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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/root/.cargo/registry/src/github.com-1ecc6299db9ec823/ryu-1.0.13/src/d2s.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>d2s.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../normalize.css"><link rel="stylesheet" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../ayu.css" disabled><link rel="stylesheet" href="../../dark.css" disabled><link rel="stylesheet" href="../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../storage.js"></script><script defer src="../../source-script.js"></script><script defer src="../../source-files.js"></script><script defer src="../../main.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../favicon.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><a class="sidebar-logo" href="../../ryu/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../ryu/index.html"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span>
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</pre><pre class="rust"><code><span class="comment">// Translated from C to Rust. The original C code can be found at
// https://github.com/ulfjack/ryu and carries the following license:
//
// Copyright 2018 Ulf Adams
//
// The contents of this file may be used under the terms of the Apache License,
// Version 2.0.
//
// (See accompanying file LICENSE-Apache or copy at
// http://www.apache.org/licenses/LICENSE-2.0)
//
// Alternatively, the contents of this file may be used under the terms of
// the Boost Software License, Version 1.0.
// (See accompanying file LICENSE-Boost or copy at
// https://www.boost.org/LICENSE_1_0.txt)
//
// Unless required by applicable law or agreed to in writing, this software
// is distributed on an &quot;AS IS&quot; BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.
</span><span class="kw">use </span><span class="kw">crate</span>::common::<span class="kw-2">*</span>;
<span class="attribute">#[cfg(not(feature = <span class="string">&quot;small&quot;</span>))]
</span><span class="kw">pub use </span><span class="kw">crate</span>::d2s_full_table::<span class="kw-2">*</span>;
<span class="kw">use </span><span class="kw">crate</span>::d2s_intrinsics::<span class="kw-2">*</span>;
<span class="attribute">#[cfg(feature = <span class="string">&quot;small&quot;</span>)]
</span><span class="kw">pub use </span><span class="kw">crate</span>::d2s_small_table::<span class="kw-2">*</span>;
<span class="kw">use </span>core::mem::MaybeUninit;
<span class="kw">pub const </span>DOUBLE_MANTISSA_BITS: u32 = <span class="number">52</span>;
<span class="kw">pub const </span>DOUBLE_EXPONENT_BITS: u32 = <span class="number">11</span>;
<span class="kw">pub const </span>DOUBLE_BIAS: i32 = <span class="number">1023</span>;
<span class="kw">pub const </span>DOUBLE_POW5_INV_BITCOUNT: i32 = <span class="number">125</span>;
<span class="kw">pub const </span>DOUBLE_POW5_BITCOUNT: i32 = <span class="number">125</span>;
<span class="attribute">#[cfg_attr(feature = <span class="string">&quot;no-panic&quot;</span>, inline)]
</span><span class="kw">pub fn </span>decimal_length17(v: u64) -&gt; u32 {
<span class="comment">// This is slightly faster than a loop.
// The average output length is 16.38 digits, so we check high-to-low.
// Function precondition: v is not an 18, 19, or 20-digit number.
// (17 digits are sufficient for round-tripping.)
