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</pre><pre class="rust ">
<span class="comment">// Copyright 2015 The Rust Project Developers. See the COPYRIGHT</span>
<span class="comment">// file at the top-level directory of this distribution and at</span>
<span class="comment">// http://rust-lang.org/COPYRIGHT.</span>
<span class="comment">//</span>
<span class="comment">// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or</span>
<span class="comment">// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license</span>
<span class="comment">// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your</span>
<span class="comment">// option. This file may not be copied, modified, or distributed</span>
<span class="comment">// except according to those terms.</span>
<span class="doccomment">//! Bit fiddling on positive IEEE 754 floats. Negative numbers aren't and needn't be handled.</span>
<span class="doccomment">//! Normal floating point numbers have a canonical representation as (frac, exp) such that the</span>
<span class="doccomment">//! value is 2<sup>exp</sup> * (1 + sum(frac[N-i] / 2<sup>i</sup>)) where N is the number of bits.</span>
<span class="doccomment">//! Subnormals are slightly different and weird, but the same principle applies.</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! Here, however, we represent them as (sig, k) with f positive, such that the value is f *</span>
<span class="doccomment">//! 2<sup>e</sup>. Besides making the "hidden bit" explicit, this changes the exponent by the</span>
<span class="doccomment">//! so-called mantissa shift.</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! Put another way, normally floats are written as (1) but here they are written as (2):</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! 1. `1.101100...11 * 2^m`</span>
<span class="doccomment">//! 2. `1101100...11 * 2^n`</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! We call (1) the **fractional representation** and (2) the **integral representation**.</span>
<span class="doccomment">//!</span>
<span class="doccomment">//! Many functions in this module only handle normal numbers. The dec2flt routines conservatively</span>
<span class="doccomment">//! take the universally-correct slow path (Algorithm M) for very small and very large numbers.</span>
<span class="doccomment">//! That algorithm needs only next_float() which does handle subnormals and zeros.</span>
<span class="kw">use</span> <span class="ident">u32</span>;
<span class="kw">use</span> <span class="ident">cmp</span>::<span class="ident">Ordering</span>::{<span class="ident">Less</span>, <span class="ident">Equal</span>, <span class="ident">Greater</span>};
<span class="kw">use</span> <span class="ident">ops</span>::{<span class="ident">Mul</span>, <span class="ident">Div</span>, <span class="ident">Neg</span>};
<span class="kw">use</span> <span class="ident">fmt</span>::{<span class="ident">Debug</span>, <span class="ident">LowerExp</span>};
<span class="kw">use</span> <span class="ident">mem</span>::<span class="ident">transmute</span>;
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">diy_float</span>::<span class="ident">Fp</span>;
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">FpCategory</span>::{<span class="ident">Infinite</span>, <span class="ident">Zero</span>, <span class="ident">Subnormal</span>, <span class="ident">Normal</span>, <span class="ident">Nan</span>};
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">Float</span>;
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">dec2flt</span>::<span class="ident">num</span>::{<span class="self">self</span>, <span class="ident">Big</span>};
<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">dec2flt</span>::<span class="ident">table</span>;
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Copy</span>, <span class="ident">Clone</span>, <span class="ident">Debug</span>)]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">Unpacked</span> {
<span class="kw">pub</span> <span class="ident">sig</span>: <span class="ident">u64</span>,
<span class="kw">pub</span> <span class="ident">k</span>: <span class="ident">i16</span>,
}
<span class="kw">impl</span> <span class="ident">Unpacked</span> {
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">sig</span>: <span class="ident">u64</span>, <span class="ident">k</span>: <span class="ident">i16</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="ident">Unpacked</span> { <span class="ident">sig</span>: <span class="ident">sig</span>, <span class="ident">k</span>: <span class="ident">k</span> }
}
}
<span class="doccomment">/// A helper trait to avoid duplicating basically all the conversion code for `f32` and `f64`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// See the parent module's doc comment for why this is necessary.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// Should **never ever** be implemented for other types or be used outside the dec2flt module.</span>
<span class="doccomment">/// Inherits from `Float` because there is some overlap, but all the reused methods are trivial.</span>
<span class="kw">pub</span> <span class="kw">trait</span> <span class="ident">RawFloat</span> : <span class="ident">Float</span> <span class="op">+</span> <span class="ident">Copy</span> <span class="op">+</span> <span class="ident">Debug</span> <span class="op">+</span> <span class="ident">LowerExp</span>
