfree_do_vec128(
	uint64x2_t numers, const struct libdivide_u64_branchfree_t *denom);
static LIBDIVIDE_INLINE int64x2_t libdivide_s64_branchfree_do_vec128(
	int64x2_t numers, const struct libdivide_s64_branchfree_t *denom);

//////// Internal Utility Functions

// Logical right shift by runtime value.
// NEON implements right shift as left shits by negative values.
static LIBDIVIDE_INLINE uint32x4_t libdivide_u32_neon_srl(uint32x4_t v, uint8_t amt)
{
	int32_t wamt = (int32_t)(amt);
	return vshlq_u32(v, vdupq_n_s32(-wamt));
}

static LIBDIVIDE_INLINE uint64x2_t libdivide_u64_neon_srl(uint64x2_t v, uint8_t amt)
{
	int64_t wamt = (int64_t)(amt);
	return vshlq_u64(v, vdupq_n_s64(-wamt));
}

// Arithmetic right shift by runtime value.
static LIBDIVIDE_INLINE int32x4_t libdivide_s32_neon_sra(int32x4_t v, uint8_t amt)
{
	int32_t wamt = (int32_t)(amt);
	return vshlq_s32(v, vdupq_n_s32(-wamt));
}

static LIBDIVIDE_INLINE int64x2_t libdivide_s64_neon_sra(int64x2_t v, uint8_t amt)
{
	int64_t wamt = (int64_t)(amt);
	return vshlq_s64(v, vdupq_n_s64(-wamt));
}

static LIBDIVIDE_INLINE int64x2_t libdivide_s64_signbits(int64x2_t v)
{
	return vshrq_n_s64(v, 63);
}

static LIBDIVIDE_INLINE uint32x4_t libdivide_mullhi_u32_vec128(uint32x4_t a, uint32_t b)
{
	// Desire is [x0, x1, x2, x3]
	uint32x4_t w1 = vreinterpretq_u32_u64(vmull_n_u32(vget_low_u32(a), b));  // [_, x0, _, x1]
	uint32x4_t w2 = vreinterpretq_u32_u64(vmull_high_n_u32(a, b));           //[_, x2, _, x3]
	return vuzp2q_u32(w1, w2);                                               // [x0, x1, x2, x3]
}

static LIBDIVIDE_INLINE int32x4_t libdivide_mullhi_s32_vec128(int32x4_t a, int32_t b)
{
	int32x4_t w1 = vreinterpretq_s32_s64(vmull_n_s32(vget_low_s32(a), b));  // [_, x0, _, x1]
	int32x4_t w2 = vreinterpretq_s32_s64(vmull_high_n_s32(a, b));           //[_, x2, _, x3]
	return vuzp2q_s32(w1, w2);                                              // [x0, x1, x2, x3]
}

static LIBDIVIDE_INLINE uint64x2_t libdivide_mullhi_u64_vec128(uint64x2_t x, uint64_t sy)
{
	// full 128 bits product is:
	// x0*y0 + (x0*y1 << 32) + (x1*y0 << 32) + (x1*y1 << 64)
	// Note x0,y0,x1,y1 are all conceptually uint32, products are 32x32->64.

	// Get low and high words. x0 contains low 32 bits, x1 is high 32 bits.
	uint64x2_t y = vdupq_n_u64(sy);
	uint32x2_t x0 = vmovn_u64(x);
	uint32x2_t y0 = vmovn_u64(y);
	uint32x2_t x1 = vshrn_n_u64(x, 32);
	uint32x2_t y1 = vshrn_n_u64(y, 32);

	// Compute x0*y0.
	uint64x2_t x0y0 = vmull_u32(x0, y0);
	uint64x2_t x0y0_hi = vshrq_n_u64(x0y0, 32);

	// Compute other intermediate products.
	uint64x2_t temp = vmlal_u32(x0y0_hi, x1, y0);  // temp = x0y0_hi + x1*y0;
	// We want to split temp into its low 32 bits and high 32 bits, both
	// in the low half of 64 bit registers.
	// Use shifts to avoid needing a reg for the mask.
	uint64x2_t temp_lo = vshrq_n_u64(vshlq_n_u64(temp, 32), 32);  // temp_lo = temp & 0xFFFFFFFF;
	uint64x2_t temp_hi = vshrq_n_u64(temp, 32);                   // temp_hi = temp >> 32;

	temp_lo = vmlal_u32(temp_lo, x0, y1);  // temp_lo += x0*y0
	temp_lo = vshrq_n_u64(temp_lo, 32);    // temp_lo >>= 32
	temp_hi = vmlal_u32(temp_hi, x1, y1);  // temp_hi += x1*y1
	uint64x2_t result = vaddq_u64(temp_hi, temp_lo);
	return result;
}

static LIBDIVIDE_INLINE int64x2_t libdivide_mullhi_s64_vec128(int64x2_t x, int64_t sy)
{
	int64x2_t p = vreinterpretq_s64_u64(
					  libdivide_mullhi_u64_vec128(vreinterpretq_u64_s64(x), (uint64_t)(sy)));
	int64x2_t y = vdupq_n_s64(sy);
	int64x2_t t1 = vandq_s64(libdivide_s64_signbits(x), y);
	int64x2_t t2 = vandq_s64(libdivide_s64_signbits(y), x);
	p = vsubq_s64(p, t1);
	p = vsubq_s64(p, t2);
	return p;
}

////////// UINT16

uint16x8_t libdivide_u16_do_vec128(uint16x8_t numers, const struct libdivide_u16_t *denom)
{
	SIMPLE_VECTOR_DIVISION(uint16_t, uint16x8_t, u16)
}

uint16x8_t libdivide_u16_branchfree_do_vec128(
	uint16x8_t numers, const struct libdivide_u16_branchfree_t *denom)
{
	SIMPLE_VECTOR_DIVISION(uint16_t, uint16x8_t, u16_branchfree)
}

////////// UINT32

uint32x4_t libdivide_u32_do_vec128(uint32x4_t numers, const struct libdivide_u32_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		return libdivide_u32_neon_srl(numers, more);
	}
	else
	{
		uint32x4_t q = libdivide_mullhi_u32_vec128(numers, denom->magic);
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// uint32_t t = ((numer - q) >> 1) + q;
			// return t >> denom->shift;
			// Note we can use halving-subtract to avoid the shift.
			uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
			uint32x4_t t = vaddq_u32(vhsubq_u32(numers, q), q);
			return libdivide_u32_neon_srl(t, shift);
		}
		else
		{
			return libdivide_u32_neon_srl(q, more);
		}
	}
}

uint32x4_t libdivide_u32_branchfree_do_vec128(
	uint32x4_t numers, const struct libdivide_u32_branchfree_t *denom)
{
	uint32x4_t q = libdivide_mullhi_u32_vec128(numers, denom->magic);
	uint32x4_t t = vaddq_u32(vhsubq_u32(numers, q), q);
	return libdivide_u32_neon_srl(t, denom->more);
}

////////// UINT64

uint64x2_t libdivide_u64_do_vec128(uint64x2_t numers, const struct libdivide_u64_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		return libdivide_u64_neon_srl(numers, more);
	}
	else
	{
		uint64x2_t q = libdivide_mullhi_u64_vec128(numers, denom->magic);
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// uint32_t t = ((numer - q) >> 1) + q;
			// return t >> denom->shift;
			// No 64-bit halving subtracts in NEON :(
			uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
			uint64x2_t t = vaddq_u64(vshrq_n_u64(vsubq_u64(numers, q), 1), q);
			return libdivide_u64_neon_srl(t, shift);
		}
		else
		{
			return libdivide_u64_neon_srl(q, more);
		}
	}
}

uint64x2_t libdivide_u64_branchfree_do_vec128(
	uint64x2_t numers, const struct libdivide_u64_branchfree_t *denom)
{
	uint64x2_t q = libdivide_mullhi_u64_vec128(numers, denom->magic);
	uint64x2_t t = vaddq_u64(vshrq_n_u64(vsubq_u64(numers, q), 1), q);
	return libdivide_u64_neon_srl(t, denom->more);
}

////////// SINT16

int16x8_t libdivide_s16_do_vec128(int16x8_t numers, const struct libdivide_s16_t *denom)
{
	SIMPLE_VECTOR_DIVISION(int16_t, int16x8_t, s16)
}

int16x8_t libdivide_s16_branchfree_do_vec128(
	int16x8_t numers, const struct libdivide_s16_branchfree_t *denom)
{
	SIMPLE_VECTOR_DIVISION(int16_t, int16x8_t, s16_branchfree)
}