</span><span class="macro">debug_assert!</span>(v &lt; <span class="number">100000000000000000</span>);
<span class="kw">if </span>v &gt;= <span class="number">10000000000000000 </span>{
<span class="number">17
</span>} <span class="kw">else if </span>v &gt;= <span class="number">1000000000000000 </span>{
<span class="number">16
</span>} <span class="kw">else if </span>v &gt;= <span class="number">100000000000000 </span>{
<span class="number">15
</span>} <span class="kw">else if </span>v &gt;= <span class="number">10000000000000 </span>{
<span class="number">14
</span>} <span class="kw">else if </span>v &gt;= <span class="number">1000000000000 </span>{
<span class="number">13
</span>} <span class="kw">else if </span>v &gt;= <span class="number">100000000000 </span>{
<span class="number">12
</span>} <span class="kw">else if </span>v &gt;= <span class="number">10000000000 </span>{
<span class="number">11
</span>} <span class="kw">else if </span>v &gt;= <span class="number">1000000000 </span>{
<span class="number">10
</span>} <span class="kw">else if </span>v &gt;= <span class="number">100000000 </span>{
<span class="number">9
</span>} <span class="kw">else if </span>v &gt;= <span class="number">10000000 </span>{
<span class="number">8
</span>} <span class="kw">else if </span>v &gt;= <span class="number">1000000 </span>{
<span class="number">7
</span>} <span class="kw">else if </span>v &gt;= <span class="number">100000 </span>{
<span class="number">6
</span>} <span class="kw">else if </span>v &gt;= <span class="number">10000 </span>{
<span class="number">5
</span>} <span class="kw">else if </span>v &gt;= <span class="number">1000 </span>{
<span class="number">4
</span>} <span class="kw">else if </span>v &gt;= <span class="number">100 </span>{
<span class="number">3
</span>} <span class="kw">else if </span>v &gt;= <span class="number">10 </span>{
<span class="number">2
</span>} <span class="kw">else </span>{
<span class="number">1
</span>}
}
<span class="comment">// A floating decimal representing m * 10^e.
</span><span class="kw">pub struct </span>FloatingDecimal64 {
<span class="kw">pub </span>mantissa: u64,
<span class="comment">// Decimal exponent&#39;s range is -324 to 308
// inclusive, and can fit in i16 if needed.
</span><span class="kw">pub </span>exponent: i32,
}
<span class="attribute">#[cfg_attr(feature = <span class="string">&quot;no-panic&quot;</span>, inline)]
</span><span class="kw">pub fn </span>d2d(ieee_mantissa: u64, ieee_exponent: u32) -&gt; FloatingDecimal64 {
<span class="kw">let </span>(e2, m2) = <span class="kw">if </span>ieee_exponent == <span class="number">0 </span>{
(
<span class="comment">// We subtract 2 so that the bounds computation has 2 additional bits.
</span><span class="number">1 </span>- DOUBLE_BIAS - DOUBLE_MANTISSA_BITS <span class="kw">as </span>i32 - <span class="number">2</span>,
ieee_mantissa,
)
} <span class="kw">else </span>{
(
ieee_exponent <span class="kw">as </span>i32 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS <span class="kw">as </span>i32 - <span class="number">2</span>,
(<span class="number">1u64 </span>&lt;&lt; DOUBLE_MANTISSA_BITS) | ieee_mantissa,
)
};
<span class="kw">let </span>even = (m2 &amp; <span class="number">1</span>) == <span class="number">0</span>;
<span class="kw">let </span>accept_bounds = even;
<span class="comment">// Step 2: Determine the interval of valid decimal representations.
</span><span class="kw">let </span>mv = <span class="number">4 </span>* m2;
<span class="comment">// Implicit bool -&gt; int conversion. True is 1, false is 0.
</span><span class="kw">let </span>mm_shift = (ieee_mantissa != <span class="number">0 </span>|| ieee_exponent &lt;= <span class="number">1</span>) <span class="kw">as </span>u32;
<span class="comment">// We would compute mp and mm like this:
// uint64_t mp = 4 * m2 + 2;
// uint64_t mm = mv - 1 - mm_shift;
// Step 3: Convert to a decimal power base using 128-bit arithmetic.
</span><span class="kw">let </span><span class="kw-2">mut </span>vr: u64;
<span class="kw">let </span><span class="kw-2">mut </span>vp: u64;
<span class="kw">let </span><span class="kw-2">mut </span>vm: u64;
<span class="kw">let </span><span class="kw-2">mut </span>vp_uninit: MaybeUninit&lt;u64&gt; = MaybeUninit::uninit();
<span class="kw">let </span><span class="kw-2">mut </span>vm_uninit: MaybeUninit&lt;u64&gt; = MaybeUninit::uninit();
<span class="kw">let </span>e10: i32;
<span class="kw">let </span><span class="kw-2">mut </span>vm_is_trailing_zeros = <span class="bool-val">false</span>;
<span class="kw">let </span><span class="kw-2">mut </span>vr_is_trailing_zeros = <span class="bool-val">false</span>;
<span class="kw">if </span>e2 &gt;= <span class="number">0 </span>{
<span class="comment">// I tried special-casing q == 0, but there was no effect on performance.
