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  • Nicely representing a floating-point number in python

    - by dln385
    I want to represent a floating-point number as a string rounded to some number of significant digits, and never using the exponential format. Essentially, I want to display any floating-point number and make sure it “looks nice”. There are several parts to this problem: I need to be able to specify the number of significant digits. The number of significant digits needs to be variable, which can't be done with with the string formatting operator. I need it to be rounded the way a person would expect, not something like 1.999999999999 I've figured out one way of doing this, though it looks like a work-round and it's not quite perfect. (The maximum precision is 15 significant digits.) >>> def f(number, sigfig): return ("%.15f" % (round(number, int(-1 * floor(log10(number)) + (sigfig - 1))))).rstrip("0").rstrip(".") >>> print f(0.1, 1) 0.1 >>> print f(0.0000000000368568, 2) 0.000000000037 >>> print f(756867, 3) 757000 Is there a better way to do this? Why doesn't Python have a built-in function for this?

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  • Convert pre-IEEE-574 C++ floating-point numbers to/from C#

    - by Richard Kucia
    Before .Net, before math coprocessors, before IEEE-574, Microsoft defined a bit pattern for floating-point numbers. Old versions of the C++ compiler happily used that definition. I am writing a C# app that needs to read/write such floating-point numbers in a file. How can I do the conversions between the 2 bit formats? I need conversion methods in both directions. This app is going to run in a PocketPC/WinCE environment. Changing the structure of the file is out-of-scope for this project. Is there a C++ compiler option that instructs it to use the old FP format? That would be ideal. I could then exchange data between the C# code and C++ code by using a null-terminated text string, and the C++ methods would be simple wrappers around sprintf and atof functions. At the very least, I'm hoping someone can reply with the bit definitions for the old FP format, so I can put together a low-level bit manipulation algorithm if necessary. Thanks.

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  • How to efficiently compare the sign of two floating-point values while handling negative zeros

    - by François Beaune
    Given two floating-point numbers, I'm looking for an efficient way to check if they have the same sign, given that if any of the two values is zero (+0.0 or -0.0), they should be considered to have the same sign. For instance, SameSign(1.0, 2.0) should return true SameSign(-1.0, -2.0) should return true SameSign(-1.0, 2.0) should return false SameSign(0.0, 1.0) should return true SameSign(0.0, -1.0) should return true SameSign(-0.0, 1.0) should return true SameSign(-0.0, -1.0) should return true A naive but correct implementation of SameSign in C++ would be: bool SameSign(float a, float b) { if (fabs(a) == 0.0f || fabs(b) == 0.0f) return true; return (a >= 0.0f) == (b >= 0.0f); } Assuming the IEEE floating-point model, here's a variant of SameSign that compiles to branchless code (at least with with Visual C++ 2008): bool SameSign(float a, float b) { int ia = binary_cast<int>(a); int ib = binary_cast<int>(b); int az = (ia & 0x7FFFFFFF) == 0; int bz = (ib & 0x7FFFFFFF) == 0; int ab = (ia ^ ib) >= 0; return (az | bz | ab) != 0; } with binary_cast defined as follow: template <typename Target, typename Source> inline Target binary_cast(Source s) { union { Source m_source; Target m_target; } u; u.m_source = s; return u.m_target; } I'm looking for two things: A faster, more efficient implementation of SameSign, using bit tricks, FPU tricks or even SSE intrinsics. An efficient extension of SameSign to three values.

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  • A* navigational mesh path finding

