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Commit 29a567f

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castarcocastarco
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Merge pull request #18 from stefanmajoor/trigo
Added Sin, Cos and Tan, by @stefanmajoor .
2 parents 1d39411 + 75ba941 commit 29a567f

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‎src/Decimal.php

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@@ -633,6 +633,123 @@ public function mod(Decimal $d, $scale = null)
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return $this->sub($div->mul($d, $scale));
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}
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/**
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* Calculates the sine of this method with the highest possible accuracy
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* Note that accuracy is limited by the accuracy of predefined PI;
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*
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* @param null $scale
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* @return Decimal sin($this)
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*/
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public function sin($scale = null) {
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// First normalise the number in the [0, 2PI] domain
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$twoPi = NumConstants::PI()->mul(Decimal::fromString("2"));
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$x = $this->mod($twoPi);
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$zero = Decimal::fromString("0");
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// PI has only 32 siginficant numbers
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$significantNumbers = is_null($scale) ? 32 : $scale;
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// Next use Maclaurin's theorem to approximate sin with high enough accuracy
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// note that the accuracy is depended on the accuracy of the given PI constant
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$faculty = Decimal::fromString("1"); // Calculates the faculty under the sign
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$loopCounter = 1; // Calculates the iteration we are in
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$xPowerN = Decimal::fromString("1"); // Calculates x^n
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$approx = Decimal::fromString("0"); // keeps track of our approximation for sin(x)
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while (true) {
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// update x^n and n! for this walkthrough
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$xPowerN = $xPowerN->mul($x);
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$faculty = $faculty->mul(Decimal::fromString((string) $loopCounter));
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// only do calculations if n is uneven
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// otherwise result is zero anyways
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if ($loopCounter % 2 === 1) {
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// calculate the absolute change in this iteration.
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$change = $xPowerN->div($faculty);
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// change should be added if x mod 4 == 1 and subtracted if x mod 4 == 3
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if ($loopCounter % 4 === 1) {
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$approx = $approx->add($change);
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} else {
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$approx = $approx->sub($change);
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}
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// Terminate the method if our change is sufficiently small
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if ($change->floor($significantNumbers)->equals($zero)) {
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return $approx->round($significantNumbers);
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}
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}
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$loopCounter++;
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}
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}
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/**
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* Calculates the cosine of this method with the highest possible accuracy
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* Note that accuracy is limited by the accuracy of predefined PI;
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*
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* @param null $scale
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* @return Decimal cos($this)
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*/
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public function cos($scale = null) {
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// First normalise the number in the [0, 2PI] domain
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$twoPi = NumConstants::PI()->mul(Decimal::fromString("2"));
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$x = $this->mod($twoPi);
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$zero = Decimal::fromString("0");
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// PI has only 32 siginficant numbers
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$significantNumbers = is_null($scale) ? 32 : $scale;
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// Next use Maclaurin's theorem to approximate sin with high enough accuracy
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// note that the accuracy is depended on the accuracy of the given PI constant
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$faculty = Decimal::fromString("1"); // Calculates the faculty under the sign
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$loopCounter = 1; // Calculates the iteration we are in
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$xPowerN = Decimal::fromString("1"); // Calculates x^n
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$approx = Decimal::fromString("1"); // keeps track of our approximation for sin(x)
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while (true) {
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// update x^n and n! for this walkthrough
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$xPowerN = $xPowerN->mul($x);
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$faculty = $faculty->mul(Decimal::fromString((string) $loopCounter));
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// only do calculations if n is uneven
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// otherwise result is zero anyways
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if ($loopCounter % 2 === 0) {
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// calculate the absolute change in this iteration.
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$change = $xPowerN->div($faculty);
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// change should be added if x mod 4 == 1 and subtracted if x mod 4 == 3
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if ($loopCounter % 4 === 0) {
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$approx = $approx->add($change);
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} else {
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$approx = $approx->sub($change);
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}
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// Terminate the method if our change is sufficiently small
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if ($change->floor($significantNumbers )->equals($zero)) {
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return $approx->round($significantNumbers);
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}
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}
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$loopCounter++;
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}
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}
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/**
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* Calculates the tangent of this method with the highest possible accuracy
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* Note that accuracy is limited by the accuracy of predefined PI;
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*
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* @param null $scale
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* @return Decimal tan($this)
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*/
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public function tan($scale = null) {
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return $this->sin($scale + 2)
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->div($this->cos($scale + 2))
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->floor($scale);
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}
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public function hasSameSign(Decimal $b) {
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return $this->isPositive() && $b->isPositive() || $this->isNegative() && $b->isNegative();
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}

‎tests/Decimal/DecimalCosTest.php

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<?php
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use Litipk\BigNumbers\Decimal as Decimal;
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/**
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* @group cos
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*/
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class DecimalCosTest extends PHPUnit_Framework_TestCase
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{
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public function cosProvider() {
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// Some values providede by mathematica
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return array(
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array('1', '0.54030230586814', '14'),
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array('123.123', '-0.82483472946164834', '17'),
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array('15000000000', '-0.72218064388924347681', '20')
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);
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}
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/**
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* @dataProvider cosProvider
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*/
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public function testSimple($nr, $answer, $digits)
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{
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$x = Decimal::fromString($nr);
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$cosX = $x->cos($digits);
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$this->assertTrue(Decimal::fromString($answer)->equals($cosX));
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}
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}

‎tests/Decimal/DecimalSinTest.php

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<?php
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use Litipk\BigNumbers\Decimal as Decimal;
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/**
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* @group sin
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*/
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class DecimalSinTest extends PHPUnit_Framework_TestCase
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{
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public function sinProvider() {
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// Some values providede by mathematica
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return array(
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array('1', '0.84147098480790', '14'),
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array('123.123', '-0.56537391969733569', '17'),
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array('15000000000', '0.69170450164193502844', '20')
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);
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}
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/**
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* @dataProvider sinProvider
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*/
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public function testSimple($nr, $answer, $digits)
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{
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$x = Decimal::fromString($nr);
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$sinX = $x->sin($digits);
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$this->assertTrue(Decimal::fromString($answer)->equals($sinX));
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}
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}

‎tests/Decimal/DecimalTanTest.php

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<?php
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use Litipk\BigNumbers\Decimal as Decimal;
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/**
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* @group tan
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*/
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class DecimalTanTest extends PHPUnit_Framework_TestCase
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{
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public function tanProvider() {
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// Some values providede by mathematica
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return array(
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array('1', '1.55740772465490', '14'),
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array('123.123', '0.68543903342472368', '17'),
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array('15000000000', '-0.95779983511717825557', '20')
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);
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}
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/**
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* @dataProvider tanProvider
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*/
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public function testSimple($nr, $answer, $digits)
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{
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$x = Decimal::fromString($nr);
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$tanX = $x->tan($digits);
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$this->assertTrue(Decimal::fromString($answer)->equals($tanX));
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}
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}

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