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### Floats
[
Datatype float-formats
Funcon binary32
Funcon binary64
Funcon binary128
Funcon decimal64
Funcon decimal128
Type floats
Funcon float
Funcon quiet-not-a-number Alias qNaN
Funcon signaling-not-a-number Alias sNaN
Funcon positive-infinity Alias pos-inf
Funcon negative-infinity Alias neg-inf
Funcon float-convert
Funcon decimal-float
Funcon float-equal
Funcon float-is-less
Funcon float-is-less-or-equal
Funcon float-is-greater
Funcon float-is-greater-or-equal
Funcon float-negate
Funcon float-absolute-value
Funcon float-add
Funcon float-subtract
Funcon float-multiply
Funcon float-multiply-add
Funcon float-divide
Funcon float-remainder
Funcon float-sqrt
Funcon float-integer-power
Funcon float-float-power
Funcon float-round-ties-to-even
Funcon float-round-ties-to-infinity
Funcon float-floor
Funcon float-ceiling
Funcon float-truncate
Funcon float-pi
Funcon float-e
Funcon float-log
Funcon float-log10
Funcon float-exp
Funcon float-sin
Funcon float-cos
Funcon float-tan
Funcon float-asin
Funcon float-acos
Funcon float-atan
Funcon float-sinh
Funcon float-cosh
Funcon float-tanh
Funcon float-asinh
Funcon float-acosh
Funcon float-atanh
Funcon float-atan2
]
/*
Floating-point numbers according to the IEEE 754 Standard (2008).
See:
- http://doi.org/10.1109/IEEESTD.2008.4610935
- https://en.wikipedia.org/wiki/IEEE_754
*/
Datatype
float-formats ::= binary32 | binary64 | binary128 | decimal64 | decimal128
Built-in Type
floats(_:float-formats)
/*
Note that for distinct formats `FF1`, `FF2`, the types `floats(FF1)` and
`floats(FF2)` are not necessarily disjoint.
*/
Built-in Funcon
float(FF:float-formats,
_:bounded-integers(0, 1), _:natural-numbers, _:integers) : =>floats(FF)
/*
Each finite number is described by three integers:
* s = a sign (zero or one),
* c = a significand (or 'coefficient'),
* q = an exponent.
The numerical value of a finite number is (-1)^s * c * b^q
where b is the base (2 or 10), also called radix.
The possible finite values that can be represented in a format
are determined by the base b, the number of digits in the significand
(precision p), and the exponent parameter emax:
* c must be an integer in the range zero through (b^p)-1
(e.g., if b=10 and p=7 then c is 0 through 9999999);
* q must be an integer such that 1-emax <= q+p-1 <= emax
(e.g., if p=7 and emax=96 then q is -101 through 90).
Note that `float(FF, S, C, Q)` is not a 1-1 operation.
*/
Built-in Funcon
quiet-not-a-number(FF:float-formats) : floats(FF)
Alias
qNaN = quiet-not-a-number
Built-in Funcon
signaling-not-a-number(FF:float-formats) : floats(FF)
Alias
sNaN = signaling-not-a-number
Built-in Funcon
positive-infinity(FF:float-formats) : floats(FF)
Alias
pos-inf = positive-infinity
Built-in Funcon
negative-infinity(FF:float-formats) : floats(FF)
Alias
neg-inf = negative-infinity
#### Conversions
Built-in Funcon
float-convert(FF1:float-formats,
FF2:float-formats, F:floats(FF1)) : =>floats(FF2)
Built-in Funcon
decimal-float(FF:float-formats,
_:strings, _:strings, _:strings) : =>floats(FF)
/*
`decimal-float(F, "M", "N", "E")` is an approximation in `floats(FF)` to the
value of 'M.N' times 10 to the power 'E', where "M.N" is decimal notation
(optionally-signed) for a fixed-point number and "E" is decimal notation
(optionally signed) for an integer. When any argument string is invalid,
the result is `quiet-not-a-number(F)`.
