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<?php |
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namespace DataValues; |
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use InvalidArgumentException; |
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/** |
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* Class for performing basic arithmetic and other transformations |
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* on DecimalValues. |
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* |
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* This uses the bcmath library if available. Otherwise, it falls back on |
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* using floating point operations. |
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* |
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* @note: this is not a genuine decimal arithmetics implementation, |
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* and should not be used for financial computations, physical simulations, etc. |
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* |
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* @see DecimalValue |
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* |
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* @since 0.1 |
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* |
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* @license GPL-2.0+ |
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* @author Daniel Kinzler |
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*/ |
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class DecimalMath { |
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/** |
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* Whether to use the bcmath library. |
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* |
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* @var bool |
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*/ |
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private $useBC; |
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/** |
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* @param bool|null $useBC Whether to use the bcmath library. If null, |
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* bcmath will automatically be used if available. |
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*/ |
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public function __construct( $useBC = null ) { |
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if ( $useBC === null ) { |
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$useBC = function_exists( 'bcscale' ); |
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} |
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$this->useBC = $useBC; |
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} |
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/** |
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* Whether this is using the bcmath library. |
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* |
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* @return bool |
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*/ |
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public function getUseBC() { |
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return $this->useBC; |
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} |
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/** |
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* @param DecimalValue $a |
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* @param DecimalValue $b |
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* |
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* @return DecimalValue |
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*/ |
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public function product( DecimalValue $a, DecimalValue $b ) { |
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if ( $this->useBC ) { |
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return $this->productWithBC( $a, $b ); |
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} |
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return $this->productWithoutBC( $a, $b ); |
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} |
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/** |
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* @param DecimalValue $a |
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* @param DecimalValue $b |
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* |
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* @return DecimalValue |
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*/ |
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private function productWithBC( DecimalValue $a, DecimalValue $b ) { |
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$scale = strlen( $a->getFractionalPart() ) + strlen( $b->getFractionalPart() ); |
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$product = bcmul( $a->getValue(), $b->getValue(), $scale ); |
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$sign = $product[0] === '-' ? '' : '+'; |
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// (Potentially) round so that the result fits into a DecimalValue |
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// Note: Product might still be to long if a*b >= 10^126 |
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$product = $this->roundDigits( $sign . $product, 126 ); |
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return new DecimalValue( $product ); |
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} |
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/** |
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* @param DecimalValue $a |
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* @param DecimalValue $b |
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* |
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* @return DecimalValue |
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*/ |
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private function productWithoutBC( DecimalValue $a, DecimalValue $b ) { |
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$product = $a->getValueFloat() * $b->getValueFloat(); |
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// Append .0 for consistency, if the result is a whole number, |
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// but $a or $b were specified with decimal places. |
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if ( |
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$product === floor( $product ) && |
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$a->getFractionalPart() . $b->getFractionalPart() !== '' |
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) { |
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$product = strval( $product ) . '.0'; |
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} |
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return new DecimalValue( $product ); |
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} |
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/** |
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* @param DecimalValue $a |
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* @param DecimalValue $b |
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* |
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* @return DecimalValue |
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*/ |
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public function sum( DecimalValue $a, DecimalValue $b ) { |
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if ( $this->useBC ) { |
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$scale = max( strlen( $a->getFractionalPart() ), strlen( $b->getFractionalPart() ) ); |
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$sum = bcadd( $a->getValue(), $b->getValue(), $scale ); |
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} else { |
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$sum = $a->getValueFloat() + $b->getValueFloat(); |
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} |
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return new DecimalValue( $sum ); |
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} |
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/** |
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* @param DecimalValue $a |
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* @param DecimalValue $b |
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* |
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* @return DecimalValue |
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*/ |
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public function min( DecimalValue $a, DecimalValue $b ) { |
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if ( $this->useBC ) { |
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$scale = max( strlen( $a->getFractionalPart() ), strlen( $b->getFractionalPart() ) ); |
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$comp = bccomp( $a->getValue(), $b->getValue(), $scale ); |
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$min = $comp > 0 ? $b : $a; |
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} else { |
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$min = min( $a->getValueFloat(), $b->getValueFloat() ); |
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$min = new DecimalValue( $min ); |
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} |
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return $min; |
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} |
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/** |
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* @param DecimalValue $a |
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* @param DecimalValue $b |
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* |
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* @return DecimalValue |
