FvgCalculations█ OVERVIEW
This library provides the core calculation engine for identifying Fair Value Gaps (FVGs) across different timeframes and for processing their interaction with price. It includes functions to detect FVGs on both the current chart and higher timeframes, as well as to check for their full or partial mitigation.
█ CONCEPTS
The library's primary functions revolve around the concept of Fair Value Gaps and their lifecycle.
Fair Value Gap (FVG) Identification
An FVG, or imbalance, represents a price range where buying or selling pressure was significant enough to cause a rapid price movement, leaving an "inefficiency" in the market. This library identifies FVGs based on three-bar patterns:
Bullish FVG: Forms when the low of the current bar (bar 3) is higher than the high of the bar two periods prior (bar 1). The FVG is the space between the high of bar 1 and the low of bar 3.
Bearish FVG: Forms when the high of the current bar (bar 3) is lower than the low of the bar two periods prior (bar 1). The FVG is the space between the low of bar 1 and the high of bar 3.
The library provides distinct functions for detecting FVGs on the current (Low Timeframe - LTF) and specified higher timeframes (Medium Timeframe - MTF / High Timeframe - HTF).
FVG Mitigation
Mitigation refers to price revisiting an FVG.
Full Mitigation: An FVG is considered fully mitigated when price completely closes the gap. For a bullish FVG, this occurs if the current low price moves below or touches the FVG's bottom. For a bearish FVG, it occurs if the current high price moves above or touches the FVG's top.
Partial Mitigation (Entry/Fill): An FVG is partially mitigated when price enters the FVG's range but does not fully close it. The library tracks the extent of this fill. For a bullish FVG, if the current low price enters the FVG from above, that low becomes the new effective top of the remaining FVG. For a bearish FVG, if the current high price enters the FVG from below, that high becomes the new effective bottom of the remaining FVG.
FVG Interaction
This refers to any instance where the current bar's price range (high to low) touches or crosses into the currently unfilled portion of an active (visible and not fully mitigated) FVG.
Multi-Timeframe Data Acquisition
To detect FVGs on higher timeframes, specific historical bar data (high, low, and time of bars at indices and relative to the higher timeframe's last completed bar) is required. The requestMultiTFBarData function is designed to fetch this data efficiently.
█ CALCULATIONS AND USE
The functions in this library are typically used in a sequence to manage FVGs:
1. Data Retrieval (for MTF/HTF FVGs):
Call requestMultiTFBarData() with the desired higher timeframe string (e.g., "60", "D").
This returns a tuple of htfHigh1, htfLow1, htfTime1, htfHigh3, htfLow3, htfTime3.
2. FVG Detection:
For LTF FVGs: Call detectFvg() on each confirmed bar. It uses high , low, low , and high along with barstate.isconfirmed.
For MTF/HTF FVGs: Call detectMultiTFFvg() using the data obtained from requestMultiTFBarData().
Both detection functions return an fvgObject (defined in FvgTypes) if an FVG is found, otherwise na. They also can classify FVGs as "Large Volume" (LV) if classifyLV is true and the FVG size (top - bottom) relative to the tfAtr (Average True Range of the respective timeframe) meets the lvAtrMultiplier.
3. FVG State Updates (on each new bar for existing FVGs):
First, check for overall price interaction using fvgInteractionCheck(). This function determines if the current bar's high/low has touched or entered the FVG's currentTop or currentBottom.
If interaction occurs and the FVG is not already mitigated:
Call checkMitigation() to determine if the FVG has been fully mitigated by the current bar's currentHigh and currentLow. If true, the FVG's isMitigated status is updated.
If not fully mitigated, call checkPartialMitigation() to see if the price has further entered the FVG. This function returns the newLevel to which the FVG has been filled (e.g., currentLow for a bullish FVG, currentHigh for bearish). This newLevel is then used to update the FVG's currentTop or currentBottom.
The calling script (e.g., fvgMain.c) is responsible for storing and managing the array of fvgObject instances and passing them to these update functions.
█ NOTES
Bar State for LTF Detection: The detectFvg() function relies on barstate.isconfirmed to ensure FVG detection is based on closed bars, preventing FVGs from being detected prematurely on the currently forming bar.
