text:
Methods of computing square roots are numerical analysis algorithms for approximating the principal, or non-negative, square root (usually denoted , , or ) of a real number. Arithmetically, it means given , a procedure for finding a number which when multiplied by itself, yields ; algebraically, it means a procedure for finding the non-negative root of the equation ; geometrically, it means given two line segments, a procedure for constructing their geometric mean.

Every real number except zero has two square roots. The principal square root of most numbers is an irrational number with an infinite decimal expansion. As a result, the decimal expansion of any such square root can only be computed to some finite-precision approximation. However, even if we are taking the square root of a perfect square integer, so that the result does have an exact finite representation, the procedure used to compute it may only return a series of increasingly accurate approximations.

The continued fraction representation of a real number can be used instead of its decimal or binary expansion and this representation has the property that the square root of any rational number (which is not already a perfect square) has a periodic, repeating expansion, similar to how rational numbers have repeating expansions in the decimal notation system.

The most common analytical methods are iterative and consist of two steps: finding a suitable starting value, followed by iterative refinement until some termination criterion is met.  The starting value can be any number, but fewer iterations will be required the closer it is to the final result.  The most familiar such method, most suited for programmatic calculation, is Newton's method, which is based on a property of the derivative in the calculus. A few methods like paper-and-pencil synthetic division and series expansion, do not require a starting value. In some applications, an integer square root is required, which is the square root rounded or truncated to the nearest integer (a modified procedure may be employed in this case).

The method employed depends on what the result is to be used for (i.e. how accurate it has to be), how much effort one is willing to put into the procedure, and what tools are at hand.  The methods may be roughly classified as those suitable for mental calculation, those usually requiring at least paper and pencil, and those which are implemented as programs to be executed on a digital electronic computer or other computing device. Algorithms may take into account convergence (how many iterations are required to achieve a specified precision), computational complexity of individual operations (i.e. division) or iterations, and error propagation (the accuracy of the final result).

Procedures for finding square roots (particularly the square root of 2) have been known since at least the period of ancient Babylon in the 17th century BCE.  Heron's method from first century Egypt was the first ascertainable algorithm for computing square root. Modern analytic methods began to be developed after introduction of the Arabic numeral system to western Europe in the early Renaissance.  Today, nearly all computing devices have a fast and accurate square root function, either as a programming language construct, a compiler intrinsic or library function, or as a hardware operator, based on one of the described procedures.

Initial estimate
Many iterative square root algorithms require an initial seed value. The seed must be a non-zero positive number; it should be between 1 and , the number whose square root is desired, because the square root must be in that range. If the seed is far away from the root, the algorithm will require more iterations. If one initializes with  (or ), then approximately  iterations will be wasted just getting the order of magnitude of the root. It is therefore useful to have a rough estimate, which may have limited accuracy but is easy to calculate. In general, the better the initial estimate, the faster the convergence.  For Newton's method (also called Babylonian or Heron's method), a seed somewhat larger than the root will converge slightly faster than a seed somewhat smaller than the root.

In general, an estimate is pursuant to an arbitrary interval known to contain the root (such as ). The estimate is a specific value of a functional approximation to  over the interval. Obtaining a better estimate involves either obtaining tighter bounds on the interval, or finding a better functional approximation to . The latter usually means using a higher order polynomial in the approximation, though not all approximations are polynomial. Common methods of estimating include scalar, linear, hyperbolic and logarithmic. A decimal base is usually used for mental or paper-and-pencil estimating. A binary base is more suitable for computer estimates.  In estimating, the exponent and mantissa are usually treated separately, as the number would be expressed in scientific notation.

Decimal estimates
Typically the number  is expressed in scientific notation as  where  and n is an integer, and the range of possible square roots is  where .

Scalar estimates
Scalar methods divide the range into intervals, and the estimate in each interval is represented by a single scalar number.  If the range is considered as a single interval, the arithmetic mean (5.5) or geometric mean () times  are plausible estimates.  The absolute and relative error for these will differ.  In general, a single scalar will be very inaccurate.  Better estimates divide the range into two or more intervals, but scalar estimates have inherently low accuracy.

For two intervals, divided geometrically, the square root  can be estimated as

This estimate has maximum absolute error of  at a = 100, and maximum relative error of 100% at a = 1.

For example, for  factored as , the estimate is . , an absolute error of 246 and relative error of almost 70%.

Linear estimates
A better estimate, and the standard method used, is a linear approximation to the function  over a small arc.  If, as above, powers of the base are factored out of the number  and the interval reduced to , a secant line spanning the arc, or a tangent line somewhere along the arc may be used as the approximation, but a least-squares regression line intersecting the arc will be more accurate.

A least-squares regression line minimizes the average difference between the estimate and the value of the function.  Its equation is . Reordering, . Rounding the coefficients for ease of computation,

That is the best estimate on average that can be achieved with a single piece linear approximation of the function  y=x2 in the interval .  It has a maximum absolute error of 1.2 at a=100, and maximum relative error of 30% at S=1 and 10.

To divide by 10, subtract one from the exponent of , or figuratively move the decimal point one digit to the left. For this formulation, any additive constant 1 plus a small increment will make a satisfactory estimate so remembering the exact number isn't a burden.  The approximation (rounded or not) using a single line spanning the range  is less than one significant digit of precision; the relative error is greater than 1/22, so less than 2 bits of information are provided. The accuracy is severely limited because the range is two orders of magnitude, quite large for this kind of estimation.

A much better estimate can be obtained by a piece-wise linear approximation: multiple line segments, each approximating some subarc of the original.  The more line segments used, the better the approximation.  The most common way is to use tangent lines; the critical choices are how to divide the arc and where to place the tangent points. An efficacious way to divide the arc from y=1 to y=100 is geometrically: for two intervals, the bounds of the intervals are the square root of the bounds of the original interval, 1*100, i.e. [1,] and [,100].  For three intervals, the bounds are the cube roots of 100: [1,], [,()2], and [()2,100], etc.  For two intervals,  = 10, a very convenient number.  Tangent lines are easy to derive, and are located at x =  and x = .  Their equations are:    and .  Inverting, the square roots are:  and . Thus for :

The maximum absolute errors occur at the high points of the intervals, at a=10 and 100, and are 0.54 and 1.7 respectively. The maximum relative errors are at the endpoints of the intervals, at a=1, 10 and 100, and are 17% in both cases.  17% or 0.17 is larger than 1/10, so the method yields less than a decimal digit of accuracy.

Hyperbolic estimates
In some cases, hyperbolic estimates may be efficacious, because a hyperbola is also a convex curve and may lie along an arc of Y = x2 better than a line. Hyperbolic estimates are more computationally complex, because they necessarily require a floating division.  A near-optimal hyperbolic approximation to x2 on the interval  is y=190/(10-x)-20.  Transposing, the square root is x = -190/(y+20)+10.  Thus for :

The floating division need be accurate to only one decimal digit, because the estimate overall is only that accurate, and can be done mentally.  A hyperbolic estimate is better on average than scalar or linear estimates. It has maximum absolute error of 1.58 at 100 and maximum relative error of 16.0% at 10.  For the worst case at a=10, the estimate is 3.67. If one starts with 10 and applies Newton-Raphson iterations straight away, two iterations will be required, yielding 3.66, before the accuracy of the hyperbolic estimate is exceeded.  For a more typical case like 75, the hyperbolic estimate is 8.00, and 5 Newton-Raphson iterations starting at 75 would be required to obtain a more accurate result.

Arithmetic estimates
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with a 5. Similarly for numbers between other squares. This method will yield a correct first digit, but it is not accurate to one digit: the first digit of the square root of 35 for example, is 5, but the square root of 35 is almost 6.

A better way is to the divide the range into intervals half way between the squares.  So any number between 25 and half way to 36, which is 30.5, estimate 5; any number greater than 30.5 up to 36, estimate 6.  The procedure only requires a little arithmetic to find a boundary number in the middle of two products from the multiplication table. Here is a reference table of those boundaries:

The final operation is to multiply the estimate  by the power of ten divided by 2, so for ,

The method implicitly yields one significant digit of accuracy, since it rounds to the best first digit.

