Metallic ratios: Difference between revisions
Content added Content deleted
m (→{{header|zkl}}: tweak) |
(Added Go) |
||
Line 146: | Line 146: | ||
=={{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}}== |
=={{header|Perl 6}}== |