<span class="op">+</span> <span class="ident">Mul</span><span class="op"><</span><span class="ident">Output</span><span class="op">=</span><span class="self">Self</span><span class="op">></span> <span class="op">+</span> <span class="ident">Div</span><span class="op"><</span><span class="ident">Output</span><span class="op">=</span><span class="self">Self</span><span class="op">></span> <span class="op">+</span> <span class="ident">Neg</span><span class="op"><</span><span class="ident">Output</span><span class="op">=</span><span class="self">Self</span><span class="op">></span>
{
<span class="kw">const</span> <span class="ident">INFINITY</span>: <span class="self">Self</span>;
<span class="kw">const</span> <span class="ident">NAN</span>: <span class="self">Self</span>;
<span class="kw">const</span> <span class="ident">ZERO</span>: <span class="self">Self</span>;
<span class="doccomment">/// Returns the mantissa, exponent and sign as integers.</span>
<span class="kw">fn</span> <span class="ident">integer_decode</span>(<span class="self">self</span>) <span class="op">-></span> (<span class="ident">u64</span>, <span class="ident">i16</span>, <span class="ident">i8</span>);
<span class="doccomment">/// Get the raw binary representation of the float.</span>
<span class="kw">fn</span> <span class="ident">transmute</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">u64</span>;
<span class="doccomment">/// Transmute the raw binary representation into a float.</span>
<span class="kw">fn</span> <span class="ident">from_bits</span>(<span class="ident">bits</span>: <span class="ident">u64</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Decode the float.</span>
<span class="kw">fn</span> <span class="ident">unpack</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">Unpacked</span>;
<span class="doccomment">/// Cast from a small integer that can be represented exactly. Panic if the integer can't be</span>
<span class="doccomment">/// represented, the other code in this module makes sure to never let that happen.</span>
<span class="kw">fn</span> <span class="ident">from_int</span>(<span class="ident">x</span>: <span class="ident">u64</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// Get the value 10<sup>e</sup> from a pre-computed table.</span>
<span class="doccomment">/// Panics for `e >= CEIL_LOG5_OF_MAX_SIG`.</span>
<span class="kw">fn</span> <span class="ident">short_fast_pow10</span>(<span class="ident">e</span>: <span class="ident">usize</span>) <span class="op">-></span> <span class="self">Self</span>;
<span class="doccomment">/// What the name says. It's easier to hard code than juggling intrinsics and</span>
<span class="doccomment">/// hoping LLVM constant folds it.</span>
<span class="kw">const</span> <span class="ident">CEIL_LOG5_OF_MAX_SIG</span>: <span class="ident">i16</span>;
<span class="comment">// A conservative bound on the decimal digits of inputs that can't produce overflow or zero or</span>
<span class="doccomment">/// subnormals. Probably the decimal exponent of the maximum normal value, hence the name.</span>
<span class="kw">const</span> <span class="ident">MAX_NORMAL_DIGITS</span>: <span class="ident">usize</span>;
<span class="doccomment">/// When the most significant decimal digit has a place value greater than this, the number</span>
<span class="doccomment">/// is certainly rounded to infinity.</span>
<span class="kw">const</span> <span class="ident">INF_CUTOFF</span>: <span class="ident">i64</span>;
<span class="doccomment">/// When the most significant decimal digit has a place value less than this, the number</span>
<span class="doccomment">/// is certainly rounded to zero.</span>
<span class="kw">const</span> <span class="ident">ZERO_CUTOFF</span>: <span class="ident">i64</span>;
<span class="doccomment">/// The number of bits in the exponent.</span>
<span class="kw">const</span> <span class="ident">EXP_BITS</span>: <span class="ident">u8</span>;
<span class="doccomment">/// The number of bits in the singificand, *including* the hidden bit.</span>
<span class="kw">const</span> <span class="ident">SIG_BITS</span>: <span class="ident">u8</span>;
<span class="doccomment">/// The number of bits in the singificand, *excluding* the hidden bit.</span>
<span class="kw">const</span> <span class="ident">EXPLICIT_SIG_BITS</span>: <span class="ident">u8</span>;
<span class="doccomment">/// The maximum legal exponent in fractional representation.</span>
<span class="kw">const</span> <span class="ident">MAX_EXP</span>: <span class="ident">i16</span>;
<span class="doccomment">/// The minimum legal exponent in fractional representation, excluding subnormals.</span>
<span class="kw">const</span> <span class="ident">MIN_EXP</span>: <span class="ident">i16</span>;
<span class="doccomment">/// `MAX_EXP` for integral representation, i.e., with the shift applied.</span>
<span class="kw">const</span> <span class="ident">MAX_EXP_INT</span>: <span class="ident">i16</span>;
<span class="doccomment">/// `MAX_EXP` encoded (i.e., with offset bias)</span>
<span class="kw">const</span> <span class="ident">MAX_ENCODED_EXP</span>: <span class="ident">i16</span>;
