[ZIP 234] Smooth Out The Block Subsidy Issuance

draft-issuance.html

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+<p><code>ZIP: 
+Title: Smooth Out The Block Subsidy Issuance
+Owners: Jason McGee &lt;jason@shieldedlabs.com&gt;
+        Mark Henderson &lt;mark@equilibrium.co&gt;
+        Tomek Piotrowski &lt;tomek@eiger.co&gt;
+        Mariusz Pilarek &lt;mariusz@eiger.co&gt;
+Original-Authors: Nathan Wilcox
+Credits: Nathan Wilcox
+         Mark Henderson
+         Jason McGee
+Status: Draft
+Category: Consensus
+Created: 2023-08-23
+License: BSD-2-Clause</code></p>
+<h1>Terminology</h1>
+<p>The key words “MUST”, “SHOULD”, “SHOULD NOT”, “MAY”, “RECOMMENDED”, “OPTIONAL”,
+and “REQUIRED” in this document are to be interpreted as described in RFC 2119. [1]</p>
+<p>"Network upgrade" - to be interpreted as described in ZIP 200. [2]</p>
+<p>“Block Subsidy” - to be interpreted as described in ZIP TBD [3]</p>
+<p>“Issuance” - to be interpreted as described in ZIP TBD [3]</p>
+<p>“We” - the ZIP authors, owners listed in the above front matter</p>
+<p>“<code>ZsfBalanceAfter(h)</code>” is the total ZEC available in the Zcash Sustainability Fund (ZSF) after the transactions
+in block <code>h</code>, described in ZIP #TODO reference#. The Sustainability Fund is used to pay out Block Subsidies
+from unmined ZEC, and other fund deposits.</p>
+<p>“<code>BLOCK_SUBSIDY_FRACTION</code>” = 41 / 100,000,000 or <code>0.00000041</code></p>
+<p>"<code>NUMBER_OF_BLOCKS_IN_4_YEARS</code>" = <code>(365.25 * 24 * 60 * 60/75 * 4)</code>, or <code>1_683_072</code></p>
+<h1>Abstract</h1>
+<p>This ZIP proposes a change to how nodes calculate the block subsidy.</p>
+<p>Instead of following a step function around the four-year halving cycle inherited
+from Bitcoin, we propose a slow exponential “smoothing” of the curve. The new issuance
+scheme would approximate the current 4 year cycle, and results in the last
+zatoshi being issued in around 114 years.</p>
+<h1>Motivation</h1>
+<p>Zcash’s economic model is inherited from Bitcoin and includes the concept of a halving
+mechanism to regulate the issuance of new coins. This approach, though foundational, invites
+ a reevaluation amid Zcash’s ongoing evolution. As the network matures, the need to address
+potential future challenges and ensure a sustained and stable economic ecosystem becomes
+apparent. The transition to a smoothed emissions curve offers an opportunity to adjust the network's
+issuance dynamics while maintaining the supply cap of 21,000,000 coins. By doing so, Zcash
+endeavors to optimize its economic framework, accommodating changing circumstances while
+maintaining predictability and stability in rewards distribution.</p>
+<p>This proposal outlines a solution to address challenges associated with the existing block
+subsidy issuance mechanism in the Zcash network. The primary goal of this proposal is to
+introduce a more predictable and stable issuance of ZEC by smoothing out the issuance
+curve while preserving the supply cap. It's important to note that this proposal does
+not seek to alter the fundamental aspects of Zcash's issuance policy. The average block
