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:

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 $a \times b \bmod m$).

The $i$-th line describes the $i$-th instruction: first, you should output a letter denoting the operation. Then output several (or zero) integers denoting the parameters to the operation. The operator and the parameters (and between parameters) should be separated by a single space.

You can output at most $10^4$ lines.