This is the first post on GeekDot about a single IC. While I did a lot of writing about ICs, mainly CPUs and FPUs, back in the BBS days (German) I stopped doing so after that and concentrated on collecting them during the following years – a true love never dies 😉
The Weitek Abacus FPUs were always special, exotic and unaffordable for the most of us. Today they additionally got a touch of a mythic being, especially as 386/486 boards featuring the special  WEITEK socket are dying out fast. Not mentioning the Abacus FPU itself.

Recently I had a mail conversation about the Abacuses and because they’re are memory mapped, I thought they might actually fit quite good into the range of my other accelerator post as the DSM860 or all those Transputer cards.

I wasn’t planning to go into all the details about the Abacus models 3167 and 4167 and went looking for a handy Wikipedia link.
To my surprise that article is pretty general and just briefly touches all product ever made by WEITEK.
So, the best source of technical information about these FPUs is the highly recommendable posting “copro16a.txt“, written by Norbert Juffa in 1994.
I’d call it the most comprehensive write-up about FPUs until that date. Because you’ll never know what happens to external links, here’s the (shortened) part about the Weitek chips:

The architecture of the Weitek chips differs significantly from the 80x87.
Strictly speaking, the Weitek Abacus 3167 and 4167 are not coprocessors in that they do not transparently extend the CPU architecture; rather, they could be described as highly-specialized, memory-mapped IO devices. But as the term "coprocessor" has been traditionally used for these chips, they will
be referred to as such here.

The Weitek coprocessors have a RISC-like architecture which has been tuned for maximum performance. Only a small instruction set has been implemented in the chip, but each instruction executes at a very high speed (usually only a few clock cycles each). [...] 
In contrast to the 80x87 family, the Weitek Abacus does not support a double extended format, has no built-in transcendental functions, and does not support denormals. The resources required to implement such features have instead been devoted to implement the basic arithmetic operations as fast as possible.

While the 80x87 coprocessors perform all internal calculations in double extended precision and therefore have about the same performance for single and double-precision calculations, the Weitek features explicit single and double-precision operations. For applications that require only single-precision operations, the Weitek can therefore provide very high performance, as single-precision operations are about twice as fast as their double-precision counterparts. Also, since the Weitek Abacus has more registers than the 80x87 coprocessors (31 versus 8), values can be kept in registers more often and have to be loaded from memory less frequently. This also leads to performance gains.
[...]

To the main CPU, the Weitek Abacus appears as a 64 KB block of memory starting at physical address 0C0000000h. Each address in this range corresponds to a coprocessor instruction. Accessing a specified memory location within this block with a MOV instruction causes the corresponding Weitek instruction to be executed. (The instructions have been cleverly assigned to memory locations in such a way that loads to consecutive coprocessor registers can make use of the 386/486 MOVS string instruction.)
This memory-mapped interface is much faster than the IO-oriented protocol that is used to couple the CPU to an 80287 or 80387 coprocessor. The Weitek's memory block can actually be assigned to any logical address using the MMU (memory management unit) in the 386/486's protected and virtual modes. This also means that the Weitek Abacus *cannot* be used in the real mode of those processors, since their physical starting address (0C0000000h) is not within the 1 MByte address range and the MMU is inoperable in real mode. However, DOS programs can make use of the Weitek by using a DOS extender or a memory manager (such as QEMM or EMM386) that runs in protected/virtual mode itself and can therefore map the Weitek's memory block to any desired location in the 1 MByte address range.

Typically the FS segment register is then set up to point to the Weitek's memory block. On the 80486, this technique has severe drawbacks, as using the FS: prefix takes an additional clock cycle, thereby nearly halving the performance of the 4167. Most DOS-based compilers exhibit this problem, so the only way around it is to code in assembly language.

Ok, so we have a good idea how the Abacuses work and how they can be used. … but what’s the story behind the company?

This is a ‘web found’ © by antiquetech.com
“Founded by Chi-Shin Wang, Edmund Sun, and Godfrey Fong (President and CEO) in 1981 in San Jose. All founders immigrated from China.
Weitek specialized in high-performance digital semiconductor components and systems for the computer and workstation industries. Weitek floating point units have been used with Inmos Transputers (Floating Point System T-series Hypercube, 1986), National Semiconductor NS32032’s (Encore Multimax, 1986), and Intel 386’s (1988). The 2048 was used in the Thinking Machines Corporations CM-2 Connection Machine. Weitek produced floating point processors for HP. HP allowed to Weitek to use it’s facilities to make chip for themselves and for their competition.”

When dramatically loosing ground to the 486DX2 Weitek moved away from the x86 platform and concentrated on SPARC CPU and FPUs as well as MIPS FPUs. That worked quite well for some time and in the 90s they finally moved into the frame buffer and graphics accelerator business. Their POWER P9000/P9100 models were quite successful but lost when players like S3 and ATI started to flex muscles.

Specs

So from our (PC-compatible) perspective there are two models of interest: The 3167 and the 4167. Basically they only differ in the bus protocol to either the Intel 386 or 486.
If you need more detailed data, I make the original specs available here for the 3167 and 4167 as PDF.
Both Abacuses clocked up to 33MHz. Especially the 4167-33MHz is very hard to find these days. That said, it might be possible to overclock a 25MHz version to 33MHz providing sufficient cooling. I found this press snippet where WEITEK proactively promoted overclocking a 33MHz to 50MHz by using a peltier element made by ICECAP – so when overclocking that by 51%, the 32% from 25 to 33MHz should be an issue:

WEITEK and ICECAP announce 33MHz version of Abacus 4167

Ram Ganapathi Mar 30 1992, 02:57 pm
WEITEK and ICECAP announce 33MHz version of Abacus 4167

Weitek Corporation and ICECAP Technologies announced today that users of 50MHz Intel 80486-based personal computers can realize a 50% performance increase for numeric-intensive applications by combining the 33 MHz version of Weitek’s Abacus 4167 math coprocessor with the ICECAP thermal management device. Superior system performance is achieved without degrading system reliability.

Using it

Applications that took advantage of the Weitek Abacus were scarce. AutoShade, Autodesk Renderman, 3-D Studio were the most prominent to use a Weitek coprocessor.
If you happen to own one, you might actually use or at least test it… so here’s the official test-suite from Weitek. It contains these tools

• DOS TSR to update the BIOS for Abacus support (if missing)
• A test tool wich checks for an Abacus presence using INT 11h BIOS calls.
• A diagnose tool
• 2 demos: A side-by-side Mandelbrot benchmark (yay!) and rendering a phong shaded beach ball
• Abacus macros for using it natively in your cool assembly code

When I find the time to pull out my Weitek-PC, I’ll post pictures of the demos… feel free to comment if you feel I’ve been missing out something.