////////// SINT32

int32x4_t libdivide_s32_do_vec128(int32x4_t numers, const struct libdivide_s32_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
		uint32_t mask = ((uint32_t)1 << shift) - 1;
		int32x4_t roundToZeroTweak = vdupq_n_s32((int)mask);
		// q = numer + ((numer >> 31) & roundToZeroTweak);
		int32x4_t q = vaddq_s32(numers, vandq_s32(vshrq_n_s32(numers, 31), roundToZeroTweak));
		q = libdivide_s32_neon_sra(q, shift);
		int32x4_t sign = vdupq_n_s32((int8_t)more >> 7);
		// q = (q ^ sign) - sign;
		q = vsubq_s32(veorq_s32(q, sign), sign);
		return q;
	}
	else
	{
		int32x4_t q = libdivide_mullhi_s32_vec128(numers, denom->magic);
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift
			int32x4_t sign = vdupq_n_s32((int8_t)more >> 7);
			// q += ((numer ^ sign) - sign);
			q = vaddq_s32(q, vsubq_s32(veorq_s32(numers, sign), sign));
		}
		// q >>= shift
		q = libdivide_s32_neon_sra(q, more & LIBDIVIDE_32_SHIFT_MASK);
		q = vaddq_s32(
				q, vreinterpretq_s32_u32(vshrq_n_u32(vreinterpretq_u32_s32(q), 31)));  // q += (q < 0)
		return q;
	}
}

int32x4_t libdivide_s32_branchfree_do_vec128(
	int32x4_t numers, const struct libdivide_s32_branchfree_t *denom)
{
	int32_t magic = denom->magic;
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
	// must be arithmetic shift
	int32x4_t sign = vdupq_n_s32((int8_t)more >> 7);
	int32x4_t q = libdivide_mullhi_s32_vec128(numers, magic);
	q = vaddq_s32(q, numers);  // q += numers

	// If q is non-negative, we have nothing to do
	// If q is negative, we want to add either (2**shift)-1 if d is
	// a power of 2, or (2**shift) if it is not a power of 2
	uint32_t is_power_of_2 = (magic == 0);
	int32x4_t q_sign = vshrq_n_s32(q, 31);  // q_sign = q >> 31
	int32x4_t mask = vdupq_n_s32(((uint32_t)1 << shift) - is_power_of_2);
	q = vaddq_s32(q, vandq_s32(q_sign, mask));  // q = q + (q_sign & mask)
	q = libdivide_s32_neon_sra(q, shift);       // q >>= shift
	q = vsubq_s32(veorq_s32(q, sign), sign);    // q = (q ^ sign) - sign
	return q;
}

////////// SINT64

int64x2_t libdivide_s64_do_vec128(int64x2_t numers, const struct libdivide_s64_t *denom)
{
	uint8_t more = denom->more;
	int64_t magic = denom->magic;
	if (magic == 0)    // shift path
	{
		uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
		uint64_t mask = ((uint64_t)1 << shift) - 1;
		int64x2_t roundToZeroTweak = vdupq_n_s64(mask);  // TODO: no need to sign extend
		// q = numer + ((numer >> 63) & roundToZeroTweak);
		int64x2_t q =
			vaddq_s64(numers, vandq_s64(libdivide_s64_signbits(numers), roundToZeroTweak));
		q = libdivide_s64_neon_sra(q, shift);
		// q = (q ^ sign) - sign;
		int64x2_t sign = vreinterpretq_s64_s8(vdupq_n_s8((int8_t)more >> 7));
		q = vsubq_s64(veorq_s64(q, sign), sign);
		return q;
	}
	else
	{
		int64x2_t q = libdivide_mullhi_s64_vec128(numers, magic);
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift
			int64x2_t sign = vdupq_n_s64((int8_t)more >> 7);  // TODO: no need to widen
			// q += ((numer ^ sign) - sign);
			q = vaddq_s64(q, vsubq_s64(veorq_s64(numers, sign), sign));
		}
		// q >>= denom->mult_path.shift
		q = libdivide_s64_neon_sra(q, more & LIBDIVIDE_64_SHIFT_MASK);
		q = vaddq_s64(
				q, vreinterpretq_s64_u64(vshrq_n_u64(vreinterpretq_u64_s64(q), 63)));  // q += (q < 0)
		return q;
	}
}

int64x2_t libdivide_s64_branchfree_do_vec128(
	int64x2_t numers, const struct libdivide_s64_branchfree_t *denom)
{
	int64_t magic = denom->magic;
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
	// must be arithmetic shift
	int64x2_t sign = vdupq_n_s64((int8_t)more >> 7);  // TODO: avoid sign extend

	// libdivide_mullhi_s64(numers, magic);
	int64x2_t q = libdivide_mullhi_s64_vec128(numers, magic);
	q = vaddq_s64(q, numers);  // q += numers

	// If q is non-negative, we have nothing to do.
	// If q is negative, we want to add either (2**shift)-1 if d is
	// a power of 2, or (2**shift) if it is not a power of 2.
	uint32_t is_power_of_2 = (magic == 0);
	int64x2_t q_sign = libdivide_s64_signbits(q);  // q_sign = q >> 63
	int64x2_t mask = vdupq_n_s64(((uint64_t)1 << shift) - is_power_of_2);
	q = vaddq_s64(q, vandq_s64(q_sign, mask));  // q = q + (q_sign & mask)
	q = libdivide_s64_neon_sra(q, shift);       // q >>= shift
	q = vsubq_s64(veorq_s64(q, sign), sign);    // q = (q ^ sign) - sign
	return q;
}

#endif

#if defined(LIBDIVIDE_AVX512)

static LIBDIVIDE_INLINE __m512i libdivide_u16_do_vec512(
	__m512i numers, const struct libdivide_u16_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_s16_do_vec512(
	__m512i numers, const struct libdivide_s16_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_u32_do_vec512(
	__m512i numers, const struct libdivide_u32_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_s32_do_vec512(
	__m512i numers, const struct libdivide_s32_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_u64_do_vec512(
	__m512i numers, const struct libdivide_u64_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_s64_do_vec512(
	__m512i numers, const struct libdivide_s64_t *denom);

static LIBDIVIDE_INLINE __m512i libdivide_u16_branchfree_do_vec512(
	__m512i numers, const struct libdivide_u16_branchfree_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_s16_branchfree_do_vec512(
	__m512i numers, const struct libdivide_s16_branchfree_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_u32_branchfree_do_vec512(
	__m512i numers, const struct libdivide_u32_branchfree_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_s32_branchfree_do_vec512(
	__m512i numers, const struct libdivide_s32_branchfree_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_u64_branchfree_do_vec512(
	__m512i numers, const struct libdivide_u64_branchfree_t *denom);
static LIBDIVIDE_INLINE __m512i libdivide_s64_branchfree_do_vec512(
	__m512i numers, const struct libdivide_s64_branchfree_t *denom);

//////// Internal Utility Functions

static LIBDIVIDE_INLINE __m512i libdivide_s64_signbits_vec512(__m512i v)
{
	;
	return _mm512_srai_epi64(v, 63);
}

static LIBDIVIDE_INLINE __m512i libdivide_s64_shift_right_vec512(__m512i v, int amt)
{
	return _mm512_srai_epi64(v, amt);
}

// Here, b is assumed to contain one 32-bit value repeated.
static LIBDIVIDE_INLINE __m512i libdivide_mullhi_u32_vec512(__m512i a, __m512i b)
{
	__m512i hi_product_0Z2Z = _mm512_srli_epi64(_mm512_mul_epu32(a, b), 32);
	__m512i a1X3X = _mm512_srli_epi64(a, 32);
	__m512i mask = _mm512_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0);
	__m512i hi_product_Z1Z3 = _mm512_and_si512(_mm512_mul_epu32(a1X3X, b), mask);
	return _mm512_or_si512(hi_product_0Z2Z, hi_product_Z1Z3);
}

// b is one 32-bit value repeated.
static LIBDIVIDE_INLINE __m512i libdivide_mullhi_s32_vec512(__m512i a, __m512i b)
{
	__m512i hi_product_0Z2Z = _mm512_srli_epi64(_mm512_mul_epi32(a, b), 32);
	__m512i a1X3X = _mm512_srli_epi64(a, 32);
	__m512i mask = _mm512_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0);
	__m512i hi_product_Z1Z3 = _mm512_and_si512(_mm512_mul_epi32(a1X3X, b), mask);
	return _mm512_or_si512(hi_product_0Z2Z, hi_product_Z1Z3);
}

// Here, y is assumed to contain one 64-bit value repeated.
static LIBDIVIDE_INLINE __m512i libdivide_mullhi_u64_vec512(__m512i x, __m512i y)
{
	// see m128i variant for comments.
	__m512i x0y0 = _mm512_mul_epu32(x, y);
	__m512i x0y0_hi = _mm512_srli_epi64(x0y0, 32);

	__m512i x1 = _mm512_shuffle_epi32(x, (_MM_PERM_ENUM)_MM_SHUFFLE(3, 3, 1, 1));
	__m512i y1 = _mm512_shuffle_epi32(y, (_MM_PERM_ENUM)_MM_SHUFFLE(3, 3, 1, 1));

	__m512i x0y1 = _mm512_mul_epu32(x, y1);
	__m512i x1y0 = _mm512_mul_epu32(x1, y);
	__m512i x1y1 = _mm512_mul_epu32(x1, y1);