The method can be extended 3 significant digits in most cases, by interpolating between the nearest squares bounding the operand.  If , then  is approximately k plus a fraction, the difference between  and k2 divided by the difference between the two squares:

  where

The final operation, as above, is to multiply the result by the power of ten divided by 2;

 is a decimal digit and  is a fraction that must be converted to decimal. It usually has only a single digit in the numerator, and one or two digits in the denominator, so the conversion to decimal can be done mentally.

Example: find the square root of 75. , so  is 75 and  is 0. From the multiplication tables, the square root of the mantissa must be 8 point something because 8 × 8 is 64, but 9 × 9 is 81, too big, so  is 8; something is the decimal representation of .  The fraction  is 75 - k2 = 11, the numerator, and 81 - k2 = 17, the denominator.  11/17 is a little less than 12/18, which is 2/3s or .67, so guess .66 (it's ok to guess here, the error is very small).  So the estimate is .  to three significant digits is 8.66, so the estimate is good to 3 significant digits.  Not all such estimates using this method will be so accurate, but they will be close.

Binary estimates
When working in the binary numeral system (as computers do internally), by expressing  as  where , the square root  can be estimated as

which is the least-squares regression line to 3 significant digit coefficients.  has maximum absolute error of 0.0408 at =2, and maximum relative error of 3.0% at =1.  A computationally convenient rounded estimate (because the coefficients are powers of 2) is:

which has maximum absolute error of 0.086 at 2 and maximum relative error of 6.1% at =0.5 and =2.0.

For , the binary approximation gives . , so the estimate has an absolute error of 19 and relative error of 5.3%.  The relative error is a little less than 1/24, so the estimate is good to 4+ bits.

An estimate for  good to 8 bits can be obtained by table lookup on the high 8 bits of , remembering that the high bit is implicit in most floating point representations, and the bottom bit of the 8 should be rounded. The table is 256 bytes of precomputed 8-bit square root values.  For example, for the index 111011012 representing 1.851562510, the entry is 101011102 representing 1.35937510, the square root of 1.851562510 to 8 bit precision (2+ decimal digits).

Babylonian method
An unknown Babylonian mathematician somehow correctly calculated the square root of 2 to three sexagesimal "digits" after the 1, but it is not known exactly how. The Babylonians knew how to approximate a hypotenuse using

(giving for example  for the diagonal of a gate whose height is  rods and whose width is  rods) and they may have used a similar approach for finding the approximation of

Heron's method

The first explicit algorithm for approximating  is known as Heron's method, after the first-century Greek mathematician Hero of Alexandria who described the method in his AD 60 work Metrica. The basic idea is that if  is an overestimate to the square root of a non-negative real number  then  will be an underestimate, or vice versa, and so the average of these two numbers may reasonably be expected to provide a better approximation (though the formal proof of that assertion depends on the inequality of arithmetic and geometric means that shows this average is always an overestimate of the square root, as noted in the article on square roots, thus assuring convergence). This is equivalent to using Newton's method to solve .

More precisely, if  is our initial guess of  and  is the error in our estimate such that , then we can expand the binomial

and solve for the error term
 since .
Therefore, we can compensate for the error and update our old estimate as

Since the computed error was not exact, this becomes our next best guess. The process of updating is iterated until desired accuracy is obtained. This is a quadratically convergent algorithm, which means that the number of correct digits of the approximation roughly doubles with each iteration. It proceeds as follows:
Begin with an arbitrary positive starting value  (the closer to the actual square root of , the better).
Let  be the average of  and  (using the arithmetic mean to approximate the geometric mean).
Repeat step 2 until the desired accuracy is achieved.
It can also be represented as:

This algorithm works equally well in the -adic numbers, but cannot be used to identify real square roots with -adic square roots; one can, for example, construct a sequence of rational numbers by this method that converges to +3 in the reals, but to −3 in the 2-adics.

Example
To calculate , where  = 125348, to six significant figures, use the rough estimation method above to get

Therefore, .

Convergence

Suppose that x0 > 0 and S > 0. Then for any natural number n, xn > 0. Let the relative error in xn be defined by

and thus

Then it can be shown that

And thus that

and consequently that convergence is assured, and quadratic.

Worst case for convergence
If using the rough estimate above with the Babylonian method, then the least accurate cases in ascending order are as follows:

Thus in any case,

Rounding errors will slow the convergence. It is recommended to keep at least one extra digit beyond the desired accuracy of the  being calculated to minimize round off error.

Bakhshali method
This method for finding an approximation to a square root was described in an ancient South Asian manuscript from Pakistan, called the Bakhshali manuscript. It is equivalent to two iterations of the Babylonian method beginning with x0. Thus, the algorithm is quartically convergent, which means that the number of correct digits of the approximation roughly quadruples with each iteration. The original presentation, using modern notation, is as follows: To calculate , let  be the initial approximation to . Then, successively iterate as:

This can be used to construct a rational approximation to the square root by beginning with an integer.  If  is an integer chosen so  is close to , and  is the difference whose absolute value is minimized, then the first iteration can be written as:

The Bakhshali method can be generalized to the computation of an arbitrary root, including fractional roots.

Example
Using the same example as given with the Babylonian method, let  Then, the first iteration gives

Likewise the second iteration gives

Digit-by-digit calculation
This is a method to find each digit of the square root in a sequence. This method is based on the binomial theorem and basically an inverse algorithm solving . It is slower than the Babylonian method, but it has several advantages:
 It can be easier for manual calculations.
 Every digit of the root found is known to be correct, i.e., it does not have to be changed later.
 If the square root has an expansion that terminates, the algorithm terminates after the last digit is found. Thus, it can be used to check whether a given integer is a square number.
 The algorithm works for any base, and naturally, the way it proceeds depends on the base chosen.
 Inconveniences are that the algorithm becomes quite unhandleable for higher roots and that it is not allowing inaccurate guesses or inaccurate sub-calculations as they, unlike the self correcting approximations like with Newtons method, lead to every following digit of the result being wrong. Furthermore this algorithm, even though being efficient enough on paper, is way too expensive for software implementations as the many calculations become larger and larger and load the memory while still only allowing digit by digit progressions leading the algorithm to become slower and slower with every following digit.

Napier's bones include an aid for the execution of this algorithm. The shifting th root algorithm is a generalization of this method.

Basic principle
First, consider the case of finding the square root of a number , that is the square of a two-digit number , where  is the tens digit and  is the units digit. Specifically:

Now using the digit-by-digit algorithm, we first determine the value of .  is the largest digit such that  is less than or equal to  from which we removed the two rightmost digits.

In the next iteration, we pair the digits, multiply  by 2, and place it in the tenth's place while we try to figure out what the value of  is.

Since this is a simple case where the answer is a perfect square root , the algorithm stops here.

The same idea can be extended to any arbitrary square root computation next. Suppose we are able to find the square root of  by expressing it as a sum of n positive numbers such that
.

By repeatedly applying the basic identity

the right-hand-side term can be expanded as

This expression allows us to find the square root by sequentially guessing the values of s. Suppose that the numbers  have already been guessed, then the m-th term of the right-hand-side of above summation is given by  where  is the approximate square root found so far. Now each new guess  should satisfy the recursion

such that  for all  with initialization  When  the exact square root has been found; if not, then the sum of s gives a suitable approximation of the square root, with  being the approximation error.

For example, in the decimal number system we have

where  are place holders and the coefficients . At any m-th stage of the square root calculation, the approximate root found so far,  and the summation term  are given by

Here since the place value of  is an even power of 10, we only need to work with the pair of most significant digits of the remaining term  at any m-th stage. The section below codifies this procedure.

It is obvious that a similar method can be used to compute the square root in number systems other than the decimal number system. For instance, finding the digit-by-digit square root in the binary number system is quite efficient since the value of  is searched from a smaller set of binary digits {0,1}. This makes the computation faster since at each stage the value of  is either  for  or  for . The fact that we have only two possible options for  also makes the process of deciding the value of  at m-th stage of calculation easier. This is because we only need to check if  for  If this condition is satisfied, then we take ; if not then  Also, the fact that multiplication by 2 is done by left bit-shifts helps in the computation.

Decimal (base 10)
Write the original number in decimal form. The numbers are written similar to the long division algorithm, and, as in long division, the root will be written on the line above. Now separate the digits into pairs, starting from the decimal point and going both left and right. The decimal point of the root will be above the decimal point of the square. One digit of the root will appear above each pair of digits of the square.

