}
	}
	var b float64
	if float64(n) <= x {
		// Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x)
		if x >= Two302 { // x > 2**302

			// (x >> n**2)
			//          Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
			//          Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
			//          Let s=sin(x), c=cos(x),
			//              xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
			//
			//                 n    sin(xn)*sqt2    cos(xn)*sqt2

// errorcheckoutput

package main

import "fmt"

// We are going to define 256 types T(n),
// such that T(n) embeds T(2n) and *T(2n+1).

func main() {
	fmt.Printf("// errorcheck\n\n")
	fmt.Printf("package p\n\n")
	fmt.Println(`import "unsafe"`)

	// Dump types.
	for n := 1; n < 256; n++ {
		writeStruct(n)
	}
	// Dump leaves
	for n := 256; n < 512; n++ {
		fmt.Printf("type T%d int\n", n)
	}

// license that can be found in the LICENSE file.

package big_test

import (
	"fmt"
	"math/big"
)

// Use the classic continued fraction for e
//
//	e = [1; 0, 1, 1, 2, 1, 1, ... 2n, 1, 1, ...]
//
// i.e., for the nth term, use
//
//	   1          if   n mod 3 != 1
//	(n-1)/3 * 2   if   n mod 3 == 1
func recur(n, lim int64) *big.Rat {
	term := new(big.Rat)
	if n%3 != 1 {
		term.SetInt64(1)

			// ok to overwrite y in place
			y = y.trunc(y, n)
		} else {
			y = nat(nil).trunc(y, n)
		}
	}
	if x.cmp(y) >= 0 {
		return z.sub(x, y)
	}
	// x - y < 0; x - y mod 2ⁿ = x - y + 2ⁿ = 2ⁿ - (y - x) = 1 + 2ⁿ-1 - (y - x) = 1 + ^(y - x).
	z = z.sub(y, x)
	for uint(len(z))*_W < n {
		z = append(z, 0)
	}
	for i := range z {
		z[i] = ^z[i]
	}
	z = z.trunc(z, n)
	return z.add(z, natOne)

entirely for the purpose of simplifying the run-time analysis, rather than
simplifying the presentation. Instead of a single algorithm that loops over
quotient digits, the paper presents two mutually-recursive algorithms, for
2n-by-n and 3n-by-2n. The paper also does not present any general (n+m)-by-n
algorithm.

The proofs in the paper are remarkably complex, especially considering that

00000040  54 bd d1 e8 02 9a ab fa  2f d1 19 e9 45 81 05 d1  |T......./...E...|
00000050  ba d2 d7 77 54 88 cc fe  14 b3 3b d1 28 15 03 03  |...wT.....;.(...|
00000060  00 1a 00 00 00 00 00 00  00 02 de 3f 93 32 6e f5  |...........?.2n.|

00000240  36 b5 b6 48 33 96 8a e3  a5 56 9b 34 16 ae 36 48  |6..H3....V.4..6H|
00000250  c5 ff 12 a7 33 f4 76 40  de d1 4b 41 ed 18 3b 04  |******@****.***..;.|
00000260  06 32 6e f3 57 c6 be 72  58 7f 78 b7 91 65 00 a8  |.2n.W..rX.x..e..|
00000270  8d 5c 7f ff 0a 62 d4 99  82 b2 6b c8 80 3e 89 30  |.\...b....k..>.0|
00000280  dd 31 60 7a 00 6e a2 13  c7 58 08 b0 d5 32 03 2e  |.1`z.n...X...2..|

00000090  f7 0d 01 01 01 05 00 03  81 8d 00 30 81 89 02 81  |...........0....|
000000a0  81 00 ba 6f aa 86 bd cf  bf 9f f2 ef 5c 94 60 78  |...o........\.`x|
000000b0  6f e8 13 f2 d1 96 6f cd  d9 32 6e 22 37 ce 41 f9  |o.....o..2n"7.A.|
000000c0  ca 5d 29 ac e1 27 da 61  a2 ee 81 cb 10 c7 df 34  |.])..'.a.......4|
000000d0  58 95 86 e9 3d 19 e6 5c  27 73 60 c8 8d 78 02 f4  |X...=..\'s`..x..|

	// values operations with respect to overflow/wrap around:
	//
	// > For unsigned integer values, the operations +, -, *, and << are
	// > computed modulo 2n, where n is the bit width of the unsigned
	// > integer's type. Loosely speaking, these unsigned integer operations
	// > discard high bits upon overflow, and programs may rely on ``wrap
	// > around''.
	//

00000090  f7 0d 01 01 01 05 00 03  81 8d 00 30 81 89 02 81  |...........0....|
000000a0  81 00 ba 6f aa 86 bd cf  bf 9f f2 ef 5c 94 60 78  |...o........\.`x|
000000b0  6f e8 13 f2 d1 96 6f cd  d9 32 6e 22 37 ce 41 f9  |o.....o..2n"7.A.|
000000c0  ca 5d 29 ac e1 27 da 61  a2 ee 81 cb 10 c7 df 34  |.])..'.a.......4|
000000d0  58 95 86 e9 3d 19 e6 5c  27 73 60 c8 8d 78 02 f4  |X...=..\'s`..x..|