	__m512i mask = _mm512_set1_epi64(0xFFFFFFFF);
	__m512i temp = _mm512_add_epi64(x1y0, x0y0_hi);
	__m512i temp_lo = _mm512_and_si512(temp, mask);
	__m512i temp_hi = _mm512_srli_epi64(temp, 32);

	temp_lo = _mm512_srli_epi64(_mm512_add_epi64(temp_lo, x0y1), 32);
	temp_hi = _mm512_add_epi64(x1y1, temp_hi);
	return _mm512_add_epi64(temp_lo, temp_hi);
}

// y is one 64-bit value repeated.
static LIBDIVIDE_INLINE __m512i libdivide_mullhi_s64_vec512(__m512i x, __m512i y)
{
	__m512i p = libdivide_mullhi_u64_vec512(x, y);
	__m512i t1 = _mm512_and_si512(libdivide_s64_signbits_vec512(x), y);
	__m512i t2 = _mm512_and_si512(libdivide_s64_signbits_vec512(y), x);
	p = _mm512_sub_epi64(p, t1);
	p = _mm512_sub_epi64(p, t2);
	return p;
}

////////// UINT16

__m512i libdivide_u16_do_vec512(__m512i numers, const struct libdivide_u16_t *denom)
{
	SIMPLE_VECTOR_DIVISION(uint16_t, __m512i, u16)
}

__m512i libdivide_u16_branchfree_do_vec512(
	__m512i numers, const struct libdivide_u16_branchfree_t *denom)
{
	SIMPLE_VECTOR_DIVISION(uint16_t, __m512i, u16_branchfree)
}

////////// UINT32

__m512i libdivide_u32_do_vec512(__m512i numers, const struct libdivide_u32_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		return _mm512_srli_epi32(numers, more);
	}
	else
	{
		__m512i q = libdivide_mullhi_u32_vec512(numers, _mm512_set1_epi32(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// uint32_t t = ((numer - q) >> 1) + q;
			// return t >> denom->shift;
			uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
			__m512i t = _mm512_add_epi32(_mm512_srli_epi32(_mm512_sub_epi32(numers, q), 1), q);
			return _mm512_srli_epi32(t, shift);
		}
		else
		{
			return _mm512_srli_epi32(q, more);
		}
	}
}

__m512i libdivide_u32_branchfree_do_vec512(
	__m512i numers, const struct libdivide_u32_branchfree_t *denom)
{
	__m512i q = libdivide_mullhi_u32_vec512(numers, _mm512_set1_epi32(denom->magic));
	__m512i t = _mm512_add_epi32(_mm512_srli_epi32(_mm512_sub_epi32(numers, q), 1), q);
	return _mm512_srli_epi32(t, denom->more);
}

////////// UINT64

__m512i libdivide_u64_do_vec512(__m512i numers, const struct libdivide_u64_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		return _mm512_srli_epi64(numers, more);
	}
	else
	{
		__m512i q = libdivide_mullhi_u64_vec512(numers, _mm512_set1_epi64(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// uint32_t t = ((numer - q) >> 1) + q;
			// return t >> denom->shift;
			uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
			__m512i t = _mm512_add_epi64(_mm512_srli_epi64(_mm512_sub_epi64(numers, q), 1), q);
			return _mm512_srli_epi64(t, shift);
		}
		else
		{
			return _mm512_srli_epi64(q, more);
		}
	}
}

__m512i libdivide_u64_branchfree_do_vec512(
	__m512i numers, const struct libdivide_u64_branchfree_t *denom)
{
	__m512i q = libdivide_mullhi_u64_vec512(numers, _mm512_set1_epi64(denom->magic));
	__m512i t = _mm512_add_epi64(_mm512_srli_epi64(_mm512_sub_epi64(numers, q), 1), q);
	return _mm512_srli_epi64(t, denom->more);
}

////////// SINT16

__m512i libdivide_s16_do_vec512(__m512i numers, const struct libdivide_s16_t *denom)
{
	SIMPLE_VECTOR_DIVISION(int16_t, __m512i, s16)
}

__m512i libdivide_s16_branchfree_do_vec512(
	__m512i numers, const struct libdivide_s16_branchfree_t *denom)
{
	SIMPLE_VECTOR_DIVISION(int16_t, __m512i, s16_branchfree)
}

////////// SINT32

__m512i libdivide_s32_do_vec512(__m512i numers, const struct libdivide_s32_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
		uint32_t mask = ((uint32_t)1 << shift) - 1;
		__m512i roundToZeroTweak = _mm512_set1_epi32(mask);
		// q = numer + ((numer >> 31) & roundToZeroTweak);
		__m512i q = _mm512_add_epi32(
						numers, _mm512_and_si512(_mm512_srai_epi32(numers, 31), roundToZeroTweak));
		q = _mm512_srai_epi32(q, shift);
		__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
		// q = (q ^ sign) - sign;
		q = _mm512_sub_epi32(_mm512_xor_si512(q, sign), sign);
		return q;
	}
	else
	{
		__m512i q = libdivide_mullhi_s32_vec512(numers, _mm512_set1_epi32(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift
			__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
			// q += ((numer ^ sign) - sign);
			q = _mm512_add_epi32(q, _mm512_sub_epi32(_mm512_xor_si512(numers, sign), sign));
		}
		// q >>= shift
		q = _mm512_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK);
		q = _mm512_add_epi32(q, _mm512_srli_epi32(q, 31));  // q += (q < 0)
		return q;
	}
}

__m512i libdivide_s32_branchfree_do_vec512(
	__m512i numers, const struct libdivide_s32_branchfree_t *denom)
{
	int32_t magic = denom->magic;
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
	// must be arithmetic shift
	__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
	__m512i q = libdivide_mullhi_s32_vec512(numers, _mm512_set1_epi32(magic));
	q = _mm512_add_epi32(q, numers);  // q += numers

	// If q is non-negative, we have nothing to do
	// If q is negative, we want to add either (2**shift)-1 if d is
	// a power of 2, or (2**shift) if it is not a power of 2
	uint32_t is_power_of_2 = (magic == 0);
	__m512i q_sign = _mm512_srai_epi32(q, 31);  // q_sign = q >> 31
	__m512i mask = _mm512_set1_epi32(((uint32_t)1 << shift) - is_power_of_2);
	q = _mm512_add_epi32(q, _mm512_and_si512(q_sign, mask));  // q = q + (q_sign & mask)
	q = _mm512_srai_epi32(q, shift);                          // q >>= shift
	q = _mm512_sub_epi32(_mm512_xor_si512(q, sign), sign);    // q = (q ^ sign) - sign
	return q;
}

////////// SINT64

__m512i libdivide_s64_do_vec512(__m512i numers, const struct libdivide_s64_t *denom)
{
	uint8_t more = denom->more;
	int64_t magic = denom->magic;
	if (magic == 0)    // shift path
	{
		uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
		uint64_t mask = ((uint64_t)1 << shift) - 1;
		__m512i roundToZeroTweak = _mm512_set1_epi64(mask);
		// q = numer + ((numer >> 63) & roundToZeroTweak);
		__m512i q = _mm512_add_epi64(
						numers, _mm512_and_si512(libdivide_s64_signbits_vec512(numers), roundToZeroTweak));
		q = libdivide_s64_shift_right_vec512(q, shift);
		__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
		// q = (q ^ sign) - sign;
		q = _mm512_sub_epi64(_mm512_xor_si512(q, sign), sign);
		return q;
	}
	else
	{
		__m512i q = libdivide_mullhi_s64_vec512(numers, _mm512_set1_epi64(magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift
			__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);
			// q += ((numer ^ sign) - sign);
			q = _mm512_add_epi64(q, _mm512_sub_epi64(_mm512_xor_si512(numers, sign), sign));
		}
		// q >>= denom->mult_path.shift
		q = libdivide_s64_shift_right_vec512(q, more & LIBDIVIDE_64_SHIFT_MASK);
		q = _mm512_add_epi64(q, _mm512_srli_epi64(q, 63));  // q += (q < 0)
		return q;
	}
}

__m512i libdivide_s64_branchfree_do_vec512(
	__m512i numers, const struct libdivide_s64_branchfree_t *denom)
{
	int64_t magic = denom->magic;
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
	// must be arithmetic shift
	__m512i sign = _mm512_set1_epi32((int8_t)more >> 7);

	// libdivide_mullhi_s64(numers, magic);
	__m512i q = libdivide_mullhi_s64_vec512(numers, _mm512_set1_epi64(magic));
	q = _mm512_add_epi64(q, numers);  // q += numers

	// If q is non-negative, we have nothing to do.
	// If q is negative, we want to add either (2**shift)-1 if d is
	// a power of 2, or (2**shift) if it is not a power of 2.
	uint32_t is_power_of_2 = (magic == 0);
	__m512i q_sign = libdivide_s64_signbits_vec512(q);  // q_sign = q >> 63
	__m512i mask = _mm512_set1_epi64(((uint64_t)1 << shift) - is_power_of_2);
	q = _mm512_add_epi64(q, _mm512_and_si512(q_sign, mask));  // q = q + (q_sign & mask)
	q = libdivide_s64_shift_right_vec512(q, shift);           // q >>= shift
	q = _mm512_sub_epi64(_mm512_xor_si512(q, sign), sign);    // q = (q ^ sign) - sign
	return q;
}