*/
#### Comparison
Built-in Funcon
float-equal(FF:float-formats,
_:floats(FF), _:floats(FF)) : =>booleans
Built-in Funcon
float-is-less(FF:float-formats,
_:floats(FF), _:floats(FF)) : =>booleans
Built-in Funcon
float-is-less-or-equal(FF:float-formats,
_:floats(FF), _:floats(FF)) : =>booleans
Built-in Funcon
float-is-greater(FF:float-formats,
_:floats(FF), _:floats(FF)) : =>booleans
Built-in Funcon
float-is-greater-or-equal(FF:float-formats,
_:floats(FF), _:floats(FF)) : =>booleans
#### Arithmetic
Built-in Funcon
float-negate(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-absolute-value(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-add(FF:float-formats, _:floats(FF), _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-subtract(FF:float-formats, _:floats(FF), _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-multiply(FF:float-formats, _:floats(FF), _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-multiply-add(FF:float-formats,
_:floats(FF), _:floats(FF), _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-divide(FF:float-formats, _:floats(FF), _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-remainder(FF:float-formats, _:floats(FF), _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-sqrt(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-integer-power(FF:float-formats, _:floats(FF), _:integers) : =>floats(FF)
Built-in Funcon
float-float-power(FF:float-formats, _:floats(FF), _:floats(FF)) : =>floats(FF)
#### Rounding
Built-in Funcon
float-round-ties-to-even(FF:float-formats, _:floats(FF)) : =>integers
Built-in Funcon
float-round-ties-to-infinity(FF:float-formats, _:floats(FF)) : =>integers
Built-in Funcon
float-floor(FF:float-formats, _:floats(FF)) : =>integers
Built-in Funcon
float-ceiling(FF:float-formats, _:floats(FF)) : =>integers
Built-in Funcon
float-truncate(FF:float-formats, _:floats(FF)) : =>integers
#### Miscellaneous
Built-in Funcon
float-pi(FF:float-formats) : =>floats(FF)
Built-in Funcon
float-e(FF:float-formats) : =>floats(FF)
Built-in Funcon
float-log(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-log10(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-exp(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-sin(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-cos(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-tan(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-asin(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-acos(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-atan(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-sinh(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-cosh(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-tanh(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-asinh(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-acosh(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-atanh(FF:float-formats, _:floats(FF)) : =>floats(FF)
Built-in Funcon
float-atan2(FF:float-formats, _:floats(FF), _:floats(FF)) : =>floats(FF)

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---
layout: default
title: "Floats"
parent: Primitive
ancestor: Funcons-beta
---
[Funcons-beta] : [Floats.cbs]
-----------------------------
### Floats
<div class="highlighter-rouge"><pre class="highlight"><code>[
<i class="keyword">Datatype</i> <span class="name"><a href="#Name_float-formats">float-formats</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_binary32">binary32</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_binary64">binary64</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_binary128">binary128</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_decimal64">decimal64</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_decimal128">decimal128</a></span>
<i class="keyword">Type</i> <span class="name"><a href="#Name_floats">floats</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float">float</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_quiet-not-a-number">quiet-not-a-number</a></span> <i class="keyword">Alias</i> <span class="name"><a href="#Name_qNaN">qNaN</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_signaling-not-a-number">signaling-not-a-number</a></span> <i class="keyword">Alias</i> <span class="name"><a href="#Name_sNaN">sNaN</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_positive-infinity">positive-infinity</a></span> <i class="keyword">Alias</i> <span class="name"><a href="#Name_pos-inf">pos-inf</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_negative-infinity">negative-infinity</a></span> <i class="keyword">Alias</i> <span class="name"><a href="#Name_neg-inf">neg-inf</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-convert">float-convert</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_decimal-float">decimal-float</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-equal">float-equal</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-is-less">float-is-less</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-is-less-or-equal">float-is-less-or-equal</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-is-greater">float-is-greater</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-is-greater-or-equal">float-is-greater-or-equal</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-negate">float-negate</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-absolute-value">float-absolute-value</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-add">float-add</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-subtract">float-subtract</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-multiply">float-multiply</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-multiply-add">float-multiply-add</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-divide">float-divide</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-remainder">float-remainder</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-sqrt">float-sqrt</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-integer-power">float-integer-power</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-float-power">float-float-power</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-round-ties-to-even">float-round-ties-to-even</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-round-ties-to-infinity">float-round-ties-to-infinity</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-floor">float-floor</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-ceiling">float-ceiling</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-truncate">float-truncate</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-pi">float-pi</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-e">float-e</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-log">float-log</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-log10">float-log10</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-exp">float-exp</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-sin">float-sin</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-cos">float-cos</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-tan">float-tan</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-asin">float-asin</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-acos">float-acos</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-atan">float-atan</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-sinh">float-sinh</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-cosh">float-cosh</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-tanh">float-tanh</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-asinh">float-asinh</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-acosh">float-acosh</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-atanh">float-atanh</a></span>
<i class="keyword">Funcon</i> <span class="name"><a href="#Name_float-atan2">float-atan2</a></span>
]</code></pre></div>
Floating-point numbers according to the IEEE 754 Standard (2008).