<span class="doccomment">/// `MIN_EXP` for integral representation, i.e., with the shift applied.</span>
<span class="kw">const</span> <span class="ident">MIN_EXP_INT</span>: <span class="ident">i16</span>;
<span class="doccomment">/// The maximum normalized singificand in integral representation.</span>
<span class="kw">const</span> <span class="ident">MAX_SIG</span>: <span class="ident">u64</span>;
<span class="doccomment">/// The minimal normalized significand in integral representation.</span>
<span class="kw">const</span> <span class="ident">MIN_SIG</span>: <span class="ident">u64</span>;
}
<span class="comment">// Mostly a workaround for #34344.</span>
<span class="macro">macro_rules</span><span class="macro">!</span> <span class="ident">other_constants</span> {
(<span class="macro-nonterminal">$</span><span class="kw">type</span>: <span class="macro-nonterminal">ident</span>) <span class="op">=></span> {
<span class="kw">const</span> <span class="ident">EXPLICIT_SIG_BITS</span>: <span class="ident">u8</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">SIG_BITS</span> <span class="op">-</span> <span class="number">1</span>;
<span class="kw">const</span> <span class="ident">MAX_EXP</span>: <span class="ident">i16</span> <span class="op">=</span> (<span class="number">1</span> <span class="op"><<</span> (<span class="self">Self</span>::<span class="ident">EXP_BITS</span> <span class="op">-</span> <span class="number">1</span>)) <span class="op">-</span> <span class="number">1</span>;
<span class="kw">const</span> <span class="ident">MIN_EXP</span>: <span class="ident">i16</span> <span class="op">=</span> <span class="op">-</span><span class="self">Self</span>::<span class="ident">MAX_EXP</span> <span class="op">+</span> <span class="number">1</span>;
<span class="kw">const</span> <span class="ident">MAX_EXP_INT</span>: <span class="ident">i16</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">MAX_EXP</span> <span class="op">-</span> (<span class="self">Self</span>::<span class="ident">SIG_BITS</span> <span class="kw">as</span> <span class="ident">i16</span> <span class="op">-</span> <span class="number">1</span>);
<span class="kw">const</span> <span class="ident">MAX_ENCODED_EXP</span>: <span class="ident">i16</span> <span class="op">=</span> (<span class="number">1</span> <span class="op"><<</span> <span class="self">Self</span>::<span class="ident">EXP_BITS</span>) <span class="op">-</span> <span class="number">1</span>;
<span class="kw">const</span> <span class="ident">MIN_EXP_INT</span>: <span class="ident">i16</span> <span class="op">=</span> <span class="self">Self</span>::<span class="ident">MIN_EXP</span> <span class="op">-</span> (<span class="self">Self</span>::<span class="ident">SIG_BITS</span> <span class="kw">as</span> <span class="ident">i16</span> <span class="op">-</span> <span class="number">1</span>);
<span class="kw">const</span> <span class="ident">MAX_SIG</span>: <span class="ident">u64</span> <span class="op">=</span> (<span class="number">1</span> <span class="op"><<</span> <span class="self">Self</span>::<span class="ident">SIG_BITS</span>) <span class="op">-</span> <span class="number">1</span>;
<span class="kw">const</span> <span class="ident">MIN_SIG</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="number">1</span> <span class="op"><<</span> (<span class="self">Self</span>::<span class="ident">SIG_BITS</span> <span class="op">-</span> <span class="number">1</span>);
<span class="kw">const</span> <span class="ident">INFINITY</span>: <span class="self">Self</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="kw">crate</span>::<span class="macro-nonterminal">$</span><span class="kw">type</span>::<span class="macro-nonterminal">INFINITY</span>;
<span class="kw">const</span> <span class="ident">NAN</span>: <span class="self">Self</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="kw">crate</span>::<span class="macro-nonterminal">$</span><span class="kw">type</span>::<span class="macro-nonterminal">NAN</span>;
<span class="kw">const</span> <span class="ident">ZERO</span>: <span class="self">Self</span> <span class="op">=</span> <span class="number">0.0</span>;
}
}
<span class="kw">impl</span> <span class="ident">RawFloat</span> <span class="kw">for</span> <span class="ident">f32</span> {
<span class="kw">const</span> <span class="ident">SIG_BITS</span>: <span class="ident">u8</span> <span class="op">=</span> <span class="number">24</span>;
<span class="kw">const</span> <span class="ident">EXP_BITS</span>: <span class="ident">u8</span> <span class="op">=</span> <span class="number">8</span>;
<span class="kw">const</span> <span class="ident">CEIL_LOG5_OF_MAX_SIG</span>: <span class="ident">i16</span> <span class="op">=</span> <span class="number">11</span>;
<span class="kw">const</span> <span class="ident">MAX_NORMAL_DIGITS</span>: <span class="ident">usize</span> <span class="op">=</span> <span class="number">35</span>;
<span class="kw">const</span> <span class="ident">INF_CUTOFF</span>: <span class="ident">i64</span> <span class="op">=</span> <span class="number">40</span>;
<span class="kw">const</span> <span class="ident">ZERO_CUTOFF</span>: <span class="ident">i64</span> <span class="op">=</span> <span class="op">-</span><span class="number">48</span>;
<span class="macro">other_constants</span><span class="macro">!</span>(<span class="ident">f32</span>);