Beginning with the left-most pair of digits, do the following procedure for each pair:

 Starting on the left, bring down the most significant (leftmost) pair of digits not yet used (if all the digits have been used, write "00") and write them to the right of the remainder from the previous step (on the first step, there will be no remainder). In other words, multiply the remainder by 100 and add the two digits. This will be the current value c.
 Find p, y and x, as follows:
 Let p be the part of the root found so far, ignoring any decimal point. (For the first step, p = 0.)
 Determine the greatest digit x such that . We will use a new variable y = x(20p + x).
 Note: 20p + x is simply twice p, with the digit x appended to the right.
 Note: x can be found by guessing what c/(20·p) is and doing a trial calculation of y, then adjusting x upward or downward as necessary.
 Place the digit  as the next digit of the root, i.e., above the two digits of the square you just brought down. Thus the next p will be the old p times 10 plus x.
 Subtract y from c to form a new remainder.
 If the remainder is zero and there are no more digits to bring down, then the algorithm has terminated. Otherwise go back to step 1 for another iteration.

Examples
Find the square root of 152.2756.

           1  2. 3  4
        /
      \/  01 52.27 56

          01                   1*1 <= 1 < 2*2                 x = 1
          01                     y = x*x = 1*1 = 1
          00 52                22*2 <= 52 < 23*3              x = 2
          00 44                  y = (20+x)*x = 22*2 = 44
             08 27             243*3 <= 827 < 244*4           x = 3
             07 29               y = (240+x)*x = 243*3 = 729
                98 56          2464*4 <= 9856 < 2465*5        x = 4
                98 56            y = (2460+x)*x = 2464*4 = 9856
                00 00          Algorithm terminates: Answer is 12.34

Binary numeral system (base 2)
This section uses the formalism from the digit-by-digit calculation section above, with the slight variation that we let , with each  or .
We iterate all , from  down to , and build up an approximate solution , the sum of all  for which we have determined the value.
To determine if  equals  or , we let . If  (i.e. the square of our approximate solution including  does not exceed the target square) then , otherwise  and .
To avoid squaring  in each step, we store the difference  and incrementally update it by setting  with .
Initially, we set  for the largest  with .

As an extra optimization, we store  and , the two terms of  in case that  is nonzero, in separate variables , :

 and  can be efficiently updated in each step:

Note that:
, which is the final result returned in the function below.

An implementation of this algorithm in C:

int32_t isqrt(int32_t n) {
    assert(("sqrt input should be non-negative", n > 0));

    // Xₙ₊₁
    int32_t x = n;

    // cₙ
    int32_t c = 0;

    // dₙ which starts at the highest power of four <= n
    int32_t d = 1 << 30; // The second-to-top bit is set.
                         // Same as ((unsigned) INT32_MAX + 1) / 2.
    while (d > n)
        d >>= 2;

    // for dₙ … d₀
    while (d != 0) {
        if (x >= c + d) {      // if Xₘ₊₁ ≥ Yₘ then aₘ = 2ᵐ
            x -= c + d;        // Xₘ = Xₘ₊₁ - Yₘ
            c = (c >> 1) + d;  // cₘ₋₁ = cₘ/2 + dₘ (aₘ is 2ᵐ)
        }
        else {
            c >>= 1;           // cₘ₋₁ = cₘ/2      (aₘ is 0)
        }
        d >>= 2;               // dₘ₋₁ = dₘ/4
    }
    return c;                  // c₋₁
}

Faster algorithms, in binary and decimal or any other base, can be realized by using lookup tables—in effect trading more storage space for reduced run time.

Exponential identity
Pocket calculators typically implement good routines to compute the exponential function and the natural logarithm, and then compute the square root of S using the identity found using the properties of logarithms () and exponentials ():

The denominator in the fraction corresponds to the nth root. In the case above the denominator is 2, hence the equation specifies that the square root is to be found. The same identity is used when computing square roots with logarithm tables or slide rules.

A two-variable iterative method
This method is applicable for finding the square root of  and converges best for .
This, however, is no real limitation for a computer based calculation, as in base 2 floating point and fixed point representations, it is trivial to multiply  by an integer power of 4, and therefore  by the corresponding power of 2, by changing the exponent or by shifting, respectively. Therefore,  can be moved to the range . Moreover, the following method does not employ general divisions, but only additions, subtractions, multiplications, and divisions by powers of two, which are again trivial to implement. A disadvantage of the method is that numerical errors accumulate, in contrast to single variable iterative methods such as the Babylonian one.

The initialization step of this method is

while the iterative steps read

Then,  (while ).

Note that the convergence of , and therefore also of , is quadratic.

The proof of the method is rather easy. First, rewrite the iterative definition of  as
.
Then it is straightforward to prove by induction that

and therefore the convergence of  to the desired result  is ensured by the convergence of  to 0, which in turn follows from .

This method was developed around 1950 by M. V. Wilkes, D. J. Wheeler and S. Gill for use on EDSAC, one of the first electronic computers. The method was later generalized, allowing the computation of non-square roots.

Iterative methods for reciprocal square roots
The following are iterative methods for finding the reciprocal square root of S which is . Once it has been found, find  by simple multiplication: . These iterations involve only multiplication, and not division. They are therefore faster than the Babylonian method. However, they are not stable. If the initial value is not close to the reciprocal square root, the iterations will diverge away from it rather than converge to it. It can therefore be advantageous to perform an iteration of the Babylonian method on a rough estimate before starting to apply these methods.

Applying Newton's method to the equation  produces a method that converges quadratically using three multiplications per step:

Another iteration is obtained by Halley's method, which is the Householder's method of order two. This converges cubically, but involves five multiplications per iteration:
, and
.
 If doing fixed-point arithmetic, the multiplication by 3 and division by 8 can implemented using shifts and adds.  If using floating-point, Halley's method can be reduced to four multiplications per iteration by precomputing  and adjusting all the other constants to compensate:
, and
.

Goldschmidt's algorithm
Some computers use Goldschmidt's algorithm to simultaneously calculate
 and
.
Goldschmidt's algorithm finds  faster than Newton-Raphson iteration on a computer with a fused multiply–add instruction and either a pipelined floating point unit or two independent floating-point units.

The first way of writing Goldschmidt's algorithm begins

  (typically using a table lookup)

and iterates

until  is sufficiently close to 1, or a fixed number of iterations.  The iterations converge to
, and
.
Note that it is possible to omit either  and  from the computation, and if both are desired then  may be used at the end rather than computing it through in each iteration.

A second form, using fused multiply-add operations, begins
  (typically using a table lookup)

and iterates

until  is sufficiently close to 0, or a fixed number of iterations.  This converges to
, and
.

Taylor series
If N is an approximation to , a better approximation can be found by using the Taylor series of the square root function:

As an iterative method, the order of convergence is equal to the number of terms used. With two terms, it is identical to the Babylonian method. With three terms, each iteration takes almost as many operations as the Bakhshali approximation, but converges more slowly. Therefore, this is not a particularly efficient way of calculation. To maximize the rate of convergence, choose N so that  is as small as possible.

Continued fraction expansion

Quadratic irrationals (numbers of the form , where a, b and c are integers), and in particular, square roots of integers, have periodic continued fractions. Sometimes what is desired is finding not the numerical value of a square root, but rather its continued fraction expansion, and hence its rational approximation. Let S be the positive number for which we are required to find the square root. Then assuming a to be a number that serves as an initial guess and r to be the remainder term, we can write  Since we have , we can express the square root of S as

By applying this expression for  to the denominator term of the fraction, we have

The numerator/denominator expansion for continued fractions (see left) is cumbersome to write as well as to embed in  text formatting systems. So mathematicians have devised several alternative notations, like

When  throughout, an even more compact notation is:

For repeating continued fractions (which all square roots of non-perfect squares do), the repetend is represented only once, with an overline to signify a non-terminating repetition of the overlined part:

For , the value of  is 1, so its representation is:

Proceeding this way, we get a generalized continued fraction for the square root as

The first step to evaluating such a fraction to obtain a root is to do numerical substitutions for the root of the number desired, and number of denominators selected. For example, in canonical form,  is 1 and for ,  is 1, so the numerical continued fraction for 3 denominators is:

Step 2 is to reduce the continued fraction from the bottom up, one denominator at a time, to yield a rational fraction whose numerator and denominator are integers. The reduction proceeds thus (taking the first three denominators):

Finally (step 3), divide the numerator by the denominator of the rational fraction to obtain the approximate value of the root:
 rounded to three digits of precision.

