Appendix 4
This appendix is in two parts:
 A list of all functions which can cause overflow.^{*}
 A note on the accuracy of the division process.
A. Functions that can cause overflow ^{*}
Title
 Function
 Circumstances causing overflow

Negate
 01, 11, 21, 31
 In the case where the number to be negated is 1.

Count
 02, 12, 22, 32
 When C(N) is 1  2^{38}

Add
 04, 14, 24, 34
 Whenever the sum is outside the range 1 to 1  2^{38}
inclusive.

Subtract
 05, 15, 25, 35
 \Whenever the difference is outside the range 1 to
1  2^{38} inclusive

Negate and Add
 07, 17, 27, 37
 /

Multiply
 52, 53
 In the case of 1 x 1 only.

Double
 54, 55
 Whenever the correct result lies out the range
1 to 1  2^{38} inclusive.

Divide
 56
 Whenever the modulus of the numerator (dividend) is greater
than that of the denominator (divisor) and in the three
cases shown in B(c) below.

^{*} This does not include "FloatingPoint Overflow":
See Appendix 5
B.
The Division Process. This note concerns the accuracy
of the result produced by the computer when the true quotient lies within
the range 1 to +1 inclusive, in function 56.
 Since the result is not rounded, when the true quotient is not
exactly expressible as a 39digit computer number, the result may
be 2^{38} less than that which would be obtained by using
a process containing a roundoff stage.
 If a and b are both positive and b > a, and if the quotient
is exactly expressible as a 39digit computer word,

 then for

a/b, a/b, 0/b
 :
 the computer results are correct,

  but for

a/b, a/b, 0/b
 :
 the computer results are 2^{38}
less than the arithmetically correct results.

 For the division ±a/±a, a > 0, the effects
of (b), combined with the fact that there is no representation
of +1, cause the results below to be produced. Note also the
result obtained for 0/0, and that the overflow indicator is
set for this case, and for both cases in which the result
of ±a/±a errs by more than 2^{38}.
Division
 Computer result
 Overflow Indicator

a/a
 1
 Set

a/a
 1
 Not Set

a/a
 12^{38}
 Set

a/a
 12^{38}
 Not Set

0/0
 2^{38}
 Set