+subsidy amount over time will remain the same and the funds for block subsidies will last
+a similar amount of time. Instead, it focuses solely on enhancing the predictability
+and consistency of the block subsidy issuance process.</p>
+<p>Smoothing the emissions curve helps ensure that the network remains economically
+viable and stable as it transitions from a traditional issuance mechanism to one
+that maintains a sustainable and predictable issuance of rewards over time. It
+prevents abrupt changes in the rate of newly issued coins, which could lead to
+disruptions in the network's economic model and potentially impact its security
+and sustainability. A smoother emissions curve allows for a more gradual and controlled
+transition, providing ZEC stakeholders and participants with a clear understanding of
+how rewards will be distributed over time.</p>
+<h1>Specification</h1>
+<p>Smoothing the issuance curve is possible using an exponential decay formula that
+satisfies the following requirements:</p>
+<h2>Issuance Goals</h2>
+<ol>
+<li>Block subsidies are monotonically decreasing, as long as <code>ZsfBalanceAfter(h)</code> is monotonically decreasing</li>
+<li>Block subsidies approximate a continuous function</li>
+<li>When <code>ZSF_BALANCE(h) &gt; 0</code> then block subsidies for block <code>h</code>
+MUST always be <code>&gt; 0</code>, preventing a final “unmined” zatoshi</li>
+<li>For any 4 year period, all paid out block subsidies MUST equal approximately
+half of <code>ZSF_BALANCE</code> at the beginning of that 4 year period</li>
+<li>This functionality MUST be introduced as part of a network upgrade</li>
+</ol>
+<p>The above requirements assume no deflationary action, i.e. that no ZEC is added
+to <code>ZSF_BALANCE</code>. They are referenced below as <strong>Rn</strong>.</p>
+<h2>Issuance Calculation</h2>
+<p>Given the block height <code>h</code> define a function <strong>S</strong>, such that:</p>
+<p><strong>S(h)</strong> = Block subsidy for a given <code>h</code>, that satisfies above requirements.</p>
+<p>Using an exponential decay function for <strong>BlockSubsidy</strong> satisfies <strong>G1</strong> and <strong>G2</strong> above:</p>
+<p><code>BlockSubsidy(h) = BLOCK_SUBSIDY_FRACTION * ZsfBalanceAfter(h - 1)</code></p>
+<p>Finally, to satisfy <strong>G3</strong> above we need to always round up to at least 1 Zatoshi
+if <code>ZsfBalanceAfter(h - 1) &gt; 0</code>:</p>
+<p><code>BlockSubsidy(h) = ceiling(BLOCK_SUBSIDY_FRACTION * ZsfBalanceAfter(h - 1))</code></p>
+<h1>Rationale</h1>
+<h2><code>BLOCK_SUBSIDY_FRACTION</code></h2>
+<p>The value <code>41 / 100_000_000</code> satisfies the approximation:</p>
+<p><code>(1 - BLOCK_SUBSIDY_FRACTION)^NUMBER_OF_BLOCKS_IN_4_YEARS ≈ 0.5</code></p>
+<p>Meaning after a period of 4 years around half of <code>ZSF_BALANCE</code> will be paid out
+as block subsidies, thus satisfying <strong>G4</strong>.</p>
+<h2>Other Notes</h2>
+<p>The suggested implementation avoids using float numbers. Rust and C++ will both round
+the result of the final division up, satisfying <strong>R3</strong> above.</p>
+<h1>Appendix: Simulation</h1>
+<p>We encourage readers to run the following Rust code, which simulates block subsidies.