// This expression is slightly faster than max(0, log10_pow2(e2) - 1).
</span><span class="kw">let </span>q = log10_pow2(e2) - (e2 &gt; <span class="number">3</span>) <span class="kw">as </span>u32;
e10 = q <span class="kw">as </span>i32;
<span class="kw">let </span>k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q <span class="kw">as </span>i32) - <span class="number">1</span>;
<span class="kw">let </span>i = -e2 + q <span class="kw">as </span>i32 + k;
vr = <span class="kw">unsafe </span>{
mul_shift_all_64(
m2,
<span class="attribute">#[cfg(feature = <span class="string">&quot;small&quot;</span>)]
</span><span class="kw-2">&amp;</span>compute_inv_pow5(q),
<span class="attribute">#[cfg(not(feature = <span class="string">&quot;small&quot;</span>))]
</span>{
<span class="macro">debug_assert!</span>(q &lt; DOUBLE_POW5_INV_SPLIT.len() <span class="kw">as </span>u32);
DOUBLE_POW5_INV_SPLIT.get_unchecked(q <span class="kw">as </span>usize)
},
i <span class="kw">as </span>u32,
vp_uninit.as_mut_ptr(),
vm_uninit.as_mut_ptr(),
mm_shift,
)
};
vp = <span class="kw">unsafe </span>{ vp_uninit.assume_init() };
vm = <span class="kw">unsafe </span>{ vm_uninit.assume_init() };
<span class="kw">if </span>q &lt;= <span class="number">21 </span>{
<span class="comment">// This should use q &lt;= 22, but I think 21 is also safe. Smaller values
// may still be safe, but it&#39;s more difficult to reason about them.
// Only one of mp, mv, and mm can be a multiple of 5, if any.
</span><span class="kw">let </span>mv_mod5 = (mv <span class="kw">as </span>u32).wrapping_sub(<span class="number">5u32</span>.wrapping_mul(div5(mv) <span class="kw">as </span>u32));
<span class="kw">if </span>mv_mod5 == <span class="number">0 </span>{
vr_is_trailing_zeros = multiple_of_power_of_5(mv, q);
} <span class="kw">else if </span>accept_bounds {
<span class="comment">// Same as min(e2 + (~mm &amp; 1), pow5_factor(mm)) &gt;= q
// &lt;=&gt; e2 + (~mm &amp; 1) &gt;= q &amp;&amp; pow5_factor(mm) &gt;= q
// &lt;=&gt; true &amp;&amp; pow5_factor(mm) &gt;= q, since e2 &gt;= q.
</span>vm_is_trailing_zeros = multiple_of_power_of_5(mv - <span class="number">1 </span>- mm_shift <span class="kw">as </span>u64, q);
} <span class="kw">else </span>{
<span class="comment">// Same as min(e2 + 1, pow5_factor(mp)) &gt;= q.
</span>vp -= multiple_of_power_of_5(mv + <span class="number">2</span>, q) <span class="kw">as </span>u64;
}
}
} <span class="kw">else </span>{
<span class="comment">// This expression is slightly faster than max(0, log10_pow5(-e2) - 1).