<span class="doccomment">/// Returns the mantissa, exponent and sign as integers.</span>
<span class="kw">fn</span> <span class="ident">integer_decode</span>(<span class="self">self</span>) <span class="op">-></span> (<span class="ident">u64</span>, <span class="ident">i16</span>, <span class="ident">i8</span>) {
<span class="kw">let</span> <span class="ident">bits</span>: <span class="ident">u32</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">transmute</span>(<span class="self">self</span>) };
<span class="kw">let</span> <span class="ident">sign</span>: <span class="ident">i8</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">bits</span> <span class="op">>></span> <span class="number">31</span> <span class="op">==</span> <span class="number">0</span> { <span class="number">1</span> } <span class="kw">else</span> { <span class="op">-</span><span class="number">1</span> };
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">exponent</span>: <span class="ident">i16</span> <span class="op">=</span> ((<span class="ident">bits</span> <span class="op">>></span> <span class="number">23</span>) <span class="op">&</span> <span class="number">0xff</span>) <span class="kw">as</span> <span class="ident">i16</span>;
<span class="kw">let</span> <span class="ident">mantissa</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">exponent</span> <span class="op">==</span> <span class="number">0</span> {
(<span class="ident">bits</span> <span class="op">&</span> <span class="number">0x7fffff</span>) <span class="op"><<</span> <span class="number">1</span>
} <span class="kw">else</span> {
(<span class="ident">bits</span> <span class="op">&</span> <span class="number">0x7fffff</span>) <span class="op">|</span> <span class="number">0x800000</span>
};
<span class="comment">// Exponent bias + mantissa shift</span>
<span class="ident">exponent</span> <span class="op">-=</span> <span class="number">127</span> <span class="op">+</span> <span class="number">23</span>;
(<span class="ident">mantissa</span> <span class="kw">as</span> <span class="ident">u64</span>, <span class="ident">exponent</span>, <span class="ident">sign</span>)
}
<span class="kw">fn</span> <span class="ident">transmute</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">u64</span> {
<span class="kw">let</span> <span class="ident">bits</span>: <span class="ident">u32</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">transmute</span>(<span class="self">self</span>) };
<span class="ident">bits</span> <span class="kw">as</span> <span class="ident">u64</span>
}
<span class="kw">fn</span> <span class="ident">from_bits</span>(<span class="ident">bits</span>: <span class="ident">u64</span>) <span class="op">-></span> <span class="ident">f32</span> {
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">bits</span> <span class="op"><</span> <span class="ident">u32</span>::<span class="ident">MAX</span> <span class="kw">as</span> <span class="ident">u64</span>, <span class="string">"f32::from_bits: too many bits"</span>);
<span class="kw">unsafe</span> { <span class="ident">transmute</span>(<span class="ident">bits</span> <span class="kw">as</span> <span class="ident">u32</span>) }
}
<span class="kw">fn</span> <span class="ident">unpack</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">Unpacked</span> {
<span class="kw">let</span> (<span class="ident">sig</span>, <span class="ident">exp</span>, <span class="ident">_sig</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">integer_decode</span>();
<span class="ident">Unpacked</span>::<span class="ident">new</span>(<span class="ident">sig</span>, <span class="ident">exp</span>)
}
<span class="kw">fn</span> <span class="ident">from_int</span>(<span class="ident">x</span>: <span class="ident">u64</span>) <span class="op">-></span> <span class="ident">f32</span> {
<span class="comment">// rkruppe is uncertain whether `as` rounds correctly on all platforms.</span>
<span class="macro">debug_assert</span><span class="macro">!</span>(<span class="ident">x</span> <span class="kw">as</span> <span class="ident">f32</span> <span class="op">==</span> <span class="ident">fp_to_float</span>(<span class="ident">Fp</span> { <span class="ident">f</span>: <span class="ident">x</span>, <span class="ident">e</span>: <span class="number">0</span> }));
<span class="ident">x</span> <span class="kw">as</span> <span class="ident">f32</span>
}
<span class="kw">fn</span> <span class="ident">short_fast_pow10</span>(<span class="ident">e</span>: <span class="ident">usize</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="ident">table</span>::<span class="ident">F32_SHORT_POWERS</span>[<span class="ident">e</span>]
}
}
<span class="kw">impl</span> <span class="ident">RawFloat</span> <span class="kw">for</span> <span class="ident">f64</span> {
<span class="kw">const</span> <span class="ident">SIG_BITS</span>: <span class="ident">u8</span> <span class="op">=</span> <span class="number">53</span>;
<span class="kw">const</span> <span class="ident">EXP_BITS</span>: <span class="ident">u8</span> <span class="op">=</span> <span class="number">11</span>;
<span class="kw">const</span> <span class="ident">CEIL_LOG5_OF_MAX_SIG</span>: <span class="ident">i16</span> <span class="op">=</span> <span class="number">23</span>;