+According to this simulation, assuming no deflationary action, block subsidies would
+last for approximately 113 years:</p>
+<h2>Rust Code</h2>
+<p>```rust
+fn main() {
+    // approximate available subsidies in August of 2023
+    let mut available_subsidies: i64 = 4671731 * 100_000_000;
+    let mut block: u32 = 0;</p>
+<pre><code>while available_subsidies &gt; 0 { 
+    let block_subsidy = (available_subsidies * 41 + 99_999_999) / 100_000_000;
+    available_subsidies -= block_subsidy;
+
+    println!(
+        "{} ({} years): {}({} ZEC) {}({} ZEC)",
+        block,                             // current block
+        block / 420_768,                   // ~ current year
+        block_subsidy,                     // block subsidy in zatoshis
+        block_subsidy / 100_000_000,       // block subsidy in ZEC
+        available_subsidies,               // available subsidies in zatoshis
+        available_subsidies / 100_000_000  // available subsidies in ZEC
+    );
+
+    block += 1;
+}
+</code></pre>
+<p>}
+```</p>
+<p>Last line of output of the above program is:</p>
+<p><code>47699804 (113 years): 1(0 ZEC) 0(0 ZEC)</code></p>
+<p>Note the addition of 99,999,999 before division to force rounding up of non-zero values.</p>
+<h1>References</h1>
+<p>[1] RFC-2119: https://datatracker.ietf.org/doc/html/rfc2119</p>
+<p>[2] ZIP-200: https://zips.z.cash/zip-0200</p>
+<p>[3] ZIP-XXX: Placeholder for the ZSF ZIP</p>

draft-issuance.md

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+```
+ZIP: 
+Title: Smooth Out The Block Subsidy Issuance
+Owners: Jason McGee <jason@shieldedlabs.com>
+        Mark Henderson <mark@equilibrium.co>
+        Tomek Piotrowski <tomek@eiger.co>
+        Mariusz Pilarek <mariusz@eiger.co>
+Original-Authors: Nathan Wilcox
+Credits: Nathan Wilcox
+         Mark Henderson
+         Jason McGee
+Status: Draft
+Category: Consensus
+Created: 2023-08-23
+License: BSD-2-Clause
+```
+
+# Terminology
+
+The key words “MUST”, “SHOULD”, “SHOULD NOT”, “MAY”, “RECOMMENDED”, “OPTIONAL”,
+and “REQUIRED” in this document are to be interpreted as described in RFC 2119. [1]
+
+"Network upgrade" - to be interpreted as described in ZIP 200. [2]
+
+“Block Subsidy” - to be interpreted as described in ZIP TBD [3]
+
+“Issuance” - to be interpreted as described in ZIP TBD [3]
+
+“We” - the ZIP authors, owners listed in the above front matter
+
+“`ZsfBalanceAfter(h)`” is the total ZEC available in the Zcash Sustainability Fund (ZSF) after the transactions
+in block `h`, described in ZIP #TODO reference#. The Sustainability Fund is used to pay out Block Subsidies
+from unmined ZEC, and other fund deposits.
+
+“`BLOCK_SUBSIDY_FRACTION`” = 41 / 100,000,000 or `0.00000041`
+
+"`NUMBER_OF_BLOCKS_IN_4_YEARS`" = `(365.25 * 24 * 60 * 60/75 * 4)`, or `1_683_072`
+
+# Abstract
+
+This ZIP proposes a change to how nodes calculate the block subsidy.
+
+Instead of following a step function around the four-year halving cycle inherited
+from Bitcoin, we propose a slow exponential “smoothing” of the curve. The new issuance
+scheme would approximate the current 4 year cycle, and results in the last
+zatoshi being issued in around 114 years.
+
+# Motivation
+
+Zcash’s economic model is inherited from Bitcoin and includes the concept of a halving
+mechanism to regulate the issuance of new coins. This approach, though foundational, invites
+ a reevaluation amid Zcash’s ongoing evolution. As the network matures, the need to address
+potential future challenges and ensure a sustained and stable economic ecosystem becomes
+apparent. The transition to a smoothed emissions curve offers an opportunity to adjust the network's
+issuance dynamics while maintaining the supply cap of 21,000,000 coins. By doing so, Zcash
+endeavors to optimize its economic framework, accommodating changing circumstances while
+maintaining predictability and stability in rewards distribution.
+
+This proposal outlines a solution to address challenges associated with the existing block
+subsidy issuance mechanism in the Zcash network. The primary goal of this proposal is to
+introduce a more predictable and stable issuance of ZEC by smoothing out the issuance
+curve while preserving the supply cap. It's important to note that this proposal does
+not seek to alter the fundamental aspects of Zcash's issuance policy. The average block
+subsidy amount over time will remain the same and the funds for block subsidies will last
+a similar amount of time. Instead, it focuses solely on enhancing the predictability
+and consistency of the block subsidy issuance process.