Higher Timeframe Data (lookahead): The requestMultiTFBarData() function uses lookahead = barmerge.lookahead_on. This means it can access historical data from the higher timeframe that corresponds to the current bar on the chart, even if the higher timeframe bar has not officially closed. This is standard for multi-timeframe analysis aiming to plot historical HTF data accurately on a lower timeframe chart.
Parameter Typing: Functions like detectMultiTFFvg and detectFvg infer the type for boolean (classifyLV) and numeric (lvAtrMultiplier) parameters passed from the main script, while explicitly typed series parameters (like htfHigh1, currentAtr) expect series data.
fvgObject Dependency: The FVG detection functions return fvgObject instances, and fvgInteractionCheck takes an fvgObject as a parameter. This UDT is defined in the FvgTypes library, making it a dependency for using FvgCalculations.
ATR for LV Classification: The tfAtr (for MTF/HTF) and currentAtr (for LTF) parameters are expected to be the Average True Range values for the respective timeframes. These are used, if classifyLV is enabled, to determine if an FVG's size qualifies it as a "Large Volume" FVG based on the lvAtrMultiplier.
MTF/HTF FVG Appearance Timing: When displaying FVGs from a higher timeframe (MTF/HTF) on a lower timeframe (LTF) chart, users might observe that the most recent MTF/HTF FVG appears one LTF bar later compared to its appearance on a native MTF/HTF chart. This is an expected behavior due to the detection mechanism in `detectMultiTFFvg`. This function uses historical bar data from the MTF/HTF (specifically, data equivalent to `HTF_bar ` and `HTF_bar `) to identify an FVG. Therefore, all three bars forming the FVG on the MTF/HTF must be fully closed and have shifted into these historical index positions relative to the `request.security` call from the LTF chart before the FVG can be detected and displayed on the LTF. This ensures that the MTF/HTF FVG is identified based on confirmed, closed bars from the higher timeframe.
█ EXPORTED FUNCTIONS
requestMultiTFBarData(timeframe)
Requests historical bar data for specific previous bars from a specified higher timeframe.
It fetches H , L , T (for the bar before last) and H , L , T (for the bar three periods prior)
from the requested timeframe.
This is typically used to identify FVG patterns on MTF/HTF.
Parameters:
timeframe (simple string) : The higher timeframe to request data from (e.g., "60" for 1-hour, "D" for Daily).
Returns: A tuple containing: .
- htfHigh1 (series float): High of the bar at index 1 (one bar before the last completed bar on timeframe).
- htfLow1 (series float): Low of the bar at index 1.
- htfTime1 (series int) : Time of the bar at index 1.
- htfHigh3 (series float): High of the bar at index 3 (three bars before the last completed bar on timeframe).
- htfLow3 (series float): Low of the bar at index 3.
- htfTime3 (series int) : Time of the bar at index 3.
detectMultiTFFvg(htfHigh1, htfLow1, htfTime1, htfHigh3, htfLow3, htfTime3, tfAtr, classifyLV, lvAtrMultiplier, tfType)
Detects a Fair Value Gap (FVG) on a higher timeframe (MTF/HTF) using pre-fetched bar data.
Parameters:
htfHigh1 (float) : High of the first relevant bar (typically high ) from the higher timeframe.
htfLow1 (float) : Low of the first relevant bar (typically low ) from the higher timeframe.
htfTime1 (int) : Time of the first relevant bar (typically time ) from the higher timeframe.
htfHigh3 (float) : High of the third relevant bar (typically high ) from the higher timeframe.
htfLow3 (float) : Low of the third relevant bar (typically low ) from the higher timeframe.
htfTime3 (int) : Time of the third relevant bar (typically time ) from the higher timeframe.
tfAtr (float) : ATR value for the higher timeframe, used for Large Volume (LV) FVG classification.
classifyLV (bool) : If true, FVGs will be assessed to see if they qualify as Large Volume.
lvAtrMultiplier (float) : The ATR multiplier used to define if an FVG is Large Volume.
tfType (series tfType enum from no1x/FvgTypes/1) : The timeframe type (e.g., types.tfType.MTF, types.tfType.HTF) of the FVG being detected.
Returns: An fvgObject instance if an FVG is detected, otherwise na.
detectFvg(classifyLV, lvAtrMultiplier, currentAtr)
Detects a Fair Value Gap (FVG) on the current (LTF - Low Timeframe) chart.