<span class="kw">const</span> <span class="ident">MAX_NORMAL_DIGITS</span>: <span class="ident">usize</span> <span class="op">=</span> <span class="number">305</span>;
<span class="kw">const</span> <span class="ident">INF_CUTOFF</span>: <span class="ident">i64</span> <span class="op">=</span> <span class="number">310</span>;
<span class="kw">const</span> <span class="ident">ZERO_CUTOFF</span>: <span class="ident">i64</span> <span class="op">=</span> <span class="op">-</span><span class="number">326</span>;
<span class="macro">other_constants</span><span class="macro">!</span>(<span class="ident">f64</span>);
<span class="doccomment">/// Returns the mantissa, exponent and sign as integers.</span>
<span class="kw">fn</span> <span class="ident">integer_decode</span>(<span class="self">self</span>) <span class="op">-></span> (<span class="ident">u64</span>, <span class="ident">i16</span>, <span class="ident">i8</span>) {
<span class="kw">let</span> <span class="ident">bits</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">transmute</span>(<span class="self">self</span>) };
<span class="kw">let</span> <span class="ident">sign</span>: <span class="ident">i8</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">bits</span> <span class="op">>></span> <span class="number">63</span> <span class="op">==</span> <span class="number">0</span> { <span class="number">1</span> } <span class="kw">else</span> { <span class="op">-</span><span class="number">1</span> };
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">exponent</span>: <span class="ident">i16</span> <span class="op">=</span> ((<span class="ident">bits</span> <span class="op">>></span> <span class="number">52</span>) <span class="op">&</span> <span class="number">0x7ff</span>) <span class="kw">as</span> <span class="ident">i16</span>;
<span class="kw">let</span> <span class="ident">mantissa</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">exponent</span> <span class="op">==</span> <span class="number">0</span> {
(<span class="ident">bits</span> <span class="op">&</span> <span class="number">0xfffffffffffff</span>) <span class="op"><<</span> <span class="number">1</span>
} <span class="kw">else</span> {
(<span class="ident">bits</span> <span class="op">&</span> <span class="number">0xfffffffffffff</span>) <span class="op">|</span> <span class="number">0x10000000000000</span>
};
<span class="comment">// Exponent bias + mantissa shift</span>
<span class="ident">exponent</span> <span class="op">-=</span> <span class="number">1023</span> <span class="op">+</span> <span class="number">52</span>;
(<span class="ident">mantissa</span>, <span class="ident">exponent</span>, <span class="ident">sign</span>)
}
<span class="kw">fn</span> <span class="ident">transmute</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">u64</span> {
<span class="kw">let</span> <span class="ident">bits</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">transmute</span>(<span class="self">self</span>) };
<span class="ident">bits</span>
}
<span class="kw">fn</span> <span class="ident">from_bits</span>(<span class="ident">bits</span>: <span class="ident">u64</span>) <span class="op">-></span> <span class="ident">f64</span> {
<span class="kw">unsafe</span> { <span class="ident">transmute</span>(<span class="ident">bits</span>) }
}
<span class="kw">fn</span> <span class="ident">unpack</span>(<span class="self">self</span>) <span class="op">-></span> <span class="ident">Unpacked</span> {
<span class="kw">let</span> (<span class="ident">sig</span>, <span class="ident">exp</span>, <span class="ident">_sig</span>) <span class="op">=</span> <span class="self">self</span>.<span class="ident">integer_decode</span>();
<span class="ident">Unpacked</span>::<span class="ident">new</span>(<span class="ident">sig</span>, <span class="ident">exp</span>)
}
<span class="kw">fn</span> <span class="ident">from_int</span>(<span class="ident">x</span>: <span class="ident">u64</span>) <span class="op">-></span> <span class="ident">f64</span> {
<span class="comment">// rkruppe is uncertain whether `as` rounds correctly on all platforms.</span>
<span class="macro">debug_assert</span><span class="macro">!</span>(<span class="ident">x</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">==</span> <span class="ident">fp_to_float</span>(<span class="ident">Fp</span> { <span class="ident">f</span>: <span class="ident">x</span>, <span class="ident">e</span>: <span class="number">0</span> }));
<span class="ident">x</span> <span class="kw">as</span> <span class="ident">f64</span>
}
<span class="kw">fn</span> <span class="ident">short_fast_pow10</span>(<span class="ident">e</span>: <span class="ident">usize</span>) <span class="op">-></span> <span class="self">Self</span> {
<span class="ident">table</span>::<span class="ident">F64_SHORT_POWERS</span>[<span class="ident">e</span>]
}
}
<span class="doccomment">/// Convert an Fp to the closest machine float type.</span>
<span class="doccomment">/// Does not handle subnormal results.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">fp_to_float</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">RawFloat</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">Fp</span>) <span class="op">-></span> <span class="ident">T</span> {
