long numerator = (long) index * (dataset.length - 1);
      // Since scale is a positive int, index is in [0, scale], and (dataset.length - 1) is a
      // non-negative int, we can do long-arithmetic on index * (dataset.length - 1) / scale to get
      // a rounded ratio and a remainder which can be expressed as ints, without risk of overflow:
      int quotient = (int) LongMath.divide(numerator, scale, RoundingMode.DOWN);

import java.io.Serializable;
import java.math.BigInteger;
import javax.annotation.CheckForNull;

/**
 * A wrapper class for unsigned {@code long} values, supporting arithmetic operations.
 *
 * <p>In some cases, when speed is more important than code readability, it may be faster simply to
 * treat primitive {@code long} values as unsigned, using the methods from {@link UnsignedLongs}.
 *

import java.io.Serializable;
import java.math.BigInteger;
import javax.annotation.CheckForNull;

/**
 * A wrapper class for unsigned {@code long} values, supporting arithmetic operations.
 *
 * <p>In some cases, when speed is more important than code readability, it may be faster simply to
 * treat primitive {@code long} values as unsigned, using the methods from {@link UnsignedLongs}.
 *

    // We extend the recursive expression for the one-variable case at Art of Computer Programming
    // vol. 2, Knuth, 4.2.2, (16) to the two-variable case. We have two value series x_i and y_i.
    // We define the arithmetic means X_n = 1/n \sum_{i=1}^n x_i, and Y_n = 1/n \sum_{i=1}^n y_i.
    // We also define the sum of the products of the differences from the means
    //           C_n = \sum_{i=1}^n x_i y_i - n X_n Y_n

<br>
<code>R0&gt;&gt;16</code>
<br>
<code>R0&lt;&lt;16</code>
<br>
<code>R0@&gt;16</code>:
For <code>&lt;&lt;</code>, left shift <code>R0</code> by 16 bits.
The other codes are <code>-&gt;</code> (arithmetic right shift),
<code>&gt;&gt;</code> (logical right shift), and
<code>@&gt;</code> (rotate right).
</li>

<li>
<code>R0-&gt;R1</code>
<br>
<code>R0&gt;&gt;R1</code>
<br>

x <= f()
^a >> b
f() || g()
x == y+1 && <-chanInt > 0
</pre>


<h3 id="Arithmetic_operators">Arithmetic operators</h3>
<p>
Arithmetic operators apply to numeric values and yield a result of the same
type as the first operand. The four standard arithmetic operators (<code>+</code>,
<code>-</code>, <code>*</code>, <code>/</code>) apply to integer,

	BFC	$29, $2, R8                              // 1f81dee7
	BFI	$29, $2, R8                              // 1881dee7
	BFI	$16, $8, R1, R2 // BFI $16, R1, $8, R2   // 1124d7e7

// synthetic arithmetic
	ADD	$0xffffffaa, R2, R3 // ADD $4294967210, R2, R3   // 55b0e0e30b3082e0
	ADD	$0xffffff55, R5     // ADD $4294967125, R5       // aab0e0e30b5085e0
	ADD.S	$0xffffffab, R2, R3 // ADD.S $4294967211, R2, R3 // 54b0e0e30b3092e0

x == y+1 &amp;&amp; &lt;-chanInt &gt; 0  // (x == (y+1)) && ((<-chanInt) > 0)
</pre>


<h3 id="Arithmetic_operators">Arithmetic operators</h3>
<p>
Arithmetic operators apply to numeric values and yield a result of the same
type as the first operand. The four standard arithmetic operators (<code>+</code>,
<code>-</code>, <code>*</code>, <code>/</code>) apply to

// the old assembler's (7a's) grammar and hand-writing complete
// instructions for each rule, to guarantee we cover the same space.

#include "../../../../../runtime/textflag.h"

TEXT	foo(SB), DUPOK|NOSPLIT, $-8

// arithmetic operations
	ADDW	$1, R2, R3
	ADDW	R1, R2, R3
	ADDW	R1, ZR, R3
	ADD	$1, R2, R3
	ADD	R1, R2, R3
	ADD	R1, ZR, R3
	ADD	$1, R2, R3
	ADDW	$1, R2
	ADDW	R1, R2
	ADD	$1, R2
	ADD	R1, R2
	ADD	R1>>11, R2

sigh.  `I only took the regular course.'

  `What was that?' inquired Alice.

  `Reeling and Writhing, of course, to begin with,' the Mock
Turtle replied; `and then the different branches of Arithmetic--
Ambition, Distraction, Uglification, and Derision.'

  `I never heard of "Uglification,"' Alice ventured to say.  `What is it?'

  The Gryphon lifted up both its paws in surprise.  `What!  Never