Parameters:
classifyLV (bool) : If true, FVGs will be assessed to see if they qualify as Large Volume.
lvAtrMultiplier (float) : The ATR multiplier used to define if an FVG is Large Volume.
currentAtr (float) : ATR value for the current timeframe, used for LV FVG classification.
Returns: An fvgObject instance if an FVG is detected, otherwise na.
checkMitigation(isBullish, fvgTop, fvgBottom, currentHigh, currentLow)
Checks if an FVG has been fully mitigated by the current bar's price action.
Parameters:
isBullish (bool) : True if the FVG being checked is bullish, false if bearish.
fvgTop (float) : The top price level of the FVG.
fvgBottom (float) : The bottom price level of the FVG.
currentHigh (float) : The high price of the current bar.
currentLow (float) : The low price of the current bar.
Returns: True if the FVG is considered fully mitigated, false otherwise.
checkPartialMitigation(isBullish, currentBoxTop, currentBoxBottom, currentHigh, currentLow)
Checks for partial mitigation of an FVG by the current bar's price action.
It determines if the price has entered the FVG and returns the new fill level.
Parameters:
isBullish (bool) : True if the FVG being checked is bullish, false if bearish.
currentBoxTop (float) : The current top of the FVG box (this might have been adjusted by previous partial fills).
currentBoxBottom (float) : The current bottom of the FVG box (similarly, might be adjusted).
currentHigh (float) : The high price of the current bar.
currentLow (float) : The low price of the current bar.
Returns: The new price level to which the FVG has been filled (e.g., currentLow for a bullish FVG).
Returns na if no new partial fill occurred on this bar.
fvgInteractionCheck(fvg, highVal, lowVal)
Checks if the current bar's price interacts with the given FVG.
Interaction means the price touches or crosses into the FVG's
current (possibly partially filled) range.
Parameters:
fvg (fvgObject type from no1x/FvgTypes/1) : The FVG object to check.
Its isMitigated, isVisible, isBullish, currentTop, and currentBottom fields are used.
highVal (float) : The high price of the current bar.
lowVal (float) : The low price of the current bar.
Returns: True if price interacts with the FVG, false otherwise.
Logic
TUF_LOGICTUF_LOGIC: Three-Value Logic for Pine Script v6
The TUF_LOGIC library implements a robust three-valued logic system (trilean logic) for Pine Script v6, providing a formal framework for reasoning about uncertain or incomplete information in financial markets. By extending beyond binary True/False states to include an explicit "Uncertain" state, this library enables more nuanced algorithmic decision-making, particularly valuable in environments characterized by imperfect information.
Core Architecture
TUF_LOGIC offers two complementary interfaces for working with trilean values:
Enum-Based API (Recommended): Leverages Pine Script v6's enum capabilities with Trilean.True , Trilean.Uncertain , and Trilean.False for improved type safety and performance.
Integer-Based API (Legacy Support): Maintains compatibility with existing code using integer values 1 (True), 0 (Uncertain), and -1 (False).
Fundamental Operations
The library provides type conversion methods for seamless interaction between integer representation and enum types ( to_trilean() , to_int() ), along with validation functions to maintain trilean invariants.
Logical Operators
TUF_LOGIC extends traditional boolean operators to the trilean domain with NOT , AND , OR , XOR , and EQUALITY functions that properly handle the Uncertain state according to the principles of three-valued logic.
The library implements three different implication operators providing flexibility for different logical requirements: IMP_K (Kleene's approach), IMP_L (Łukasiewicz's approach), and IMP_RM3 (Relevant implication under RM3 logic).
Inspired by Tarski-Łukasiewicz's modal logic formulations, TUF_LOGIC includes modal operators: MA (Modal Assertion) evaluates whether a state is possibly true; LA (Logical Assertion) determines if a state is necessarily true; and IA (Indeterminacy Assertion) identifies explicitly uncertain states.
The UNANIMOUS operator evaluates trilean values for complete agreement, returning the consensus value if one exists or Uncertain otherwise. This function is available for both pairs of values and arrays of trilean values.
Practical Applications
TUF_LOGIC excels in financial market scenarios where decision-making must account for uncertainty. It enables technical indicator consensus by combining signals with different confidence levels, supports multi-timeframe analysis by reconciling potentially contradictory signals, enhances risk management by explicitly modeling uncertainty, and handles partial information systems where some data sources may be unreliable.
