ieee-754 | 易学教程

Floating Point to Binary Value(C++)

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问题 I want to take a floating point number in C++, like 2.25125, and a int array filled with the binary value that is used to store the float in memory (IEEE 754). So I could take a number, and end up with a int num[16] array with the binary value of the float: num[0] would be 1 num[1] would be 1 num[2] would be 0 num[3] would be 1 and so on... Putting an int into an array isn't difficult, just the process of getting the binary value of a float is where I'm stuck. Can you just read the binary in

Is it safe to assume floating point is represented using IEEE754 floats in C?

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问题 Floating point is implementation defined in the C. So there isn't any guarantees. Our code needs to be portable, we are discussing whether or not acceptable to use IEEE754 floats in our protocol. For performance reasons it would be nice if we don't have to convert back and forth between a fixed point format when sending or receiving data. While I know that there can be differences between platforms and architectures regarding the size of long or wchar_t . But I can't seem to find any specific

Why does division by zero in IEEE754 standard results in Infinite value?

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I'm just curious, why in IEEE-754 any non zero float number divided by zero results in infinite value? It's a nonsense from the mathematical perspective. So I think that correct result for this operation is NaN. Function f(x) = 1/x is not defined when x=0, if x is a real number. For example, function sqrt is not defined for any negative number and sqrt(-1.0f) if IEEE-754 produces a NaN value. But 1.0f/0 is Inf . But for some reason this is not the case in IEEE-754 . There must be a reason for this, maybe some optimization or compatibility reasons. So what's the point? It's a nonsense from the

Usefulness of signaling NaN?

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问题 I've recently read up quite a bit on IEEE 754 and the x87 architecture. I was thinking of using NaN as a "missing value" in some numeric calculation code I'm working on, and I was hoping that using signaling NaN would allow me to catch a floating point exception in the cases where I don't want to proceed with "missing values." Conversely, I would use quiet NaN to allow the "missing value" to propagate through a computation. However, signaling NaNs don't work as I thought they would based on

How do I convert from a decimal number to IEEE 754 single-precision floating-point format?

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问题 How would I go about manually changing a decimal (base 10) number into IEEE 754 single-precision floating-point format? I understand that there is three parts to it, a sign, an exponent, and a mantissa. I just don't completely understand what the last two parts actually represent. 回答1: Find the largest power of 2 which is smaller than your number, e.g if you start with x = 10.0 then 2 3 = 8, so the exponent is 3. The exponent is biased by 127 so this means the exponent will be represented as

Algorithm to convert an IEEE 754 double to a string?

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Many programming languages that use IEEE 754 doubles provide a library function to convert those doubles to strings. For example, C has sprintf , C++ has stringstream , Java has Double.toString , etc. Internally, how are these functions implemented? That is, what algorithm(s) are they using to convert the double into a string representation, given that they are often subject to programmer-chosen precision limitations? Thanks! The code used by various software environments to convert floating-point numbers to string representations is typically based on the following publications (the work by

What is difference between quiet NaN and signaling NaN?

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I have read about floating-point and I understand that NaN could results from operations. but I can't understand what are these concepts exactly. What is difference? Which one can be produced during C++ programming? As a programmer, could I write a program cause a sNaN? When an operation results in a quiet NaN, there is no indication that anything is unusual until the program checks the result and sees a NaN. That is, computation continues without any signal from the floating point unit (FPU) or library if floating-point is implemented in software. A signalling NaN will produce a signal,

What is a subnormal floating point number?

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isnormal() reference page tells : Determines if the given floating point number arg is normal, i.e. is neither zero, subnormal, infinite, nor NaN. A number being zero, infinite or NaN is clear what it means. But it also says subnormal. When is a number subnormal? In the IEEE754 standard, floating point numbers are represented as binary scientific notation, x = M × 2 e . Here M is the mantissa and e is the exponent . Mathematically, you can always choose the exponent so that 1 ≤ M < 2.* However, since in the computer representation the exponent can only have a finite range, there are some

Float precision bits

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问题 In this wiki article it shows 23 bits for precision, 8 for exponent, and 1 for sign Where is the hidden 24th bit in float type that makes (23+1) for 7 significand digits? 回答1: Floating point numbers are usually normalized. Consider, for example, scientific notation as most of us learned it in school. You always scale the exponent so there's exactly one digit before the decimal point. For example, instead of 123.456, you write 1.23456x10 2 . Floating point on a computer is normally handled

Denormalized Numbers - IEEE 754 Floating Point

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问题 So I'm trying to learn more about Denormalized numbers as defined in the IEEE 754 standard for Floating Point numbers. I've already read several articles thanks to Google search results, and I've gone through several StackOverFlow posts. However I still have some questions unanswered. First off, just to review my understanding of what a Denormalized float is: Numbers which have fewer bits of precision, and are smaller (in magnitude) than normalized numbers Essentially, a denormalized float