I want to check whether a float is actually 32 or 64bits (and the number of bits of a numpy float array). There should be a built-in, but just didn't find out... Show
Sven Marnach 543k114 gold badges914 silver badges816 bronze badges asked Nov 21, 2011 at 17:43
Hailiang ZhangHailiang Zhang 16.2k21 gold badges66 silver badges112 bronze badges 0
Properties of a Python The items of a NumPy array might have different size, but you can
check their size in bytes by
answered Nov 21, 2011 at 17:45
Sven MarnachSven Marnach 543k114 gold badges914 silver badges816 bronze badges 5 numpy.finfo lists sizes and other attributes of float32 ..., including
will print e.g.
(Try float16 and float128 too.) answered Nov 21, 2011 at 18:51
2
answered May 15, 2013 at 0:30
gggggggg 2,1541 gold badge15 silver badges19 bronze badges The range of floating point values is available in the As Sven says, for CPython
So this is not necessarily the case for other Python implementations. answered Nov 21, 2011 at 18:00 0
"+1" because one digit in the mantissa is stored implicitly. answered Oct 28, 2020 at 0:49
This chapter discusses how to store data, and how to compute values from data. The topics are variables, memory, data types, expressions, and operators. It’s useful to be able to store values in the computer’s memory for later use. A variable is a name that refers to a location in the computer’s memory where a piece of information can be stored. A simple example: The statement
Later, when the value of the variable is needed (in the In Python, each variable must be assigned a value before that variable can be used. Variable names vs. stringsStrings have quotation marks around them so that it is clear that the string is to be considered a string value, and not a variable name. What does the following code print? Is there an error in the code? Using variables to change code behaviorWe’ll see soon how to use variables to compute and store values. But one important use of variables is to change the behavior of code. First, we write the code in terms of some variables. Changing the values of those variables then changes the behavior of the code. The example below shows how this
works. First, run the code. Then change the value of Exercise: big smileObjective: Use variables to allow behavior of code to be changed easily. The code below will draw a smiley face on the screen, and you can use the variables Test your code by changing variable values a few times to draw the smiley face at different locations at both small and large scales. Choosing good variable namesVariable names are sequences of letters, digits, and underscores. The first letter cannot be a digit, and variable names cannot contain spaces. Python is case-sensitive: uppercase and lowercase letters are considered to be different characters in variable names, so that the names By convention, letters appearing in
variable names in Python are all lowercase. If you want to make up a variable name from multiple words, use the underscore character Variable assignment with ‘=’The equals sign used to assign a value to a variable is not the same as the equals sign you see in mathematics. In mathematics, the equals sign is used to write down facts: the expression or variable on the left-hand side of the equation is now, and always will be, equal to the expression or variable on the right-hand side. In mathematics, x = 5 is a fine equation. So is x = 6. But if I gave you both equations, you’d say I screwed up, because then x would equal both 5 and 6, and it just can’t. But in Python, the following works just fine: The
So the first line of code copies the value 5 into the variable Here are a few statements that wouldn’t work in mathematics, but do work in Python: In mathematics, x = x + 1 would mean something like “x is the number that is one greater than itself”. That sounds like something that Captain Kirk used to make a computer explode in Star Trek. There is no such number. In Python, there’s no problem. Evaluate the expression on the right-hand side. Fine—because When you see or write an equals sign in Python, do not think “mathematically equals.” Say in your mind, “assignment operator.” Compute the value on the right-hand side. Put the computed value into the variable on the left-hand side. Will the code How memory worksMemory in a computer is basically a long sequence of 0s and 1s, or binary digits: bits. You can think of a very long row of on/off switches. Since each switch value doesn’t give much information (only a 0 or a 1), it’s useful to refer to groups of bits. A group of eight sequential bits is called a byte. On a Mac or PC, each byte has its own address, a number associated with it that we can use to refer to that byte. The byte at address 0 is the first byte in memory; the byte at address 1 is the second, and so forth. (Computer scientists often start counting at 0. Believe it or not, we often find it easier to start counting at 0 than starting at 1.) Wait – how do we refer to a location in memory? Do we use variable names or addresses? The answer is both. You have a Hinman box number. I can refer to your mailbox directly by number (address), or I can use your name to refer to the box, assuming that I have a directory that tells me what box number is associated with your name. Python acts as the directory that keeps track of the correspondence between variable names and memory addresses where the contents of the variables can be found. Integer typesI just said that memory is a string of 0s and 1s. How in the world are we going to represent the number 42 by a string of 0s and 1s? Python uses a special code, relying on how to represent numbers in base 2, or binary. Let’s not worry too much about how to represent numbers in binary, but I’ll just tell you that 42 in base 2 is 101010. Here are various integers in binary:
The first thing to notice about these binary representations is that their lengths differ. The integer 6 needs only three bits, but the integer 999 needs ten bits. To be safe, Python allocates a fixed number of bytes of space in memory for each variable of a normal integer type, which is known as Let’s say you had only one byte of memory. How many different patterns of 0s and 1s can represent integers in eight bits? Let’s count them:
It looks like there are 28 = 256 different patterns. I could use my one byte to represent 256 unique integer numbers, because each integer would need its own bit pattern. If I had two bytes, I could represent 216 = 65,536 different integer numbers. With four bytes (the usual amount of memory allocated
to each Note: When you are typing in large integers, whether it’s as part of your program, as console input, or as input anywhere else, do not include commas. Do not type The long int typeIf you want to store a number larger than 2,147,483,647, Python can do it, using the In Python, every datum has a type. But we don’t have to say what the type is; Python can figure it out for itself. The floating-point typeThe floating-point type is like scientific notation, e.g., 6.02 × 1023. Since you can’t type a superscript in plain text for Python, if an exponent on the 10 is needed, you would write it like this: Notice that we omit the 10, but it’s understood; 6.02e23 is not 6.0223 (6.02 raised to the power 23), but instead is 6.02 × 1023. Floating-point numbers are stored with three parts:
The floating-point type (or “float type” for short) is used for numbers that have
fractional parts or are too large to store in a Floating-point numbers get less precise the further you get from 0The difference between 0.01 and 0.02 is, relatively, a lot (100%), but the relative difference between (6.02e23 + 0.01) and (6.02e23 + 0.02) is not a lot, at least compared with the size of the numbers involved. For this reason, the 264 floating-point numbers are not evenly distributed on the real number line. More of them are allocated near 0 than near numbers with larger magnitudes. When you type in a number with a decimal point, or create one through some mathematical operation, the computer finds a floating-point number close to the correct number. Small fractions are likely to be lost in this rounding process for real numbers that are very large, since the nearest floating-point number that the computer can represent may be relatively quite far away. Expressions and operatorsYou can use Python to compute. The program The plus-sign is called an operator. An operator takes one or more operands, computes a result, and makes that result available to Python for further use. In this example, the operand on the left is 18, and the operand on the right is 24. An expression is an operator and its operands; we say that the expression can be evaluated to give a single value. In our
example, the expression is An expression can be an operand to an operator: Here, the expression The character Arithmetic operators such as For example: Integer divisionThere are two types of division, and each is sometimes useful. Integer division takes two integers and evaluates to an integer. Floating-point division takes two floating-point numbers (numbers with a decimal point) and evaluates to a floating-point number. Remember word problems like this? At the Lake Morey Skate-athon, I skate around an oval ice track that is four miles long. I carry a card, and for every full lap I skate, I get my card stamped. If I start at 12:00 noon and skate at 10 miles per hour, how many stamps will I have at 3:00 pm? At 3:00 pm, I will have skated 3 × 10 miles, or 30 miles. Dividing 4 into 30 gives 7 laps, and hence 7 stamps, with half a lap (2/4 of a lap) left over. In Python version 2, the program:
gives the result ‘7’: integer division. In Python 3, the operator Using integer division when you want floating-point division is a very common mistake in Python 2. The best solution is to start your code with the statement:
Operators defined on integer and floating-point types: +, -, *, /, %The operators defined on integer and floating-types types are
The mod operator in Python is unusual in that it can take
floating-point operands. (Most other programming languages that support a mod operator insist on only integer operands.) For example, The string typeThere are many different types of data to store. Integers are one type; letters of the alphabet are another. The “string” type of data represents one or more letters of the alphabet, symbols (such as When you type a string value into Python, it must be surrounded by quotes, so that the string does not look like the name of a variable. We call The quotes say that “hello” is a string, and not a variable name. More examples: The quotes just identify the data as a string; the quotes aren’t part of the string. Python is unusual in that you can use either single quotes or double quotes around the string, as long as you use the same kind of quotes before and after a given string. So the following lines do the same thing: But String concatenationThe plus sign (“ What if there are strings on each side? Then the plus sign is the string-concatenation operator. Concatenation means to “combine two strings together”. Internal representation of stringsGiven that the memory of a computer stores only sequences of 0s and 1s, then how does Python store a string in memory? Python uses a code to convert a string into a binary representation of the string when the string is stored. When the string is retrieved, Python uses the code in reverse to convert back from binary into the string. Which code does Python use? Python version 2.7 (the version we use for this class), uses a popular code called the American Standard Code for
Information Interchange, or ASCII. Each character (string of length 1) uses eight bits, or one byte. For example, the ASCII code for the character If you’d like to see a full table of ASCII character codes, click here. You rarely need to know a character’s ASCII code. Converting between typesThere are
a few special functions that convert between types of data: Sometimes conversions are performed automatically by Python behind the scenes, much as what happens when one of the operands for division is a floating-point number and the other is an int. For example, if you try to add a float and an int, the int is converted to a float before addition: The boolean typeThere’s
one another type of data, called a Coding styleWe’ve already discussed comments, which are one tool to make reading and understanding programs easier. Another way to improve understandability is to use meaningful names for variables. For instance, consider the following code: What does it do? We could tell by running it, or we could add comments. Or we
could use more descriptive names than Without using comments, we’ve improved the understandability of the code considerably. This is not to say that comments should be jettisoned completely in favor of meaningful names! Rather, the two strategies work together. Next, consider this code, with meaningful names: It’s easy to see what it does because of the names we’ve chosen. But it could be better, especially the constant floating-point values we’ve stuck in there. Presumably, we’re confident in our ability to calculate 4.0 * 3.0 / pi (notice that I have to make sure that at least one of 4 and 3 is a float so that I don’t get integer division), but if we make a mistake, it’s going to be very difficult to track down. Here, we’ve replaced the number 3.14 with a variable Some constants are so widely-used that Python defines them for us. For instance: An
added benefit of using Python’s Bonus coverage: The function typeA function is itself a data type in Python. You can think of the name of the function as a variable that contains the address of the function’s lines of code. What this means is that other variables can also store a reference to the function. Here is an example: We have already seen another example. We wrote the Is Python float 64Python float values are represented as 64-bit double-precision values. The maximum value any floating-point number can be is approx 1.8 x 10308. Any number greater than this will be indicated by the string inf in Python.
Are Python floats 32 bit?Python's floating-point numbers are usually 64-bit floating-point numbers, nearly equivalent to np.
How many bytes is a double in Python?Data Types and Sizes. Is a float 4 bytes?Single-precision values with float type have 4 bytes, consisting of a sign bit, an 8-bit excess-127 binary exponent, and a 23-bit mantissa.
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