By providing a mathematically sound framework for reasoning about uncertainty, TUF_LOGIC elevates trading system design beyond simplistic binary logic, allowing for more sophisticated decision-making that better reflects real-world market complexity.
Library "TUF_LOGIC"
Three-Value Logic (TUF: True, Uncertain, False) implementation for Pine Script.
This library provides a comprehensive set of logical operations supporting trilean logic systems,
including Kleene, Łukasiewicz, and RM3 implications. Compatible with Pine v6 enums.
method validate(self)
Ensures a valid trilean integer value by clamping to the appropriate range .
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The integer value to validate.
Returns: An integer value guaranteed to be within the valid trilean range.
method to_trilean(self)
Converts an integer value to a Trilean enum value.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The integer to convert (typically -1, 0, or 1).
Returns: A Trilean enum value: True (1), Uncertain (0), or False (-1).
method to_int(self)
Converts a Trilean enum value to its corresponding integer representation.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The Trilean enum value to convert.
Returns: Integer value: 1 (True), 0 (Uncertain), or -1 (False).
method NOT(self)
Negates a trilean integer value (NOT operation).
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The integer value to negate.
Returns: Negated integer value: 1 -> -1, 0 -> 0, -1 -> 1.
method NOT(self)
Negates a Trilean enum value (NOT operation).
Namespace types: series Trilean
Parameters:
self (series Trilean) : The Trilean enum value to negate.
Returns: Negated Trilean: True -> False, Uncertain -> Uncertain, False -> True.
method AND(self, comparator)
Logical AND operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The first integer value.
comparator (int) : The second integer value to compare with.
Returns: Integer result of the AND operation (minimum value).
method AND(self, comparator)
Logical AND operation for Trilean enum values following three-valued logic.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The first Trilean enum value.
comparator (series Trilean) : The second Trilean enum value to compare with.
Returns: Trilean result of the AND operation.
method OR(self, comparator)
Logical OR operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The first integer value.
comparator (int) : The second integer value to compare with.
Returns: Integer result of the OR operation (maximum value).
method OR(self, comparator)
Logical OR operation for Trilean enum values following three-valued logic.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The first Trilean enum value.
comparator (series Trilean) : The second Trilean enum value to compare with.
Returns: Trilean result of the OR operation.
method EQUALITY(self, comparator)
Logical EQUALITY operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The first integer value.
comparator (int) : The second integer value to compare with.
Returns: Integer representation (1/-1) indicating if values are equal.
method EQUALITY(self, comparator)
Logical EQUALITY operation for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The first Trilean enum value.
comparator (series Trilean) : The second Trilean enum value to compare with.
Returns: Trilean.True if both values are equal, Trilean.False otherwise.
method XOR(self, comparator)
Logical XOR (Exclusive OR) operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The first integer value.
comparator (int) : The second integer value to compare with.
Returns: Integer result of the XOR operation.
method XOR(self, comparator)
Logical XOR (Exclusive OR) operation for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The first Trilean enum value.
comparator (series Trilean) : The second Trilean enum value to compare with.
Returns: Trilean result of the XOR operation.
method IMP_K(self, comparator)
Material implication using Kleene's logic for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The antecedent integer value.
comparator (int) : The consequent integer value.
Returns: Integer result of Kleene's implication operation.
method IMP_K(self, comparator)
Material implication using Kleene's logic for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The antecedent Trilean enum value.
comparator (series Trilean) : The consequent Trilean enum value.
Returns: Trilean result of Kleene's implication operation.
method IMP_L(self, comparator)
Logical implication using Łukasiewicz's logic for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The antecedent integer value.
comparator (int) : The consequent integer value.
Returns: Integer result of Łukasiewicz's implication operation.
method IMP_L(self, comparator)
Logical implication using Łukasiewicz's logic for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The antecedent Trilean enum value.
comparator (series Trilean) : The consequent Trilean enum value.
Returns: Trilean result of Łukasiewicz's implication operation.
method IMP_RM3(self, comparator)
Logical implication using RM3 logic for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The antecedent integer value.
comparator (int) : The consequent integer value.