</span><span class="kw">let </span>q = log10_pow5(-e2) - (-e2 &gt; <span class="number">1</span>) <span class="kw">as </span>u32;
e10 = q <span class="kw">as </span>i32 + e2;
<span class="kw">let </span>i = -e2 - q <span class="kw">as </span>i32;
<span class="kw">let </span>k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
<span class="kw">let </span>j = q <span class="kw">as </span>i32 - k;
vr = <span class="kw">unsafe </span>{
mul_shift_all_64(
m2,
<span class="attribute">#[cfg(feature = <span class="string">&quot;small&quot;</span>)]
</span><span class="kw-2">&amp;</span>compute_pow5(i <span class="kw">as </span>u32),
<span class="attribute">#[cfg(not(feature = <span class="string">&quot;small&quot;</span>))]
</span>{
<span class="macro">debug_assert!</span>(i &lt; DOUBLE_POW5_SPLIT.len() <span class="kw">as </span>i32);
DOUBLE_POW5_SPLIT.get_unchecked(i <span class="kw">as </span>usize)
},
j <span class="kw">as </span>u32,
vp_uninit.as_mut_ptr(),
vm_uninit.as_mut_ptr(),
mm_shift,
)
};
vp = <span class="kw">unsafe </span>{ vp_uninit.assume_init() };
vm = <span class="kw">unsafe </span>{ vm_uninit.assume_init() };
<span class="kw">if </span>q &lt;= <span class="number">1 </span>{
<span class="comment">// {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
// mv = 4 * m2, so it always has at least two trailing 0 bits.
</span>vr_is_trailing_zeros = <span class="bool-val">true</span>;
<span class="kw">if </span>accept_bounds {
<span class="comment">// mm = mv - 1 - mm_shift, so it has 1 trailing 0 bit iff mm_shift == 1.
</span>vm_is_trailing_zeros = mm_shift == <span class="number">1</span>;
} <span class="kw">else </span>{
<span class="comment">// mp = mv + 2, so it always has at least one trailing 0 bit.
</span>vp -= <span class="number">1</span>;
}
} <span class="kw">else if </span>q &lt; <span class="number">63 </span>{
<span class="comment">// TODO(ulfjack): Use a tighter bound here.
// We want to know if the full product has at least q trailing zeros.
// We need to compute min(p2(mv), p5(mv) - e2) &gt;= q
// &lt;=&gt; p2(mv) &gt;= q &amp;&amp; p5(mv) - e2 &gt;= q
// &lt;=&gt; p2(mv) &gt;= q (because -e2 &gt;= q)
</span>vr_is_trailing_zeros = multiple_of_power_of_2(mv, q);
}
}
<span class="comment">// Step 4: Find the shortest decimal representation in the interval of valid representations.
</span><span class="kw">let </span><span class="kw-2">mut </span>removed = <span class="number">0i32</span>;
<span class="kw">let </span><span class="kw-2">mut </span>last_removed_digit = <span class="number">0u8</span>;
<span class="comment">// On average, we remove ~2 digits.
</span><span class="kw">let </span>output = <span class="kw">if </span>vm_is_trailing_zeros || vr_is_trailing_zeros {
<span class="comment">// General case, which happens rarely (~0.7%).
