14 Feb
2006
14 Feb
'06
10:14 p.m.
Don North wrote:
Jerome H. Fine wrote:
Jerome Fine replies:
I suggest that you might not be aware of the exact implementation
of the PDP-11 integer "Div" instruction when an overflow occurs.
Please be aware there is no one "PDP-11 microcode". The internals and
microflows of each machine are different, except for the 11/45-55 and
11/70 which are very closely related implementations (same basic core
CPU). Some of the VLSI CPUs also tend to behave the same as they are
based on the same core CPU (F11, J11, etc).
How the DIV instruction behaves in boundary conditions (ie, when the
true quotient can not be represented in 16b) can, but may not, be CPU
specific. Some CPUs may generate the correct 16 LSB of the 32b
quotient. Others may not. The PDP-11 programmers guide for various
CPUs indicates that the only affect one can count on is that the 'V'
bit is set.
In practice, given the standard shift/subtract algorithms for binary
division, it is probably the case that the 16b quotient is a true
subset of the 32b quotient. However, there is no easy way to prove
this without examining the microcode on each machine, or writing a
test program and running it on each machine.
SIMH implements PDP-11 DIV as:
case 1: /* DIV */
if (!CPUO (OPT_EIS)) {
setTRAP (TRAP_ILL);
break;
}
src2 = dstreg? R[dstspec]: ReadW (GeteaW (dstspec));
src = (((uint32) R[srcspec]) << 16) | R[srcspec | 1];
if (src2 == 0) {
N = 0; /* J11,11/70
compat */
Z = V = C = 1; /* N = 0, Z = 1 */
break;
}
if ((src == 020000000000) && (src2 == 0177777)) {
V = 1; /* J11,11/70
compat */
N = Z = C = 0; /* N = Z = 0 */
break;
}
if (GET_SIGN_W (src2)) src2 = src2 | ~077777;
if (GET_SIGN_W (R[srcspec])) src = src | ~017777777777;
--> dst = src / src2;
N = (dst < 0); /* N set on 32b
result */
if ((dst > 077777) || (dst < -0100000)) {
V = 1; /* J11,11/70
compat */
Z = C = 0; /* Z = C = 0 */
====>> break;
}
--> R[srcspec] = dst & 0177777;
--> R[srcspec | 1] = (src - (src2 * dst)) & 0177777;
Z = GET_Z (dst);
V = C = 0;
break;
which would appear that the 16b quotient returned is the 16 LSB of the
correct 32b quotient.
Actually I read the C code wrong. If overflow is detected,
the 'break;'
jumps out of the code and no registers are modified.
So SIMH does NOT modify any registers if the V-bit has been set.
I checked the 11/34 MAINDEC EIS diagnostic. For the DIV tests, the
result registers are NOT checked if the Vbit is set.
The diagnostic does not verify that the registers are unchanged; it
assumes the registers are UNDEFINED if V is set.
I ran some simple DIV tests on a real 11/44:
Johnny
Billquist wrote:
"Jerome H. Fine" wrote:
I have noticed what may be an interesting result when I use the
PDP-11 Integer Divide Instruction "Div". Since I have noticed
at least one individual who worked on the microcode for the
PDP-11, perhaps there is an explicit "Yes / No" answer to my
question:
Since this actually have nothing to do with the microcode, and
actually is nothing specific with the PDP-11 DIV instruction, just
about anyone should be able to answer definitely. >>s 1000
(Program)
DIV Test of 'div r2,r0'
..R0.. ..R1.. ..R2.. ....NUM... ..DEN.. => ..R0.. ..R1.. ..R2.. NZVC
..QUO.. ..REM..
000003 000004 000003 196612. 3. => 000003 000004 000003
0010 3. 4.
000000 000000 000000 0. 0. => 000000 000000 000000
0011 0. 0. <-- Zbit clear
000001 000001 000000 65537. 0. => 000001 000001 000000
0011 1. 1. <-- Zbit clear
000000 001000 000010 512. 8. => 000100 000000 000010
0000 64. 0.
000000 001234 000021 668. 17. => 000047 000005 000021
0000 39. 5.
000010 001234 005432 524956. 2842. => 000270 003754 005432
0000 184. 2028.
012345 012345 054321 350557413. 22737. => 036071 051134 054321 0000
15417. 21084.
012345 012345 000005 350557413. 5. => 012345 012345 000005 0010
5349. 5349.
000000 040000 000002 16384. 2. => 020000 000000 000002 0000
8192. 0.
000000 100000 000002 32768. 2. => 040000 000000 000002 0000
16384. 0.
000001 000000 000002 65536. 2. => 100000 000000 000002 0010
-32768. 0. <-- R0 changed, Vbit set
000002 000000 000002 131072. 2. => 000002 000000 000002
0010 2. 0.
Goodbye
(Console)
Halted at 165146
and an 11/44 under the latest SIMH:
local[625] pdp11 divtest.ini
PDP-11 simulator V3.5-0
DIV Test of 'div r2,r0'
..R0.. ..R1.. ..R2.. ....NUM... ..DEN.. => ..R0.. ..R1.. ..R2.. NZVC
..QUO.. ..REM..
