float: Floating point precision

  • Floating point numbers have limited precision.
  • It depends on the system, PHP typically uses the IEEE 754 double precision format, which will give a maximum relative error due to rounding in the order of 1.11e-16.
  • Non elementary arithmetic operations may give larger errors, and, of course, error propagation must be considered when several operations are compounded.
  • Additionally, rational numbers that are exactly representable as floating point numbers in base 10, like 0.1 or 0.7, do not have an exact representation as floating point numbers in base 2, which is used internally, no matter the size of the mantissa.
  • Floor((0.1+0.7)*10) will usually return 7 instead of the expected 8, since the internal representation will be something like 7.9999999999999991118....
  • Never trust floating number results to the last digit, and do not compare floating point numbers directly for equality.

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Floating point precision

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