The actual value of  is 1.41 to three significant digits. The relative error is 0.17%, so the rational fraction is good to almost three digits of precision.  Taking more denominators gives successively better approximations: four denominators yields the fraction , good to almost 4 digits of precision, etc.

The following are examples of square roots, their simple continued fractions, and their first terms  called convergents  up to and including denominator 99:

In general, the larger the denominator of a rational fraction, the better the approximation. It can also be shown that truncating a continued fraction yields a rational fraction that is the best approximation to the root of any fraction with denominator less than or equal to the denominator of that fraction  e.g., no fraction with a denominator less than or equal to 70 is as good an approximation to  as 99/70.

Lucas sequence method
the Lucas sequence of the first kind Un(P,Q) is defined by the recurrence relations:and the characteristic equation of it is:it has the discriminant  and the roots:all that yield the following positive value:so when we want , we can choose  and , and then calculate  using   and for large value of .

The most effective way to calculate  and is:Summary:then when :

Approximations that depend on the floating point representation

A number is represented in a floating point format as  which is also called scientific notation. Its square root is  and similar formulae would apply for cube roots and logarithms. On the face of it, this is no improvement in simplicity, but suppose that only an approximation is required: then just  is good to an order of magnitude. Next, recognise that some powers, , will be odd, thus for 3141.59 = 3.14159 rather than deal with fractional powers of the base, multiply the mantissa by the base and subtract one from the power to make it even. The adjusted representation will become the equivalent of 31.4159 so that the square root will be .

If the integer part of the adjusted mantissa is taken, there can only be the values 1 to 99, and that could be used as an index into a table of 99 pre-computed square roots to complete the estimate. A computer using base sixteen would require a larger table, but one using base two would require only three entries: the possible bits of the integer part of the adjusted mantissa are 01 (the power being even so there was no shift, remembering that a normalised floating point number always has a non-zero high-order digit) or if the power was odd, 10 or 11, these being the first two bits of the original mantissa. Thus, 6.25 = 110.01 in binary, normalised to 1.1001 × 22 an even power so the paired bits of the mantissa are 01, while .625 = 0.101 in binary normalises to 1.01 × 2−1 an odd power so the adjustment is to 10.1 × 2−2 and the paired bits are 10. Notice that the low order bit of the power is echoed in the high order bit of the pairwise mantissa. An even power has its low-order bit zero and the adjusted mantissa will start with 0, whereas for an odd power that bit is one and the adjusted mantissa will start with 1. Thus, when the power is halved, it is as if its low order bit is shifted out to become the first bit of the pairwise mantissa.

A table with only three entries could be enlarged by incorporating additional bits of the mantissa. However, with computers, rather than calculate an interpolation into a table, it is often better to find some simpler calculation giving equivalent results. Everything now depends on the exact details of the format of the representation, plus what operations are available to access and manipulate the parts of the number. For example, Fortran offers an EXPONENT(x) function to obtain the power. Effort expended in devising a good initial approximation is to be recouped by thereby avoiding the additional iterations of the refinement process that would have been needed for a poor approximation. Since these are few (one iteration requires a divide, an add, and a halving) the constraint is severe.

Many computers follow the IEEE (or sufficiently similar) representation, and a very rapid approximation to the square root can be obtained for starting Newton's method. The technique that follows is based on the fact that the floating point format (in base two) approximates the base-2 logarithm. That is

So for a 32-bit single precision floating point number in IEEE format (where notably, the power has a bias of 127 added for the represented form) you can get the approximate logarithm by interpreting its binary representation as a 32-bit integer, scaling it by , and removing a bias of 127, i.e.

For example, 1.0 is represented by a hexadecimal number 0x3F800000, which would represent  if taken as an integer. Using the formula above you get , as expected from . In a similar fashion you get 0.5 from 1.5 (0x3FC00000).

To get the square root, divide the logarithm by 2 and convert the value back. The following program demonstrates the idea. Note that the exponent's lowest bit is intentionally allowed to propagate into the mantissa.  One way to justify the steps in this program is to assume  is the exponent bias and  is the number of explicitly stored bits in the mantissa and then show that

/* Assumes that float is in the IEEE 754 single precision floating point format */
#include <stdint.h>
float sqrt_approx(float z)
{
	union { float f; uint32_t i; } val = {z};	/* Convert type, preserving bit pattern */
	/*
	 * To justify the following code, prove that
	 *
	 * ((((val.i / 2^m) - b) / 2) + b) * 2^m = ((val.i - 2^m) / 2) + ((b + 1) / 2) * 2^m)
	 *
	 * where
	 *
	 * b = exponent bias
	 * m = number of mantissa bits
	 */
	val.i -= 1 << 23;	/* Subtract 2^m. */
	val.i >>= 1;		/* Divide by 2. */
	val.i += 1 << 29;	/* Add ((b + 1) / 2) * 2^m. */

	return val.f;		/* Interpret again as float */
}

The three mathematical operations forming the core of the above function can be expressed in a single line.  An additional adjustment can be added to reduce the maximum relative error.  So, the three operations, not including the cast, can be rewritten as
	val.i = (1 << 29) + (val.i >> 1) - (1 << 22) + a;

where a is a bias for adjusting the approximation errors. For example, with a = 0 the results are accurate for even powers of 2 (e.g. 1.0), but for other numbers the results will be slightly too big (e.g. 1.5 for 2.0 instead of 1.414... with 6% error). With a = −0x4B0D2, the maximum relative error is minimized to ±3.5%.

If the approximation is to be used for an initial guess for Newton's method to the equation , then the reciprocal form shown in the following section is preferred.

Reciprocal of the square root

A variant of the above routine is included below, which can be used to compute the reciprocal of the square root, i.e.,  instead, was written by Greg Walsh. The integer-shift approximation produced a relative error of less than 4%, and the error dropped further to 0.15% with one iteration of Newton's method on the following line. In computer graphics it is a very efficient way to normalize a vector.

float invSqrt(float x) {
    float xhalf = 0.5f * x;
    union {
        float x;
        int i;
    } u;
    u.x = x;
    u.i = 0x5f375a86 - (u.i >> 1);
    /* The next line can be repeated any number of times to increase accuracy */
    u.x = u.x * (1.5f - xhalf * u.x * u.x);
    return u.x;
}

Some VLSI hardware implements inverse square root using a second degree polynomial estimation followed by a Goldschmidt iteration.

Negative or complex square
If S < 0, then its principal square root is

If S = a+bi where a and b are real and b ≠ 0, then its principal square root is

This can be verified by squaring the root.
Here

is the modulus of S. The principal square root of a complex number is defined to be the root with the non-negative real part.

See also
 Alpha max plus beta min algorithm
 nth root algorithm
 Square root of 2
 Integer square root

Notes

References

Bibliography

External links

 Square roots by subtraction
 Integer Square Root Algorithm by Andrija Radović
 Personal Calculator Algorithms I : Square Roots (William E. Egbert), Hewlett-Packard Journal (May 1977) : page 22
 Calculator to learn the square root

Root-finding algorithms
Computer arithmetic algorithms

redpajama_set_name: RedPajamaWikipedia


Practicing/experimenting with different expressions and hair shapes for this character. Hair needs work clearly, very happy that Klingon's prefer messy hair... Rendered using ZBrush BPR with minimal touch ups in Photoshop.


Did you mean flights from Memmingen Allgäu?
Skyscanner is simple and fast. And it's free to use! Compare low cost flights then book your airline tickets to Memmingen Allgäu directly by clicking through to agency and airline sites.
Browse through our flight offers below, or use the search box to enter your travel dates and let us find the cheapest flights to Memmingen Allgäu or wherever you want to go.
Why not add a hotel after you've arrived at Memmingen Allgäu? For the best hotel deals, head on over to Skyscanner Hotels where Skyscanner searches all the best hotel suppliers to bring you the best rates.


