You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


Q:

Alternatives for compile-time floating-point initialization

I'm currently working on a template-meta-programming based implementation of floating-point arithmetic. The template which represent compile-time float values is as follows:
template<bool S , std::int16_t E , std::uint64_t M>
struct number{};

Since initializing such values using hardcoded mantissas, exponents, etc, is a cumbersome and bug-prone process I have written a template for converting decimal values to floating-point ones:
template<std::int64_t INT , std::uint64_t DECS>
struct decimal{};

Where the first parameter represents the integral part and the second the fractional digits. I think this is a common and well known way.
However this pattern suffers from some issues (How I enter negative less-than-one numbers?), where one of the most annoying for me is the fact that there is no way to enter zero digits just after the comma, i.e., numbers like 0.00032.
I'm C++11 aware, and I was thinking about a user-defined-literal + decltype() approach (Even with a macro #define FLOAT(x) decltype(x_MY_LITERAL)) but I'm not sure that approach is possible in all contexts, I mean, if the literal + decltype is evaluable in the context of a template parameter.  
Even if that could work, I want to know if there are other possible approaches for this problem. So, what alternatives are there for floating-point-like initialization at compile-time via tmp?

Attemped alternatives:
Just for completeness shake, I will describe the alternatives I have implemented, how they work, and its consts and pros. The question itself remains open, to allow anybody to add more alternatives.
Some background
First I will describe the features I have used, just to make sure everybody understand the code.
My library, The Turbo Metaprogramming Library, is based on three principles:

Type template parameters only: Being completely generic mixing type parameters, value parameters, and template-template parameters is really hard (Near impossible), so this library uses type parameters only. Whenever is necessary to use values or templates, the library provides wrappers to pass such parameters through boxing.
Uniform expression evaluation: One of the first needs when working in a programming language is a way to evaluate expressions and take its value. Turbo provides the tml::evalmetafunction, which takes any kind of expression and returns (evaluates) its value.
Generic algorithms and metafunctions customized via template specialization: Whenever I can I use C++11 template aliases to avoid the cumbersome typename ::type construction. My convention is to define implementation templates (The metafunctions which really do the work) on a nested impl namespace, and a C++11 template alias to the result on the current namespace. Since such aliases return the result directly, they are not evaluable on a complex expression (Consider a metafunction instantation add<X,Y>, where X and Y are variables of a lambda. If add was an alias to the result, that doesn't work because the evaluation has no sense. If we need the expression (metafunction) instead of its result directly, my convention was to put an alias to the metafunction on a func nested namespace . 

Here are some examples:
using bits = tml::util::sizeof_bits<int>; //bits is a size_t integral constant with the 
                                          //size on bits of an int

//A metafunction which returns the size on bits of a type doubled
using double_size = tml::lambda<_1 , tml::mul<tml::util::func::sizeof_bits<_1>,tml::Int<2>> >;

using int_double_size = tml::eval<double_size,int>; //Read as "double_size(int)"

tml is the main namespace of the library, and floating-point features are exposed on the tml::floating namespace.
TL;DR

tml::eval takes any expression and evaluates it, returning its value. Its a C++11 template alias, so typename ::type is not needed.
tml::integral_constant (Just an alias of std::integral_constant) is the de-facto value wrapper for passing value parameters as type parameters through boxing. The library has the convention of using type-parameters only (There are wrappers for template-template parameters too, see tml::lazy and tml::bind).

Attempt 1: From integer
Here we define a metafunction integer which returns a floating-point value from an integer  one:
template<std::int64_t mantissa , sign_t S = (sign_t)(mantissa >= 0)>
struct integer
{
    using m   = tml::floating::number<S,0,static_cast<mantissa_t>((mantissa >= 0) ? mantissa : -mantissa)>;
    using hsb = tml::floating::highest_set_bit<m>;
    static constexpr const exponent_t exp = hsb::value - 31;

    using result = tml::floating::number<S,exp,(m::mantissa << (31 - hsb::value))>; //Note the number is normalized
};

What it does is to take the integral value directly, use it as mantissa, and normalize the number explicitly computing the highest (most significant) set bit, shifting the mantissa acordingly.
An example of its ussage could be:
using ten = tml::floating::integer<10>;

Advantages:

Efficiency: No extra complex computations are required to obtain the equivalent floating point number. The only relevant operation is the call to highest_set_bit.
The number is normalized by default (Regarding on efficiency too). Also there are no precision issues (At least not for small values).

Disadvantages:

Only works with integral values.