    - by theguywholikeslinux
    So I've been making this top down 2D java game in this framework called Greenfoot [1] and I've been working on the AI for the guys you are gonna fight. I want them to be able to move around the world realistically so I soon realized, amongst a couple of other things, I would need some kind of pathfinding. I have made two A* prototypes. One is grid based and then I made one that works with waypoints so now I need to work out a way to get from a 2d "map" of the obstacles/buildings to a graph of nodes that I can make a path from. The actual pathfinding seems fine, just my open and closed lists could use a more efficient data structure, but I'll get to that if and when I need to. I intend to use a navigational mesh for all the reasons out lined in this post on ai-blog.net [2]. However, the problem I have faced is that what A* thinks is the shortest path from the polygon centres/edges is not necessarily the shortest path if you travel through any part of the node. To get a better idea you can see the question I asked on stackoverflow [3]. I got a good answer concerning a visibility graph. I have since purchased the book (Computational Geometry: Algorithms and Applications [4]) and read further into the topic, however I am still in favour of a navigational mesh (See "Managing Complexity" [5] from Amit’s Notes about Path-Finding [6]). (As a side note, maybe I could possibly use Theta* to convert multiple waypoints into one straight line if the first and last are not obscured. Or each time I move back check to the waypoint before last to see if I can go straight from that to this) So basically what I want is a navigational mesh where once I have put it through a funnel algorithm (e.g. this one from Digesting Duck [7]) I will get the true shortest path, rather than get one that is the shortest path following node to node only, but not the actual shortest given that you can go through some polygons and skip nodes/edges. Oh and I also want to know how you suggest storing the information concerning the polygons. For the waypoint prototype example I made I just had each node as an object and stored a list of all the other nodes you could travel to from that node, I'm guessing that won't work with polygons? and how to I tell if a polygon is open/traversable or if it is a solid object? How do I store which nodes make up the polygon? Finally, for the record: I do want to programme this by myself from scratch even though there are already other solutions available and I don't intend to be (re) using this code in anything other than this game so it does not matter that it will inevitably be poor quality. http://greenfoot.org http://www.ai-blog.net/archives/000152.html http://stackoverflow.com/q/7585515/ http://www.cs.uu.nl/geobook/ http://theory.stanford.edu/~amitp/GameProgramming/MapRepresentations.html http://theory.stanford.edu/~amitp/GameProgramming/ http://digestingduck.blogspot.com/2010/03/simple-stupid-funnel-algorithm.html

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  • Floating point inaccuracy examples

    - by David Rutten
    How do you explain floating point inaccuracy to fresh programmers and laymen who still think computers are infinitely wise and accurate? Do you have a favourite example or anecdote which seems to get the idea across much better than an precise, but dry, explanation? How is this taught in Computer Science classes?

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  • Why differs floating-point precision in C# when separated by parantheses and when separated by state

    - by Andreas Larsen
    I am aware of how floating point precision works in the regular cases, but I stumbled on an odd situation in my C# code. Why aren't result1 and result2 the exact same floating point value here? const float A; // Arbitrary value const float B; // Arbitrary value float result1 = (A*B)*dt; float result2 = (A*B); result2 *= dt; From this page I figured float arithmetic was left-associative and that this means values are evaluated and calculated in a left-to-right manner. The full source code involves XNA's Quaternions. I don't think it's relevant what my constants are and what the VectorHelper.AddPitchRollYaw() does. The test passes just fine if I calculate the delta pitch/roll/yaw angles in the same manner, but as the code is below it does not pass: X Expected: 0.275153548f But was: 0.275153786f [TestFixture] internal class QuaternionPrecisionTest { [Test] public void Test() { JoystickInput input; input.Pitch = 0.312312432f; input.Roll = 0.512312432f; input.Yaw = 0.912312432f; const float dt = 0.017001f; float pitchRate = input.Pitch * PhysicsConstants.MaxPitchRate; float rollRate = input.Roll * PhysicsConstants.MaxRollRate; float yawRate = input.Yaw * PhysicsConstants.MaxYawRate; Quaternion orient1 = Quaternion.Identity; Quaternion orient2 = Quaternion.Identity; for (int i = 0; i < 10000; i++) { float deltaPitch = (input.Pitch * PhysicsConstants.MaxPitchRate) * dt; float deltaRoll = (input.Roll * PhysicsConstants.MaxRollRate) * dt; float deltaYaw = (input.Yaw * PhysicsConstants.MaxYawRate) * dt; // Add deltas of pitch, roll and yaw to the rotation matrix orient1 = VectorHelper.AddPitchRollYaw( orient1, deltaPitch, deltaRoll, deltaYaw); deltaPitch = pitchRate * dt; deltaRoll = rollRate * dt; deltaYaw = yawRate * dt; orient2 = VectorHelper.AddPitchRollYaw( orient2, deltaPitch, deltaRoll, deltaYaw); } Assert.AreEqual(orient1.X, orient2.X, "X"); Assert.AreEqual(orient1.Y, orient2.Y, "Y"); Assert.AreEqual(orient1.Z, orient2.Z, "Z"); Assert.AreEqual(orient1.W, orient2.W, "W"); } } Granted, the error is small and only presents itself after a large number of iterations, but it has caused me some great headackes.

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  • Can one use polygon() or equivalent in lattice and ggplot2 plots?

    - by Alex Reynolds
    Is it possible to annotate lattice (or ggplot2) figures with elements created with polygon() (or elements created with a similar function) from the graphics library? I'm not too familiar with either library beyond examples of simple graphs posted on the web and printed in Deepayan Sarkar's book. Therefore, while I have code for what I've been doing in R with the graphics library, pointing me to relevant, equivalent functions and usage examples for lattice or ggplot2 specifically would be appreciated. Thanks.