000003 000004 000003 196612. 3. => 000003 000004 000003
0010 3. 4.
000000 000000 000000 0. 0. => 000000 000000 000000
0111 0. 0. <-- Zbit set
000001 000001 000000 65537. 0. => 000001 000001 000000
0111 1. 1. <-- Zbit set
000000 001000 000010 512. 8. => 000100 000000 000010
0000 64. 0.
000000 001234 000021 668. 17. => 000047 000005 000021
0000 39. 5.
000010 001234 005432 524956. 2842. => 000270 003754 005432
0000 184. 2028.
012345 012345 054321 350557413. 22737. => 036071 051134 054321 0000
15417. 21084.
012345 012345 000005 350557413. 5. => 012345 012345 000005 0010
5349. 5349.
000000 040000 000002 16384. 2. => 020000 000000 000002 0000
8192. 0.
000000 100000 000002 32768. 2. => 040000 000000 000002 0000
16384. 0.
000001 000000 000002 65536. 2. => 000001 000000 000002
0010 1. 0. <-- R0 unchanged, Vbit set
000002 000000 000002 131072. 2. => 000002 000000 000002
0010 2. 0.
Goodbye
HALT instruction, PC: 000010 (000012)
Goodbye
local[626]
the interesting case is the (65536. / 2.) computation where the real
11/44 generates the correct unsigned quotient in R0, but also sets the Vbit.
In most cases however it appears that if DIV overflows the quo and rem
registers are unaltered and the Vbit is set.
SIMH and a real 11/44 (mostly) behave this way. The behavior below found
by Jerome may be an anomaly seen in E11.
Please see below!
I agree that the above code is the "correct" method to ensure
a valid result. BUT, that is NOT what I am attempting to determine.
Specifically, I have found that the following code also works:
Mov R0,R3
Div (R2),R0 ; First Divide Instruction
Tst R1
Bne Somewhere - since the quotient is not of interest when a
non-zero remainder
Mov R0,-(SP)
Mov R3,R1
Clr R0
Div (R2),R0 ; Second Divide Instruction
Mov (SP)+,R1
At this point, R0 / R1 now contains 32 bit quotient IF the first
"Div" instruction places the low order 16 bits of the 32 bit
quotient into R0. I have found this result in practice and since
there is a VERY HIGH probability that the remainder is NOT
zero, the above code is MUCH faster.
Again, the specific question is IF the quotient of the "Div" instruction
is the low order 16 bits of a 32 bit quotient all of the time or just
when the high order 16 bits are all zero????????
I learned that also, but the observation is not relevant
to my question.
I realize that the DEC manual description of the "Div" instruction
does not address the situation when the quotient exceeds 65535
(decimal) or 16 bits, but again, perhaps someone who knows
the microcode might have an answer.
I AGREE!! It would have been "nice" though if
DEC knew where the value was and made that high
order 16 bits available via the next instruction
if the user needed it. That information would
also have exactly defined whether or not the low
order 16 bits of the quotient and the remainder
were correct all of the time. Any comments on these
TWO observations?
I realize that the instruction set is long past being
subject to change in DEC hardware, but that does not
mean that an emulator could not manage to make a few
small but vital improvements. And certainly, at least
in SIMH, it is possible to examine the code to determine
the answer to my original question. Does anyone have
the code for the "Div" emulation in SIMH and what does
happen when the high order 16 bits of the quotient are
non-zero?
Sincerely yours,
Jerome Fine
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If I
divide 196612 by 3 - i.e. "Div (R2),R0" where R0 = 3, R1 = 4,
(R2) = 3
the result (in addition to the condition bits) is
R0 = 1, R1 = 1
which is
exactly correct if the quotient is regarded as a
32 bit result
with R0 being
the low order 16 bits of that result and the high
order 32 bits are
somewhere
else - probably inaccessible as far as
programming is concerned,
but easily
obtained by:
Mov R1-(SP) ; Save low order 16 bits of dividend
Mov R0,R1 ; Divide high order 16 bits
Clr R0 ; of dividend
Div (R2),R0 ; by the divisor
Mov R0,R3 ; Save high order 16 bits of quotient
Mov R1,R0 ; Divide the remainder
Mov (SP)+,R1 ; of the dividend
Div (R2),R0 ; by the divisor
i.e. R3 now contains the high order 16 bits of the 32 bit quotient
with R0 holding the low order 16 bits of the 32 bit quotient
What you have
implemented here, as well as described, is the exact
way you should have been taught how to do division on paper in
elementary school.
Yes, that algorithm is valid, and can be extended to arbitrary
sizes, as long as you remember the full method. Can
anyone confirm what I have found in practice?
Certainly. It's basic math, the
way it's taught in elementary school.
That was atleast the first way I was taught how do do divides on big
numbers on paper. Even
better would be a method of retrieving the high
order 16 bits of the quotient in a manner which takes
fewer instructions and without a second divide instruction!
I doubt you'll find it.