The determination whether or not a person need towards carry out business by using a custom-made home designer is yours to make towards make, nonetheless it's a little something you need to definitely always check, specially in event you wish a new custom made, personal home. But if your corporation requires some sort of lot involving high-priced inventory to operate you actually might come to be retaining upwards an upcoming difficulty when you attend easily sell. When you have opted to start with your company own organization, on the list of highly first stuff which you try to deliver can be to focus on a organization application.
As soon as it is because of him your organization, choosing most effective industrial roofing on Lamb Nation, TX can be a complicated preference. When a good small business is actually born, delicious responsibilities an online business proprietor needs to shoulder. Eventhough it's critical to realize that you will have to buy from a California custom family home builder, you may be wondering exactly why you must hence. Commencing plus holding a good company can't ever be a individual surpassed exertion, primarily whenever you aren't interested in the actual good results about your business. When it again is because of him organization, a lot of consumers are looking for the nearly all suitable industry as the particular one who is actually going to make the absolute most cash with the exact the very least , efforts. A great number of small business is completed over the Online world applying distinct technological know-how. Generating a growing web site supplier is actually plenty for deliver the results.
A good number of individuals crash in business since they will make preventable mistakes! Currently, a corporation determines a strong extra aid to enhance it has the yields in addition to boost a effectiveness and that help support can just only come to be offered via concept. When you do not get content with how important things are taking place in your individual business, then carefully consider delivering the idea along with IT assist. You're the companhy, you're the exact loved types together with if you're the very track record the fact that prospects believe in. Basically the business seems to have the power to get freedom inside your reach. Simply If everyone would enjoy to brew a maintainable provider which will you're allowed to replicate by the factor involving 10, 000, Management competencies are essential. On-line internet business will certainly not need you to pay out significant amounts of investment.
A knowledge room can provide typically the ability for many individuals to job collectively in addition to publish data files that must be protected meant for assorted purposes. The very internet files room will be shielded through security activities that definitely will be released clear inside agreement. With a digital files room provides needed stability to make it easy for you in order to behavior your own personal organization with no fear with your security and safety break or possibly personal information burglary. It can possibly present the capacity share files. A digital files room and also online digital price space stipulates the exact capacity to deliver necessary papers and data files when they may needed instantly.
A data files room stipulates the skills regarding many consumers for you to team up and write about records of which has to be secure for a few people purposes. Some sort of safeguarded data files place may well be going to possibly be an option with the celebration the need is discovered towards transmit facts from 4 organization to another. A protect data living room enables you actually to protect the material whenever discussing it with individuals that need it. An excellent the ability to transmit and be given information when safeguarding the additional privacy of the records. Any digital package space, due diligence space, or possibly data room in your home can deliver you all the advantages for your contract storage capability without requiring to rent payments the bodily space and even manually set up the files. Read more: .


Kingsbury and awards chair Don Cusic.
Will the Circle Be Unbroken: Country Music in America, edited by Paul Kingsbury and Alanna Nash and published by DK Publishing has been announced as the winner of the Belmont Book Award. The award given annually by Belmont University honors the writer and the editor of the Best Book on Country Music. The presentation occurred on Friday, May 25, at a special awards luncheon held during the International Country Music Conference held at Belmont May 24-26.
The book Will the Circle Be Unbroken is a project of the Country Music Hall of Fame and Foundation, whose photos were used extensively in this comprehensive history of country music.
The award is determined by a blue ribbon panel of experts. Books published in the previous calendar year are eligible and a wide variety of books on country music are considered, from scholarly studies of various aspects of country music to biographies and autobiographies.


Watch the Snow Diamond Select 2018 Alpaca Auction LIVE!
We encourage you to make your reservation early, as October is a popular season in the Bend Redmond area.
Beautiful resort setting midway between Bend & Redmond.


To the college student: Take a hard look at your college ID card. That sheet of precious polymers is worth thousands of dollars and oodles of fun. Our job is to help you unlock that potential. With the right know-how and attitude, you can join us in reaping the benefits of being the indebted and sleep-deprived college students we are. College happens, make the best of it.
To anyone else: Welcome! Okay, so you don't have a college ID card, don't worry! We have enough resources here that you're bound to come across something that you'll make good use of. So go on, explore.
Hewsoft was founded in June of 2004 by Mario Magaña and Nicholas Ramos. Its purpose was to educate the community about the growing technological influence. As we continued to grow and expand our share of experiences, we developed resources and services that best fit that mission. Starting with a single operations unit, Media, Hewsoft was solely responsible for yearly video productions aimed at social and education venues. In 2005, Hewsoft had its largest organizational expansion. This was matched with two new units, Web and Originals. Previous Media video production-related operations moved into the new Originals unit as Originals was to deal with all in-house creative productions, while Web with all Internet and technology-related mediums and services, including maintenance of the Hewsoft website, and finally Media with maintaining a catalog of multi-medium resources to make them easily accessible via the website. For about four years, there were no major changes to the brand and structure of Hewsoft. Then, in the spring of 2009, a major project was announced to rebrand and restructure Hewsoft.
The three main units remained, but with very different goals. A new logo was unveiled during the summer of 2009; the first major refresh of the original conception from 2004. Soon after, Hewsoft launched its brand new website, built completely from the ground up so that it could fully comply with modern web coding and multi-browser and platform standards. With an upgraded mission focused around the modern college student, the Hewsoft Social, Dashboard, and Sandbox brands were developed to deliver the new message. With various Hewsofties (guys and gals who run Hewsoft) studying at the University of California, Los Angeles, UCLA was the first college campus to be supported by Social and Dashboard, two brands with a focus on local and college-specific services. However, there are current plans to add the University of California, Santa Barbara [UCSB], University of California, Riverside [UCR], University of California, San Diego [UCSD], and the University of Southern California [USC].
As you may have noticed, we currently don't offer products for sale. That is not our active goal. We employ certain online advertising mechanisms across our site to fund just enough resources to keep the site running.
Hewsoft © 2012. All Rights Reserved.