+
+Smoothing the emissions curve helps ensure that the network remains economically
+viable and stable as it transitions from a traditional issuance mechanism to one
+that maintains a sustainable and predictable issuance of rewards over time. It
+prevents abrupt changes in the rate of newly issued coins, which could lead to
+disruptions in the network's economic model and potentially impact its security
+and sustainability. A smoother emissions curve allows for a more gradual and controlled
+transition, providing ZEC stakeholders and participants with a clear understanding of
+how rewards will be distributed over time.
+
+
+
+# Specification
+
+Smoothing the issuance curve is possible using an exponential decay formula that
+satisfies the following requirements:
+
+## Issuance Goals
+
+1. Block subsidies are monotonically decreasing, as long as `ZsfBalanceAfter(h)` is monotonically decreasing
+2. Block subsidies approximate a continuous function
+3. When `ZSF_BALANCE(h) > 0` then block subsidies for block `h`
+MUST always be `> 0`, preventing a final “unmined” zatoshi
+4. For any 4 year period, all paid out block subsidies MUST equal approximately
+half of `ZSF_BALANCE` at the beginning of that 4 year period
+5. This functionality MUST be introduced as part of a network upgrade
+
+The above requirements assume no deflationary action, i.e. that no ZEC is added
+to `ZSF_BALANCE`. They are referenced below as **Rn**.
+
+## Issuance Calculation
+
+Given the block height `h` define a function **S**, such that:
+
+**S(h)** = Block subsidy for a given `h`, that satisfies above requirements.
+
+Using an exponential decay function for **BlockSubsidy** satisfies **G1** and **G2** above:
+
+`BlockSubsidy(h) = BLOCK_SUBSIDY_FRACTION * ZsfBalanceAfter(h - 1)`
+
+Finally, to satisfy **G3** above we need to always round up to at least 1 Zatoshi
+if `ZsfBalanceAfter(h - 1) > 0`:
+
+`BlockSubsidy(h) = ceiling(BLOCK_SUBSIDY_FRACTION * ZsfBalanceAfter(h - 1))`
+
+# Rationale
+
+## `BLOCK_SUBSIDY_FRACTION`
+
+The value `41 / 100_000_000` satisfies the approximation:
+
+`(1 - BLOCK_SUBSIDY_FRACTION)^NUMBER_OF_BLOCKS_IN_4_YEARS ≈ 0.5`
+
+Meaning after a period of 4 years around half of `ZSF_BALANCE` will be paid out
+as block subsidies, thus satisfying **G4**.
+
+
+## Other Notes
+
+The suggested implementation avoids using float numbers. Rust and C++ will both round
+the result of the final division up, satisfying **R3** above.
+
+# Appendix: Simulation
+
+We encourage readers to run the following Rust code, which simulates block subsidies.
+According to this simulation, assuming no deflationary action, block subsidies would
+last for approximately 113 years:
+
+## Rust Code
+
+```rust
+fn main() {
+    // approximate available subsidies in August of 2023
+    let mut available_subsidies: i64 = 4671731 * 100_000_000;
+    let mut block: u32 = 0;
+
+    while available_subsidies > 0 { 
+        let block_subsidy = (available_subsidies * 41 + 99_999_999) / 100_000_000;
+        available_subsidies -= block_subsidy;
+
+        println!(
+            "{} ({} years): {}({} ZEC) {}({} ZEC)",
+            block,                             // current block
+            block / 420_768,                   // ~ current year
+            block_subsidy,                     // block subsidy in zatoshis
+            block_subsidy / 100_000_000,       // block subsidy in ZEC
+            available_subsidies,               // available subsidies in zatoshis
+            available_subsidies / 100_000_000  // available subsidies in ZEC
+        );
+
+        block += 1;
+    }   
+}
+```
+
+Last line of output of the above program is:
+
+`47699804 (113 years): 1(0 ZEC) 0(0 ZEC)`
+
+Note the addition of 99,999,999 before division to force rounding up of non-zero values.
+
+
+# References
+
+[1] RFC-2119: https://datatracker.ietf.org/doc/html/rfc2119
+
+[2] ZIP-200: https://zips.z.cash/zip-0200
+
+[3] ZIP-XXX: Placeholder for the ZSF ZIP