<span class="kw">let</span> <span class="ident">x</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">normalize</span>();
<span class="comment">// x.f is 64 bit, so x.e has a mantissa shift of 63</span>
<span class="kw">let</span> <span class="ident">e</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">e</span> <span class="op">+</span> <span class="number">63</span>;
<span class="kw">if</span> <span class="ident">e</span> <span class="op">></span> <span class="ident">T</span>::<span class="ident">MAX_EXP</span> {
<span class="macro">panic</span><span class="macro">!</span>(<span class="string">"fp_to_float: exponent {} too large"</span>, <span class="ident">e</span>)
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">e</span> <span class="op">></span> <span class="ident">T</span>::<span class="ident">MIN_EXP</span> {
<span class="ident">encode_normal</span>(<span class="ident">round_normal</span>::<span class="op"><</span><span class="ident">T</span><span class="op">></span>(<span class="ident">x</span>))
} <span class="kw">else</span> {
<span class="macro">panic</span><span class="macro">!</span>(<span class="string">"fp_to_float: exponent {} too small"</span>, <span class="ident">e</span>)
}
}
<span class="doccomment">/// Round the 64-bit significand to T::SIG_BITS bits with half-to-even.</span>
<span class="doccomment">/// Does not handle exponent overflow.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">round_normal</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">RawFloat</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">Fp</span>) <span class="op">-></span> <span class="ident">Unpacked</span> {
<span class="kw">let</span> <span class="ident">excess</span> <span class="op">=</span> <span class="number">64</span> <span class="op">-</span> <span class="ident">T</span>::<span class="ident">SIG_BITS</span> <span class="kw">as</span> <span class="ident">i16</span>;
<span class="kw">let</span> <span class="ident">half</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="number">1</span> <span class="op"><<</span> (<span class="ident">excess</span> <span class="op">-</span> <span class="number">1</span>);
<span class="kw">let</span> (<span class="ident">q</span>, <span class="ident">rem</span>) <span class="op">=</span> (<span class="ident">x</span>.<span class="ident">f</span> <span class="op">>></span> <span class="ident">excess</span>, <span class="ident">x</span>.<span class="ident">f</span> <span class="op">&</span> ((<span class="number">1</span> <span class="op"><<</span> <span class="ident">excess</span>) <span class="op">-</span> <span class="number">1</span>));
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">q</span> <span class="op"><<</span> <span class="ident">excess</span> <span class="op">|</span> <span class="ident">rem</span>, <span class="ident">x</span>.<span class="ident">f</span>);
<span class="comment">// Adjust mantissa shift</span>
<span class="kw">let</span> <span class="ident">k</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">e</span> <span class="op">+</span> <span class="ident">excess</span>;
<span class="kw">if</span> <span class="ident">rem</span> <span class="op"><</span> <span class="ident">half</span> {
<span class="ident">Unpacked</span>::<span class="ident">new</span>(<span class="ident">q</span>, <span class="ident">k</span>)
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">rem</span> <span class="op">==</span> <span class="ident">half</span> <span class="op">&&</span> (<span class="ident">q</span> <span class="op">%</span> <span class="number">2</span>) <span class="op">==</span> <span class="number">0</span> {
<span class="ident">Unpacked</span>::<span class="ident">new</span>(<span class="ident">q</span>, <span class="ident">k</span>)
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">q</span> <span class="op">==</span> <span class="ident">T</span>::<span class="ident">MAX_SIG</span> {
<span class="ident">Unpacked</span>::<span class="ident">new</span>(<span class="ident">T</span>::<span class="ident">MIN_SIG</span>, <span class="ident">k</span> <span class="op">+</span> <span class="number">1</span>)
} <span class="kw">else</span> {
<span class="ident">Unpacked</span>::<span class="ident">new</span>(<span class="ident">q</span> <span class="op">+</span> <span class="number">1</span>, <span class="ident">k</span>)
}
}
<span class="doccomment">/// Inverse of `RawFloat::unpack()` for normalized numbers.</span>
<span class="doccomment">/// Panics if the significand or exponent are not valid for normalized numbers.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">encode_normal</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">RawFloat</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">Unpacked</span>) <span class="op">-></span> <span class="ident">T</span> {
<span class="macro">debug_assert</span><span class="macro">!</span>(<span class="ident">T</span>::<span class="ident">MIN_SIG</span> <span class="op"><=</span> <span class="ident">x</span>.<span class="ident">sig</span> <span class="op">&&</span> <span class="ident">x</span>.<span class="ident">sig</span> <span class="op"><=</span> <span class="ident">T</span>::<span class="ident">MAX_SIG</span>,
<span class="string">"encode_normal: significand not normalized"</span>);