Returns: Integer result of the RM3 implication operation.
method IMP_RM3(self, comparator)
Logical implication using RM3 logic for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The antecedent Trilean enum value.
comparator (series Trilean) : The consequent Trilean enum value.
Returns: Trilean result of the RM3 implication operation.
method MA(self)
Modal Assertion (MA) operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The integer value to evaluate.
Returns: 1 if the value is 1 or 0, -1 if the value is -1.
method MA(self)
Modal Assertion (MA) operation for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The Trilean enum value to evaluate.
Returns: Trilean.True if value is True or Uncertain, Trilean.False if value is False.
method LA(self)
Logical Assertion (LA) operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The integer value to evaluate.
Returns: 1 if the value is 1, -1 otherwise.
method LA(self)
Logical Assertion (LA) operation for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The Trilean enum value to evaluate.
Returns: Trilean.True if value is True, Trilean.False otherwise.
method IA(self)
Indeterminacy Assertion (IA) operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The integer value to evaluate.
Returns: 1 if the value is 0, -1 otherwise.
method IA(self)
Indeterminacy Assertion (IA) operation for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The Trilean enum value to evaluate.
Returns: Trilean.True if value is Uncertain, Trilean.False otherwise.
method UNANIMOUS(self, comparator)
Evaluates the unanimity between two trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The first integer value.
comparator (int) : The second integer value.
Returns: Integer value of self if both values are equal, 0 (Uncertain) otherwise.
method UNANIMOUS(self, comparator)
Evaluates the unanimity between two Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The first Trilean enum value.
comparator (series Trilean) : The second Trilean enum value.
Returns: Value of self if both values are equal, Trilean.Uncertain otherwise.
method UNANIMOUS(self)
Evaluates the unanimity among an array of trilean integer values.
Namespace types: array
Parameters:
self (array) : The array of integer values.
Returns: First value if all values are identical, 0 (Uncertain) otherwise.
method UNANIMOUS(self)
Evaluates the unanimity among an array of Trilean enum values.
Namespace types: array
Parameters:
self (array) : The array of Trilean enum values.
Returns: First value if all values are identical, Trilean.Uncertain otherwise.
Advanced Multi-Timeframe Trading System (Risk Managed)Description:
This strategy is an original approach that combines two main analytical components to identify potential trade opportunities while simulating realistic trading conditions:
1. Market Trend Analysis via an Approximate Hurst Exponent
• What It Does:
The strategy computes a rough measure of market trending using an approximate Hurst exponent. A value above 0.5 suggests persistent, trending behavior, while a value below 0.5 indicates a tendency toward mean-reversion.
• How It’s Used:
The Hurst exponent is calculated on both the chart’s current timeframe and a higher timeframe (default: Daily) to capture both local and broader market dynamics.
2. Fibonacci Retracement Levels
• What It Does:
Using daily high and low data from a selected timeframe (default: Daily), the script computes key Fibonacci retracement levels.
• How It’s Used:
• The 61.8% level (Golden Ratio) serves as a key threshold:
• A long entry is signaled when the price crosses above this level if the daily Hurst exponent confirms a trending market.
• The 38.2% level is used to identify short-entry opportunities when the price crosses below it and the daily Hurst indicates non-trending conditions.
Signal Logic:
• Long Entry:
When the price crosses above the 61.8% Fibonacci level (Golden Ratio) and the daily Hurst exponent is greater than 0.5, suggesting a trending market.
• Short Entry:
When the price crosses below the 38.2% Fibonacci level and the daily Hurst exponent is less than 0.5, indicating a less trending or potentially reversing market.
Risk Management & Trade Execution:
• Stop-Loss:
Each trade is risk-managed with a stop-loss set at 2% below (for longs) or above (for shorts) the entry price. This ensures that no single trade risks more than a small, sustainable portion of the account.
• Take Profit:
A take profit order targets a risk-reward ratio of 1:2 (i.e., the target profit is twice the amount risked).
• Position Sizing:
Trades are executed with a fixed position size equal to 10% of account equity.
• Trade Frequency Limits:
• Daily Limit: A maximum of 5 trades per day
• Overall Limit: No more than 510 trades during the backtesting period (e.g., since 2019)
These limits are imposed to simulate realistic trading frequency and to avoid overtrading in backtest results.
