ieee-754

问题 What is the biggest "no-floating" integer that can be stored in an IEEE 754 double type without losing precision ? 回答1: The biggest/largest integer that can be stored in a double without losing precision is the same as the largest possible value of a double. That is, DBL_MAX or approximately 1.8 × 10 308 (if your double is an IEEE 754 64-bit double). It's an integer. It's represented exactly. What more do you want? Go on, ask me what the largest integer is, such that it and all smaller

问题 This question already has answers here : Efficient way to round double precision numbers to a lower precision given in number of bits (2 answers) Closed last year . I would like to introduce some artificial precision loss into two numbers being compared to smooth out minor rounding errors so that I don't have to use the Math.abs(x - y) < eps idiom in every comparison involving x and y . Essentially, I want something that behaves similarly to down-casting a double to a float and then up

问题 As we know, because of the limited precision of double, the following two calculation may not give the exact the same value : A / B / C and A / ( B * C ) My question is even with the same two variable, A & B, can the compiler guarantee every time A / B yield the same value ? Or I should ask in the code, can we guarantee the following statement always return true: If ( A / B == A / B ) 回答1: A guarantee of behavior for a compiler requires some document specifying the behavior. The answer

问题 i am learning IEEE-754 representation of numbers. I know how to convert from binary to IEEE and on vice versa. Now i am trying to figure out how to find out how many numbers in single precision are for instance between 2 and 3. So, the sign will be the same for both. Fraction will be a combination i think and exponent is dependent from a proper number(because of shifts). WHat would be a clever way to do it right ? I would be grateful for any help. 回答1: Using a handy online IEEE-754 conversion

问题 I know that floating point values in JavaScript are stored with a binary base-2 format specified in IEEE 754. To me, this means that when I assign the literal value .1 to a variable, the value actually stored will be 0.100000001490116119384765625 (or some high-precision number like that--my math may be wrong). But counter to that assumption, the console.log of a stored value does not reflect this. The following code: var a = 0.1; console.log(a); ...when executed in Chrome, and probably other

问题 Why is 0 11110 1111111111 and not 0 11111 1111111111 the highest half precision number? 回答1: Because an exponent field of 11111 2 is reserved for infinities and NaNs. Section 3.4 of the IEEE 754-2008 standard says: The range of the encoding’s biased exponent E shall include: every integer between 1 and 2 w − 2, inclusive, to encode normal numbers the reserved value 0 to encode ±0 and subnormal numbers the reserved value 2 w − 1 to encode ±∞ and NaNs. Here "w" is the width of the exponent

问题 I'm looking the best way to transform a float number to its decimal representation in C. I'll try to give you an example: the user introduces a number in IEEE754 (1 1111111 10101...) and the program has to return the decimal representation (ex. 25.6) I've tried with masks, and bitwise operations, but I haven't got any logical result. 回答1: I believe the following is performing the operation you describe: I use the int as an intermediate representation because it has the same number of bits as

问题 The best way I've found to produce a decimal.Decimal number with a specific number of significant figures is the one used to initialize the variable kluge below: import decimal THIS_IS_JUST_AN_EXAMPLE = 0.00001/3.0 with decimal.localcontext() as c: c.prec = 5 kluge = decimal.Decimal(THIS_IS_JUST_AN_EXAMPLE) + decimal.Decimal(0) naive = decimal.Decimal(THIS_IS_JUST_AN_EXAMPLE) print repr(kluge) print repr(naive) # Decimal('0.0000033333') # Decimal('0

问题 I write code in LINUX RHEL 64bit, and use C++98. I have an array of floating point values, and I wanted to 'mark' some values to be 'invalid'. One possible solution is to use another bit-array to tell if the corresponding value is valid. I was wondering if we can use any special double value. The link Why does IEEE 754 reserve so many NaN values? says that there are lot of NaN values. Can we use any value reserved for my problem? I only need one bit in the payload to indicate if a double

问题 I'm struggling with converting a 32-bit hex expression into a single precision number in Matlab. The num2hex function works fine for both. For example, >> b = 0.4 b = 0.400000000000000 >> class(b) ans = double >> num2hex(b) ans = 3fd999999999999a >> num2hex(single(b)) ans = 3ecccccd However, this does not work the other way around. The hex2num function only converts hexadecimal expression into doubles. So, >> b = 0.4 b = 0.400000000000000 >> num2hex(single(b)) ans = 3ecccccd >> hex2num(ans)