Integer division on ARM processors is done using the SDIV and UDIV instructions for signed and unsigned division respectively. Here is a detailed guide on how integer division works on ARM and how to utilize the division instructions.

## Overview of Integer Division on ARM

On ARM processors, integer division is done in the Arithmetic Logic Unit (ALU) which contains circuitry to perform basic arithmetic and logical operations. When a division instruction is executed, the two integer operands are passed to the ALU which then performs the division operation on them.

ARM has two division instructions:

- SDIV: Signed Divide – Performs signed integer division, taking into account the sign of the operands.
- UDIV: Unsigned Divide – Performs unsigned integer division, treating the operands as positive values.

Both instructions divide a 32-bit operand (the numerator) by a 32-bit operand (the denominator) and return a 32-bit result. The remainder of the division is discarded.

Some key points regarding integer division on ARM:

- The execution time of SDIV and UDIV is variable and depends on the values of the operands. More cycles are required for larger operands.
- Division by zero leads to undefined behavior on ARM. This should always be avoided through proper input validation.
- The ARM architecture uses restoring division to perform SDIV and UDIV. This algorithm produces one bit of the result per iteration.
- Many ARM processors do not have a hardware divider and use a software library routine for division. This leads to very high division latencies.
- Some ARM processors like Cortex-A series have an integer divider unit for improved performance. But division is still slower than other arithmetic operations.

## Signed Division (SDIV)

The SDIV instruction performs signed integer division, taking into account the signs of the two operands. The instruction divides the 32-bit numerator (N) by the 32-bit denominator (D) and returns a 32-bit result (R).

The pseudocode for SDIV is: if D == 0 then UNPREDICTABLE; if (N == INT_MIN) and (D == -1) then R = INT_MIN; else R = N / D;

The key behaviors are:

- If the denominator is 0, the result is unpredictable (typically traps).
- If N is -2^31 and D is -1, ignoring signs causes overflow. So INT_MIN / -1 = INT_MIN is defined.
- In other cases, a standard signed division is performed while preserving sign.

For positive operands, SDIV works like unsigned division. But when the signs of N and D differ, the result sign follows these rules:

- If N >= 0, R >= 0
- If D >= 0, R <= 0

Some examples: SDIV R0, R1, R2 R1 = 15, R2 = 4 -> R0 = 3 R1 = -15, R2 = 4 -> R0 = -3 R1 = 4, R2 = -3 -> R0 = -1 R1 = -4, R2 = -3 -> R0 = 1 R1 = -2147483648, R2 = -1 -> R0 = -2147483648 (INT_MIN / -1)

## Unsigned Division (UDIV)

The UDIV instruction performs unsigned integer division, treating both operands as positive values. As with SDIV, the 32-bit numerator (N) is divided by the 32-bit denominator (D) to produce a 32-bit result (R).

The pseudocode for UDIV is: if D == 0 then UNPREDICTABLE; R = N / D;

Again, divide by 0 leads to undefined behavior. For non-zero D, standard unsigned division is performed, equivalent to: R = floor(N / D)

Some examples: UDIV R0, R1, R2 R1 = 15, R2 = 4 -> R0 = 3 R1 = 4, R2 = 15 -> R0 = 0 R1 = 0x80000000, R2 = 0x40000000 -> R0 = 0x2

## Performing Division in ARM Assembly

To perform integer division in ARM Assembly, the SDIV and UDIV instructions are used. Here are some examples: // Signed division MOV R0, #15 MOV R1, #4 SDIV R2, R0, R1 // R2 = 15 / 4 = 3 // Unsigned division MOV R3, #0x80000000 MOV R4, #0x40000000 UDIV R5, R3, R4 // R5 = 0x20000000

Some key points on using SDIV/UDIV in assembly:

- Operands must be in registers, not immediates.
- Results go to a register, not memory.
- Remainder is discarded, just the quotient is produced.
- Division flags like overflow/carry are not set by SDIV/UDIV.
- Slower than other arithmetic ops, may take over 10 cycles.

## Improving Division Performance on ARM

Integer division is generally costly on ARM processors. Here are some techniques to improve division performance in ARM programs:

- Use architecture with hardware divide – Cortex-A series is faster for division compared to Cortex-M.
- Replace divisions by constants with multiplications – e.g. x/4 => x>>2.
- Use reciprocal multiplication instead of division where possible.
- Avoid divisions inside tight loops. Try moving them outside the loop.
- unroll/paralleize loops with multiple divisions.
- Use optimized division routines from CMSIS libraries for Cortex-M.
- If integer-only is okay, use fixed-point math instead of floating point division.
- For compilers, use speed optimization flags like -O3 to enhance division code.

## Doing Division in C/C++ on ARM

For C/C++ code running on ARM, integer division can be performed using the / and % operators, along with typecasting.

Examples: int a = 15, b = 4; int c = a / b; // Signed division 15 / 4 unsigned int x = 0x80000000, y = 0x40000000; unsigned int z = x / y; // Unsigned division int p = -15; int q = 4; int r = p / q; // Signed division -15 / 4 = -3 int s = -2147483648 / -1; // Handle INT_MIN / -1 properly

The %= operator is used to obtain the remainder. And typecasting can be used to specify signed/unsigned division: int i = 15 % 4; // Remainder = 3 unsigned u = -1; int s = (int)u; // Typecast to signed

The compiler handles selecting SDIV or UDIV based on the operand types. Optimization flags like -O3 can be used to enhance division performance.

## Handling Division by Zero

Attempting to divide by zero with SDIV or UDIV leads to undefined behavior on ARM. This could result in a crash, exception, or other unexpected results.

To avoid this, input validation is necessary in code that performs division. Here are some ways to check for zero before dividing in C/C++ on ARM: if(y == 0) { // Handle divide by zero } else { x / y; // Proceed with divide } // Use ternary operator z = (y == 0) ? 0 : x / y; // Use preprocessor macro #define DIV(x, y) ((y) == 0 ? 0 : (x) / (y)) int r = DIV(x, y);

The ARM interrupt controller can also be configured to trigger an exception on divide by zero. The IDE/debugger can break execution when the exception occurs.

## Division Operations in ARM NEON

ARM NEON is a SIMD instruction set extension for ARM Cortex-A series processors. It provides instructions to perform division on multiple values simultaneously.

NEON provides vector signed and unsigned divide instructions:

- VDIV – Divide elements of two vectors.
- VDIVQ – Divide quadword vectors.

For example: int32x4_t num = {15, -15, 4, -4}; int32x4_t den = {4, 4, -3, -3}; int32x4_t res = vdivq_s32(num, den); // res = {3, -3, -1, 1}

NEON division uses the integer division unit and has lower throughput than multiplication. But it enables parallel division of multiple values, accelerating workflows like video processing.

## Summary

Here are the key points on integer division in ARM processors:

- SDIV and UDIV instructions are used for signed and unsigned division.
- Division takes multiple cycles and is slower than other arithmetic.
- Hardware divide units in Cortex-A series improve performance.
- Divide by zero leads to undefined behavior and must be avoided.
- Techniques like loop unrolling, avoiding division, and using NEON help increase speed.
- C/C++ relies on the compiler to use SDIV/UDIV based on operand types.
- Input validation is necessary to watch for divide by zero.

Understanding the division instructions, behavior, and performance is key to utilizing this operation efficiently in ARM programs.