</span><span class="kw">loop </span>{
<span class="kw">let </span>vp_div10 = div10(vp);
<span class="kw">let </span>vm_div10 = div10(vm);
<span class="kw">if </span>vp_div10 &lt;= vm_div10 {
<span class="kw">break</span>;
}
<span class="kw">let </span>vm_mod10 = (vm <span class="kw">as </span>u32).wrapping_sub(<span class="number">10u32</span>.wrapping_mul(vm_div10 <span class="kw">as </span>u32));
<span class="kw">let </span>vr_div10 = div10(vr);
<span class="kw">let </span>vr_mod10 = (vr <span class="kw">as </span>u32).wrapping_sub(<span class="number">10u32</span>.wrapping_mul(vr_div10 <span class="kw">as </span>u32));
vm_is_trailing_zeros &amp;= vm_mod10 == <span class="number">0</span>;
vr_is_trailing_zeros &amp;= last_removed_digit == <span class="number">0</span>;
last_removed_digit = vr_mod10 <span class="kw">as </span>u8;
vr = vr_div10;
vp = vp_div10;
vm = vm_div10;
removed += <span class="number">1</span>;
}
<span class="kw">if </span>vm_is_trailing_zeros {
<span class="kw">loop </span>{
<span class="kw">let </span>vm_div10 = div10(vm);
<span class="kw">let </span>vm_mod10 = (vm <span class="kw">as </span>u32).wrapping_sub(<span class="number">10u32</span>.wrapping_mul(vm_div10 <span class="kw">as </span>u32));
<span class="kw">if </span>vm_mod10 != <span class="number">0 </span>{
<span class="kw">break</span>;
}
<span class="kw">let </span>vp_div10 = div10(vp);
<span class="kw">let </span>vr_div10 = div10(vr);
<span class="kw">let </span>vr_mod10 = (vr <span class="kw">as </span>u32).wrapping_sub(<span class="number">10u32</span>.wrapping_mul(vr_div10 <span class="kw">as </span>u32));
vr_is_trailing_zeros &amp;= last_removed_digit == <span class="number">0</span>;
last_removed_digit = vr_mod10 <span class="kw">as </span>u8;
vr = vr_div10;
vp = vp_div10;
vm = vm_div10;
removed += <span class="number">1</span>;
}
}
<span class="kw">if </span>vr_is_trailing_zeros &amp;&amp; last_removed_digit == <span class="number">5 </span>&amp;&amp; vr % <span class="number">2 </span>== <span class="number">0 </span>{
<span class="comment">// Round even if the exact number is .....50..0.
</span>last_removed_digit = <span class="number">4</span>;
}
<span class="comment">// We need to take vr + 1 if vr is outside bounds or we need to round up.
</span>vr + ((vr == vm &amp;&amp; (!accept_bounds || !vm_is_trailing_zeros)) || last_removed_digit &gt;= <span class="number">5</span>)
<span class="kw">as </span>u64
} <span class="kw">else </span>{
<span class="comment">// Specialized for the common case (~99.3%). Percentages below are relative to this.
</span><span class="kw">let </span><span class="kw-2">mut </span>round_up = <span class="bool-val">false</span>;
<span class="kw">let </span>vp_div100 = div100(vp);
<span class="kw">let </span>vm_div100 = div100(vm);
<span class="comment">// Optimization: remove two digits at a time (~86.2%).
</span><span class="kw">if </span>vp_div100 &gt; vm_div100 {
<span class="kw">let </span>vr_div100 = div100(vr);
<span class="kw">let </span>vr_mod100 = (vr <span class="kw">as </span>u32).wrapping_sub(<span class="number">100u32</span>.wrapping_mul(vr_div100 <span class="kw">as </span>u32));
round_up = vr_mod100 &gt;= <span class="number">50</span>;
vr = vr_div100;
vp = vp_div100;
vm = vm_div100;
removed += <span class="number">2</span>;
}
<span class="comment">// Loop iterations below (approximately), without optimization above:
// 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
// Loop iterations below (approximately), with optimization above:
// 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
</span><span class="kw">loop </span>{
<span class="kw">let </span>vp_div10 = div10(vp);
<span class="kw">let </span>vm_div10 = div10(vm);
<span class="kw">if </span>vp_div10 &lt;= vm_div10 {
<span class="kw">break</span>;
}
<span class="kw">let </span>vr_div10 = div10(vr);
<span class="kw">let </span>vr_mod10 = (vr <span class="kw">as </span>u32).wrapping_sub(<span class="number">10u32</span>.wrapping_mul(vr_div10 <span class="kw">as </span>u32));
round_up = vr_mod10 &gt;= <span class="number">5</span>;
vr = vr_div10;
vp = vp_div10;
vm = vm_div10;
removed += <span class="number">1</span>;
}
<span class="comment">// We need to take vr + 1 if vr is outside bounds or we need to round up.
</span>vr + (vr == vm || round_up) <span class="kw">as </span>u64
};
<span class="kw">let </span>exp = e10 + removed;
FloatingDecimal64 {
exponent: exp,
mantissa: output,
}
}
</code></pre></div>
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