<span class="comment">// Remove the hidden bit</span>
<span class="kw">let</span> <span class="ident">sig_enc</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">sig</span> <span class="op">&</span> <span class="op">!</span>(<span class="number">1</span> <span class="op"><<</span> <span class="ident">T</span>::<span class="ident">EXPLICIT_SIG_BITS</span>);
<span class="comment">// Adjust the exponent for exponent bias and mantissa shift</span>
<span class="kw">let</span> <span class="ident">k_enc</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">k</span> <span class="op">+</span> <span class="ident">T</span>::<span class="ident">MAX_EXP</span> <span class="op">+</span> <span class="ident">T</span>::<span class="ident">EXPLICIT_SIG_BITS</span> <span class="kw">as</span> <span class="ident">i16</span>;
<span class="macro">debug_assert</span><span class="macro">!</span>(<span class="ident">k_enc</span> <span class="op">!=</span> <span class="number">0</span> <span class="op">&&</span> <span class="ident">k_enc</span> <span class="op"><</span> <span class="ident">T</span>::<span class="ident">MAX_ENCODED_EXP</span>,
<span class="string">"encode_normal: exponent out of range"</span>);
<span class="comment">// Leave sign bit at 0 ("+"), our numbers are all positive</span>
<span class="kw">let</span> <span class="ident">bits</span> <span class="op">=</span> (<span class="ident">k_enc</span> <span class="kw">as</span> <span class="ident">u64</span>) <span class="op"><<</span> <span class="ident">T</span>::<span class="ident">EXPLICIT_SIG_BITS</span> <span class="op">|</span> <span class="ident">sig_enc</span>;
<span class="ident">T</span>::<span class="ident">from_bits</span>(<span class="ident">bits</span>)
}
<span class="doccomment">/// Construct a subnormal. A mantissa of 0 is allowed and constructs zero.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">encode_subnormal</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">RawFloat</span><span class="op">></span>(<span class="ident">significand</span>: <span class="ident">u64</span>) <span class="op">-></span> <span class="ident">T</span> {
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">significand</span> <span class="op"><</span> <span class="ident">T</span>::<span class="ident">MIN_SIG</span>, <span class="string">"encode_subnormal: not actually subnormal"</span>);
<span class="comment">// Encoded exponent is 0, the sign bit is 0, so we just have to reinterpret the bits.</span>
<span class="ident">T</span>::<span class="ident">from_bits</span>(<span class="ident">significand</span>)
}
<span class="doccomment">/// Approximate a bignum with an Fp. Rounds within 0.5 ULP with half-to-even.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">big_to_fp</span>(<span class="ident">f</span>: <span class="kw-2">&</span><span class="ident">Big</span>) <span class="op">-></span> <span class="ident">Fp</span> {
<span class="kw">let</span> <span class="ident">end</span> <span class="op">=</span> <span class="ident">f</span>.<span class="ident">bit_length</span>();
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">end</span> <span class="op">!=</span> <span class="number">0</span>, <span class="string">"big_to_fp: unexpectedly, input is zero"</span>);
<span class="kw">let</span> <span class="ident">start</span> <span class="op">=</span> <span class="ident">end</span>.<span class="ident">saturating_sub</span>(<span class="number">64</span>);
<span class="kw">let</span> <span class="ident">leading</span> <span class="op">=</span> <span class="ident">num</span>::<span class="ident">get_bits</span>(<span class="ident">f</span>, <span class="ident">start</span>, <span class="ident">end</span>);
<span class="comment">// We cut off all bits prior to the index `start`, i.e., we effectively right-shift by</span>
<span class="comment">// an amount of `start`, so this is also the exponent we need.</span>
<span class="kw">let</span> <span class="ident">e</span> <span class="op">=</span> <span class="ident">start</span> <span class="kw">as</span> <span class="ident">i16</span>;
<span class="kw">let</span> <span class="ident">rounded_down</span> <span class="op">=</span> <span class="ident">Fp</span> { <span class="ident">f</span>: <span class="ident">leading</span>, <span class="ident">e</span>: <span class="ident">e</span> }.<span class="ident">normalize</span>();
<span class="comment">// Round (half-to-even) depending on the truncated bits.</span>
<span class="kw">match</span> <span class="ident">num</span>::<span class="ident">compare_with_half_ulp</span>(<span class="ident">f</span>, <span class="ident">start</span>) {
<span class="ident">Less</span> <span class="op">=></span> <span class="ident">rounded_down</span>,
<span class="ident">Equal</span> <span class="kw">if</span> <span class="ident">leading</span> <span class="op">%</span> <span class="number">2</span> <span class="op">==</span> <span class="number">0</span> <span class="op">=></span> <span class="ident">rounded_down</span>,
<span class="ident">Equal</span> <span class="op">|</span> <span class="ident">Greater</span> <span class="op">=></span> <span class="kw">match</span> <span class="ident">leading</span>.<span class="ident">checked_add</span>(<span class="number">1</span>) {
