Re: [New Release] Vector Magic Serial Number
Rapheal Pinto
You cannot rely on a std::vector being any particular size. The size can even change between debug and release modes. Typically a vector is implemented with three pointers but it does have to. In this case if you have a 64 bit system your vector could have 2 pointers. One to the data and one to a struct that has the other information in it. If you are going to need the size of the vector for something in your program then you should just use sizeof(std::vector) and not use a "magic" number.
ChatGPT, a proprietary instruction-following model, was released in November 2022 and took the world by storm. The model was trained on trillions of words from the web, requiring massive numbers of GPUs to develop. This quickly led to Google and other companies releasing their own proprietary instruction-following models. In February 2023, Meta released the weights for a set of high-quality (but not instruction-following) language models called LLaMA to academic researchers, trained for over 80,000 GPU-hours each. Then, in March, Stanford built the Alpaca model, which was based on LLaMA, but tuned on a small dataset of 50,000 human-like questions and answers that, surprisingly, made it exhibit ChatGPT-like interactivity.
The inverse square root of a floating point number is used in digital signal processing to normalize a vector, scaling it to length 1 to produce a unit vector.[14] For example, computer graphics programs use inverse square roots to compute angles of incidence and reflection for lighting and shading. 3D graphics programs must perform millions of these calculations every second to simulate lighting. When the code was developed in the early 1990s, most floating point processing power lagged the speed of integer processing.[7] This was troublesome for 3D graphics programs before the advent of specialized hardware to handle transform and lighting. Computation of square roots usually depends upon many division operations, which for floating point numbers are computationally expensive. The fast inverse square generates a good approximation with only one division step.
The advantages in speed offered by the fast inverse square root trick came from treating the 32-bit floating-point word[note 1] as an integer, then subtracting it from a "magic" constant, 0x5F3759DF.[7][19][20][21] This integer subtraction and bit shift results in a bit pattern which, when re-defined as a floating-point number, is a rough approximation for the inverse square root of the number. One iteration of Newton's method is performed to gain some accuracy, and the code is finished. The algorithm generates reasonably accurate results using a unique first approximation for Newton's method; however, it is much slower and less accurate than using the SSE instruction rsqrtss on x86 processors also released in 1999.[1][22]
It is not known precisely how the exact value for the magic number was determined. Chris Lomont developed a function to minimize approximation error by choosing the magic number R \displaystyle R over a range. He first computed the optimal constant for the linear approximation step as 0x5F37642F, close to 0x5F3759DF, but this new constant gave slightly less accuracy after one iteration of Newton's method.[30] Lomont then searched for a constant optimal even after one and two Newton iterations and found 0x5F375A86, which is more accurate than the original at every iteration stage.[30] He concluded by asking whether the exact value of the original constant was chosen through derivation or trial and error.[31] Lomont said that the magic number for 64-bit IEEE754 size type double is 0x5FE6EC85E7DE30DA, but it was later shown by Matthew Robertson to be exactly 0x5FE6EB50C7B537A9.[32]
R operates on named data structures. The simplest suchstructure is the numeric vector, which is a single entityconsisting of an ordered collection of numbers. To set up a vectornamed x, say, consisting of five numbers, namely 10.4, 5.6, 3.1,6.4 and 21.7, use the R command
The elementary arithmetic operators are the usual +, -,*, / and ^ for raising to a power.In addition all of the common arithmetic functions are available.log, exp, sin, cos, tan, sqrt,and so on, all have their usual meaning.max and min select the largest and smallest elements of avector respectively.range is a function whose value is a vector of length two, namelyc(min(x), max(x)).length(x) is the number of elements in x,sum(x) gives the total of the elements in x,and prod(x) their product.
Components are always numbered and may always be referred to assuch. Thus if Lst is the name of a list with four components,these may be individually referred to as Lst[[1]],Lst[[2]], Lst[[3]] and Lst[[4]]. If, further,Lst[[4]] is a vector subscripted array then Lst[[4]][1] isits first entry.
Produces a histogram of the numeric vector x. A sensible numberof classes is usually chosen, but a recommendation can be given with thenclass= argument. Alternatively, the breakpoints can bespecified exactly with the breaks= argument. If theprobability=TRUE argument is given, the bars represent relativefrequencies divided by bin width instead of counts.