Attempt 2: Decimal initialization
This alternative uses a pair of integral values to represent the integral and fractional parts of the number respectively:
template<std::int64_t INTEGRAL , std::uint64_t FRACTIONAL>
struct decimal{ ... };

using pi = decimal<3,141592654>;

What it does is to compute the value of the integral part (Just call to integer, the previous attempt) and the value of the fractional part.
The value of the fractional part is the value of the integer adjusted until the radix point is at the beginning of the number. In other words:
                       integer<fractional_part>
fractional_value = ________________________________
                          10^number_of_digits

Then the value of the number is just the sum of both values:
result = integer_part_value + fractional_value

The number of digits of an integral number is log10(number) + 1. I have ended up with a log10 metafunction for integral values that doesn't require recursion:
template<typename N>
struct log10
{
    using result = tml::Int<(0  <= N::value && N::value < 10)  ? 0 :
                            (10 <= N::value && N::value < 100) ? 1 :
                            ...
                           >;
} 

So it has O(1) complexity (Measuring template instantation depth, of course).
With this metafunction, the formula above becomes:
//First some aliases, to make the code more handy:
using integral_i   = tml::integral_constant<std::int64_t,INTEGRAL>;
using integral_f   = tml::floating::integer<INTEGRAL>;
using fractional_f = tml::floating::integer<FRACTIONAL>;
using ten          = tml::floating::integer<10>;
using one          = tml::Int<1>;

using fractional_value = tml::eval<tml::div<fractional_f , 
                                            tml::pow<ten,
                                                     tml::add<tml::log10<integral_i>,
                                                              one
                                                             >
                                                    >
                                           >
                                  > 

And then the result is:
 using result = tml::eval<tml::add<integral_f,fractional_value>>;

Advantages

Allows instancing non-integral values like 12.123.

Disadvantages:

Performance: tml::pow is recursive, with a complexity of O(n). tml::div for floating-point values is implemented as a multiplication of the numerator by the reciprocal of the denominator. That reciprocal is computed by a Newton-Raphson approximation (Five iterations by default).
Precision issues: The sequential multiplications done to compute the power could lead to accumulative minor precision issues. The same for the Newton-Raphson approximation done to compute the division.
The notation is limited: There is no way to specify numbers with trailing zeros after the point, say 13.0004, since an integer literal 0004 is not valid.  

Attempt 3 (3.1 and 3.2): Decimal scientific notation
Instead of writing the number using hardcoded digits, we use decimal (Power of 10) scientific notation to initialize floating-point numbers:
using pi = tml::floating::decimal_sci<3141592654,-9>; //3141592654 x 10^-9

To compute the number you only have to take the value of the significant, and multiply it by the corresponding power of 10:
template<std::int64_t S , std::int64_t E>
struct decimal_sci
{
    using significant = tml::floating::integer<S>;
    using power       = tml::eval<tml::pow<tml::floating::integer<10>,tml::Int<E>>>;

    using result = tml::eval<tml::mul<significant,power>>;
};

There is an improvement for this attempt, which treats the given significant if it was normalized to one integer digit only. So a value 0.0034565432 could be written as (34565432 , -3) instead of (34565432 , -11).
I call it tml::floating::decimal_scinorm:
template<std::int64_t S , std::int64_t E = 0>
struct decimal_scinorm
{
    using significant_i = tml::integral_constant<std::int64_t,S>;
    using exponent_i    = tml::integral_constant<std::int64_t,E>;

    using adjust  = tml::eval<tml::log10<significant_i>>;
    using new_exp = tml::eval<tml::sub<exponent_i,adjust>>;

    using result = typename decimal_sci<S,new_exp::value>::result;
};

using pi = tml::floating::decimal_scinorm<3141592654>; //3.141592654
using i  = tml::floating::decimal_scinorm<999999,-4>;  //0.000999999

Advantages

Leads with wide numbers, with heading zeros included, in a simple way.
Uses a well known notation, no syntactic tricks involved.

Disadvantages

Poor precision with very large/small numbers (Well, thats expected since thats how scientific-notation works). Note the floating-point internal computations could lead to accumulative precision errors, proportional to the length (of the mantissa) and exponent of the number. Are the same precision errors of the attempts above (From the usage of tml::pow, tml::div, etc).

A:

You might want to use user-defined literals. According to cppreference.com, it

Allows integer, floating-point, character, and string literals to produce objects of user-defined type by defining a user-defined
  suffix.

(see also http://en.cppreference.com/w/cpp/language/user_literal). This way, you could make the expression
123.456_mysuffix

yield whatever type you want, if you define the literal operator for _mysuffix. With that operator, you can access the input 123.456 either as a (standard c++) floating point number or you can do the necessary conversion from the raw string as a const char* yourself.
EDIT: After reading your edited question and realizing what kind of template meta-programming you were talking about, I just wanted to emphasize that the literal can also be accessed as a parameter pack of char template parameters. You might be able to integrate this into your compile time framework.