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Q: Speed of Intel 8087 co-processor in FLOPS ($100) ( Answered 5 out of 5 stars,   0 Comments )
Subject: Speed of Intel 8087 co-processor in FLOPS ($100)
Category: Computers > Hardware
Asked by: questionaskcomputers-ga
List Price: $100.00
Posted: 11 Jul 2005 19:43 PDT
Expires: 10 Aug 2005 19:43 PDT
Question ID: 542435
Need to know how fast the 8087 co-processor was for floating point
1)add, 2)multiple, 3)divide.  I think they used 32-bit floating point
representation, please confirm.  Answer must include pointer to an
authoritative source that I can quote, such as a ref manual, a
technical article, an intel spec sheet, or the like.

Request for Question Clarification by maniac-ga on 12 Jul 2005 19:07 PDT
Hello Questionaskcomputers,

I found several references that quote floating point multiply timing
for the 8088 / 8087 combination. The references for other instructions
are much more limited but I have a few more comprehensive sources
(timing for all 8087 instructions) that agree with the multiply

None of these are particularly authoritative but the agreement in
times is encouraging - the consistency would indicate the results are

Intel by the way does not appear to have any authoritative references
on line for the 8087. I found a few references to 80287 and 80387
processors (directly on Intel's site or copies on other sites) but
nothing that appears to be directly generated by Intel on the 8087.
There are technical articles describing the 8087 but nothing like an
intel specification sheet (or reference manual). Please let me know if
this would be a problem in answering your question (or you wish to
adjust the price for a less authoritative answer).


Clarification of Question by questionaskcomputers-ga on 12 Jul 2005 20:43 PDT
Hello maniac-ga,

Glad to know you are on the case.  Give me all the info you have in a
coherent form.  Note that I am interested in 8086/8087 combo, not 8088
(although presumably performance of the 8087 is the same).  I am OK
with keeping the price at 100 for a well-written description of what
you have learned with pointers to whatever your sources have been.
Subject: Re: Speed of Intel 8087 co-processor in FLOPS ($100)
Answered By: maniac-ga on 13 Jul 2005 19:18 PDT
Rated:5 out of 5 stars
Hello Questionaskcomputers,

Perhaps the most complete and straight forward reference is at

this appears to be duplicated at

They all appear to be created by "John Allen" (view the web page
source), perhaps from Northrup Grumman - see
for a message on one of the sites referring with that name, but that
is speculation on my part.

Let me explain the first reference and how I matched it to some
technical articles written in the 1980's to verify that the timing
appears to be correct.

Scroll down to FMUL for a complete example. The values in the table
are in CPU cycles - so for a 8 Mhz 8087, a cycle would take 0.125
microseconds each. Converting to microseconds, the values for the 8087
would be calculated as:
               8087 in microseconds
  fmul reg s    11.250 to 13.125
  fmul reg      16.250 to 18.125
  fmul mem32    13.750 to 15.625 + EA
  fmul mem64    19.250 to 21.000 + EA
  fmulp reg s   11.750 to 13.500
  fmulp reg     16.750 to 18.500

where the "s" suffix indicates a value with 40 trailing zeros in the
fraction and EA refers to the time to calculate the effective address.
From the integer page at
the time for effective address calculations is as follows.

  EA = cycles to calculate the Effective Address
        base   = 5   BP+DI or BX+SI = 7   BP+DI+disp or BX+SI+disp = 11
        index  = 5   BX+DI or BP+SI = 8   BX+DI+disp or BP+SI+disp = 12
        disp   = 6   segment override = +2

a reasonable value to use is 8-10 cycles on average, so adding a
microsecond to the values in my table would be a quick approximation
to the typical execution time.

To convert to FLOPS, do a calculation like
  1/.000020  (for a typical 64 bit multiply)
to get 50,000 FLOPS for 64 bit multiplies.

If you have Microsoft Excel, I suggest a simple spreadsheet; something like

A1 = 'HZ'
B1 = 8000000
(select B1, use Insert -> Name... -> Define and define the name HZ to
refer to cell B1)
A2 = 'CycleTime'
B2 = =1/HZ

Then you can define rows like

A5 = (Name of instruction)  [e.g., fmul reg s]
B5 = (lower value of cycles)  [e.g., 90]
C5 = (upper value of cycles) [e.g., 105]
D5 = =B5*CycleTime
E5 = =C5*CycleTime
F5 = 1/D5
G5 = 1/E5

to compute the values needed and can vary the HZ value to get results
for another CPU speed (e.g., 4700000 for 4.7 MHz.

To make it look nice, I formatted columns D and E to be a number with
10 digits after the decimal point and columns F and G to be a number
with 0 digits after the decimal point.

I have a spreadsheet built like this (but cannot post it directly on
Google Answers - let me know if you want a copy and I can put it on a
public location for you to download if needed.

The technical articles I found were a series titled "DTACK GROUNDED"
which has several articles in the early 1980's that describe the
development of the 8087 and has some timing information. Search for
to find archives at

I find it interesting to note that this series of journals is for
"simple 68000 systems" yet has quite a bit of performance data for
Intel processors as well.

See #17
and scroll down to page 1, column 2 for an article titled "Math Chips
Revisited". It talks about a claim made by Intel that a floating point
multiply can be done in 19 microseconds (and scoffs at the claim).
Note if you set HZ to 4.7 MHz and use the 90 cycles from fmul reg s,
you get 19.149 microseconds - pretty close to the claimed 19

The article claims that a fpmul takes 27 microseconds. You can get
this result by setting HZ to 4.7 MHz and use the 130 cycles from fmul
reg to get 27.656 microseconds - again close to the claimed 27

As a cross check, see #19
and scroll down to page 8, column 1 for an article titled "Truth In
Advertising". It indicates an Intel advertisement for 1.7 microseconds
(should be 17 microseconds) for an 8 MHz 8087 for a double precision
multiply. Adjusting HZ to 8 MHz and looking at the fmul values, I see
a range of 16.250 to 18.125 (as I showed above), so 17 microseconds
matches the values I calculated.

Another comparative reference is at
which describes "FLOPS" for the 8087 in 1983 as roughly 30,000 - the
data I calculated for timing can justify that kind of value.

To answer your specific question for performance of an 8087 for 32 bit
floating point add, multiply, and divide, some typical values are:

     Cycles             Seconds                FLOPS      Microseconds 
    Minimum Maximum   Minimum      Maximum  Minimum Maximum Min   Max
fadd   70      100 0.0000087500 0.0000125000 114286  80000  8.75  12.5
fdiv  193      203 0.0000241250 0.0000253750  41451  39409 24.125 25.375
fmul  130      145 0.0000162500 0.0000181250  61538  55172 16.25  18.125

the above are for an 8 MHz 8087. Similar results can be calculated for
other execution rates.

The searches I used for this answer included:
  8087 floating point multiply timing
  8087 cycles floating point multiply add divide
  8087 fmul fdiv fadd microseconds
  8087 fmul fdiv fadd cycles
  "FPU instruction timings" (to find multiple sources of the reference data)

[a couple fruitless searches... had some intersesting information but
no complete results]
  8087 timing
  8087 cycles  

If some part of the answer is unclear, you need further information,
or want the spreadsheet I prepared, please make a request for
clarification. i would be glad to help you as needed.
questionaskcomputers-ga rated this answer:5 out of 5 stars

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