Backtesting Parameters:
• Initial Capital: $10,000
• Commission: 0.1% per trade
• Slippage: 1 tick per bar
These settings aim to reflect the conditions faced by the average trader and help ensure that the backtesting results are realistic and not misleading.
Chart Overlays & Visual Aids:
• Fibonacci Levels:
The key Fibonacci retracement levels are plotted on the chart, and the zone between the 61.8% and 38.2% levels is highlighted to show a key retracement area.
• Market Trend Background:
The chart background is tinted green when the daily Hurst exponent indicates a trending market (value > 0.5) and red otherwise.
• Information Table:
An on-chart table displays key parameters such as the current Hurst exponent, daily Hurst value, the number of trades executed today, and the global trade count.
Disclaimer:
Past performance is not indicative of future results. This strategy is experimental and provided solely for educational purposes. It is essential that you backtest and paper trade using your own settings before considering any live deployment. The Hurst exponent calculation is an approximation and should be interpreted as a rough gauge of market behavior. Adjust the parameters and risk management settings according to your personal risk tolerance and market conditions.
Additional Notes:
• Originality & Usefulness:
This script is an original mashup that combines trend analysis with Fibonacci retracement methods. The description above explains how these components work together to provide trading signals.
• Realistic Results:
The strategy uses realistic account sizes, commission rates, slippage, and risk management rules to generate backtesting results that are representative of real-world trading.
• Educational Purpose:
This script is intended to support the TradingView community by offering insights into combining multiple analysis techniques in one strategy. It is not a “get-rich-quick” system but rather an educational tool to help traders understand risk management and trade signal logic.
By using this script, you acknowledge that trading involves risk and that you are responsible for testing and adjusting the strategy to fit your own trading environment. This publication is fully open source, and any modifications should include proper attribution if significant portions of the code are reused.
MathOperatorLibrary "MathOperator"
Methods to handle operators.
method add(value_a, value_b)
Add value a to b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method subtract(value_a, value_b)
subtract value b from a.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method multiply(value_a, value_b)
multiply value a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method divide(value_a, value_b)
divide value a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method remainder(value_a, value_b)
remainder of a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method equal(value_a, value_b)
equality of value a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method not_equal(value_a, value_b)
inequality of value a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method over(value_a, value_b)
value a is over b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method under(value_a, value_b)
value a is under b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method over_equal(value_a, value_b)
value a is over equal b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method under_equal(value_a, value_b)
value a is under equal b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method and_(value_a, value_b)
logical and of a with b
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method or_(value_a, value_b)
logical or of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method not_(value_a)
logical not of a.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
Returns: bool.
method xor_(value_a, value_b)
logical xor of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method xnor_(value_a, value_b)
logical xnor of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method nand_(value_a, value_b)
logical nand of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method nor_(value_a, value_b)
logical nor of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
TUF_LOGICThe TUF_LOGIC library incorporates three-valued logic (also known as trilean logic) into Pine Script, enabling the representation of states beyond the binary True and False to include an 'Uncertain' state. This addition is particularly apt for financial market contexts where information may not always be black or white, accommodating scenarios of partial or ambiguous data.
Key Features:
Trilean Data Type: Defines a tri type, facilitating the representation of True (1), Uncertain (0), and False (-1) states, thus accommodating a more nuanced approach to logical evaluation.
Validation and Conversion: Includes methods like validate, to ensure trilean variables conform to expected states, and to_bool, for converting trilean to boolean values, enhancing interoperability with binary logic systems.
Core Logical Operations: Extends traditional logical operators (AND, OR, NOT, XOR, EQUALITY) to work within the trilean domain, enabling complex conditionals that reflect real-world uncertainties.
Specialized Logical Operations:
Implication Operators: Features IMP_K (Kleene's), IMP_L (Łukasiewicz's), and IMP_RM3, offering varied approaches to logical implication within the trilean framework.
Possibility, Necessity, and Contingency Operators: Implements MA ("it is possible that..."), LA ("it is necessary that..."), and IA ("it is unknown/contingent that..."), derived from Tarski-Łukasiewicz's modal logic attempts, enriching the library with modal logic capabilities.
Unanimity Functions: The UNANIMOUS operator assesses complete agreement among trilean values, useful for scenarios requiring consensus or uniformity across multiple indicators or conditions.
