Metallic ratios: Difference between revisions
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=={{header|Go}}==
<lang go>package main
import (
"fmt"
"math/big"
)
var names = [10]string{"Platinum", "Golden", "Silver", "Bronze", "Copper",
"Nickel", "Aluminium", "Iron", "Tin", "Lead"}
func lucas(b int64) {
fmt.Printf("Lucas sequence for %s ratio, where b = %d:\n", names[b], b)
fmt.Print("First 15 elements: ")
var x0, x1 int64 = 1, 1
fmt.Printf("%d, %d", x0, x1)
for i := 1; i <= 13; i++ {
x2 := b*x1 + x0
fmt.Printf(", %d", x2)
x0, x1 = x1, x2
}
fmt.Println()
}
func metallic(b int64) {
lucas(b)
x0, x1, x2, bb := big.NewInt(1), big.NewInt(1), big.NewInt(0), big.NewInt(b)
ratio := big.NewRat(1, 1)
iters := 0
prev := ratio.FloatString(32)
for {
iters++
x2.Mul(bb, x1)
x2.Add(x2, x0)
this := ratio.SetFrac(x2, x1).FloatString(32)
if prev == this {
plural := "s"
if iters == 1 {
plural = " "
}
fmt.Printf("Value to 32 dp after %2d iteration%s: %s\n\n", iters, plural, this)
return
}
prev = this
x0.Set(x1)
x1.Set(x2)
}
}
func main() {
for b := int64(0); b < 10; b++ {
metallic(b)
}
}</lang>
{{out}}
<pre>
First 15 elements: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Value to 32 dp after 1 iteration : 1.00000000000000000000000000000000
Lucas sequence for Golden ratio, where b = 1:
First 15 elements: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610
Value to 32 dp after 78 iterations: 1.61803398874989484820458683436564
Lucas sequence for Silver ratio, where b = 2:
First 15 elements: 1, 1, 3, 7, 17, 41, 99, 239, 577, 1393, 3363, 8119, 19601, 47321, 114243
Value to 32 dp after 44 iterations: 2.41421356237309504880168872420970
Lucas sequence for Bronze ratio, where b = 3:
First 15 elements: 1, 1, 4, 13, 43, 142, 469, 1549, 5116, 16897, 55807, 184318, 608761, 2010601, 6640564
Value to 32 dp after 34 iterations: 3.30277563773199464655961063373525
Lucas sequence for Copper ratio, where b = 4:
First 15 elements: 1, 1, 5, 21, 89, 377, 1597, 6765, 28657, 121393, 514229, 2178309, 9227465, 39088169, 165580141
Value to 32 dp after 28 iterations: 4.23606797749978969640917366873128
Lucas sequence for Nickel ratio, where b = 5:
First 15 elements: 1, 1, 6, 31, 161, 836, 4341, 22541, 117046, 607771, 3155901, 16387276, 85092281, 441848681, 2294335686
Value to 32 dp after 25 iterations: 5.19258240356725201562535524577016
Lucas sequence for Aluminium ratio, where b = 6:
First 15 elements: 1, 1, 7, 43, 265, 1633, 10063, 62011, 382129, 2354785, 14510839, 89419819, 551029753, 3395598337, 20924619775
Value to 32 dp after 23 iterations: 6.16227766016837933199889354443272
Lucas sequence for Iron ratio, where b = 7:
First 15 elements: 1, 1, 8, 57, 407, 2906, 20749, 148149, 1057792, 7552693, 53926643, 385039194, 2749201001, 19629446201, 140155324408
Value to 32 dp after 22 iterations: 7.14005494464025913554865124576352
Lucas sequence for Tin ratio, where b = 8:
First 15 elements: 1, 1, 9, 73, 593, 4817, 39129, 317849, 2581921, 20973217, 170367657, 1383914473, 11241683441, 91317382001, 741780739449
Value to 32 dp after 20 iterations: 8.12310562561766054982140985597408
Lucas sequence for Lead ratio, where b = 9:
First 15 elements: 1, 1, 10, 91, 829, 7552, 68797, 626725, 5709322, 52010623, 473804929, 4316254984, 39320099785, 358197153049, 3263094477226
Value to 32 dp after 20 iterations: 9.10977222864644365500113714088140
</pre>
=={{header|Perl 6}}==
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