#endif

#if defined(LIBDIVIDE_AVX2)

static LIBDIVIDE_INLINE __m256i libdivide_u16_do_vec256(
	__m256i numers, const struct libdivide_u16_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_s16_do_vec256(
	__m256i numers, const struct libdivide_s16_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_u32_do_vec256(
	__m256i numers, const struct libdivide_u32_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_s32_do_vec256(
	__m256i numers, const struct libdivide_s32_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_u64_do_vec256(
	__m256i numers, const struct libdivide_u64_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_s64_do_vec256(
	__m256i numers, const struct libdivide_s64_t *denom);

static LIBDIVIDE_INLINE __m256i libdivide_u16_branchfree_do_vec256(
	__m256i numers, const struct libdivide_u16_branchfree_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_s16_branchfree_do_vec256(
	__m256i numers, const struct libdivide_s16_branchfree_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_u32_branchfree_do_vec256(
	__m256i numers, const struct libdivide_u32_branchfree_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_s32_branchfree_do_vec256(
	__m256i numers, const struct libdivide_s32_branchfree_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_u64_branchfree_do_vec256(
	__m256i numers, const struct libdivide_u64_branchfree_t *denom);
static LIBDIVIDE_INLINE __m256i libdivide_s64_branchfree_do_vec256(
	__m256i numers, const struct libdivide_s64_branchfree_t *denom);

//////// Internal Utility Functions

// Implementation of _mm256_srai_epi64(v, 63) (from AVX512).
static LIBDIVIDE_INLINE __m256i libdivide_s64_signbits_vec256(__m256i v)
{
	__m256i hiBitsDuped = _mm256_shuffle_epi32(v, _MM_SHUFFLE(3, 3, 1, 1));
	__m256i signBits = _mm256_srai_epi32(hiBitsDuped, 31);
	return signBits;
}

// Implementation of _mm256_srai_epi64 (from AVX512).
static LIBDIVIDE_INLINE __m256i libdivide_s64_shift_right_vec256(__m256i v, int amt)
{
	const int b = 64 - amt;
	__m256i m = _mm256_set1_epi64x((uint64_t)1 << (b - 1));
	__m256i x = _mm256_srli_epi64(v, amt);
	__m256i result = _mm256_sub_epi64(_mm256_xor_si256(x, m), m);
	return result;
}

// Here, b is assumed to contain one 32-bit value repeated.
static LIBDIVIDE_INLINE __m256i libdivide_mullhi_u32_vec256(__m256i a, __m256i b)
{
	__m256i hi_product_0Z2Z = _mm256_srli_epi64(_mm256_mul_epu32(a, b), 32);
	__m256i a1X3X = _mm256_srli_epi64(a, 32);
	__m256i mask = _mm256_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0);
	__m256i hi_product_Z1Z3 = _mm256_and_si256(_mm256_mul_epu32(a1X3X, b), mask);
	return _mm256_or_si256(hi_product_0Z2Z, hi_product_Z1Z3);
}

// b is one 32-bit value repeated.
static LIBDIVIDE_INLINE __m256i libdivide_mullhi_s32_vec256(__m256i a, __m256i b)
{
	__m256i hi_product_0Z2Z = _mm256_srli_epi64(_mm256_mul_epi32(a, b), 32);
	__m256i a1X3X = _mm256_srli_epi64(a, 32);
	__m256i mask = _mm256_set_epi32(-1, 0, -1, 0, -1, 0, -1, 0);
	__m256i hi_product_Z1Z3 = _mm256_and_si256(_mm256_mul_epi32(a1X3X, b), mask);
	return _mm256_or_si256(hi_product_0Z2Z, hi_product_Z1Z3);
}

// Here, y is assumed to contain one 64-bit value repeated.
static LIBDIVIDE_INLINE __m256i libdivide_mullhi_u64_vec256(__m256i x, __m256i y)
{
	// see m128i variant for comments.
	__m256i x0y0 = _mm256_mul_epu32(x, y);
	__m256i x0y0_hi = _mm256_srli_epi64(x0y0, 32);

	__m256i x1 = _mm256_shuffle_epi32(x, _MM_SHUFFLE(3, 3, 1, 1));
	__m256i y1 = _mm256_shuffle_epi32(y, _MM_SHUFFLE(3, 3, 1, 1));

	__m256i x0y1 = _mm256_mul_epu32(x, y1);
	__m256i x1y0 = _mm256_mul_epu32(x1, y);
	__m256i x1y1 = _mm256_mul_epu32(x1, y1);

	__m256i mask = _mm256_set1_epi64x(0xFFFFFFFF);
	__m256i temp = _mm256_add_epi64(x1y0, x0y0_hi);
	__m256i temp_lo = _mm256_and_si256(temp, mask);
	__m256i temp_hi = _mm256_srli_epi64(temp, 32);

	temp_lo = _mm256_srli_epi64(_mm256_add_epi64(temp_lo, x0y1), 32);
	temp_hi = _mm256_add_epi64(x1y1, temp_hi);
	return _mm256_add_epi64(temp_lo, temp_hi);
}

// y is one 64-bit value repeated.
static LIBDIVIDE_INLINE __m256i libdivide_mullhi_s64_vec256(__m256i x, __m256i y)
{
	__m256i p = libdivide_mullhi_u64_vec256(x, y);
	__m256i t1 = _mm256_and_si256(libdivide_s64_signbits_vec256(x), y);
	__m256i t2 = _mm256_and_si256(libdivide_s64_signbits_vec256(y), x);
	p = _mm256_sub_epi64(p, t1);
	p = _mm256_sub_epi64(p, t2);
	return p;
}

////////// UINT16

__m256i libdivide_u16_do_vec256(__m256i numers, const struct libdivide_u16_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		return _mm256_srli_epi16(numers, more);
	}
	else
	{
		__m256i q = _mm256_mulhi_epu16(numers, _mm256_set1_epi16(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			__m256i t = _mm256_adds_epu16(_mm256_srli_epi16(_mm256_subs_epu16(numers, q), 1), q);
			return _mm256_srli_epi16(t, (more & LIBDIVIDE_16_SHIFT_MASK));
		}
		else
		{
			return _mm256_srli_epi16(q, more);
		}
	}
}

__m256i libdivide_u16_branchfree_do_vec256(
	__m256i numers, const struct libdivide_u16_branchfree_t *denom)
{
	__m256i q = _mm256_mulhi_epu16(numers, _mm256_set1_epi16(denom->magic));
	__m256i t = _mm256_adds_epu16(_mm256_srli_epi16(_mm256_subs_epu16(numers, q), 1), q);
	return _mm256_srli_epi16(t, denom->more);
}

////////// UINT32

__m256i libdivide_u32_do_vec256(__m256i numers, const struct libdivide_u32_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		return _mm256_srli_epi32(numers, more);
	}
	else
	{
		__m256i q = libdivide_mullhi_u32_vec256(numers, _mm256_set1_epi32(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// uint32_t t = ((numer - q) >> 1) + q;
			// return t >> denom->shift;
			uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
			__m256i t = _mm256_add_epi32(_mm256_srli_epi32(_mm256_sub_epi32(numers, q), 1), q);
			return _mm256_srli_epi32(t, shift);
		}
		else
		{
			return _mm256_srli_epi32(q, more);
		}
	}
}

__m256i libdivide_u32_branchfree_do_vec256(
	__m256i numers, const struct libdivide_u32_branchfree_t *denom)
{
	__m256i q = libdivide_mullhi_u32_vec256(numers, _mm256_set1_epi32(denom->magic));
	__m256i t = _mm256_add_epi32(_mm256_srli_epi32(_mm256_sub_epi32(numers, q), 1), q);
	return _mm256_srli_epi32(t, denom->more);
}

////////// UINT64

__m256i libdivide_u64_do_vec256(__m256i numers, const struct libdivide_u64_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		return _mm256_srli_epi64(numers, more);
	}
	else
	{
		__m256i q = libdivide_mullhi_u64_vec256(numers, _mm256_set1_epi64x(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// uint32_t t = ((numer - q) >> 1) + q;
			// return t >> denom->shift;
			uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
			__m256i t = _mm256_add_epi64(_mm256_srli_epi64(_mm256_sub_epi64(numers, q), 1), q);
			return _mm256_srli_epi64(t, shift);
		}
		else
		{
			return _mm256_srli_epi64(q, more);
		}
	}
}

__m256i libdivide_u64_branchfree_do_vec256(
	__m256i numers, const struct libdivide_u64_branchfree_t *denom)
{
	__m256i q = libdivide_mullhi_u64_vec256(numers, _mm256_set1_epi64x(denom->magic));
	__m256i t = _mm256_add_epi64(_mm256_srli_epi64(_mm256_sub_epi64(numers, q), 1), q);
	return _mm256_srli_epi64(t, denom->more);
}