This library is developed to support scenarios in financial trading and analysis where decisions might hinge on more than binary outcomes. By incorporating modal logic aspects and providing a framework for handling uncertainty through the MA, LA, and IA operations, TUF_LOGIC bridges the gap between classical binary logic and the realities of uncertain information, making it a valuable tool for developing sophisticated trading strategies and analytical models.
Library "TUF_LOGIC"
3VL Implementation (TUF stands for True, Uncertain, False.)
method validate(self)
Ensures a valid trilean variable. This works by clamping the variable to the range associated with the trilean type.
Namespace types: tri
Parameters:
self (tri)
Returns: Validated trilean object.
method to_bool(self)
Converts a trilean object into a boolean object. True -> True, Uncertain -> na, False -> False.
Namespace types: tri
Parameters:
self (tri)
Returns: A boolean variable.
method NOT(self)
Negates the trilean object. True -> False, Uncertain -> Uncertain, False -> True
Namespace types: tri
Parameters:
self (tri)
Returns: Negated trilean object.
method AND(self, comparator)
Logical AND operation for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The first trilean object.
comparator (tri) : The second trilean object to compare with.
Returns: `tri` Result of the AND operation as a trilean object.
method OR(self, comparator)
Logical OR operation for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The first trilean object.
comparator (tri) : The second trilean object to compare with.
Returns: `tri` Result of the OR operation as a trilean object.
method EQUALITY(self, comparator)
Logical EQUALITY operation for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The first trilean object.
comparator (tri) : The second trilean object to compare with.
Returns: `tri` Result of the EQUALITY operation as a trilean object, True if both are equal, False otherwise.
method XOR(self, comparator)
Logical XOR (Exclusive OR) operation for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The first trilean object.
comparator (tri) : The second trilean object to compare with.
Returns: `tri` Result of the XOR operation as a trilean object.
method IMP_K(self, comparator)
Material implication using Kleene's logic for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The antecedent trilean object.
comparator (tri) : The consequent trilean object.
Returns: `tri` Result of the implication operation as a trilean object.
method IMP_L(self, comparator)
Logical implication using Łukasiewicz's logic for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The antecedent trilean object.
comparator (tri) : The consequent trilean object.
Returns: `tri` Result of the implication operation as a trilean object.
method IMP_RM3(self, comparator)
Logical implication using RM3 logic for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The antecedent trilean object.
comparator (tri) : The consequent trilean object.
Returns: `tri` Result of the RM3 implication as a trilean object.
method MA(self)
Evaluates to True if the trilean object is either True or Uncertain, False otherwise.
Namespace types: tri
Parameters:
self (tri) : The trilean object to evaluate.
Returns: `tri` Result of the operation as a trilean object.
method LA(self)
Evaluates to True if the trilean object is True, False otherwise.
Namespace types: tri
Parameters:
self (tri) : The trilean object to evaluate.
Returns: `tri` Result of the operation as a trilean object.
method IA(self)
Evaluates to True if the trilean object is Uncertain, False otherwise.
Namespace types: tri
Parameters:
self (tri) : The trilean object to evaluate.
Returns: `tri` Result of the operation as a trilean object.
UNANIMOUS(self, comparator)
Evaluates the unanimity between two trilean values.
Parameters:
self (tri) : The first trilean value.
comparator (tri) : The second trilean value.
Returns: `tri` Returns True if both values are True, False if both are False, and Uncertain otherwise.
method UNANIMOUS(self)
Evaluates the unanimity among an array of trilean values.
Namespace types: array
Parameters:
self (array) : The array of trilean values.
Returns: `tri` Returns True if all values are True, False if all are False, and Uncertain otherwise.
tri
Three Value Logic (T.U.F.), or trilean. Can be True (1), Uncertain (0), or False (-1).
Fields:
v (series int) : Value of the trilean variable. Can be True (1), Uncertain (0), or False (-1).
xor logical operatorLibrary "xor"
xor(a, b)
xor: Exclusive or, or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false).
Parameters:
a : first argument
b : second argument
Returns: returns xor (true only if a and b are true, but not both)
Example:
true xor true = false
true xor false = true
false xor true = true
false xor false = false
Example - Switching LineExample of manipulating a float series to:
• switch from one source to another
• maintain a level by referencing itself
This script publication is intended for:
• Educational Purposes
Who is it for?
Anyone who wants to learn how to change the position or state of an active float series.
