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0.2.0 float16ext
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Rob Tillaart
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c6851e9ae3
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82f164b6bb
@ -6,6 +6,12 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/)
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and this project adheres to [Semantic Versioning](http://semver.org/).
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## [0.2.0] - 2024-04-18
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- sync with float16 version 0.3.0
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- remove printable interface to fix issue #12 float 16 (footprint).
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----
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## [0.1.0] - 2024-03-06
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- initial version based upon float16
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@ -19,17 +19,33 @@ This **experimental** library defines the float16ext (2 byte) data type, includi
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function to and from float32 type. It is an extension to the float16 library.
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Reference -https://en.wikipedia.org/wiki/Half-precision_floating-point_format#ARM_alternative_half-precision
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The library implements the **Printable** interface so one can directly print the
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float16ext values in any stream e.g. Serial.
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The primary usage of the float16ext data type is to efficiently store and transport
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a floating point number. As it uses only 2 bytes where float and double have typical
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4 and 8 bytes, gains can be made at the price of range and precision.
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Note that float16ext only has ~3 significant digits.
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To print a float16, one need to convert it with toFloat(), toDouble() or toString(decimals).
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The latter allows concatenation and further conversion to an char array.
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#### Difference with float16
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In pre 0.3.0 version the Printable interface was implemented, but it has been removed
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as it caused excessive memory usage when declaring arrays of float16.
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#### ARM alternative half-precision
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-https://en.wikipedia.org/wiki/Half-precision_floating-point_format#ARM_alternative_half-precision
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_ARM processors support (via a floating point control register bit)
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an "alternative half-precision" format, which does away with the
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special case for an exponent value of 31 (111112).[10] It is almost
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identical to the IEEE format, but there is no encoding for infinity or NaNs;
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instead, an exponent of 31 encodes normalized numbers in the range 65536 to 131008._
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Implemented in https://github.com/RobTillaart/float16ext class.
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#### Difference with float16 and float16ext
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The float16ext library has an extended range as it supports values from +- 65504
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to +- 131008.
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@ -44,25 +60,73 @@ Although they share a lot of code float16 and float16ext should not be mixed.
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In the future these libraries might merge / derive one from the other.
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#### Breaking change 0.2.0
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Version 0.3.0 has a breaking change. The **Printable** interface is removed as
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it causes larger than expected arrays of float 16 (See #16). On ESP8266 every
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float16 object was 8 bytes and on AVR it was 5 bytes instead of the expected 2 bytes.
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To support printing the class added two new conversion functions:
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```cpp
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f16.toFloat();
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f16.toString(decimals);
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Serial.println(f16.toFloat(), 4);
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Serial.println(f16.toString(4));
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```
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This keeps printing relative easy.
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The footprint of the library is now smaller and one can now create compact array's
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of float16 elements using only 2 bytes per element.
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## Specifications
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layout is same as float16.
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layout is same as float16, however the range is different.
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| attribute | value | notes |
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|:----------|:-------------|:--------|
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| size | 2 bytes | layout s eeeee mmmmmmmmmm (1, 5, 10)
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| sign | 1 bit |
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| exponent | 5 bit |
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| mantissa | 10 bit | ~ 3 digits
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| minimum | 5.96046 E−8 | smallest positive number.
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| | 1.0009765625 | 1 + 2^−10 = smallest number larger than 1.
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| maximum | 131008 |
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| | |
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| Attribute | Value | Notes |
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|:------------|:----------------|:--------|
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| size | 2 bytes | layout s eeeee mmmmmmmmmm (1, 5, 10)
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| sign | 1 bit |
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| exponent | 5 bit |
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| mantissa | 10 bit | 3 - 4 digits
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| minimum | ±5.96046 E−8 | smallest number.
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| | ±1.0009765625 | 1 + 2^−10 = smallest number larger than 1.
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| maximum | ±131008 |
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| | |
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± = ALT 0177
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#### Example values
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Source: https://en.wikipedia.org/wiki/Half-precision_floating-point_format
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```cpp
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/*
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SIGN EXP MANTISSA
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0 01111 0000000000 = 1
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0 01111 0000000001 = 1 + 2−10 = 1.0009765625 (next smallest float after 1)
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1 10000 0000000000 = −2
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0 11110 1111111111 = 65504 (max half precision)
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0 00001 0000000000 = 2−14 ≈ 6.10352 × 10−5 (minimum positive normal)
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0 00000 1111111111 = 2−14 - 2−24 ≈ 6.09756 × 10−5 (maximum subnormal)
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0 00000 0000000001 = 2−24 ≈ 5.96046 × 10−8 (minimum positive subnormal)
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0 00000 0000000000 = 0
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1 00000 0000000000 = −0
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0 01101 0101010101 = 0.333251953125 ≈ 1/3
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*/
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```
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#### Related
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- https://github.com/RobTillaart/float16
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- https://github.com/RobTillaart/float16ext
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- https://github.com/RobTillaart/fraction
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- https://en.wikipedia.org/wiki/Half-precision_floating-point_format
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@ -74,28 +138,35 @@ layout is same as float16.