////////// SINT16

__m256i libdivide_s16_do_vec256(__m256i numers, const struct libdivide_s16_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		uint16_t shift = more & LIBDIVIDE_16_SHIFT_MASK;
		uint16_t mask = ((uint16_t)1 << shift) - 1;
		__m256i roundToZeroTweak = _mm256_set1_epi16(mask);
		// q = numer + ((numer >> 15) & roundToZeroTweak);
		__m256i q = _mm256_add_epi16(
						numers, _mm256_and_si256(_mm256_srai_epi16(numers, 15), roundToZeroTweak));
		q = _mm256_srai_epi16(q, shift);
		__m256i sign = _mm256_set1_epi16((int8_t)more >> 7);
		// q = (q ^ sign) - sign;
		q = _mm256_sub_epi16(_mm256_xor_si256(q, sign), sign);
		return q;
	}
	else
	{
		__m256i q = _mm256_mulhi_epi16(numers, _mm256_set1_epi16(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift
			__m256i sign = _mm256_set1_epi16((int8_t)more >> 7);
			// q += ((numer ^ sign) - sign);
			q = _mm256_add_epi16(q, _mm256_sub_epi16(_mm256_xor_si256(numers, sign), sign));
		}
		// q >>= shift
		q = _mm256_srai_epi16(q, more & LIBDIVIDE_16_SHIFT_MASK);
		q = _mm256_add_epi16(q, _mm256_srli_epi16(q, 15));  // q += (q < 0)
		return q;
	}
}

__m256i libdivide_s16_branchfree_do_vec256(
	__m256i numers, const struct libdivide_s16_branchfree_t *denom)
{
	int16_t magic = denom->magic;
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_16_SHIFT_MASK;
	// must be arithmetic shift
	__m256i sign = _mm256_set1_epi16((int8_t)more >> 7);
	__m256i q = _mm256_mulhi_epi16(numers, _mm256_set1_epi16(magic));
	q = _mm256_add_epi16(q, numers);  // q += numers

	// If q is non-negative, we have nothing to do
	// If q is negative, we want to add either (2**shift)-1 if d is
	// a power of 2, or (2**shift) if it is not a power of 2
	uint16_t is_power_of_2 = (magic == 0);
	__m256i q_sign = _mm256_srai_epi16(q, 15);  // q_sign = q >> 15
	__m256i mask = _mm256_set1_epi16(((uint16_t)1 << shift) - is_power_of_2);
	q = _mm256_add_epi16(q, _mm256_and_si256(q_sign, mask));  // q = q + (q_sign & mask)
	q = _mm256_srai_epi16(q, shift);                          // q >>= shift
	q = _mm256_sub_epi16(_mm256_xor_si256(q, sign), sign);    // q = (q ^ sign) - sign
	return q;
}

////////// SINT32

__m256i libdivide_s32_do_vec256(__m256i numers, const struct libdivide_s32_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
		uint32_t mask = ((uint32_t)1 << shift) - 1;
		__m256i roundToZeroTweak = _mm256_set1_epi32(mask);
		// q = numer + ((numer >> 31) & roundToZeroTweak);
		__m256i q = _mm256_add_epi32(
						numers, _mm256_and_si256(_mm256_srai_epi32(numers, 31), roundToZeroTweak));
		q = _mm256_srai_epi32(q, shift);
		__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
		// q = (q ^ sign) - sign;
		q = _mm256_sub_epi32(_mm256_xor_si256(q, sign), sign);
		return q;
	}
	else
	{
		__m256i q = libdivide_mullhi_s32_vec256(numers, _mm256_set1_epi32(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift
			__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
			// q += ((numer ^ sign) - sign);
			q = _mm256_add_epi32(q, _mm256_sub_epi32(_mm256_xor_si256(numers, sign), sign));
		}
		// q >>= shift
		q = _mm256_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK);
		q = _mm256_add_epi32(q, _mm256_srli_epi32(q, 31));  // q += (q < 0)
		return q;
	}
}

__m256i libdivide_s32_branchfree_do_vec256(
	__m256i numers, const struct libdivide_s32_branchfree_t *denom)
{
	int32_t magic = denom->magic;
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
	// must be arithmetic shift
	__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
	__m256i q = libdivide_mullhi_s32_vec256(numers, _mm256_set1_epi32(magic));
	q = _mm256_add_epi32(q, numers);  // q += numers

	// If q is non-negative, we have nothing to do
	// If q is negative, we want to add either (2**shift)-1 if d is
	// a power of 2, or (2**shift) if it is not a power of 2
	uint32_t is_power_of_2 = (magic == 0);
	__m256i q_sign = _mm256_srai_epi32(q, 31);  // q_sign = q >> 31
	__m256i mask = _mm256_set1_epi32(((uint32_t)1 << shift) - is_power_of_2);
	q = _mm256_add_epi32(q, _mm256_and_si256(q_sign, mask));  // q = q + (q_sign & mask)
	q = _mm256_srai_epi32(q, shift);                          // q >>= shift
	q = _mm256_sub_epi32(_mm256_xor_si256(q, sign), sign);    // q = (q ^ sign) - sign
	return q;
}

////////// SINT64

__m256i libdivide_s64_do_vec256(__m256i numers, const struct libdivide_s64_t *denom)
{
	uint8_t more = denom->more;
	int64_t magic = denom->magic;
	if (magic == 0)    // shift path
	{
		uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
		uint64_t mask = ((uint64_t)1 << shift) - 1;
		__m256i roundToZeroTweak = _mm256_set1_epi64x(mask);
		// q = numer + ((numer >> 63) & roundToZeroTweak);
		__m256i q = _mm256_add_epi64(
						numers, _mm256_and_si256(libdivide_s64_signbits_vec256(numers), roundToZeroTweak));
		q = libdivide_s64_shift_right_vec256(q, shift);
		__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
		// q = (q ^ sign) - sign;
		q = _mm256_sub_epi64(_mm256_xor_si256(q, sign), sign);
		return q;
	}
	else
	{
		__m256i q = libdivide_mullhi_s64_vec256(numers, _mm256_set1_epi64x(magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift
			__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);
			// q += ((numer ^ sign) - sign);
			q = _mm256_add_epi64(q, _mm256_sub_epi64(_mm256_xor_si256(numers, sign), sign));
		}
		// q >>= denom->mult_path.shift
		q = libdivide_s64_shift_right_vec256(q, more & LIBDIVIDE_64_SHIFT_MASK);
		q = _mm256_add_epi64(q, _mm256_srli_epi64(q, 63));  // q += (q < 0)
		return q;
	}
}

__m256i libdivide_s64_branchfree_do_vec256(
	__m256i numers, const struct libdivide_s64_branchfree_t *denom)
{
	int64_t magic = denom->magic;
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
	// must be arithmetic shift
	__m256i sign = _mm256_set1_epi32((int8_t)more >> 7);

	// libdivide_mullhi_s64(numers, magic);
	__m256i q = libdivide_mullhi_s64_vec256(numers, _mm256_set1_epi64x(magic));
	q = _mm256_add_epi64(q, numers);  // q += numers

	// If q is non-negative, we have nothing to do.
	// If q is negative, we want to add either (2**shift)-1 if d is
	// a power of 2, or (2**shift) if it is not a power of 2.
	uint32_t is_power_of_2 = (magic == 0);
	__m256i q_sign = libdivide_s64_signbits_vec256(q);  // q_sign = q >> 63
	__m256i mask = _mm256_set1_epi64x(((uint64_t)1 << shift) - is_power_of_2);
	q = _mm256_add_epi64(q, _mm256_and_si256(q_sign, mask));  // q = q + (q_sign & mask)
	q = libdivide_s64_shift_right_vec256(q, shift);           // q >>= shift
	q = _mm256_sub_epi64(_mm256_xor_si256(q, sign), sign);    // q = (q ^ sign) - sign
	return q;
}

#endif

#if defined(LIBDIVIDE_SSE2)

static LIBDIVIDE_INLINE __m128i libdivide_u16_do_vec128(
	__m128i numers, const struct libdivide_u16_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_s16_do_vec128(
	__m128i numers, const struct libdivide_s16_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_u32_do_vec128(
	__m128i numers, const struct libdivide_u32_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_s32_do_vec128(
	__m128i numers, const struct libdivide_s32_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_u64_do_vec128(
	__m128i numers, const struct libdivide_u64_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_s64_do_vec128(
	__m128i numers, const struct libdivide_s64_t *denom);

static LIBDIVIDE_INLINE __m128i libdivide_u16_branchfree_do_vec128(
	__m128i numers, const struct libdivide_u16_branchfree_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_s16_branchfree_do_vec128(
	__m128i numers, const struct libdivide_s16_branchfree_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_u32_branchfree_do_vec128(
	__m128i numers, const struct libdivide_u32_branchfree_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_s32_branchfree_do_vec128(
	__m128i numers, const struct libdivide_s32_branchfree_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_u64_branchfree_do_vec128(
	__m128i numers, const struct libdivide_u64_branchfree_t *denom);
static LIBDIVIDE_INLINE __m128i libdivide_s64_branchfree_do_vec128(
	__m128i numers, const struct libdivide_s64_branchfree_t *denom);