text:
IOWA BEEF PACKERS, INC. v. THOMPSON
IOWA BEEF PACKERS, INC. v. THOMPSON, 405 U.S. 228 (1972)
IOWA BEEF PACKERS, INC. v. THOMPSON(1972)
Court's grant of certiorari to decide whether employees may sue for overtime allegedly withheld in violation of the Fair Labor Standards Act if the complaint of that violation was also subject to grievance and arbitration provisions of a collective-bargaining agreement held improvidently granted in view of subsequent disclosure that those provisions did not apply to all disputes, but merely those based on violations of the agreement.
185 N. W. 2d 738, certiorari dismissed as improvidently granted.
Louis S. Goldberg argued the cause for petitioner. With him on the brief was P. L. Nymann.
Raymond Edward Franck argued the cause and filed a brief for respondents.
A. Raymond Randolph, Jr., argued the cause pro hac vice for the United States as amicus curiae urging affirmance. With him on the brief were Solicitor General Griswold and Richard F. Schubert.
Respondents brought this suit in an Iowa District Court under 16 (b) of the Fair Labor Standards Act, 52 Stat. 1069, as amended, 29 U.S.C. 216 (b), to recover overtime compensation allegedly not paid by their petitioner employer in violation of the overtime provisions of the Act, 29 U.S.C. 207 (a) (1). The District Court denied petitioner's motion to dismiss the action for failure of respondents to exhaust the grievance arbitration procedures provided in a collective-bargaining agreement between petitioner and respondents' union and awarded respondents the overtime claimed plus costs and attorneys' fees. The Supreme Court of Iowa affirmed. 185 [405 U.S. 228, 229] N. W. 2d 738 (1971). We granted certiorari, 404 U.S. 820 (1971).
The collective-bargaining agreement required petitioner to provide a lunch period for each employee no later than five hours from the start of an employee's shift. Petitioner provided the lunch period but required the employees to remain on call during the period. Respondents did not choose, as perhaps under the contract was open to them, to make the requirement the basis of a grievance for alleged violation either of the lunch-period provision or of the hours-of-work provision, Art. VII, requiring time and one-half for hours worked over eight in any day or 40 in any week. They claimed instead that, because of the requirement, the Fair Labor Standards Act, as a matter of law, rendered the lunch period "work" time, whether or not actually worked, for the purpose of determining whether petitioner violated its statutory obligation to pay overtime rates for work hours over 40 in any work week. See Armour & Co. v. Wantock, 323 U.S. 126 (1944). The grievance thus pertained not to an alleged violation of the agreement but to an alleged violation of the Fair Labor Standards Act.
In U.S. Bulk Carriers v. Arguelles, 400 U.S. 351 (1971), the Court held that a seaman could sue in federal court for wages under 46 U.S.C. 596 without invoking grievance and arbitration procedures under a collective-bargaining agreement that provided for resolution of all disputes and grievances, not merely those based on alleged violations of the contract. We granted certiorari in this case to decide whether, similarly, employees may sue in court to recover overtime allegedly withheld in violation of the Fair Labor Standards Act, if their complaint of alleged statutory violation is also subject to resolution under grievance and arbitration provisions of a collective-bargaining agreement. It developed at oral argument, however, that the grievance and arbitration [405 U.S. 228, 230] provisions, Art. XX of the collective-bargaining agreement involved in this case, do not have the broad scope of the procedures in Arguelles, but apply only to grievances "pertaining to a violation of the Agreement." Moreover, the issues as presented by petitioner provide no occasion to address, and we intimate no view upon, the question whether, although the statutory claim is not subject to contract arbitration, pursuit of the statutory remedy is nevertheless barred because respondents might have made the requirement to be on call the basis of a grievance for alleged violation of the lunch period or overtime provision of the collective-bargaining agreement. In these circumstances, which were not fully apprehended at the time certiorari was granted, the writ of certiorari will be dismissed as improvidently granted. The Monrosa v. Carbon Black, Inc., 359 U.S. 180, 183 (1959).
MR. JUSTICE DOUGLAS, dissenting.
The arbitration clause in this collective agreement reaches "a grievance pertaining to a violation of the Agreement." The agreement covered both the lunch period 1 and overtime. 2
The Iowa Supreme Court held that "[t]he present controversy is undoubtedly arbitrable" under the collective agreement. Given the presumption favoring liberal construction of arbitration clauses, Steelworkers v. Warrior & Gulf Co., 363 U.S. 574, 582 -583, we should defer to [405 U.S. 228, 231] that ruling. Even under that construction, it seems that a suit for overtime allegedly withheld in violation of the Fair Labor Standards Act, 29 U.S.C. 207 (a) (1) is maintainable. That would mean affirming the Iowa Supreme Court. U.S. Bulk Carriers v. Arguelles, 400 U.S. 351 , which kept the courthouse door open, would seem to control this case. 3
An affirmance would follow, a fortiori, if this collective agreement be construed as not requiring arbitration of this FLSA claim. For then it would seem that the worker would have a choice to sue under the statute or to proceed to arbitration on his contractual claim arising out of the same dispute.
The petition, however, is not dismissed for those reasons but for a wholly different one. It is said that there was a requirement to be "on call" and that that duty conflicted with the lunch or overtime provisions of the agreement. The difficulty is twofold: there was no "on call" grievance ever tendered so far as the record [405 U.S. 228, 232] shows; moreover, the agreement concededly does not cover any "on call" requirement or duty. So there is no conflict between statutory remedy and remedy by arbitration and the difficulty posed is imaginary.
We should "dismiss as improvidently granted" only in exceptional situations and where all nine members of the Court agree. In all other cases the merits of the controversy should be decided. The present case on its facts is simple and uncomplicated; and a decision on the merits is apparently important to unions and employer alike.
[ Footnote 1 ] Article XIV, 1, states:
"A lunch period shall be provided no later than five (5) hours from the start of an employee's shift, except when the shift does not exceed five and one-half (5 1/2) hours."
[ Footnote 2 ] Article VII, 3, states:
"Time and one-half (1 1/2) will be paid for hours worked in excess of eight (8) in any day. Time and one-half (1 1/2) will be paid for all hours worked in excess of forty (40) in any one week."
[ Footnote 3 ] The Iowa Supreme Court properly stated:
"We doubt that the general Congressional intent favoring arbitration can stand against the specific Congressional intent which is manifest in the Fair Labor Standards Act provisions giving employees strong and detailed rights in court. We think Congress intended that workmen should have free access to the courts in FLSA cases. We are the more persuaded of that view by the broad Congressional policy expressed in 2 of FLSA, 29 U.S.C.A. 202. There the objectives of the act are set forth, and those objectives encompass more than simply wage relief for employees; they include broad economic considerations - improvement in commerce among the states. The remedies provided by the act are part of the Congressional scheme to obtain employer compliance with the act and hence achievement of those broader objectives. We believe that if Congressional intent to allow a seaman to arbitrate or sue at his option is manifest in the seaman's act involved in Arguelles, as the Court held there, then an intent to give workmen such an option is also manifest in the Fair Labor Standards Act." 185 N. W. 2d 738, 742. [405 U.S. 228, 233]