Sometimes we want to identify particular points on a plot, ratherthan their positions. For example, we may wish the user to select someobservation of interest from a graphical display and then manipulatethat observation in some way. Given a number of (x, y)coordinates in two numeric vectors x and y, we could usethe identify() function as follows:
The identify() functions performs no plotting itself, but simplyallows the user to move the mouse pointer and click the left mousebutton near a point. If there is a point near the mouse pointer it willbe marked with its index number (that is, its position in thex/y vectors) plotted nearby. Alternatively, you could usesome informative string (such as a case name) as a highlight by usingthe labels argument to identify(), or disable markingaltogether with the plot = FALSE argument. When the process isterminated (see above), identify() returns the indices of theselected points; you can use these indices to extract the selectedpoints from the original vectors x and y.
When activating Vector Magic, the caster focuses the magical energies that dwell throughout their frame intently, projecting them outwards ever-so-slightly with the user's energies superimposing themselves over the wielder of this magic's body, acting as an invisible armor composed entirely of arcane power of sorts which is compressed upon their frame. This invisible armor allows the caster to instantly induce the fusion of eternano ambient within the atmosphere and the magical energy that makes up the defense shrouding their frame - however, instead of the usual activation methods of magic, Vector Magic allows the caster to, well, affect vectors, which are a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another; specifically, and thus constant fusion of the magical energies that compose the invisible armor and stray eternano, the caster modify the vector values of anything that they come into contact with - however, their control over vectors is mainly in regards to Euclidean vectors, which are used to represent physical quantities that have both magnitude and direction. As long as "something goes somewhere" and energy combination is in play, with Vector Magic, the caster can induce a similar effect.
Vector Magic is a naturally defensive type of magic that offers superior protection than almost every other form of defensive magic, including those such as Barrier Magic and even the basic spell known as Defenser, the power of Vector Magic allows it's caster to completely redirect an opposing vector (something with direction and magnitude) away from himself, or otherwise reduce the energy from something coming in contact with the invisible barrier projected by this magic to zero, rendering it inert and completely harmless. The defensive power of Vector Magic is exceptional to say the least; practitioners of this magic are capable of redirecting anything with a vector including light, sound, heat, electricity, and even gravity, all of which provides a nearly undefeatable defense when combating wizards. As defense is the primary function of Vector Magic, exceptionally skilled users, rare as they are, are capable of introducing a filter-like system into this magic that allows those skilled users to instantly redirect anything that isn't listed within the filter; the filters actual purpose is to protect the user as this magic would naturally redirect everything with a vector including oxygen and such other things as that.
The defensive applications of this magic are essentially without end and are all exceptionally powerful, easily being able to stop pretty much anything that may cause harm to its user and render it completely harmless. Even the most powerful of magic spells are rendered useless when pitted against a user of Vector Magic, but the defenses are not without weakness. Vector Magic is unable to deal with an attack that has already penetrated the area that sits between the outermost shell of the projected barrier and the user should it already be there before the barrier is completely erected. Vector Magic's defensive capabilities are also shown to rely entirely upon the projected barrier of the magic, meaning that should an attack or vector not make contact with it Vector Magic will fail to activate and act accordingly with its casters commands.
Vector Magic, while a primarily defensive magic can also be used offensively to astounding results; simple motions and actions can become exceedingly deadly, all while maintaining a powerful defense. The offensive usages of Vector Magic allow its caster to increase the magnitude of the vectors of objects, such as a small pebble, being capable of launching it like a cannonball. Users of Vector Magic who utilize it for offensive purposes are able to project the barrier that is used by this magic and shirk it down until it may only surround their fists; this allows even the simplest touches to cause severe and highly grievous wounds with only the lightest of feather touches. By surrounding only their fists with the barrier that is produced by this magic to work, they are able to use even the faintest of touches to cause extreme damage to objects; the fist sized barriers allow casters to make only the slightest of contact while still obtaining the maximum of results, such as being able to lightly poke an opponent in the chest and wend them flying several hundred feet backwards, and with enough force to shatter stone and metal like wet tissue paper. A weak punch with no force to it can hurl an opponent into the ground with enough force to leave a large crater in its wake. Other offensive usages of Vector Magic allow a caster to use a pseudo-form of Gravity Magic by increasing the gravitational vectors surround their opposition, or they can lower it, but this usage has a highly limited range of use and is primarily used by the caster by lowering the gravitational vectors around themselves. Vector Magic users can also very easily create varying sized earthquakes by manipulating the vectors that their feet apply to the ground, this allows even the lightest of touches to the ground cause severe shaking and disorientation, as well as users being able to make the ground violently erupt upwards and explode.
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