//////// Internal Utility Functions

// Implementation of _mm_srai_epi64(v, 63) (from AVX512).
static LIBDIVIDE_INLINE __m128i libdivide_s64_signbits_vec128(__m128i v)
{
	__m128i hiBitsDuped = _mm_shuffle_epi32(v, _MM_SHUFFLE(3, 3, 1, 1));
	__m128i signBits = _mm_srai_epi32(hiBitsDuped, 31);
	return signBits;
}

// Implementation of _mm_srai_epi64 (from AVX512).
static LIBDIVIDE_INLINE __m128i libdivide_s64_shift_right_vec128(__m128i v, int amt)
{
	const int b = 64 - amt;
	__m128i m = _mm_set1_epi64x((uint64_t)1 << (b - 1));
	__m128i x = _mm_srli_epi64(v, amt);
	__m128i result = _mm_sub_epi64(_mm_xor_si128(x, m), m);
	return result;
}

// Here, b is assumed to contain one 32-bit value repeated.
static LIBDIVIDE_INLINE __m128i libdivide_mullhi_u32_vec128(__m128i a, __m128i b)
{
	__m128i hi_product_0Z2Z = _mm_srli_epi64(_mm_mul_epu32(a, b), 32);
	__m128i a1X3X = _mm_srli_epi64(a, 32);
	__m128i mask = _mm_set_epi32(-1, 0, -1, 0);
	__m128i hi_product_Z1Z3 = _mm_and_si128(_mm_mul_epu32(a1X3X, b), mask);
	return _mm_or_si128(hi_product_0Z2Z, hi_product_Z1Z3);
}

// SSE2 does not have a signed multiplication instruction, but we can convert
// unsigned to signed pretty efficiently. Again, b is just a 32 bit value
// repeated four times.
static LIBDIVIDE_INLINE __m128i libdivide_mullhi_s32_vec128(__m128i a, __m128i b)
{
	__m128i p = libdivide_mullhi_u32_vec128(a, b);
	// t1 = (a >> 31) & y, arithmetic shift
	__m128i t1 = _mm_and_si128(_mm_srai_epi32(a, 31), b);
	__m128i t2 = _mm_and_si128(_mm_srai_epi32(b, 31), a);
	p = _mm_sub_epi32(p, t1);
	p = _mm_sub_epi32(p, t2);
	return p;
}

// Here, y is assumed to contain one 64-bit value repeated.
static LIBDIVIDE_INLINE __m128i libdivide_mullhi_u64_vec128(__m128i x, __m128i y)
{
	// full 128 bits product is:
	// x0*y0 + (x0*y1 << 32) + (x1*y0 << 32) + (x1*y1 << 64)
	// Note x0,y0,x1,y1 are all conceptually uint32, products are 32x32->64.

	// Compute x0*y0.
	// Note x1, y1 are ignored by mul_epu32.
	__m128i x0y0 = _mm_mul_epu32(x, y);
	__m128i x0y0_hi = _mm_srli_epi64(x0y0, 32);

	// Get x1, y1 in the low bits.
	// We could shuffle or right shift. Shuffles are preferred as they preserve
	// the source register for the next computation.
	__m128i x1 = _mm_shuffle_epi32(x, _MM_SHUFFLE(3, 3, 1, 1));
	__m128i y1 = _mm_shuffle_epi32(y, _MM_SHUFFLE(3, 3, 1, 1));

	// No need to mask off top 32 bits for mul_epu32.
	__m128i x0y1 = _mm_mul_epu32(x, y1);
	__m128i x1y0 = _mm_mul_epu32(x1, y);
	__m128i x1y1 = _mm_mul_epu32(x1, y1);

	// Mask here selects low bits only.
	__m128i mask = _mm_set1_epi64x(0xFFFFFFFF);
	__m128i temp = _mm_add_epi64(x1y0, x0y0_hi);
	__m128i temp_lo = _mm_and_si128(temp, mask);
	__m128i temp_hi = _mm_srli_epi64(temp, 32);

	temp_lo = _mm_srli_epi64(_mm_add_epi64(temp_lo, x0y1), 32);
	temp_hi = _mm_add_epi64(x1y1, temp_hi);
	return _mm_add_epi64(temp_lo, temp_hi);
}

// y is one 64-bit value repeated.
static LIBDIVIDE_INLINE __m128i libdivide_mullhi_s64_vec128(__m128i x, __m128i y)
{
	__m128i p = libdivide_mullhi_u64_vec128(x, y);
	__m128i t1 = _mm_and_si128(libdivide_s64_signbits_vec128(x), y);
	__m128i t2 = _mm_and_si128(libdivide_s64_signbits_vec128(y), x);
	p = _mm_sub_epi64(p, t1);
	p = _mm_sub_epi64(p, t2);
	return p;
}

////////// UINT26

__m128i libdivide_u16_do_vec128(__m128i numers, const struct libdivide_u16_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		return _mm_srli_epi16(numers, more);
	}
	else
	{
		__m128i q = _mm_mulhi_epu16(numers, _mm_set1_epi16(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			__m128i t = _mm_adds_epu16(_mm_srli_epi16(_mm_subs_epu16(numers, q), 1), q);
			return _mm_srli_epi16(t, (more & LIBDIVIDE_16_SHIFT_MASK));
		}
		else
		{
			return _mm_srli_epi16(q, more);
		}
	}
}

__m128i libdivide_u16_branchfree_do_vec128(
	__m128i numers, const struct libdivide_u16_branchfree_t *denom)
{
	__m128i q = _mm_mulhi_epu16(numers, _mm_set1_epi16(denom->magic));
	__m128i t = _mm_adds_epu16(_mm_srli_epi16(_mm_subs_epu16(numers, q), 1), q);
	return _mm_srli_epi16(t, denom->more);
}

////////// UINT32

__m128i libdivide_u32_do_vec128(__m128i numers, const struct libdivide_u32_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		return _mm_srli_epi32(numers, more);
	}
	else
	{
		__m128i q = libdivide_mullhi_u32_vec128(numers, _mm_set1_epi32(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// uint32_t t = ((numer - q) >> 1) + q;
			// return t >> denom->shift;
			uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
			__m128i t = _mm_add_epi32(_mm_srli_epi32(_mm_sub_epi32(numers, q), 1), q);
			return _mm_srli_epi32(t, shift);
		}
		else
		{
			return _mm_srli_epi32(q, more);
		}
	}
}

__m128i libdivide_u32_branchfree_do_vec128(
	__m128i numers, const struct libdivide_u32_branchfree_t *denom)
{
	__m128i q = libdivide_mullhi_u32_vec128(numers, _mm_set1_epi32(denom->magic));
	__m128i t = _mm_add_epi32(_mm_srli_epi32(_mm_sub_epi32(numers, q), 1), q);
	return _mm_srli_epi32(t, denom->more);
}

////////// UINT64

__m128i libdivide_u64_do_vec128(__m128i numers, const struct libdivide_u64_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		return _mm_srli_epi64(numers, more);
	}
	else
	{
		__m128i q = libdivide_mullhi_u64_vec128(numers, _mm_set1_epi64x(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// uint32_t t = ((numer - q) >> 1) + q;
			// return t >> denom->shift;
			uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
			__m128i t = _mm_add_epi64(_mm_srli_epi64(_mm_sub_epi64(numers, q), 1), q);
			return _mm_srli_epi64(t, shift);
		}
		else
		{
			return _mm_srli_epi64(q, more);
		}
	}
}

__m128i libdivide_u64_branchfree_do_vec128(
	__m128i numers, const struct libdivide_u64_branchfree_t *denom)
{
	__m128i q = libdivide_mullhi_u64_vec128(numers, _mm_set1_epi64x(denom->magic));
	__m128i t = _mm_add_epi64(_mm_srli_epi64(_mm_sub_epi64(numers, q), 1), q);
	return _mm_srli_epi64(t, denom->more);
}

////////// SINT16

__m128i libdivide_s16_do_vec128(__m128i numers, const struct libdivide_s16_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		uint16_t shift = more & LIBDIVIDE_16_SHIFT_MASK;
		uint16_t mask = ((uint16_t)1 << shift) - 1;
		__m128i roundToZeroTweak = _mm_set1_epi16(mask);
		// q = numer + ((numer >> 15) & roundToZeroTweak);
		__m128i q =
			_mm_add_epi16(numers, _mm_and_si128(_mm_srai_epi16(numers, 15), roundToZeroTweak));
		q = _mm_srai_epi16(q, shift);
		__m128i sign = _mm_set1_epi16((int8_t)more >> 7);
		// q = (q ^ sign) - sign;
		q = _mm_sub_epi16(_mm_xor_si128(q, sign), sign);
		return q;
	}
	else
	{
		__m128i q = _mm_mulhi_epi16(numers, _mm_set1_epi16(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift
			__m128i sign = _mm_set1_epi16((int8_t)more >> 7);
			// q += ((numer ^ sign) - sign);
			q = _mm_add_epi16(q, _mm_sub_epi16(_mm_xor_si128(numers, sign), sign));
		}
		// q >>= shift
		q = _mm_srai_epi16(q, more & LIBDIVIDE_16_SHIFT_MASK);
		q = _mm_add_epi16(q, _mm_srli_epi16(q, 15));  // q += (q < 0)
		return q;
	}
}

