Computation - Task 9

Let $x_t$ denote the result of the $t$-th instruction. The permitted instructions, their syntax, and the result $x_t$ are listed below.

Here $s(x) = \frac{1}{1 + e^{-x}}$, where $e = 2.718281828459045\ldots$ is the base of the natural logarithm.

The P, M, and * operators carry a penalty. See the grading section for details.

The operations have finite precision. Results are accurate only up to 90 digits after the decimal point, and the rest is rounded. Likewise, the argument $c$ of the adding constant instruction can have at most 90 digits in its decimal part.

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

For each instruction, the parameters $i$ and $j$ must be smaller than the current instruction number $t$. Instructions run in order, one at a time.

Task 1: Given $a, b$ with $|a|, |b| \leq 10^9$, where $a$ and $b$ have at most 9 digits in their decimal parts, compute $-2a-2b$.

Task 2: Given $a$ with $|a| \leq 10^9$, where $a$ has at most 9 digits in its decimal part, compute $\frac{1}{1+e^{17a}}$.

Task 3: Given $a$ with $|a| \leq 10^9$, where $a$ has at most 9 digits in its decimal part, compute $-1$ if $a < 0$, $0$ if $a = 0$, and $1$ if $a > 0$.

Task 4: Given $a$ with $|a| \leq 10^9$, where $a$ has at most 9 digits in its decimal part, compute the absolute value $|a|$.

Task 5: Given $a_1, \ldots, a_{32}$ with each $a_i \in \{0,1\}$, read $a_1a_2 \cdots a_{32}$ as a binary number, where $a_1$ is the most significant bit and $a_{32}$ is the least significant bit. Compute its value in base 10.

Task 6: Given an integer $a$ with $0 \leq a < 2^{32}$, output 32 integers giving the binary representation of $a$. Print the most significant bit first and the least significant bit last. If $a$ has fewer than 32 bits, add leading 0s.

Task 7: Given integers $a, b$ with $0 \leq a, b < 2^{32}$, compute the bitwise XOR of $a$ and $b$.

Task 8: Given $a$ with $|a| \leq 10^9$, where $a$ has at most 9 digits in its decimal part, output $\frac{a}{10}$.

Task 9: Given $a_1, \ldots, a_{16}$ with $|a_i| \leq 10^9$, where each $a_i$ has at most 9 digits in its decimal part, print 16 real numbers that are the values $a_1, \ldots, a_{16}$ sorted in ascending order.

Task 10: Given integers $a, b, m$ with $0 \leq a, b < 2^{32}$ and $1 \leq m < 2^{32}$, compute the remainder when $a \times b$ is divided by $m$, that is, $a \times b \bmod m$.

The $i$-th line describes the $i$-th instruction. First, output a letter for the operation. Then output zero or more integers for its parameters. Put a single space between the operator and each parameter.

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