See:
- http://doi.org/10.1109/IEEESTD.2008.4610935
- https://en.wikipedia.org/wiki/IEEE_754
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Datatype</i>
<span class="name"><span id="Name_float-formats">float-formats</span></span> ::= <span id="Name_binary32">binary32</span> | <span id="Name_binary64">binary64</span> | <span id="Name_binary128">binary128</span> | <span id="Name_decimal64">decimal64</span> | <span id="Name_decimal128">decimal128</span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Type</i>
<span class="name"><span id="Name_floats">floats</span></span>(_:<span class="name"><a href="#Name_float-formats">float-formats</a></span>)</code></pre></div>
Note that for distinct formats <code><i class="var">FF<sub class="sub">1</sub></i></code>, <code><i class="var">FF<sub class="sub">2</sub></i></code>, the types <code><span class="name"><a href="#Name_floats">floats</a></span>(<i class="var">FF<sub class="sub">1</sub></i>)</code> and
<code><span class="name"><a href="#Name_floats">floats</a></span>(<i class="var">FF<sub class="sub">2</sub></i>)</code> are not necessarily disjoint.
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float">float</span></span>(<span id="Variable372_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>,
_:<span class="name"><a href="../Integers/index.html#Name_bounded-integers">bounded-integers</a></span>(0, 1), _:<span class="name"><a href="../Integers/index.html#Name_natural-numbers">natural-numbers</a></span>, _:<span class="name"><a href="../Integers/index.html#Name_integers">integers</a></span>) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable425_FF"><i class="var">FF</i></span>)</code></pre></div>
Each finite number is described by three integers:
* s = a sign (zero or one),
* c = a significand (or 'coefficient'),
* q = an exponent.
The numerical value of a finite number is (-1)^s * c * b^q
where b is the base (2 or 10), also called radix.
The possible finite values that can be represented in a format
are determined by the base b, the number of digits in the significand
(precision p), and the exponent parameter emax:
* c must be an integer in the range zero through (b^p)-1
(e.g., if b=10 and p=7 then c is 0 through 9999999);
* q must be an integer such that 1-emax <= q+p-1 <= emax
(e.g., if p=7 and emax=96 then q is -101 through 90).
Note that <code><span class="name"><a href="#Name_float">float</a></span>(<i class="var">FF</i>, <i class="var">S</i>, <i class="var">C</i>, <i class="var">Q</i>)</code> is not a 1-1 operation.