__m128i libdivide_s16_branchfree_do_vec128(
	__m128i numers, const struct libdivide_s16_branchfree_t *denom)
{
	int16_t magic = denom->magic;
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_16_SHIFT_MASK;
	// must be arithmetic shift
	__m128i sign = _mm_set1_epi16((int8_t)more >> 7);
	__m128i q = _mm_mulhi_epi16(numers, _mm_set1_epi16(magic));
	q = _mm_add_epi16(q, numers);  // q += numers

	// If q is non-negative, we have nothing to do
	// If q is negative, we want to add either (2**shift)-1 if d is
	// a power of 2, or (2**shift) if it is not a power of 2
	uint16_t is_power_of_2 = (magic == 0);
	__m128i q_sign = _mm_srai_epi16(q, 15);  // q_sign = q >> 15
	__m128i mask = _mm_set1_epi16(((uint16_t)1 << shift) - is_power_of_2);
	q = _mm_add_epi16(q, _mm_and_si128(q_sign, mask));  // q = q + (q_sign & mask)
	q = _mm_srai_epi16(q, shift);                       // q >>= shift
	q = _mm_sub_epi16(_mm_xor_si128(q, sign), sign);    // q = (q ^ sign) - sign
	return q;
}

////////// SINT32

__m128i libdivide_s32_do_vec128(__m128i numers, const struct libdivide_s32_t *denom)
{
	uint8_t more = denom->more;
	if (!denom->magic)
	{
		uint32_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
		uint32_t mask = ((uint32_t)1 << shift) - 1;
		__m128i roundToZeroTweak = _mm_set1_epi32(mask);
		// q = numer + ((numer >> 31) & roundToZeroTweak);
		__m128i q =
			_mm_add_epi32(numers, _mm_and_si128(_mm_srai_epi32(numers, 31), roundToZeroTweak));
		q = _mm_srai_epi32(q, shift);
		__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
		// q = (q ^ sign) - sign;
		q = _mm_sub_epi32(_mm_xor_si128(q, sign), sign);
		return q;
	}
	else
	{
		__m128i q = libdivide_mullhi_s32_vec128(numers, _mm_set1_epi32(denom->magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift
			__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
			// q += ((numer ^ sign) - sign);
			q = _mm_add_epi32(q, _mm_sub_epi32(_mm_xor_si128(numers, sign), sign));
		}
		// q >>= shift
		q = _mm_srai_epi32(q, more & LIBDIVIDE_32_SHIFT_MASK);
		q = _mm_add_epi32(q, _mm_srli_epi32(q, 31));  // q += (q < 0)
		return q;
	}
}

__m128i libdivide_s32_branchfree_do_vec128(
	__m128i numers, const struct libdivide_s32_branchfree_t *denom)
{
	int32_t magic = denom->magic;
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_32_SHIFT_MASK;
	// must be arithmetic shift
	__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
	__m128i q = libdivide_mullhi_s32_vec128(numers, _mm_set1_epi32(magic));
	q = _mm_add_epi32(q, numers);  // q += numers

	// If q is non-negative, we have nothing to do
	// If q is negative, we want to add either (2**shift)-1 if d is
	// a power of 2, or (2**shift) if it is not a power of 2
	uint32_t is_power_of_2 = (magic == 0);
	__m128i q_sign = _mm_srai_epi32(q, 31);  // q_sign = q >> 31
	__m128i mask = _mm_set1_epi32(((uint32_t)1 << shift) - is_power_of_2);
	q = _mm_add_epi32(q, _mm_and_si128(q_sign, mask));  // q = q + (q_sign & mask)
	q = _mm_srai_epi32(q, shift);                       // q >>= shift
	q = _mm_sub_epi32(_mm_xor_si128(q, sign), sign);    // q = (q ^ sign) - sign
	return q;
}

////////// SINT64

__m128i libdivide_s64_do_vec128(__m128i numers, const struct libdivide_s64_t *denom)
{
	uint8_t more = denom->more;
	int64_t magic = denom->magic;
	if (magic == 0)    // shift path
	{
		uint32_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
		uint64_t mask = ((uint64_t)1 << shift) - 1;
		__m128i roundToZeroTweak = _mm_set1_epi64x(mask);
		// q = numer + ((numer >> 63) & roundToZeroTweak);
		__m128i q = _mm_add_epi64(
						numers, _mm_and_si128(libdivide_s64_signbits_vec128(numers), roundToZeroTweak));
		q = libdivide_s64_shift_right_vec128(q, shift);
		__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
		// q = (q ^ sign) - sign;
		q = _mm_sub_epi64(_mm_xor_si128(q, sign), sign);
		return q;
	}
	else
	{
		__m128i q = libdivide_mullhi_s64_vec128(numers, _mm_set1_epi64x(magic));
		if (more & LIBDIVIDE_ADD_MARKER)
		{
			// must be arithmetic shift
			__m128i sign = _mm_set1_epi32((int8_t)more >> 7);
			// q += ((numer ^ sign) - sign);
			q = _mm_add_epi64(q, _mm_sub_epi64(_mm_xor_si128(numers, sign), sign));
		}
		// q >>= denom->mult_path.shift
		q = libdivide_s64_shift_right_vec128(q, more & LIBDIVIDE_64_SHIFT_MASK);
		q = _mm_add_epi64(q, _mm_srli_epi64(q, 63));  // q += (q < 0)
		return q;
	}
}

__m128i libdivide_s64_branchfree_do_vec128(
	__m128i numers, const struct libdivide_s64_branchfree_t *denom)
{
	int64_t magic = denom->magic;
	uint8_t more = denom->more;
	uint8_t shift = more & LIBDIVIDE_64_SHIFT_MASK;
	// must be arithmetic shift
	__m128i sign = _mm_set1_epi32((int8_t)more >> 7);

	// libdivide_mullhi_s64(numers, magic);
	__m128i q = libdivide_mullhi_s64_vec128(numers, _mm_set1_epi64x(magic));
	q = _mm_add_epi64(q, numers);  // q += numers

	// If q is non-negative, we have nothing to do.
	// If q is negative, we want to add either (2**shift)-1 if d is
	// a power of 2, or (2**shift) if it is not a power of 2.
	uint32_t is_power_of_2 = (magic == 0);
	__m128i q_sign = libdivide_s64_signbits_vec128(q);  // q_sign = q >> 63
	__m128i mask = _mm_set1_epi64x(((uint64_t)1 << shift) - is_power_of_2);
	q = _mm_add_epi64(q, _mm_and_si128(q_sign, mask));  // q = q + (q_sign & mask)
	q = libdivide_s64_shift_right_vec128(q, shift);     // q >>= shift
	q = _mm_sub_epi64(_mm_xor_si128(q, sign), sign);    // q = (q ^ sign) - sign
	return q;
}

#endif

/////////// C++ stuff

#ifdef __cplusplus

enum Branching
{
	BRANCHFULL,  // use branching algorithms
	BRANCHFREE   // use branchfree algorithms
};

namespace detail
{
enum Signedness
{
	SIGNED,
	UNSIGNED,
};

#if defined(LIBDIVIDE_NEON)
// Helper to deduce NEON vector type for integral type.
template <int _WIDTH, Signedness _SIGN>
struct NeonVec {};

template <>
struct NeonVec<16, UNSIGNED>
{
	typedef uint16x8_t type;
};

template <>
struct NeonVec<16, SIGNED>
{
	typedef int16x8_t type;
};

template <>
struct NeonVec<32, UNSIGNED>
{
	typedef uint32x4_t type;
};

template <>
struct NeonVec<32, SIGNED>
{
	typedef int32x4_t type;
};

template <>
struct NeonVec<64, UNSIGNED>
{
	typedef uint64x2_t type;
};

template <>
struct NeonVec<64, SIGNED>
{
	typedef int64x2_t type;
};

template <typename T>
struct NeonVecFor
{
	// See 'class divider' for an explanation of these template parameters.
	typedef typename NeonVec<sizeof(T) * 8, (((T)0 >> 0) > (T)(-1) ? SIGNED : UNSIGNED)>::type type;
};

#define LIBDIVIDE_DIVIDE_NEON(ALGO, INT_TYPE)                    \
    LIBDIVIDE_INLINE typename NeonVecFor<INT_TYPE>::type divide( \
        typename NeonVecFor<INT_TYPE>::type n) const {           \
        return libdivide_##ALGO##_do_vec128(n, &denom);          \
    }
#else
#define LIBDIVIDE_DIVIDE_NEON(ALGO, INT_TYPE)
#endif