redpajama_set_name: RedPajamaCommonCrawl


Discussion in 'Asia' started by amelia88, Apr 21, 2016.
I know that in an ideal world we would all have the time to stop for long, fancy meals - but let's be honest, sometimes when we travel I'm sure we have all thought to ourselves "okay - fast food it is!"
Do you have any favorites in Asia? I really loved Coco's Curry in Japan (so good!) and Beef bowls from Yoshinoya and Sukiya. They're cheap too, but I feel like they're way better than the fast food equivalents I would get here at home in the States.
I didn't really get a chance to experience much in other countries when it comes to fast food but I would love to get your favorites in case I'm in those countries at some point!
The gyuudon places are definitely my favorite. I'm a big fan of Yoshinoya... super cheap, delicious, and filling! Coco's Curry is also pretty good, but they don't have a close location near me so I don't go often.
In terms of burgers and stuff, a lot of the Japanese fast food chains are lacking. That's mainly because they use the beef/pork mixed with onion patty and that tastes off to me. It's fine as a hamburger steak (hamburg), but I prefer beef patties. I'd say Freshness Burger is probably the best Japanese fast food chain in terms of burgers and fries. But they're also a little pricier because they aim to be "healthy".
Mine would be Tokyo Tokyo because I love eating Japanese food. And the best thing about this place, they have unlimited rice. So for a person like me who loves to eat a lot, Tokyo Tokyo is heaven-sent. Yoshinoya is also a great place, but they don't offer unlimited rice. Another favorite of mine is Chow King. They sell Chinese food though. I love their Nai Cha. There was a time that I got so addicted to it that I buy Nai Cha from them every day.
The Food Republic in Tung Chung, Hongkong is my favorite when it comes to fast food. It is a mix of Chinese, of course, and Asian plus continental dishes. I always order the fried Taiwanese dumplings which is like the Japanese gyouza while my husband's favorite is the rice toppings of a Portuguese cuisine. What's nice in Food Republic is the competitive prices not to mention the authentic taste. It also has a big dining area so you need not wait for vacant tables unlike in other fast foods. And another plus, which we had sampled, was the fine dining which is located in the far corner - they have good steaks there.
Let's start with my country, the Philippines: My favourite fast food here is Jollibee. I think they have some chains in Hong Kong, America and Vietnam. My favourite here is the Spaghetti and Chicken meal. Their spaghetti is quite sweet with some hotdogs in it, it's more specifically for children. Their chicken is very delicious, it's crunchy outside but very juicy inside. I also love their "palabok" but I don't think it's available outside our country.
My favourite fast food chain in Japan would have to be Pepper Lunch. It's a restaurant where you they cook the meals in your sizzling plate in front of you. There's a variety of meals and you can choose which sauce you'd prefer either honey sauce or garlic soy sauce.
In South Korea, it has to be BonChon. I particularly love their JapChae, yum! But their chickens are delicious as well, you can choose which flavour you want as well. Their fish fingers are very soft inside but crunchy outside.
It's great that these fast food chains are also available here in my country. That's why I can enjoy these foods whenever I want. I will try out your suggestions as well if ever I'm in the countries you have mentioned.
@Coco I loooooved Pepper Lunch too!! They had it in a mall that I visited, and I thought it was great. I ordered one with a hamburger steak, and it came with rice, carrots, beans, corn and some noodles all for less than 1000 yen from memory - super tasty and great value too! I think I must have had the garlic soy sauce - they just gave me one by default! But it was so yummy!
I haven't tried the other fast food places you mentioned but I'll be sure to give them a try if I come across them in my travels!
Fast Food places are my go to dining for me. In as much as I'd like to experiment, I've the tendency to go for the more familiar. Also, they're cheaper, I think!
While in Seoul, Lotteria is a gift for me. During that travel to South Korea, I have not developed the taste for Korean foods yet.
The picture below is of a Lotteria branch somewhere in Ho Chi Minh in Vietnam. I like it here because the food agrees with my Filipino taste bud.
Another favorite in Seoul is Paris Baguette Cafe. Who wouldn't want these for breakfast?
I think these two places are savior to those who can't subsist on noodles and everything spicy.
In the other countries, Mc Do is also a very familiar place. I like that each country you visit, there is a different kind of offering. Like the McSpaghetti. I think this is an ONLY in the Philippines meal. In HK, they carry corn kernels/black burger which I have not seen offered in my home country.
KFC is also another go to place. I wish the breakfast they offer in Singapore be made available in the Philippines. Unless I'm mistaken, I don't think we have this kind of breakfast meal in our KFC branches. I stand corrected if they're being offered now. NOTE if you're in Thailand, be careful when ordering SPICY. They really mean HOT and SPICY. I can tolerate their HOT and SPICY in my country, but it was an altogether different matter in Bangkok. Literally, you're going to be asking for milk when you order their hot and spicy. It will really burn your tongue!
Oh my god. I live in Japan and we have Lotteria here and it never looks like that (the picture sararas posted). Lotteria looks a lot better outside of Japan even though it started here... in Japan, they serve pretty mediocre burgers and they don't have steak sets like the one pictured.
I agree with you. Lotteria is pretty disappointing in Japan right now. Even McDonald's does a better job!
My favorite fast food comes from Yoshinoya. Being vegetarian, I love their lunch bowls. My other favorite doesn't come from a fast food chain at all, but rather the Aeon supermarkets. I adore their sushi rolls.
@sararas thanks so much for the great pictures - I've never seen a KFC that sells waffles! That's bizarre to me, although it's kinda cool at the same time - I love waffles, so I'll never complain about them being found more commonly than expected!
The meal at Paris Baguette café looks great, too! A good variety of things - I like when breakfasts include some sweet and some savory so you can get the best of both worlds!
I have never eaten any Asian fast food - at least, I don't think I have. Would that include thing like Wagamama and Yo Sushi? I cannot think of any other outlets in the UK that sell what could be considered fast food, Asian style. I am not a fan of sushi as I can't really get my head around the idea of eating raw fish, but I love noodles.
I wish we have Lotteria here in the PH. What I like is the little side dish. The picture shown is actually not steak (not the real one at least), but something similar to a burger patty. But I thought the taste was OK though.
If it's any consideration, I think Mister Donuts in Japan are way better than what what we have here in the PH. It's really sad. But I think I saw an outlet in our capital city Manila, that is at least a lot closer to the Japan branches. Unfortunately, it hasn't reached at my home province of Cebu yet.
Oh, no problem! Glad to share with the others. I second you with the KFC breakfast meal. I love waffles, too. But being Filipino ,waffles for breakfast cannot tramp our beloved rice.So, I understand why marketing would not even consider offering this meal to our country.
I also would like to share this picture of Dunkin Donuts from a branch in Seoul.
The bun tastes and has a muffin-like texture. I can't remember what's in between the bun though, except the cheese.(Probably burger patty). I don't think we have this in our country. Also, what's notable in this Dunkin Donuts in Seoul is the establishment's atmosphere is comparable to a Starbucks or Coffee Bean. Our Dunkin Donut outlets are truly far from it.
I love Pepper Lunch from Japan! It's a bit pricey for a rice meal but it's really good and tasty. I love the honey sauce too. I like BonChon too 'cause the chicken tastes one of a kind. It's sweet but crisp and tasty. The JapChae is great too. Affordable.
We have Tokyo Tokyo and Chowking here in the Philippines that are family favorites. Tokyo Tokyo, obviously the fast food take for Japanese food, serves bento boxes of main dish, side dish, a serving of rice and vegetables and soup. The desert is not bad either. They also have sushi and ramen. My favorites are the prawn tempura and pork tonkatsy bento boxes. At Chowking, the choices are catered more to the Filipinos taste. Rice meals, noodles and dim sum are the best sellers here. I have a soft spot for breaded pork chop and an order of Chicharap prawn crackers.
Some of my favourite although not necessarily fastfood here in Seoul are from Yogertpresso (near exit 3 in Hongdae) and a local place I head to for brunch sometimes, here are some pictures!
Even the "hamburg" (that's what a hamburger steak is called in Japan) isn't available in Lotteria Japan. They just have the basic stuff and it's not so good. As for Mister Donuts, it's decent but I still think Krispy Kreme wins for donuts.
I didn't know Yoshinoya had vegetarian options. Is it a regional thing?
My favorite favorite Asian fast food the Chinese place in the mall. I can not spell the name correctly. So I will not mention it. But, it is a good place to eat. You can get a full box of rice and meats for $8.00. The customer service is always excellent. I like trying the different flavors of chicken. My mouth gets wet just thinking about the place. I miss going to the place. I haven't went there in a long time. I will again when I get the time.
Some other amazing 'fast food' dishes in Korea would be tteokbokki (it's some sort of spicy rice cakes) and my favourite, samgyeopsal!
It's fun getting a glimpse into foods around the world!
I can't say it is very Korean either as they don't usually have breakfast, but there are plenty of bean dishes in here, especially red sweet beans which can be eaten with ice cream and rice cakes (patbingsu), it is definitely one of the best traditional things you can try in Korea!
I think I'd enjoy that yogurt minus the strawberry/blueberry though. I'm waffle/pancake fanatic, so what you have right there is PURE LOVE! Something I would thoroughly enjoy and could finish in just a few gulps, haha!
Agree, Krispy Kreme offers way better-tasting donuts than Mister Donuts. My comparison really is more on the place itself. The set-up of the whole cafe. The ambiance and all that. Mister Donuts PH just doesn't have the vibe that most coffee shops have. I could say the same thing to our local Dunkin Donuts, too. Although I love their donuts more here as they're cheaper.
Speaking of donuts, if I've more budget I'll go for JCo among all these donut shops.
Regarding the comment on 'regional thing', I really do believe that meal offerings do deal with regional tastes. The franchise may be for the brand, but I think the companies make consideration on the local market's taste. After all, the local market is the target consumers. They have to adapt some of the meal offerings to suit the locals. Otherwise, the franchise may die on its own as it won't survive the competition.
Very true. Plus in the case of Japan, there are some products that are exclusive to a prefecture/region and you can't get it anywhere else. So usually fast food chains will create new food items based on the ingredients available in their prefecture. For example, in Okinawa I saw a lot of purple sweet potato products at their fast food restaurants. They even had purple sweet potato fries which is an Okinawa exclusive. I didn't try it, but it must've been good because there was a long line.
Your reply makes me recall of a Mc Do story. I could no longer remember the book that I read before, but it did narrate how the Mc Donalds Philippine franchise managed to include a "spaghetti meal" in their menu line up. If my memory serves me, it took the Philippine McDo franchise holder 2 years to convince McDo Headquarters to include it in the Philippine's McDo Menu. To those who doesn't know, it's only in the Philippines that McDo didn't beat the local fast food brand. For most Filipinos, Jollibee (a local brand) will always be the number 1 brand. Among its famous meal is the "Jolly Spaghetti." Thus, for McDo to compete with the local brand, they had to introduce their own version of a spaghetti meal, and they call it "McSpaghetti".
We try to adapt our menu to reflect different tastes and local traditions for every country in which we have restaurants. We're keen to respect cultural differences and so every country has its own policy of developing menu items.
You will still be able to buy the most iconic items on our menu, such as our famous Big Mac, wherever you are in the world, and every single one of our restaurants meets the same high quality standards we take pride in.
Jollibee in the Philippines is pretty good. Their food is relatively more sweet than Western food because of the palette of Filipino people but they serve burgers, hotdogs and chicken just like any other fast food restaurant. I like hawker restaurants in Singapore and Hong Kong because they're fast, cheap and tasty with a Chinese kick.
My favorite Asian food? I vote for som tam. This is a spicy salad made in Thailand. Different regions in Thailand have different recipes. The Thais can tell the difference. I can't. All som tam is dynamite to me. I mean, they put chillies into it, by the handfuls. When I order my som tam, I also make sure that they only put just one chilli in it. This has made the hawkers look strangely at me on many occasions. Here's a picture of som tam.
One of my friends is a Thai American and her mom makes an AMAZING green papaya salad!!
Thai food has to be one of my favorites. It's always so flavorsome!
Good to know that som tam has got another fan. How's the taste like, to you? Was it too spicy? In Malaysia, which borders Thailand, there are also shops selling som tam. However, the taste has been modified to suit the Malaysian taste buds. In short, the Malaysian version is not that spicy. In Thailand, even the Thais sweat when they eat som tam. However, they maintain that if it's not spicy enough, then there's no point in eating som tam. Myself, much as I like som tam, I can think of many other ways of committing suicide.


