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Rating 3.5 stars · Review by J.R. Bookwalter

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PDF OCR X is a simple drag-and-drop utility for Mac OS X and Windows, that converts your PDFs and images into text documents.

//pull out element 2.0 float element = m[1][0]; //pull out column vector <1.0, 3.0> float2 firstCol = m[0];

(mod p )

The arithmetic operators are overloaded for matrices, too. In this case, multiplication of matrices with the same dimension actually performs matrix multiplication, not per-element multiplication. Multiplication of vectors and matrices with the proper dimension in the proper order also performs matrix multiplication. For example,



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float2x2 * float2x2 -> float2x2 //multiplies 2x2 matrix by 2x2 matrix, yielding 2x2 matrix float2 * float2x2 -> float2 //multiplies 1x2 matrix by 2x2 matrix, yielding 1x2 matrix (row vector) float2x2 * float2 -> float2 //multiplies 2x2 matrix by 2x1 matrix, yielding 2x1 matrix (column vector) float * float2x2 -> float2x2 //multiplies scalar by 2x2 matrix, yielding 2x2 matrix

(mod p )

Recognition rate (%) 100 80 60 40

Manipulating whole vectors and matrices at a time is not only concise and fast, but applicable to 3D graphics and some image processing algorithms.

a' (mod p ) = (g")b (mod p ) = g a b (mod p ) .

Suitable only for input images, Pixel Bender includes image types for images with various numbers of color channels.





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Pretty much the only thing you can do with an image is sample it, using the three sample functions listed toward the end of Table 38-2. This yields a pixel of the corresponding number of channels.

Figure 6.2: Difie Hellman key exchange. Trudy sees ga (mod p ) and g6 (mod p ) and she breaks the key exchange protocol if she can find gab (mod p ) . To do 50, it appears that she must find a from ga (mod p ) or b from gb (mod p ) . Therefore, the strength of the DiffieHcllinan key exchange protocol is believed to depend on the computational

Unfortunately, Pixel Bender on Flash doesn t support arrays. Instead, you could try to encode a series of oat values in an n 1 one-channel image (image1). Regions are not yet available.

(a) Recognition rate (%) 60 55 50 45 40 35 2 3 4

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Pixel Bender provides a suite of mathematical functions, all of which are overloaded to work with vectors of any dimension when it makes sense. For example, log() can take the logarithm of a number if passed a float, but it also takes the logarithm of four numbers at once if passed a float4. I signify that any dimension of oat may be passed with the (purely notational) type floatn. So few functions are de ned that they can be summarized in Table 38-2.

complexity of solving the discrete logarithm problem. That is, there is no efficient solution to the problem of finding y given ICY (mod p ) , the base z and the modulus p . Suppose, for example, we want to solve the equation 2" = 9 (mod 11). Since the numbers are so small, this is easy to solve by exhaustively searching through all of the possible exponents. We see that

TABLE 38-2

floatn radians(floatn d) floatn degrees(floatn r) floatn sin(floatn r) floatn cos(floatn r) floatn tan(floatn r) floatn asin(floatn x) floatn acos(floatn x) floatn atan(floatn slope) floatn atan(floatn y, floatn x) floatn pow(floatn a, floatn b) floatn exp(floatn x) floatn exp2(floatn x) floatn log(floatn x) floatn log2(floatn x) floatn sqrt(floatn x) floatn inverseSqrt(floatn x) floatn abs(floatn x) floatn sign(floatn x) floatn floor(floatn x) floatn ceil (floatn x) floatn fract(floatn x) floatn mod(floatn a, floatn b) floatn min(floatn a, floatn b) floatn max(floatn a, floatn b)

2 (mod 11)

Converts d degrees to radians Converts r radians to degrees Sine; r is in radians Cosine Tangent Arcsine Arccosine Arctangent Arctangent Raises ab Raises e x Raises 2x Natural logarithm of x Base 2 logarithm of x Positive square root of x Reciprocal of the positive square root of x Absolute value of x Sign of x. Returns -1.0, 0.0, or 1.0 Rounds down x to nearest whole number Rounds up x to nearest whole number Fractional part of x Returns a modulo b, remainder of a divided by b Minimum of the two arguments Maximum of the two arguments

MCE (UNIT)

TABLE 38-2

22 = 4 (mod 11) 23 = 8 (mod 11) 24 = 16 = 5 (mod 11) 25 = 5 . 2

(continued )

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