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#### Constructors
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- **float16ext(void)** defaults to zero.
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- **float16ext(void)** defaults value to zero.
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- **float16ext(double f)** constructor.
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- **float16ext(const float16ext &f)** copy constructor.
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#### Conversion
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- **double toDouble(void)** convert to double (or float).
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- **double toDouble(void)** convert value to double or float (if the same e.g. UNO).
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- **float toFloat(void)** convert value to float.
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- **String toString(unsigned int decimals = 2)** convert value to a String with decimals.
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Please note that the accuracy is only 3-4 digits for the whole number so use decimals
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with care.
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#### Export and store
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To serialize the internal format e.g. to disk, two helper functions are available.
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- **uint16_t getBinary()** get the 2 byte binary representation.
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- **void setBinary(uint16_t u)** set the 2 bytes binary representation.
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- **size_t printTo(Print& p) const** Printable interface.
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- **void setDecimals(uint8_t d)** idem, used for printTo.
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- **uint8_t getDecimals()** idem.
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Note the setDecimals takes one byte per object which is not efficient for arrays of float16ext.
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See array example for efficient storage using set/getBinary() functions.
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#### Compare
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Standard compare functions. Since 0.1.5 these are quite optimized,
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so it is fast to compare e.g. 2 measurements.
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The library implement the standard compare functions.
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These are optimized, so it is fast to compare 2 float16ext values.
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Note: comparison with a float or double always include a conversion.
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You can improve performance by converting e.g. a threshold only once before comparison.
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- **bool operator == (const float16ext& f)**
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- **bool operator != (const float16ext& f)**
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@ -120,14 +191,14 @@ Not planned to optimize these.
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- **float16ext& operator \*= (const float16ext& f)**
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- **float16ext& operator /= (const float16ext& f)**
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negation operator.
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Negation operator.
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- **float16ext operator - ()** fast negation.
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Math helpers.
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- **int sign()** returns 1 == positive, 0 == zero, -1 == negative.
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- **bool isZero()** returns true if zero. slightly faster than **sign()**.
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## Notes
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The float16ext does not support INF or NAN.
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## Future
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@ -135,7 +206,7 @@ negation operator.
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#### Must
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- update documentation.
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- keep in sync with float16 lib
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- keep in sync with float16 lib where possible.
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#### Should
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@ -21,8 +21,6 @@ void setup()
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// Serial.print("FLOAT16EXT_LIB_VERSION: ");
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// Serial.println(FLOAT16EXT_LIB_VERSION);
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f16.setDecimals(10);
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print_all();
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Serial.println("\ndone");
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@ -43,7 +41,7 @@ void print_all()
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f16.setBinary(x);
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Serial.print(x);
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Serial.print("\t");
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Serial.print(f16);
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Serial.print(f16.toString(4));
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Serial.println();
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}
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}
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@ -21,8 +21,6 @@ void setup()
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Serial.print("FLOAT16EXT_LIB_VERSION: ");
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Serial.println(FLOAT16EXT_LIB_VERSION);
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f16.setDecimals(10);
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print_all();
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Serial.println("\ndone");
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@ -47,7 +45,7 @@ void print_all()
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Serial.print("\t");
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Serial.print(f16.toDouble(), 10);
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Serial.print("\t");
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Serial.print(f16);
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Serial.print(f16.toString(10));
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Serial.println();
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}
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@ -59,7 +57,7 @@ void print_all()
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Serial.print("\t");
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Serial.print(f16.toDouble(), 10);
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Serial.print("\t");
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Serial.print(f16);
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Serial.print(f16.toString(10));
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Serial.println();
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}
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}
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@ -21,8 +21,6 @@ void setup()
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Serial.print("FLOAT16EXT_LIB_VERSION: ");
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Serial.println(FLOAT16EXT_LIB_VERSION);
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f16.setDecimals(6);
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test_all();
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Serial.println("\ndone");
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@ -1,7 +1,7 @@
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//
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// FILE: float16ext.cpp
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// AUTHOR: Rob Tillaart
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// VERSION: 0.1.0
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// VERSION: 0.2.0
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// PURPOSE: library for Float16s for Arduino
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// URL: http://en.wikipedia.org/wiki/Half-precision_floating-point_format
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@ -15,18 +15,26 @@ float16ext::float16ext(double f)
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_value = f32tof16(f);
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}
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// PRINTING
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size_t float16ext::printTo(Print& p) const
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{
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double d = this->f16tof32(_value);
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return p.print(d, _decimals);
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}
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//////////////////////////////////////////////////////////
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//
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// CONVERTING & PRINTING
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//
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double float16ext::toDouble() const
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{
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return f16tof32(_value);
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}
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float float16ext::toFloat() const
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{
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return f16tof32(_value);
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}
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String float16ext::toString(unsigned int decimals) const
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{
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return String((double)f16tof32(_value), decimals);
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}
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//////////////////////////////////////////////////////////
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//
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@ -172,12 +180,7 @@ float float16ext::f16tof32(uint16_t _value) const
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{
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return sgn ? -0 : 0;
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}
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// NAN & INF
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// if (exp == 0x001F)
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// {
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// if (man == 0) return sgn ? -INFINITY : INFINITY;
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// else return NAN;
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// }
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// NAN & INF not supported
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// NORMAL
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if (exp > 0)
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@ -2,7 +2,7 @@
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//
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// FILE: float16ext.h
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// AUTHOR: Rob Tillaart
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// VERSION: 0.1.0
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// VERSION: 0.2.0
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// PURPOSE: Arduino library to implement float16ext data type.
