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The number 0, the strings "0" and "", the empty list (), and the special value undef evaluate to false. [8] All else evaluates to true. Lua has a Boolean data type, but non-Boolean values can also behave as Booleans. The non-value nil evaluates to false, whereas every other data type value evaluates to true.
For 8-bit integers the table of quarter squares will have 2 9 −1=511 entries (one entry for the full range 0..510 of possible sums, the differences using only the first 256 entries in range 0..255) or 2 9 −1=511 entries (using for negative differences the technique of 2-complements and 9-bit masking, which avoids testing the sign of ...
char * pc [10]; // array of 10 elements of 'pointer to char' char (* pa)[10]; // pointer to a 10-element array of char The element pc requires ten blocks of memory of the size of pointer to char (usually 40 or 80 bytes on common platforms), but element pa is only one pointer (size 4 or 8 bytes), and the data it refers to is an array of ten ...
Karatsuba multiplication of az+b and cz+d (boxed), and 1234 and 567 with z=100. Magenta arrows denote multiplication, amber denotes addition, silver denotes subtraction and cyan denotes left shift. (A), (B) and (C) show recursion with z=10 to obtain intermediate values. The Karatsuba algorithm is a fast multiplication algorithm.
In mathematics and mathematical logic, Boolean algebra is a branch of algebra.It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.
Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing B by B + c 1 − 3c 2 will cause them to be renumbered from 0 through 9 and 4 through 23, respectively. Taking advantage of this feature, some languages (like FORTRAN 77) specify that array indices begin at 1, as in mathematical ...
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Another array data type, intended for numerical use (especially to represent vectors and matrices); the C++ standard allows specific optimizations for this intended purpose. According to Josuttis, valarray was badly designed, by people "who left the [C++ standard] committee a long time before the standard was finished", and expression template ...