Thursday, July 17, 2008

Computer Accumulator

In a computer's central processing unit (CPU), an accumulator is a register in which intermediate arithmetic and logic results are stored. Without a register like an accumulator, it would be necessary to write the result of each calculation (addition, multiplication, shift, etc.) to main memory, perhaps only to be read right back again for use in the next operation. Access to main memory is slower than access to a register like the accumulator because the technology used for the large main memory is slower (but cheaper) than that used for a register.

The canonical example for accumulator use is summing a list of numbers. The accumulator is initially set to zero, then each number in turn is added to the value in the accumulator. Only when all numbers have been added is the result held in the accumulator written to main memory or to another, non-accumulator, CPU register.

An accumulator machine, also called a 1-operand machine, or a CPU with accumulator-based architecture, is a kind of CPU in which -- although it may have several registers -- the CPU always stores the results of most calculations in one special register -- typically called "the" accumulator of that CPU. Historically almost all early computers were accumulator machines; and many microcontrollers still popular as of 2008 (such as the Freescale 68HC12 and the PICmicro) are accumulator machines.

Modern CPUs are typically 2-operand or 3-operand machines -- the additional operands specify which one of many general purpose registers (also called "general purpose accumulators"[1]) are used as the source and destination for calculations. These CPUs are not considered "accumulator machines".

The characteristic which distinguishes one register as being the accumulator of a computer architecture is that the accumulator (if the architecture were to have one) would be used as an implicit operand for arithmetic instructions. For instance, a CPU might have an instruction like:

ADD memaddress

This instruction would add the value read from the memory location at memaddress to the value from the accumulator, placing the result in the accumulator. The accumulator is not identified in the instruction by a register number; it is implicit in the instruction and no other register can be specified in the instruction. Some architectures use a particular register as an accumulator in some instructions, but other instructions use register numbers for explicit operand specification.

In the common x86 microprocessor architecture, the 32-bit EAX register (or one of its subcomponents AX or AL, or part or all of the separate 32-bit EDX register for multiplication of large numbers) is an accumulator in some arithmetic instructions, such as MUL and DIV, but in other arithmetic instructions EAX is one of several registers that can be specified. For instance, MUL ecx will multiply the contents of 32-bit register ECX by those of EAX and split the result between EAX and EDX (for 64 bits total, avoiding overflow). ADD, however, accepts two arguments: ADD ecx, edx will add ECX and EDX and place the result in ECX, and likewise for most registers.

History of the computer accumulator

Historical convention dedicates a register to "the accumulator", an "arithmetic organ" that literally accumulates its number during a sequence of arithmetic operations:

"The first part of our arithmetic organ ... should be a parallel storage organ which can receive a number and add it to the one already in it, which is also able to clear its contents and which can store what it contains. We will call such an organ an Accumulator. It is quite conventional in principle in past and present computing machines of the most varied types, e.g. desk multipliers, standard IBM counters, more modern relay machines, the ENIAC" (Goldstine and von Neumann, 1946; p. 98 in Bell and Newell 1971).

Just a few of the instructions are, for example (with some modern interpretation):

Clear accumulator and add number from memory location x

Clear accumulator and subtract number from memory location x

Add number copied from memory location x to the contents of the accumulator

Subtract number copied from memory location x to the contents of the accumulator

Clear accumulator and shift contents of register into accumulator

No convention exists regarding the names for operations from registers to accumulator and from accumulator to registers. Tradition (e.g. Knuth's (1973) imaginary MIX computer), for example, uses two instructions called LOAD ACCUMULATOR from memory/register (e.g. "LDA r") and STORE ACCUMULATOR in register/memory (e.g. "STA r"). Knuth's model has many other instructions as well.