Tap into the digital media craze and brand your business today by providing your tech-savvy clients with a custom printed Skinit card. With this card, they can purchase the items they need to personalize their cell phone, iPod or PDA. Our custom printed skins are designed to fit the contours and buttons of your device. Customers can choose from thousands of top sports, entertainment or collegiate branded skins or can design their own skin through our photo upload module.


text:
Q: Copying large files on the same disk - increasing the buffer I'm on OS X, and I'm copying a large amount of data from one partition to another.
Because of the nature of a magnetic disk, I feel this would go much faster if I can get 'cp' to use a huge buffer of a few hundred megs.
Is this easily possible at all? I'm copying several directories recursively.

A: No matter what you do in between, shuffling data within solid-state memory chips, the processes of reading and writing a magnetic/mechanical disk, which requires physically moving pieces of metal, will take orders of magnitude more time, and there's no way to avoid that.

redpajama_set_name: RedPajamaStackExchange


text:
Home»Featured»The Experience 17: When and where to watch on DStv, GOtv
The Experience 17: When and where to watch on DStv, GOtv
By The Eagle Online December 2, 2022 No Comments0 Views
The 17th edition of The Experience, which holds on Friday (today) will be broadcast live on DStv and GOtv.
Regarded as the biggest gospel concert worldwide, it is convened by Paul Adefarasin, Lead Pastor, House on The Rock, Lagos.
This year's edition will feature some of the biggest names in Christian music, including: Mercy Chinwo, Eben, Don Moen, Nathaniel Bassey, Chandler Moore, Travis Green, Tope Alabi, Sinach, Moses Bliss, Dunsi Oyekan, Phil Thompson, Donnie McClurkin, Mr. M & Revelation, and The Lagos Metropolitan Gospel Choir.
"The Experience Lagos is one of the most anticipated events on our festive calendar. We are excited to be able to bring back the concert by airing this year's edition to our DStv and GOtv subscribers Live, on the Holiday Channel. This is the perfect concert for believers, and Gospel music fans alike," says Dr. Busola Tejumola, Head of Content and Channels, West Africa, MultiChoice.
There will be a variety of comedy performances as well as goodwill messages and intercessory prayers.
This year's edition will bring together internationally renowned artists, luminaries and icons, all united under the banner of Jesus Christ.
Experience 17 will be streamed Live on the Holiday Channel on DStv Channel 198 and GOtv Channel 53 on December 2, 2022 at 7pm (WAT).
Busola Tejumola Chandler Moore Don Moen Donnie McClurkin DSTV Dunsi Oyekan Eben GoTV HOUSE ON THE ROCK Mercy Chinwo Moses Bliss Mr. M & Revelation Multichoice Nathaniel Bassey Paul Adefarasin Phil Thompson Sinach The Experience TOPE ALABI Travis Green
Emergency responders battle fire at Lagos market
A leader like Jacinda Ardern, by Azu Ishiekwene


I just finished my second week of the 6 week cycle. I have definatly noticed a difference with my workouts, and recovery. My muscle fatigue and soreness definatly don't last as long. I have more energy during the day, and I even have energy to play with my kids after a 10 hr day at work and the gym.
I also noticed that I sleep much better, and wake up in the morning refreshed.
Have been using Elite Testo now for almost 2 months which is a decent time to evaluate any supplement. Along with a good diet and exercise program, as well as rest, I am noticing some good benefits and gains. Energy seems to be up as do my workouts as I am lasting longer even though I am performing harder sessions. Recovery periods seem to be less painful too.
We want you to have a chance to take your health to the next level and try our products for 60 days. If you don't love one of our products, simply contact my team at myelitehealth.co.uk/help-support and we'll happily refund you.
Want to start enjoying the benefits of collagen protein?
Include one serving in your morning smoothie.
Add to baking dishes, muffins, bars or pancakes to increase protein intake.
Replace other protein powder with this.
Create a chia coconut collagen pudding.
Take one serving of collagen pre- or post-workout.
Many standard formulas fail to harness the true power of natural vitamins and minerals that can contribute to testosterone function. In fact the whole market is choc-full of dodgy players peddling sub-par products. You can see from our reviews and the products that we offer that we are a real UK business with thousands of happy customers.
Elite Testo combines a range of research proven ingredients in their purest and most potent forms.
Elite Testo is a cutting-edge, t-booster with one aim - to elevate your overall performance in and out of the gym. Formulated by our experts to smash the performance of any legal test booster available on the market.
Struggling for energy? Struggling to build real muscle? Elite Testo is a category leading testo supplement that may be the 'missing link' you need.
Elite Testo is a category leading testo supplement, exhaustively formulated by our experts to boost your testosterone naturally.
1. Cremades, Ruzafa C, Monserrat F, López-Contreras AJ, Peñafiel R (2004). Influence of dietary arginine.
2. Ovidiu A. Galescu, MD, MS,1 Melissa K. Crocker, MD,1,2 Anne M. Altschul,1 Shannon E. Marwitz, BS,1 Sheila M. Brady, MSN, CRNP,1 and Jack A. Yanovski, MD, PhD. A Pilot Study of the Effects of Niacin Administration on Free Fatty Acid and Muscle Growth.
*Minus shipping & handling, when applicable. Applicable on purchases from store.draxe.com only.
We want you to have a chance to take your health to the next level and try our products for 60 days. If you don't love one of our products, simply contact my team at 0845 8620595 or myelitehealth.co.uk/help-support and we'll happily refund you.
Disclaimer: All discussion about results on this website are based on individual findings where each circumstance is completely unique and may not be similar or the same as you. Vitamin supplements are not intended to treat or prevent any disease. Food supplements must not replace a balanced and varied diet, and a healthy lifestyle.


Innotribe opened its Startup Challenge for Africa and is currently looking for the best startups to showcase their products during SWIFT's African Regional Conference (ARC) to be held in Mauritius from 17-19 May.
SWIFT announced early this week that the Innotribe Startup Challenge for Africa is open for applications and for the second year running, the Innotribe Startup Challenge for Africa will be part of SWIFT's African Regional Conference.
The Innotribe Startup Challenge gives young African financial technology startups, the opportunity to showcase their products and receive expert coaching and mentoring. Twelve companies will be selected to compete in the event, with three finalists selected to attend Sibos, SWIFT's annual global financial services conference. At Sibos, which takes place from 26-29 September in Geneva, the finalists will share the stage with fintech experts and receive a US$10,000 cash prize each.
"Through the Startup Challenge, we want to spotlight innovation playing a role in the future of the financial industry across the African continent and provide an opportunity for young fintech companies to use Innotribe's network and alumni to help them develop to the best of their potential," he added.
Launched in 2011, the Startup Challenge has become one of the leading global startup competitions, connecting the financial services industry with more than 650 fintech startups around the world and reaching over 4,000 audience members through global showcases and networking events.
Last year for the first time Innotribe, SWIFT's innovation arm, partnered with ARC to bring the Startup Challenge to Africa, showcasing vibrant businesses and a genuine spirit of innovation. It highlighted how much SWIFT's member institutions are keen to understand the fintech innovation that is happening in their own communities and the importance for local startups to benefit from in-depth industry feedback and gain exposure at a global stage.