fmod and %

[Zunbeltz Izaola]

Hi,

I have a problem with % operation. It returns a incorrect value in
this case:
1.0

where the returned value should be -2.77555756156e-17.

The documentation says that there is same errors due to roundoff and
suggest to use fmod from math module.
-2.77555756156e-17

Ok, but when i try the following:
-0.32768000000000003

but i want to get the result % gives
0.67232000000000003

what is going wrong? Any suggestions

Thanks in advance

 

[Jeff Epler]

fmod and % have a different rule about the sign of the returned value.
This is documented both in the language reference and in the library
reference, in the appropriate spots.

http://python.org/doc/current/ref/binary.html#l2h-411
The % (modulo) operator yields the remainder from the division of
the first argument by the second. The numeric arguments are first
converted to a common type. A zero right argument raises the
ZeroDivisionError exception. The arguments may be floating point
numbers, e.g., 3.14%0.7 equals 0.34 (since 3.14 equals 4*0.7 + 0.34.)
The modulo operator always yields a result with the same sign as its
second operand (or zero); the absolute value of the result is strictly
smaller than the absolute value of the second operand

[Footnote: While abs(x%y) < abs(y) is true mathematically, for
floats it may not be true numerically due to roundoff. For example,
and assuming a platform on which a Python float is an IEEE 754
double-precision number, in order that -1e-100 % 1e100 have the
same sign as 1e100, the computed result is -1e-100 + 1e100, which
is numerically exactly equal to 1e100. Function fmod() in the math
module returns a result whose sign matches the sign of the first
argument instead, and so returns -1e-100 in this case. Which approach
is more appropriate depends on the application.]

http://python.org/doc/current/lib/module-math.html#l2h-1105
fmod(x, y)
Return fmod(x, y), as defined by the platform C library. Note that
the Python expression x % y may not return the same result.

Jeff

 

[Terry Reedy]

Hi,

I have a problem with % operation. It returns a incorrect value in
this case:

1.0

where the returned value should be -2.77555756156e-17.

Wrong. As per the docs, x % positive number is defined as being positive
and <= that positive number. So above should be about 1.0 - 2.8e17, which,
for 32 bit machines, is 1.0, which is exactly what you got
1.0.

as with

1.0

whereas 0.99999999999999989

0.67232000000000003

And this is 1.0 - .32768

Terry J. Reedy