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_quiet-not-a-number">quiet-not-a-number</span></span>(<span id="Variable527_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>) : <span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable542_FF"><i class="var">FF</i></span>)
<i class="keyword">Alias</i>
<span class="name"><span id="Name_qNaN">qNaN</span></span> = <span class="name"><a href="#Name_quiet-not-a-number">quiet-not-a-number</a></span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_signaling-not-a-number">signaling-not-a-number</span></span>(<span id="Variable560_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>) : <span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable575_FF"><i class="var">FF</i></span>)
<i class="keyword">Alias</i>
<span class="name"><span id="Name_sNaN">sNaN</span></span> = <span class="name"><a href="#Name_signaling-not-a-number">signaling-not-a-number</a></span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_positive-infinity">positive-infinity</span></span>(<span id="Variable593_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>) : <span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable608_FF"><i class="var">FF</i></span>)
<i class="keyword">Alias</i>
<span class="name"><span id="Name_pos-inf">pos-inf</span></span> = <span class="name"><a href="#Name_positive-infinity">positive-infinity</a></span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_negative-infinity">negative-infinity</span></span>(<span id="Variable626_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>) : <span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable641_FF"><i class="var">FF</i></span>)
<i class="keyword">Alias</i>
<span class="name"><span id="Name_neg-inf">neg-inf</span></span> = <span class="name"><a href="#Name_negative-infinity">negative-infinity</a></span></code></pre></div>
#### Conversions
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-convert">float-convert</span></span>(<span id="Variable679_FF1"><i class="var">FF<sub class="sub">1</sub></i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>,
<span id="Variable689_FF2"><i class="var">FF<sub class="sub">2</sub></i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, <span id="Variable698_F"><i class="var">F</i></span>:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable704_FF1"><i class="var">FF<sub class="sub">1</sub></i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable728_FF2"><i class="var">FF<sub class="sub">2</sub></i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_decimal-float">decimal-float</span></span>(<span id="Variable744_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>,
_:<span class="name"><a href="../../Composite/Strings/index.html#Name_strings">strings</a></span>, _:<span class="name"><a href="../../Composite/Strings/index.html#Name_strings">strings</a></span>, _:<span class="name"><a href="../../Composite/Strings/index.html#Name_strings">strings</a></span>) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable787_FF"><i class="var">FF</i></span>)</code></pre></div>
<code><span class="name"><a href="#Name_decimal-float">decimal-float</a></span>(<i class="var">F</i>, "M", "N", "E")</code> is an approximation in <code><span class="name"><a href="#Name_floats">floats</a></span>(<i class="var">FF</i>)</code> to the
value of 'M.N' times 10 to the power 'E', where "M.N" is decimal notation
(optionally-signed) for a fixed-point number and "E" is decimal notation
(optionally signed) for an integer. When any argument string is invalid,
the result is <code><span class="name"><a href="#Name_quiet-not-a-number">quiet-not-a-number</a></span>(<i class="var">F</i>)</code>.
#### Comparison
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-equal">float-equal</span></span>(<span id="Variable889_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>,
_:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable902_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable920_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="../Booleans/index.html#Name_booleans">booleans</a></span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-is-less">float-is-less</span></span>(<span id="Variable949_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>,
_:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable962_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable980_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="../Booleans/index.html#Name_booleans">booleans</a></span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-is-less-or-equal">float-is-less-or-equal</span></span>(<span id="Variable1009_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>,
_:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1022_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1040_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="../Booleans/index.html#Name_booleans">booleans</a></span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-is-greater">float-is-greater</span></span>(<span id="Variable1069_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>,
_:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1082_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1100_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="../Booleans/index.html#Name_booleans">booleans</a></span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-is-greater-or-equal">float-is-greater-or-equal</span></span>(<span id="Variable1129_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>,
_:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1142_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1160_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="../Booleans/index.html#Name_booleans">booleans</a></span></code></pre></div>
#### Arithmetic
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-negate">float-negate</span></span>(<span id="Variable1202_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1215_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1237_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-absolute-value">float-absolute-value</span></span>(<span id="Variable1253_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1266_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1288_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-add">float-add</span></span>(<span id="Variable1304_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1317_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1335_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1358_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-subtract">float-subtract</span></span>(<span id="Variable1374_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1387_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1405_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1428_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-multiply">float-multiply</span></span>(<span id="Variable1444_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1457_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1475_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1498_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-multiply-add">float-multiply-add</span></span>(<span id="Variable1514_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>,
_:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1527_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1545_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1563_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1587_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-divide">float-divide</span></span>(<span id="Variable1603_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1616_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1634_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1657_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-remainder">float-remainder</span></span>(<span id="Variable1673_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1686_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1704_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1727_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-sqrt">float-sqrt</span></span>(<span id="Variable1743_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1756_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1778_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-integer-power">float-integer-power</span></span>(<span id="Variable1794_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1807_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="../Integers/index.html#Name_integers">integers</a></span>) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1838_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-float-power">float-float-power</span></span>(<span id="Variable1854_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1867_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1885_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1908_FF"><i class="var">FF</i></span>)</code></pre></div>
#### Rounding
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-round-ties-to-even">float-round-ties-to-even</span></span>(<span id="Variable1943_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1956_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="../Integers/index.html#Name_integers">integers</a></span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-round-ties-to-infinity">float-round-ties-to-infinity</span></span>(<span id="Variable1984_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable1997_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="../Integers/index.html#Name_integers">integers</a></span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-floor">float-floor</span></span>(<span id="Variable2025_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2038_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="../Integers/index.html#Name_integers">integers</a></span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-ceiling">float-ceiling</span></span>(<span id="Variable2066_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2079_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="../Integers/index.html#Name_integers">integers</a></span></code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-truncate">float-truncate</span></span>(<span id="Variable2107_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2120_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="../Integers/index.html#Name_integers">integers</a></span></code></pre></div>
#### Miscellaneous
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-pi">float-pi</span></span>(<span id="Variable2161_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2177_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-e">float-e</span></span>(<span id="Variable2193_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2209_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-log">float-log</span></span>(<span id="Variable2225_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2238_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2260_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-log10">float-log10</span></span>(<span id="Variable2276_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2289_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2311_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-exp">float-exp</span></span>(<span id="Variable2327_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2340_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2362_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-sin">float-sin</span></span>(<span id="Variable2378_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2391_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2413_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-cos">float-cos</span></span>(<span id="Variable2429_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2442_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2464_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-tan">float-tan</span></span>(<span id="Variable2480_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2493_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2515_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-asin">float-asin</span></span>(<span id="Variable2531_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2544_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2566_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-acos">float-acos</span></span>(<span id="Variable2582_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2595_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2617_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-atan">float-atan</span></span>(<span id="Variable2633_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2646_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2668_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-sinh">float-sinh</span></span>(<span id="Variable2684_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2697_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2719_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-cosh">float-cosh</span></span>(<span id="Variable2735_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2748_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2770_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-tanh">float-tanh</span></span>(<span id="Variable2786_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2799_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2821_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-asinh">float-asinh</span></span>(<span id="Variable2837_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2850_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2872_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-acosh">float-acosh</span></span>(<span id="Variable2888_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2901_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2923_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-atanh">float-atanh</span></span>(<span id="Variable2939_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2952_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable2974_FF"><i class="var">FF</i></span>)</code></pre></div>
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
<span class="name"><span id="Name_float-atan2">float-atan2</span></span>(<span id="Variable2990_FF"><i class="var">FF</i></span>:<span class="name"><a href="#Name_float-formats">float-formats</a></span>, _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable3003_FF"><i class="var">FF</i></span>), _:<span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable3021_FF"><i class="var">FF</i></span>)) : =><span class="name"><a href="#Name_floats">floats</a></span>(<span id="Variable3044_FF"><i class="var">FF</i></span>)</code></pre></div>
____
From the [PLanCompS Project] | [CBS-beta issues...] | [Suggest an improvement...]
[Floats.cbs]: Floats.cbs
"CBS SOURCE FILE"
[Funcons-beta]: /CBS-beta/docs/Funcons-beta
"FUNCONS-BETA"
[Unstable-Funcons-beta]: /CBS-beta/docs/Unstable-Funcons-beta
"UNSTABLE-FUNCONS-BETA"
[Languages-beta]: /CBS-beta/docs/Languages-beta
"LANGUAGES-BETA"
[Unstable-Languages-beta]: /CBS-beta/docs/Unstable-Languages-beta
"UNSTABLE-LANGUAGES-BETA"
[CBS-beta]: /CBS-beta "CBS-BETA"
[PLanCompS Project]: https://plancomps.github.io
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[CBS-beta issues...]: https://github.com/plancomps/CBS-beta/issues
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