Intel 8087

The Intel 8087, announced in 1980, was the first x87 floating-point coprocessor for the 8086 line of microprocessors.^[4][5]

The purpose of the 8087 was to speed up computations for floating-point arithmetic, such as addition, subtraction, multiplication, division, and square root. It also computed transcendental functions such as exponential, logarithmic or trigonometric calculations, and besides floating-point it could also operate on large binary and decimal integers. The performance enhancements were from approximately 20% to over 500%, depending on the specific application. The 8087 could perform about 50,000 FLOPS^[4] using around 2.4 watts.^[5] Only arithmetic operations benefited from installation of an 8087; computers used only with such applications as word processing, for example, would not benefit from the extra expense (around $150^[6]) and power consumption of an 8087.

Die of Intel 8087.

The 8087 was an advanced IC for its time, pushing the limits of period manufacturing technology. Initial yields were extremely low.

The sales of the 8087 received a significant boost when IBM included a coprocessor socket on the IBM PC motherboard. Due to a shortage of chips, IBM did not actually offer the 8087 as an option for the PC until it had been on the market for six months. Development of the 8087 led to the IEEE 754-1985 standard for floating-point arithmetic. There were later x87 coprocessors for the 80186 (not used in PC-compatibles), 80286, 80386, and 80386SX processors. Starting with the 80486, the later Intel x86 processors did not use a separate floating point coprocessor; floating point functions were provided integrated with the processor.

Design and development

Intel had previously manufactured the 8231 Arithmetic processing unit, and the 8232 Floating Point Processor. These were designed for use with 8080 or similar processors and used an 8-bit data bus. They were interfaced to a host system either through programmed I/O or a DMA controller.^[7]

The 8087 was initially conceived by Bill Pohlman, the engineering manager at Intel who oversaw the development of the 8086 chip. Bill took steps to be sure that the 8086 chip could support a yet-to-be-developed math chip.

In 1977 Pohlman got the go ahead to design the 8087 math chip. Bruce Ravenel was assigned as architect, and John Palmer was hired to be co-architect and mathematician for the project. The two came up with a revolutionary design with 64 bits of mantissa and 16 bits of exponent for the longest format real number, with a stack architecture CPU and 8 80-bit stack registers, with a computationally rich instruction set. The design solved a few outstanding known problems in numerical computing and numerical software: rounding error problems were eliminated for 64-bit operands, and numerical mode conversions were solved for all 64-bit numbers. Palmer credited William Kahan's writings on floating point as a significant influence on their design.^[8]

The 8087 design initially met a cool reception in Santa Clara due to its aggressive design. Eventually, the design was assigned to Intel Israel, and Rafi Nave was assigned to lead the implementation of the chip. Palmer, Ravenel and Nave were awarded patents for the design.^[9] Robert Koehler and John Bayliss were also awarded a patent for the technique where some instructions with a particular bit pattern were offloaded to the coprocessor.^[10]

The 8087 had 45,000 transistors and was manufactured as a 3 μm depletion load HMOS circuit. It worked in tandem with the 8086 or 8088 and introduced about 60 new instructions. Most 8087 assembly mnemonics begin with F, such as FADD, FMUL, FCOM and so on, making them easily distinguishable from 8086 instructions. The binary encodings for all 8087 instructions begin with the bit pattern 11011, decimal 27, the same as the ASCII character ESC although in the higher order bits of a byte; similar instruction prefixes are also sometimes referred to as "escape codes". When the 8088 saw the escape code, it would defer to the 8087 until it was ready.

The codes are encoded in 6 bits across 2 bytes, beginning with the escape sequence:

 ┌───────────┬───────────┐
 │ 1101 1xxx │ mmxx xrrr │
 └───────────┴───────────┘

The first three x's are the first three bits of the floating point opcode. Then two m's, then the latter half three bits of the floating point opcode, followed by three r's. The m's and r's specify the addressing mode information.^[11]

Application programs had to be written to make use of the special floating point instructions. At run time, software could detect the coprocessor and use it for floating point operations. When detected absent, similar floating point functions had to be calculated in software or the whole coprocessor could be emulated in software for more precise numerical compatibility.^[6]

Registers

Simplified 8087 microarchitecture.

The x87 family does not use a directly addressable register set such as the main registers of the x86 processors; instead, the x87 registers form an eight-level deep stack structure^[12] ranging from st0 to st7, where st0 is the top. The x87 instructions operate by pushing, calculating, and popping values on this stack. However, dyadic operations such as FADD, FMUL, FCMP, and so on may either implicitly use the topmost st0 and st1, or it may use st0 together with an explicit memory operand or register; the st0 register may thus be used as an accumulator (i.e. as a combined destination and left operand) and can also be exchanged with any of the eight stack registers using an instruction called FXCH stX (codes D9C8..D9CF_h). This makes the x87 stack usable as seven freely addressable registers plus an accumulator. This is especially applicable on superscalar x86 processors (Pentium of 1993 and later) where these exchange instructions are optimized down to a zero clock penalty.

