This FAQ is based on a question and answers that appeared on
Why does the mod(x,y) function sometimes give puzzling results?
Why is mod(0.3,0.1) not equal to 0?
Results of the mod(x,y) function
Nicholas J. Cox, Durham University, UK
Thomas J. Steichen, RJRT
April 2001; updated February 2003; minor revisions September 2005
function (see [D] functions) is equivalent to x − y *
floor(x/y). Here floor() returns the
largest integer not greater than its argument so that floor(2) = 2,
floor(2.3) = 2, floor(−2) = −2, and
floor(−2.3) = −3. In other words, it is the remainder on
dividing x by y. It is obvious that 0.3 is a multiple of 0.1 and that the
result should be 0, but given
. display mod(0.3,0.1)
Stata shows 0.1.
Is this is a bug? Not really, but the result is unlikely to be what you
want. It arises because int(0.3/0.1) = 2 to machine precision, and
not 3, as expected from ordinary arithmetic. Hence, 0.1 is shown as the
remainder or modulus.
Let us explain in more detail. Numbers like 0.3 and 0.1 cannot be held as
exact binary equivalents; see [U] 13.10 Precision and problems
therein. To show this, we will use %21.18f as a display format, which
lets us see the underlying values with pretty much the same precision as Stata.
(Stata also provides a special %21x format that shows the exact value
in a special hexadecimal format, which you may wish to explore. This format
was first available late in the product cycle of Stata 6.0. See also [U]
12.2 Numbers and [U] 12.5.1 Numeric formats.)
. di %21.18f .3
. di %21.18f .1
We are using essentially every bit here to get the closest machine decimal
approximation we can to the true decimals 0.3 and 0.1. Clearly, neither
number is represented exactly in the machine.
If we compare
. di %21.18f .3/.1
. di %21.18f 3
it is also clear that, in machine decimal, 3 is not equal to 0.3/0.1. This
occurs because 3 can be represented accurately while 0.3/0.1 is just a
smidgen smaller due to the approximations required to represent 0.3 and 0.1.
Clearly, the integer portion of 0.3/0.1 = 2.999999999999999600 is 2, with
the consequence that mod(0.3,0.1) is shown as 0.1 (more precisely, it
is 0.099999999999999978 in machine decimal, but Stata's default display
format rounds it to 0.1).
Users may get better results using float( ) and round( ), but
perhaps the best advice is cautionary: it is safest not to try precision
work using small fractional arguments to mod( ). You may be better
advised to work at an equivalent problem using integers.
Stata for Windows
Stata for Unix
Stata for Mac