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:

Does std::scientific always result in normalized scientific notation for floating-point numbers?

Scientific notation defines how numbers should be displayed using a sign, a number and an exponent but it does not state that the visualization is normalized.
An example: -2.34e-2 (normalized scientific notation) is the same as -0.234e-1 (scientific notation)
Can I rely on the following code always producing the normalized outcome?
Edit: except NAN and INF as pointed out in the answers.
template<typename T>
static std::string toScientificNotation(T number, unsigned significantDigits)
{
    if (significantDigits > 0) {
        significantDigits--;
    }
    std::stringstream ss;
    ss.precision(significantDigits);
    ss << std::scientific << number;
    return ss.str();
}

If yes, please list a section in the C++ documentation/standard stating that it is not platform/implementation-defined. Since the value of 0 is also represented differently I'm afraid that certain very small numbers (denormalized?!) could be visualized differently. On my platform with my compiler it currently works for std::numeric_limits::min(), denorm_min().
Note: I use this to find the order of magnitude of a number without messing with all the quirky details of floating point number analysis. I wanted the standard library do it for me :-)

A:

Can I rely on the following code always producing the normalized outcome?

There are no guarantee of it, no. Better said: the Standard does not impose a guarantee as strong as you wish here was.
std::scientific is only quoted on the following relevant parts:

[floatfield.manip]:2

ios_base& scientific(ios_base& str);  

Effects: Calls str.setf(ios_­base​::​scientific, ios_­base​::​floatfield).
Returns: str.

Table 101 — fmtflags effects

| Element    | Effect(s) if set                                       |
| ...        | ...                                                    |
| scientific | generates floating-point output in scientific notation |
| ...        | ...                                                    |

A:

Yes, except for zero, infinity and NaN.
The C++ standard refers to the C standard for formatting, which requires normalized scientific notation.

[floatfield.manip]/2

ios_base& scientific(ios_base& str);

Effects: Calls str.setf(ios_­base​::​scientific, ios_­base​::​floatfield).
Returns: str.

[ostream.inserters.arithmetic]/1 (partial)

operator<<(float val);
operator<<(double val);
operator<<(long double val);

Effects: The classes num_­get<> and num_­put<> handle locale-dependent numeric formatting and parsing. These inserter functions use the imbued locale value to perform numeric formatting. When val is of type ..., double, long double, ..., the formatting conversion occurs as if it performed the following code fragment:
bool failed = use_facet<
  num_put<charT, ostreambuf_iterator<charT, traits>>
    >(getloc()).put(*this, *this, fill(), val).failed();

When val is of type float the formatting conversion occurs as if it performed the following code fragment:
bool failed = use_facet<
  num_put<charT, ostreambuf_iterator<charT, traits>>
    >(getloc()).put(*this, *this, fill(),
      static_cast<double>(val)).failed();

[facet.num.put.virtuals]/1:5.1 (partial)

Stage 1:
The first action of stage 1 is to determine a conversion specifier. The tables that describe this determination use the following local variables
fmtflags flags = str.flags();
fmtflags floatfield = (flags & (ios_base::floatfield));

For conversion from a floating-point type, the function determines the floating-point conversion specifier as indicated in Table 70.
Table 70 — Floating-point conversions
| State                                            | stdio equivalent |
| ------------------------------------------------ | ---------------- |
| floatfield == ios_­base​::​scientific && !uppercase | %e               |
| floatfield == ios_­base​::​scientific               | %E               |

The representations at the end of stage 1 consists of the char's that would be printed by a call of printf(s, val) where s is the conversion specifier determined above.

C11 n1570 [7.21.6.1]:8.4

e,E
A double argument representing a floating-point number is converted in the
  style [−]d.ddde±dd, where there is one digit (which is nonzero if the
  argument is nonzero) before the decimal-point character and the number of
  digits after it is equal to the precision; if the precision is missing, it is taken as 6; if the precision is zero and the # flag is not specified, no decimal-point
  character appears. The value is rounded to the appropriate number of digits. The E conversion specifier produces a number with E instead of e
  introducing the exponent. The exponent always contains at least two digits,
  and only as many more digits as necessary to represent the exponent. If the
  value is zero, the exponent is zero.
A double argument representing an infinity or NaN is converted in the style of an f or F conversion specifier.