IEEE floating point standard

When Intel designed the 8087, it aimed to make a standard floating-point format for future designs. An important aspect of the 8087 from a historical perspective was that it became the basis for the IEEE 754 floating-point standard. The 8087 did not implement the eventual IEEE 754 standard in all its details, as the standard was not finished until 1985, but the 80387 did. The 8087 provided two basic 32/64-bit floating-point data types and an additional extended 80-bit internal temporary format (that could also be stored in memory) to improve accuracy over large and complex calculations. Apart from this, the 8087 offered an 80-bit/18-digit packed BCD (binary coded decimal) format and 16, 32, and 64-bit integer data types.^[12]

Infinity

The 8087 handles infinity values by either affine closure or projective closure (selected via the status register). With affine closure, positive and negative infinities are treated as different values. With projective closure, infinity is treated as an unsigned representation for very small or very large numbers.^[13] These two methods of handling infinity were incorporated into the draft version of the IEEE 754 floating-point standard. However, projective closure was dropped from the later formal issue of IEEE 754-1985. The 80287 retained projective closure as an option, but the 80387 and subsequent floating point processors (including the 80187) only supported affine closure.

Coprocessor interface

The 8087 differed from subsequent Intel coprocessors in that it was directly connected to the address and data buses. The 8088/86 looked for instructions that commenced with the '11011' sequence and relinquished control to the coprocessor. The coprocessor handed control back once the execution of the coprocessor instruction was complete. There was a potential crash problem if the coprocessor instruction failed to decode to one that the coprocessor understood. Intel's later coprocessors did not connect to the buses in the same way, but were handed the instructions by the main processor. This yielded an execution time penalty, but the potential crash problem was avoided because the main processor would ignore the instruction if the coprocessor refused to accept it. The 8087 was able to detect whether it was connected to an 8088 or an 8086 by monitoring the data bus during the reset cycle.

The 8087 was, in theory, capable of working concurrently while the 8086/8 processes additional instructions. In practice, there was the potential for a bus crash if both processors attempted to access either bus simultaneously. The assembler would automatically insert an 'FWAIT' instruction after each and every coprocessor opcode forcing the 8086/8 to halt execution until the 8087 signalled that it had finished.^[14] This limitation was removed from later designs.

Models and second sources

Intel 8087 Math Coprocessor Pinout

Intel 8087 coprocessors were fabricated in two variants, one with ceramic side-brazed DIP (CerDIP) and one in hermetic DIP (PDIP), and were designed to operate in the following temperature ranges:

• C, D, QC and QD prefixes: 0 °C to +70 °C (Commercial use).
• LC, LD, TC and TD prefixes: −40 °C to +85 °C (Industrial use).
• MC and MD prefixes: −55 °C to +125 °C (Military use).

All models of the 8087 had a 40 pin DIP package and operated on 5 volts, consuming around 2.4 watts. Unlike later Intel coprocessors, the 8087 had to run at the same clock speed as the main processor.^[6] Suffixes on the part number identified the clock speed:

• 

  The original 5 MHz Intel C8087

• 

  The original 5 MHz Intel D8087

• 

  An 8 MHz Intel D8087-2

• 

  An Intel 5 MHz C8087-3

The part was second-sourced by AMD as AMD 8087^[2] and by Cyrix as Cyrix 8087.^[3] The clone K1810WM87 of the 8087 was produced in the Soviet Union.^[15]

Successors

Just as the 8088 and 8086 processors were superseded by later parts, so was the 8087 superseded. Other Intel coprocessors were the 80287, 80387, and the 80187. Starting with the 80486, the later Intel processors did not use a separate floating point coprocessor; virtually all included it on the main processor die, with the significant exception of the 80486SX which was a modified 80486DX with the FPU disabled. The 80487 was in fact a full blown i486DX chip with an extra pin. When installed, it disabled the 80486SX CPU. The 80486DX, Pentium, and later processors include floating-point functionality on the CPU core.

Complete FPU Instruction set of the 8087

Abbreviations:

• f32: 32 bit IEEE-754 floating point number
• f64: 64 bit IEEE-754 floating point number
• f80: 80 bit IEEE-754 floating point number
• i16: 16 bit signed integer
• i32: 32 bit signed integer
• i64: 64 bit signed integer
• bcd: 80 bit signed BCD integer
• u16: 16 bit status or control word
• env: FPU environment state
• stt: complete FPU state (FPU environment + eight 80 bit floating point registers)

Table contains complete FPU instruction set of 8087, 80287, 80387 and the last extension on Pentium based FPUs.

References

Bibliography

• Sanchez, Julio; Canton, Maria P. (2007). Software Solutions for Engineers and Scientists. CRC Press. ISBN 1-4200-4302-1. 

External links

• Intel 80x87 math coprocessors at cpu-collection.de
• Coprocessor.info: 8087 math coprocessor history information and pictures
• Datasheet for the Intel 8087 Math Coprocessor