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  • Floating point mantissa bias

    - by user69514
    Does anybody know how to go out solving this problem? * a = 1.0 × 2^9 * b = -1.0 × 2^9 * c = 1.0 × 2^1 Using the floating-point (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 16, a normalized mantissa of 8 bits, and a single sign bit for the number), perform the following two calculations, paying close attention to the order of operations. * b + (a + c) = ? * (b + a) + c = ?

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  • Point of Sale how to add quantity v2

    - by Jimmy nguyen
    Problem - I have Point of Sale V9 -intuit When ringing up a customer by using a barcode scanner for 1 item and the customer wants multiple of that same item but the receipt shows a long list of that same item. How can I get that program to set it where it would just self update without having to physically touching the keyboard or mouse I would pretty much want it to be user friendly Also if there is a code for this where do I put in the code?

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  • Real life example fo Floating Point error

    - by Rob
    Is there any examples of a company that was burned by floating point data that caused a rounding issue? We're implementing a new system and all the monetary values are stored in floats. I think if i can show actual examples of why this has failed it'll have more weight than the theory of why the values can't be stored properly.

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  • Floating point arithmetics restricted to integers

    - by user396672
    I use doubles for a uniform implementation of some arithmetic calculations. These calculations may be actually applied to integers too, but there are no C++-like templates in Java and I don't want to duplicate the implementation code, so I simply use "double" version for ints. Does JVM spec guarantees the correctness of integer operations such a <=,=, +, -, *, and / (in case of remainder==0) when the operations are emulated as corresponding floating point ops? (Any integer, of course, has reasonable size to be represented in double's mantissa)

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  • Floating point computer - Trouble with getting back correct results

    - by Francisco P.
    Having trouble with a challenge. Let's say I have a theoretical, base 10, floating point calculator with the following characteristics Only 3 digits for mantissa 1 digit for exponent Sign for mantissa and exponent How would this machine compute the following? 300 + \sum_{i=1}^{100} 0.2 The correct result is 320. The machine's result is 300. But why? Can't get where the 20 goes goes missing... Thanks for your time.

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  • Custom Floating Point Representation

    - by Abion47
    I'm trying to write a parser that will read a particular file type, and I need to map the different data types to C# equivalents. Most of them aren't that difficult, but I'm having trouble wrapping my head around what "int16 with a bias of 14" means. I've deduced that it's some kind of floating point type, so my best bet would be to write a converter that would map it to a float, double, or decimal type. I'm not sure where to take it from here, though.

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  • OOP Design of items in a Point-of-Sale system

    - by Jonas
    I am implementing a Point-of-Sale system. In the system I represent an Item in three places, and I wounder how I should represent them in OOP. First I have the WarehouseItem, that contains price, purchase price, info about the supplier, suppliers price, info about the product and quantity in warehouse. Then I have CartItem, which contains the same fields as WarehouseItem, but adds NrOfItems and Discount. And finally I have ReceiptItem, thats contains an item where I have stripped of info about the supplier, and only contains the price that was payed. Are there any OOP-recommendations, best-practices or design patterns that I could apply for this? I don't really know if CartItem should contain (wrap) an WarehouseItem, or extend it, or if I just should copy the fields that I need. Maybe I should create an Item-class where I keep all common fields, and then extend it to WarehouseItem, CartItem and ReceiptItem. Sometimes I think that it is good to keep the field of the item and just display the information that is needed.

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  • Another floating point question

    - by jeffmax329
    I have read most of the posts on here regarding floating point, and I understand the basic underlying issue that using IEEE 754 (and just by the nature of storing numbers in binary) certain fractions cannot be represented. I am trying to figure out the following: If both Python and JavaScript use the IEEE 754 standard, why is it that executing the following in Python .1 + .1 Results in 0.20000000000000001 (which is to be expected) Where as in Javascript (in at least Chrome and Firefox) the answer is .2 However performing .1 + .2 In both languages results in 0.30000000000000004 In addition, executing var a = 0.3; in JavaScript and printing a results in 0.3 Where as doing a = 0.3 in Python results in 0.29999999999999999 I would like to understand the reason for this difference in behavior. In addition, many of the posts on OS link to a JavaScript port of Java's BigDecimal, but the link is dead. Does anyone have a copy?

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  • Using write to print floating point numbers.

    - by Tom
    Hi, As an exercise to achieve something larger, i'm trying to use write to print a floating point number. I haven't done this in a while. I must be doing something wrong because I cant get it to work. Here is my code #include <unistd.h> int main(){ float f = 4.5; write(1,&f,sizeof float); return 0; } However, when running it im getting ?@ Any thoughts? Thanks in advance.