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// half-precision floating point format,
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// used for efficient storage and transport.
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@ -11,10 +11,10 @@
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#include "Arduino.h"
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#define FLOAT16EXT_LIB_VERSION (F("0.1.0"))
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#define FLOAT16EXT_LIB_VERSION (F("0.2.0"))
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class float16ext: public Printable
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class float16ext
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{
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public:
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// Constructors
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@ -22,16 +22,14 @@ public:
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float16ext(double f);
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float16ext(const float16ext &f) { _value = f._value; };
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// Conversion
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// Conversion and printing
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double toDouble(void) const;
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// access the 2 byte representation.
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uint16_t getBinary() { return _value; };
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void setBinary(uint16_t u) { _value = u; };
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float toFloat() const;
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String toString(unsigned int decimals = 2) const; // keep esp32 happy.
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// Printable
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size_t printTo(Print& p) const;
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void setDecimals(uint8_t d) { _decimals = d; };
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uint8_t getDecimals() { return _decimals; };
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// access the 2 byte representation.
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uint16_t getBinary() { return _value; };
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void setBinary(uint16_t u) { _value = u; };
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// equalities
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bool operator == (const float16ext& f);
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@ -62,13 +60,12 @@ public:
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// CORE CONVERSION
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// should be private but for testing...
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// should be private, needed for testing.
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float f16tof32(uint16_t) const;
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uint16_t f32tof16(float) const;
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private:
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uint8_t _decimals = 4;
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uint16_t _value;
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};
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@ -1,4 +1,4 @@
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# Syntax Colouring Map For float16
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# Syntax Colouring Map For float16ext
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# Data types (KEYWORD1)
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@ -7,11 +7,11 @@ float16ext KEYWORD1
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# Methods and Functions (KEYWORD2)
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toDouble KEYWORD2
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toFloat KEYWORD2
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toString KEYWORD2
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getBinary KEYWORD2
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setBinary KEYWORD2
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setDecimals KEYWORD2
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getDecimals KEYWORD2
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sign KEYWORD2
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isZero KEYWORD2
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@ -15,7 +15,7 @@
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"type": "git",
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"url": "https://github.com/RobTillaart/float16ext.git"
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},
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"version": "0.1.0",
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"version": "0.2.0",
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"license": "MIT",
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"frameworks": "*",
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"platforms": "*",
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@ -1,5 +1,5 @@
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name=float16ext
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version=0.1.0
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version=0.2.0
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author=Rob Tillaart <rob.tillaart@gmail.com>
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maintainer=Rob Tillaart <rob.tillaart@gmail.com>
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sentence=Arduino library to implement float16ext data type.
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@ -85,6 +85,16 @@ unittest(test_constructor)
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}
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unittest(test_sizeof)
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{
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float16ext value(1);
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float16ext arr[10];
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assertEqual(2, sizeof(value));
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assertEqual(20, sizeof(arr));
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}
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unittest(test_compare_equal)
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{
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float16ext a(1);
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@ -153,19 +163,12 @@ unittest(test_conversion)
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}
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unittest(test_printable)
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unittest(test_toString)
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{
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float16ext f16(123.456);
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// test default value.
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assertEqual(4, f16.getDecimals());
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for (int i = 0; i < 6; i++)
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{
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f16.setDecimals(i);
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assertEqual(i, f16.getDecimals());
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}
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// TODO
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// printable? how to test?
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float16ext f16(-123.456);
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fprintf(stderr, "note the limited accuracy (~4 digits).\n");
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assertNotEqual("-123.456", f16.toString(3));
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assertEqual("-123.4", f16.toString(1));
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}
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@ -184,17 +187,19 @@ unittest(test_all_values)
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b = a.toDouble();
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if (x != b.getBinary()) // assert would give 65K lines output!
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{
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fprintf(stderr, "fail at %d\n", x);
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fprintf(stderr, "fail at %d != %d\n", x, b.getBinary());
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}
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}
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fprintf(stderr, "test all negative patterns\n");
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fprintf(stderr, "only fails -0\n");
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for (uint32_t x = 0x8000; x < 0xFFFF; x++)
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{
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a.setBinary(x);
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b = a.toDouble();
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if (x != b.getBinary())
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{
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fprintf(stderr, "fail at %d\n", x);
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fprintf(stderr, "fail at %d != %d\n", x, b.getBinary());
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}
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}
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}
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