<span class="prelude-val">Some</span>(<span class="ident">f</span>) <span class="op">=></span> <span class="ident">Fp</span> { <span class="ident">f</span>: <span class="ident">f</span>, <span class="ident">e</span>: <span class="ident">e</span> }.<span class="ident">normalize</span>(),
<span class="prelude-val">None</span> <span class="op">=></span> <span class="ident">Fp</span> { <span class="ident">f</span>: <span class="number">1</span> <span class="op"><<</span> <span class="number">63</span>, <span class="ident">e</span>: <span class="ident">e</span> <span class="op">+</span> <span class="number">1</span> },
}
}
}
<span class="doccomment">/// Find the largest floating point number strictly smaller than the argument.</span>
<span class="doccomment">/// Does not handle subnormals, zero, or exponent underflow.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">prev_float</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">RawFloat</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">T</span>) <span class="op">-></span> <span class="ident">T</span> {
<span class="kw">match</span> <span class="ident">x</span>.<span class="ident">classify</span>() {
<span class="ident">Infinite</span> <span class="op">=></span> <span class="macro">panic</span><span class="macro">!</span>(<span class="string">"prev_float: argument is infinite"</span>),
<span class="ident">Nan</span> <span class="op">=></span> <span class="macro">panic</span><span class="macro">!</span>(<span class="string">"prev_float: argument is NaN"</span>),
<span class="ident">Subnormal</span> <span class="op">=></span> <span class="macro">panic</span><span class="macro">!</span>(<span class="string">"prev_float: argument is subnormal"</span>),
<span class="ident">Zero</span> <span class="op">=></span> <span class="macro">panic</span><span class="macro">!</span>(<span class="string">"prev_float: argument is zero"</span>),
<span class="ident">Normal</span> <span class="op">=></span> {
<span class="kw">let</span> <span class="ident">Unpacked</span> { <span class="ident">sig</span>, <span class="ident">k</span> } <span class="op">=</span> <span class="ident">x</span>.<span class="ident">unpack</span>();
<span class="kw">if</span> <span class="ident">sig</span> <span class="op">==</span> <span class="ident">T</span>::<span class="ident">MIN_SIG</span> {
<span class="ident">encode_normal</span>(<span class="ident">Unpacked</span>::<span class="ident">new</span>(<span class="ident">T</span>::<span class="ident">MAX_SIG</span>, <span class="ident">k</span> <span class="op">-</span> <span class="number">1</span>))
} <span class="kw">else</span> {
<span class="ident">encode_normal</span>(<span class="ident">Unpacked</span>::<span class="ident">new</span>(<span class="ident">sig</span> <span class="op">-</span> <span class="number">1</span>, <span class="ident">k</span>))
}
}
}
}
<span class="comment">// Find the smallest floating point number strictly larger than the argument.</span>
<span class="comment">// This operation is saturating, i.e. next_float(inf) == inf.</span>
<span class="comment">// Unlike most code in this module, this function does handle zero, subnormals, and infinities.</span>
<span class="comment">// However, like all other code here, it does not deal with NaN and negative numbers.</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">next_float</span><span class="op"><</span><span class="ident">T</span>: <span class="ident">RawFloat</span><span class="op">></span>(<span class="ident">x</span>: <span class="ident">T</span>) <span class="op">-></span> <span class="ident">T</span> {
<span class="kw">match</span> <span class="ident">x</span>.<span class="ident">classify</span>() {
<span class="ident">Nan</span> <span class="op">=></span> <span class="macro">panic</span><span class="macro">!</span>(<span class="string">"next_float: argument is NaN"</span>),
<span class="ident">Infinite</span> <span class="op">=></span> <span class="ident">T</span>::<span class="ident">INFINITY</span>,
<span class="comment">// This seems too good to be true, but it works.</span>
<span class="comment">// 0.0 is encoded as the all-zero word. Subnormals are 0x000m...m where m is the mantissa.</span>
<span class="comment">// In particular, the smallest subnormal is 0x0...01 and the largest is 0x000F...F.</span>
<span class="comment">// The smallest normal number is 0x0010...0, so this corner case works as well.</span>
<span class="comment">// If the increment overflows the mantissa, the carry bit increments the exponent as we</span>
<span class="comment">// want, and the mantissa bits become zero. Because of the hidden bit convention, this</span>
<span class="comment">// too is exactly what we want!</span>
<span class="comment">// Finally, f64::MAX + 1 = 7eff...f + 1 = 7ff0...0 = f64::INFINITY.</span>
<span class="ident">Zero</span> <span class="op">|</span> <span class="ident">Subnormal</span> <span class="op">|</span> <span class="ident">Normal</span> <span class="op">=></span> {
<span class="kw">let</span> <span class="ident">bits</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">transmute</span>();
<span class="ident">T</span>::<span class="ident">from_bits</span>(<span class="ident">bits</span> <span class="op">+</span> <span class="number">1</span>)
}
}
}
</pre>
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