• Choose a category
• All
• Classic-Fiction

Of course, computers are supposed to make things easy for people, so the chore of writing a bunch of routines to do floating-point arithmetic seems at odds with the goal. That's the beauty of software, though. Once somebody writes the floating-point routines for a particular machine, other people can use them. Floating-point arithmetic is so important to scientific and engineering applications that it's traditionally been given a very high priority. In the early days of computers, writing floating-point routines was always one of the first software jobs when a new type of computer was built.

In fact, it even makes sense to implement computer machine-code instructions that perform floating-point arithmetic directly! Obviously, that's easier to say than to do. But that's how important floating-point calculations are. If you can implement floating-point arithmetic in hardware—similar to the multiply and divide instructions in 16-bit microprocessors—all floating-point calculations done on the machine will be faster.

The first commercial computer that included floating-point hardware as an option was the IBM 704 in 1954. The 704 stored all numbers as 36-bit values. For floating-point numbers, that broke down to a 27-bit significand, an 8-bit exponent, and a sign bit. The floating-point hardware could do addition, subtraction, multiplication, and division. Other floating-point functions had to be implemented in software.

Hardware floating-point arithmetic came to the desktop in 1980, when Intel released the 8087 Numeric Data Coprocessor chip, a type of integrated circuit usually referred to these days as a math coprocessor or a floating-point unit (FPU). The 8087 is called a coprocessor because it couldn't be used by itself. It could be used only in conjunction with the 8086 and 8088, Intel's first 16-bit microprocessors.

The 8087 is a 40-pin chip that uses many of the same signals as the 8086 and 8088 chips. The microprocessor and the math coprocessor are connected by means of these signals. When the CPU reads a special instruction—called ESC for Escape—the coprocessor takes over and executes the next machine code, which indicates one of 68 instructions that include trigonometry, exponents, and logarithms. Data types are based on the IEEE standard. At the time, the 8087 was considered to be the most sophisticated integrated circuit ever made.

You can think of the coprocessor as a little self-contained computer. In response to a particular floating-point machine code instruction (for example, FSQRT to calculate a square root), the coprocessor internally executes its own series of instructions coded in ROM. These internal instructions are called microcode. The instructions generally loop, so the result of the calculation isn't immediately available. Still, however, the math coprocessor is usually at least 10 times faster than the equivalent routines done in software.

The motherboard of the original IBM PC had a 40-pin socket for an 8087 chip right next to the 8088 chip. Unfortunately, this socket was empty. Users who needed the extra floating-point speed had to buy an 8087 separately and install it themselves. Even after installation of the math coprocessor, not all applications could be expected to run faster. Some applications—such as word processors—have very little need for floating-point arithmetic. Others, such as spreadsheet programs, can use floating-point calculation much more, and these programs should run faster, but not all of them did.

You see, programmers had to write specific code for the coprocessor that used the coprocessor's machine-code instructions. Because a math coprocessor wasn't a standard piece of hardware, many programmers didn't bother to do so. After all, they had to write their own floating-point subroutines anyway (because most people didn't have a math coprocessor installed), so it became extra work—not less work—to support the 8087 chip. Eventually, programmers learned to write their applications to use the math coprocessor if it was present on the