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  • Floating point innacuracies

    - by Greg
    While writing a function which will perform some operation with each number in a range I ran into some problems with floating point inaccuracies. The problem can be seen in the code below: #include <iostream> using namespace std; int main() { double start = .99999, end = 1.00001, inc = .000001; int steps = (end - start) / inc; for(int i = 0; i <= steps; ++i) { cout << (start + (inc * i)) << endl; } } The problem is that the numbers the above program outputs look like this: 0.99999 0.999991 0.999992 0.999993 0.999994 0.999995 0.999996 0.999997 0.999998 0.999999 1 1 1 1 1 1.00001 1.00001 1.00001 1.00001 1.00001 1.00001 They only appear to be correct up to the first 1. What is the proper way to solve this problem?

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  • Why do game engines convert models to triangles compared to keeping it as four side polygon

    - by Grant
    I've worked using maya for animation and more film orientated projects however I am also focusing on my studies on video game development (eventually want to be either programmer or some sort of TD with programming and 3D skills). Anyways, I was talking with one of my professor and we couldn't figure out why all game engines (that I know of) convert to triangles. Anyone happen to know why game engines convert to triangles compared to leaving the models as four sided polygons? Also what are the pros and cons (if any) of doing this? Thanks in advance.

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  • converting 2d grid of squares to polygon nav mesh

    - by Roflha
    I haven't actually started programming for this one yet, but I wanted to see how I would go about doing this anyway. Say I have a 2D matrix of squares, all of the same size, some traversable and some not. How would I go about creating a navigation mesh of polygons from this grid. Is there any reading I can look at until I get a chance to get to my computer or should I just give it a go. My idea was to take the non-traversable squares out and extend lines from there edges to make polygons.. that's all I have got so far. Any advice?

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  • Find max integer size that a floating point type can handle without loss of precision

    - by Checkers
    Double has range more than a 64-bit integer, but its precision is less dues to its representation (since double is 64-bit as well, it can't fit more actual values). So, when representing larger integers, you start to lose precision in the integer part. #include <boost/cstdint.hpp> #include <limits> template<typename T, typename TFloat> void maxint_to_double() { T i = std::numeric_limits<T>::max(); TFloat d = i; std::cout << std::fixed << i << std::endl << d << std::endl; } int main() { maxint_to_double<int, double>(); maxint_to_double<boost::intmax_t, double>(); maxint_to_double<int, float>(); return 0; } This prints: 2147483647 2147483647.000000 9223372036854775807 9223372036854775800.000000 2147483647 2147483648.000000 Note how max int can fit into a double without loss of precision and boost::intmax_t (64-bit in this case) cannot. float can't even hold an int. Now, the question: is there a way in C++ to check if the entire range of a given integer type can fit into a loating point type without loss of precision? Preferably, it would be a compile-time check that can be used in a static assertion, and would not involve enumerating the constants the compiler should know or can compute.

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  • floating point equality in Python and in general

    - by eric.frederich
    I have a piece of code that behaves differently depending on whether I go through a dictionary to get conversion factors or whether I use them directly. The following piece of code will print 1.0 == 1.0 -> False But if you replace factors[units_from] with 10.0 and factors[units_to ] with 1.0 / 2.54 it will print 1.0 == 1.0 -> True #!/usr/bin/env python base = 'cm' factors = { 'cm' : 1.0, 'mm' : 10.0, 'm' : 0.01, 'km' : 1.0e-5, 'in' : 1.0 / 2.54, 'ft' : 1.0 / 2.54 / 12.0, 'yd' : 1.0 / 2.54 / 12.0 / 3.0, 'mile' : 1.0 / 2.54 / 12.0 / 5280, 'lightyear' : 1.0 / 2.54 / 12.0 / 5280 / 5.87849981e12, } # convert 25.4 mm to inches val = 25.4 units_from = 'mm' units_to = 'in' base_value = val / factors[units_from] ret = base_value * factors[units_to ] print ret, '==', 1.0, '->', ret == 1.0 Let me first say that I am pretty sure what is going on here. I have seen it before in C, just never in Python but since Python in implemented in C we're seeing it. I know that floating point numbers will change values going from a CPU register to cache and back. I know that comparing what should be two equal variables will return false if one of them was paged out while the other stayed resident in a register. Questions What is the best way to avoid problems like this?... In Python or in general. Am I doing something completely wrong? Side Note This is obviously part of a stripped down example but what I'm trying to do is come with with classes of length, volume, etc that can compare against other objects of the same class but with different units. Rhetorical Questions If this is a potentially dangerous problem since it makes programs behave in an undetermanistic matter, should compilers warn or error when they detect that you're checking equality of floats Should compilers support an option to replace all float equality checks with a 'close enough' function? Do compilers already do this and I just can't find the information.

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