Computation - Task 4

Given a task, you should write a program that solves the task using the instructions below. Let $x\_t$ denote the result of the $t$ -th instruction. The permitted instructions, the syntax, and the result $x\_t$ are given below:

Name	Operator	Parameters	Effects
Input	`I`	N/A	Read a real number from the terminal and make the number $x\_t$
Output	`O`	$i$	Print $x\_i$ to the terminal, and $x\_t = x\_i$
Addition	`+`	$i \quad j$	$x\_t = x\_i + x\_j$
Adding constant	`C`	$i \quad c$	$x\_t = x\_i +c$
Negate	`-`	$i$	$x\_t = -x\_i$
Left shift	`<`	$i \quad k$	$x\_t = x\_i \cdot 2^k$
Right shift	`>`	$i \quad k$	$x\_t = x\_i \cdot 2^{-k}$
S	`S`	$i$	$x\_t = s(x\_i)$
Comparison	`P`	$i \quad j$	$x\_t = \left\\{ \begin{array}{ll} -1 & \quad x\_i < x\_j \\\ 0 & \quad x\_i = x\_j \\\ 1 & \quad x\_i > x\_j \end{array} \right.$
Max	`M`	$i \quad j$	$x\_t = \left\\{ \begin{array}{ll} x\_i & \quad x\_i > x\_j \\\ x\_j & \quad x\_i \leq x\_j \\\ \end{array} \right.$
Multiplication	`*`	$i \quad j$	$x\_i = x\_i \cdot x\_j$

Here, the definition of $s(x)$ is given below where $e = 2.718281828459045\ldots$ is the base of natural logarithm:

$\displaystyle s(x) = \frac{1}{1 + e^{-x}}.$

Notice there is a penalty for using the P, M, and * operators. See details below in the "grading" section.

For each instruction, the parameters $i$ and $j$ must be smaller than the current instruction number $t$ . The instructions are executed in the order, one by one.

The operations have finite precision: in particular, the results are only accurate up to 90 digits after the decimal point and the rest will be rounded. Similarly, the argument $c$ to the adding constant instruction can have at most 90 digits in its decimal part.

For left shift and right shift instructions, $k$ must be a non-negative integer not exceeding 10000.

The ten tasks are given below:

Task 1: Given $a,b$ where $|a|, |b| \leq 10^9$ and $a,b$ have at most 9 digits in their decimal parts, compute $-2a-2b$ .
Task 2: Given $a$ where $|a| \leq 10^9$ and $a$ has at most 9 digits in its decimal part, compute $\frac{1}{1+e^{17a}}$ .
Task 3: Given $a$ where $|a| \leq 10^9$ and $a$ has at most 9 digits in its decimal part, compute $\left\\{ \begin{array}{ll} -1 & \quad a < 0\\\ 0 & \quad a = 0\\\ 1 & \quad a > 0 \end{array} \right.$ .
Task 4: Given $a$ where $|a| \leq 10^9$ and $a$ has at most 9 digits in its decimal part, compute the absolute value of $a$ , $|a|$ .
Task 5: Given $a\_1,\ldots,a\_{32}$ where $a\_1,\ldots,a\_{32} \in \\{0,1\\}$ , treat $a\_1a\_2 \cdots a\_{32}$ as a binary number where $a\_1$ is the most significant bit and $a\_{32}$ is the least significant bit, compute the corresponding value (in base 10).
Task 6: Given integer $a$ where $0 \leq a < 2^{32}$ , output 32 integers denoting $a$ in base 2 representation. The most significant bit should be printed first and the least significant bit should be printed last. If $a$ has less than 32 bits in its binary representation, add leading 0s.
Task 7: Given integers $a,b$ where $0 \leq a,b < 2^{32}$ , compute the bitwise XOR of $a$ and $b$ .
Task 8: Given $a$ where $|a| \leq 10^9$ and $a$ has at most 9 digits in its decimal part, output $\frac{a}{10}$ .
Task 9: Given $a\_1,\ldots,a\_{16}$ where $|a\_i| \leq 10^9$ and $a\_i$ has at most 9 digits in its decimal part, print 16 real numbers representing the result of sorting $a\_1,\ldots,a\_{16}$ in ascending order.
Task 10: Given integers $a,b,m$ where $0 \leq a,b < 2^{32}$ , $1 \leq m < 2^{32}$ , compute the remainder after dividing $a \times b$ by $m$ (i.e. compute $a \times b \bmod m$ ).

Computation - Task 4

문제

출력