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Java Forum / General / October 2006How to find the "next" number (precision and java)
Hello everybody! I have the following question: Given a double number, can I calculate the next closest double that can represented from Java's float implementation ? e.g. If I have the number 1.500000000000000000000000000000000000000011111111111000000000000000000000000000000000000000000000000000 and the precision is 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 then the next number would be 1.500000000000000000000000000000000000000011111111111000000000000000000000000000000000000000000000000001 Can I do something like this or the precision is not the same for all numbers? Thanks in advance! > Hello everybody! I have the following question: > Given a double number, can I calculate the next closest double that can > represented from Java's float implementation ? What? float or double? > e.g. If I have the number 1.500000000000000000000000000000000000000011111111111000000000000000000000000000000000000000000000000000 > and the precision is 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 > then the next number would be 1.500000000000000000000000000000000000000011111111111000000000000000000000000000000000000000000000000001 floats have 7 digits precision, doubles have 15 digits precision. That is TOTAL digits, not digits after the decimal point. That means, first number would be 1.5, second number would be 0, and the third again 1.5 > Can I do something like this or the precision is not the same for all > numbers? Depends. relative precision is the same for all doubles/floats, absolute precision (the one you seem to refer to) is not. Have a look at java.lang.Math.ulp(double) or java.lang.Math.ulp(float). If thats not what you want, have a look at java.math.BigDecimal. Thanks Boris! I'm on to it > Hello everybody! I have the following question: > Given a double number, can I calculate the next closest double that can [quoted text clipped - 10 lines] > > Thanks in advance! The absolute value of the gap between adjacent doubles varies with magnitude. Floating point carries a fixed number of significant bits, so large numbers have bigger gaps between them than small numbers. It is sometimes called the "ulp", unit in last place, of the number, and is a useful concept in talking and thinking about floating point precision. If you want to know it for a specific number, use Math.ulp(). In simple cases (not infinities, NaNs, Double.MAX_VALUE), you can find the next double up by adding one to the bit pattern: long bits = Double.doubleToLongBits(in); double up = Double.longBitsToDouble(bits+1); Patricia Thank you Patricia for your answer! I had to read the IEEE 754 standard to fully understand what you had already explained to me! It was exactly what I was looking for! > Thank you Patricia for your answer! I had to read the IEEE 754 standard > to fully understand what you had already explained to me! It was > exactly what I was looking for! I am still lost.* What is the actual (/ultimate) purpose of gaining the next double? * Not that that matters to the OP or their stated problem, but I am interested. Andrew T. >> Thank you Patricia for your answer! I had to read the IEEE 754 standard >> to fully understand what you had already explained to me! It was [quoted text clipped - 6 lines] > * Not that that matters to the OP or their stated problem, > but I am interested. I don't know about the OP's interest, but I am interested in the gaps between adjacent numbers as a means to the end of understanding floating point behavior. The precision of many of the java.lang.Math methods is defined in terms of the ulp for the input. The most accurate operations, including simple arithmetic, produce an answer, if rounding is needed, that is one of the pair of doubles that bracket the infinitely precise result. Patricia > Thank you Patricia for your answer! I had to read the IEEE 754 standard > to fully understand what you had already explained to me! It was > exactly what I was looking for! You have my sympathy. What understanding I have of IEEE floating point came partly from reading the standard, many times. Patricia > > Thank you Patricia for your answer! I had to read the IEEE 754 standard > > to fully understand what you had already explained to me! It was > > exactly what I was looking for! > > You have my sympathy. What understanding I have of IEEE floating point > came partly from reading the standard, many times. (chuckle) BTW - Thanks for the response on the other (sub)thread. Andrew T. Free MagazinesGet these publications absolutely FREE for up to 12 months. There are no hidden fees and no obligation. Simply choose a title, complete the application form and submit it. Read more ...
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