#if defined(LIBDIVIDE_SSE2)
#define LIBDIVIDE_DIVIDE_SSE2(ALGO)                     \
    LIBDIVIDE_INLINE __m128i divide(__m128i n) const {  \
        return libdivide_##ALGO##_do_vec128(n, &denom); \
    }
#else
#define LIBDIVIDE_DIVIDE_SSE2(ALGO)
#endif

#if defined(LIBDIVIDE_AVX2)
#define LIBDIVIDE_DIVIDE_AVX2(ALGO)                     \
    LIBDIVIDE_INLINE __m256i divide(__m256i n) const {  \
        return libdivide_##ALGO##_do_vec256(n, &denom); \
    }
#else
#define LIBDIVIDE_DIVIDE_AVX2(ALGO)
#endif

#if defined(LIBDIVIDE_AVX512)
#define LIBDIVIDE_DIVIDE_AVX512(ALGO)                   \
    LIBDIVIDE_INLINE __m512i divide(__m512i n) const {  \
        return libdivide_##ALGO##_do_vec512(n, &denom); \
    }
#else
#define LIBDIVIDE_DIVIDE_AVX512(ALGO)
#endif

// The DISPATCHER_GEN() macro generates C++ methods (for the given integer
// and algorithm types) that redirect to libdivide's C API.
#define DISPATCHER_GEN(T, ALGO)                                                       \
    libdivide_##ALGO##_t denom;                                                       \
    LIBDIVIDE_INLINE dispatcher() {}                                                  \
    LIBDIVIDE_INLINE dispatcher(T d) : denom(libdivide_##ALGO##_gen(d)) {}            \
    LIBDIVIDE_INLINE T divide(T n) const { return libdivide_##ALGO##_do(n, &denom); } \
    LIBDIVIDE_INLINE T recover() const { return libdivide_##ALGO##_recover(&denom); } \
    LIBDIVIDE_DIVIDE_NEON(ALGO, T)                                                    \
    LIBDIVIDE_DIVIDE_SSE2(ALGO)                                                       \
    LIBDIVIDE_DIVIDE_AVX2(ALGO)                                                       \
    LIBDIVIDE_DIVIDE_AVX512(ALGO)

// The dispatcher selects a specific division algorithm for a given
// width, signedness, and ALGO using partial template specialization.
template <int _WIDTH, Signedness _SIGN, Branching _ALGO>
struct dispatcher {};

template <>
struct dispatcher<16, SIGNED, BRANCHFULL>
{
	DISPATCHER_GEN(int16_t, s16)
};
template <>
struct dispatcher<16, SIGNED, BRANCHFREE>
{
	DISPATCHER_GEN(int16_t, s16_branchfree)
};
template <>
struct dispatcher<16, UNSIGNED, BRANCHFULL>
{
	DISPATCHER_GEN(uint16_t, u16)
};
template <>
struct dispatcher<16, UNSIGNED, BRANCHFREE>
{
	DISPATCHER_GEN(uint16_t, u16_branchfree)
};
template <>
struct dispatcher<32, SIGNED, BRANCHFULL>
{
	DISPATCHER_GEN(int32_t, s32)
};
template <>
struct dispatcher<32, SIGNED, BRANCHFREE>
{
	DISPATCHER_GEN(int32_t, s32_branchfree)
};
template <>
struct dispatcher<32, UNSIGNED, BRANCHFULL>
{
	DISPATCHER_GEN(uint32_t, u32)
};
template <>
struct dispatcher<32, UNSIGNED, BRANCHFREE>
{
	DISPATCHER_GEN(uint32_t, u32_branchfree)
};
template <>
struct dispatcher<64, SIGNED, BRANCHFULL>
{
	DISPATCHER_GEN(int64_t, s64)
};
template <>
struct dispatcher<64, SIGNED, BRANCHFREE>
{
	DISPATCHER_GEN(int64_t, s64_branchfree)
};
template <>
struct dispatcher<64, UNSIGNED, BRANCHFULL>
{
	DISPATCHER_GEN(uint64_t, u64)
};
template <>
struct dispatcher<64, UNSIGNED, BRANCHFREE>
{
	DISPATCHER_GEN(uint64_t, u64_branchfree)
};
}  // namespace detail

#if defined(LIBDIVIDE_NEON)
// Allow NeonVecFor outside of detail namespace.
template <typename T>
struct NeonVecFor
{
	typedef typename detail::NeonVecFor<T>::type type;
};
#endif

// This is the main divider class for use by the user (C++ API).
// The actual division algorithm is selected using the dispatcher struct
// based on the integer width and algorithm template parameters.
template <typename T, Branching ALGO = BRANCHFULL>
class divider
{
private:
	// Dispatch based on the size and signedness.
	// We avoid using type_traits as it's not available in AVR.
	// Detect signedness by checking if T(-1) is less than T(0).
	// Also throw in a shift by 0, which prevents floating point types from being passed.
	typedef detail::dispatcher<sizeof(T) * 8,
			(((T)0 >> 0) > (T)(-1) ? detail::SIGNED : detail::UNSIGNED), ALGO>
			dispatcher_t;

public:
	// We leave the default constructor empty so that creating
	// an array of dividers and then initializing them
	// later doesn't slow us down.
	divider() {}

	// Constructor that takes the divisor as a parameter
	LIBDIVIDE_INLINE divider(T d) : div(d) {}

	// Divides n by the divisor
	LIBDIVIDE_INLINE T divide(T n) const
	{
		return div.divide(n);
	}

	// Recovers the divisor, returns the value that was
	// used to initialize this divider object.
	T recover() const
	{
		return div.recover();
	}

	bool operator==(const divider<T, ALGO> &other) const
	{
		return div.denom.magic == other.denom.magic && div.denom.more == other.denom.more;
	}

	bool operator!=(const divider<T, ALGO> &other) const
	{
		return !(*this == other);
	}

	// Vector variants treat the input as packed integer values with the same type as the divider
	// (e.g. s32, u32, s64, u64) and divides each of them by the divider, returning the packed
	// quotients.
#if defined(LIBDIVIDE_SSE2)
	LIBDIVIDE_INLINE __m128i divide(__m128i n) const
	{
		return div.divide(n);
	}
#endif
#if defined(LIBDIVIDE_AVX2)
	LIBDIVIDE_INLINE __m256i divide(__m256i n) const
	{
		return div.divide(n);
	}
#endif
#if defined(LIBDIVIDE_AVX512)
	LIBDIVIDE_INLINE __m512i divide(__m512i n) const
	{
		return div.divide(n);
	}
#endif
#if defined(LIBDIVIDE_NEON)
	LIBDIVIDE_INLINE typename NeonVecFor<T>::type divide(typename NeonVecFor<T>::type n) const
	{
		return div.divide(n);
	}
#endif

private:
	// Storage for the actual divisor
	dispatcher_t div;
};

// Overload of operator / for scalar division
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE T operator/(T n, const divider<T, ALGO> &div)
{
	return div.divide(n);
}

// Overload of operator /= for scalar division
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE T &operator/=(T &n, const divider<T, ALGO> &div)
{
	n = div.divide(n);
	return n;
}

// Overloads for vector types.
#if defined(LIBDIVIDE_SSE2)
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE __m128i operator/(__m128i n, const divider<T, ALGO> &div)
{
	return div.divide(n);
}

template <typename T, Branching ALGO>
LIBDIVIDE_INLINE __m128i operator/=(__m128i &n, const divider<T, ALGO> &div)
{
	n = div.divide(n);
	return n;
}
#endif
#if defined(LIBDIVIDE_AVX2)
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE __m256i operator/(__m256i n, const divider<T, ALGO> &div)
{
	return div.divide(n);
}

template <typename T, Branching ALGO>
LIBDIVIDE_INLINE __m256i operator/=(__m256i &n, const divider<T, ALGO> &div)
{
	n = div.divide(n);
	return n;
}
#endif
#if defined(LIBDIVIDE_AVX512)
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE __m512i operator/(__m512i n, const divider<T, ALGO> &div)
{
	return div.divide(n);
}

template <typename T, Branching ALGO>
LIBDIVIDE_INLINE __m512i operator/=(__m512i &n, const divider<T, ALGO> &div)
{
	n = div.divide(n);
	return n;
}
#endif

#if defined(LIBDIVIDE_NEON)
template <typename T, Branching ALGO>
LIBDIVIDE_INLINE typename NeonVecFor<T>::type operator/(
	typename NeonVecFor<T>::type n, const divider<T, ALGO> &div)
{
	return div.divide(n);
}

template <typename T, Branching ALGO>
LIBDIVIDE_INLINE typename NeonVecFor<T>::type operator/=(
	typename NeonVecFor<T>::type &n, const divider<T, ALGO> &div)
{
	n = div.divide(n);
	return n;
}
#endif

#if __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1900)
// libdivide::branchfree_divider<T>
template <typename T>
using branchfree_divider = divider<T, BRANCHFREE>;
#endif

}  // namespace libdivide

#endif  // __cplusplus

#if defined(_MSC_VER)
#pragma warning(pop)
#endif

#endif  // LIBDIVIDE_H