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*/ |
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public function max( DecimalValue $a, DecimalValue $b ) { |
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if ( $this->useBC ) { |
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$scale = max( strlen( $a->getFractionalPart() ), strlen( $b->getFractionalPart() ) ); |
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$comp = bccomp( $a->getValue(), $b->getValue(), $scale ); |
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$max = $comp > 0 ? $a : $b; |
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} else { |
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$max = max( $a->getValueFloat(), $b->getValueFloat() ); |
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$max = new DecimalValue( $max ); |
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} |
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return $max; |
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} |
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/** |
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* Returns the given value, with any insignificant digits removed or zeroed. |
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* |
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* Rounding is applied using the "round half away from zero" rule (that is, +0.5 is |
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* rounded to +1 and -0.5 is rounded to -1). |
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* |
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* @since 0.1 |
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* |
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* @param DecimalValue $decimal |
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* @param int $significantDigits The number of digits to retain, counting the decimal point, |
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* but not counting the leading sign. |
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* |
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* @throws InvalidArgumentException |
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* @return DecimalValue |
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*/ |
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public function roundToDigit( DecimalValue $decimal, $significantDigits ) { |
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$value = $decimal->getValue(); |
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$rounded = $this->roundDigits( $value, $significantDigits ); |
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return new DecimalValue( $rounded ); |
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} |
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/** |
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* Returns the given value, with any insignificant digits removed or zeroed. |
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* |
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* Rounding is applied using the "round half away from zero" rule (that is, +0.5 is |
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* rounded to +1 and -0.5 is rounded to -1). |
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* |
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* @since 0.1 |
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* |
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* @param DecimalValue $decimal |
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* @param int $significantExponent The exponent of the last significant digit, |
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* e.g. -1 for "keep the first digit after the decimal point", or 2 for |
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* "zero the last two digits before the decimal point". |
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* |
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* @throws InvalidArgumentException |
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* @return DecimalValue |
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*/ |
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public function roundToExponent( DecimalValue $decimal, $significantExponent ) { |
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//NOTE: the number of digits to keep (without the leading sign) |
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// is the same as the exponent's offset (with the leaqding sign). |
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$digits = $this->getPositionForExponent( $significantExponent, $decimal ); |
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return $this->roundToDigit( $decimal, $digits ); |
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} |
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/** |
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* Returns the (zero based) position for the given exponent in |
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* the given decimal string, counting the decimal point and the leading sign. |
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* |
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* @example: the position of exponent 0 in "+10.03" is 2. |
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* @example: the position of exponent 1 in "+210.03" is 2. |
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* @example: the position of exponent -2 in "+1.037" is 4. |
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* |
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* @param int $exponent |
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* @param DecimalValue $decimal |
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* |
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* @return int |
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*/ |
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public function getPositionForExponent( $exponent, DecimalValue $decimal ) { |
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$decimal = $decimal->getValue(); |
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$pointPos = strpos( $decimal, '.' ); |
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if ( $pointPos === false ) { |
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$pointPos = strlen( $decimal ); |
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} |
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// account for leading sign |
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$pointPos--; |
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if ( $exponent < 0 ) { |
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// account for decimal point |
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$position = $pointPos + 1 - $exponent; |
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} else { |
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// make sure we don't remove more digits than are there |
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$position = max( 0, $pointPos - $exponent ); |
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} |
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return $position; |
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} |
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/** |
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* Returns the given value, with any insignificant digits removed or zeroed. |
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* |
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* Rounding is applied using the "round half away from zero" rule (that is, +0.5 is |
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* rounded to +1 and -0.5 is rounded to -1). |
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* |
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* @see round() |
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* |
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* @param string $value |
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* @param int $significantDigits |
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* |
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* @throws InvalidArgumentException if $significantDigits is smaller than 0 |
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* @return string |
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*/ |
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private function roundDigits( $value, $significantDigits ) { |
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if ( !is_int( $significantDigits ) || $significantDigits < 0 ) { |
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throw new InvalidArgumentException( '$significantDigits must be a non-negative integer' ); |
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} |
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// keeping no digits results in zero. |
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if ( $significantDigits === 0 ) { |
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return '+0'; |
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} |
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$len = strlen( $value ); |
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// keeping all digits means no rounding |
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if ( $significantDigits >= $len - 1 ) { |
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return $value; |
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} |
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// whether the last character is already part of the integer part of the decimal value |
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$i = min( $significantDigits + 1, $len ); // account for the sign |
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$ch = $i < $len ? $value[$i] : '0'; |
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if ( $ch === '.' ) { |
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// NOTE: we expect the input to be well formed, so it cannot end with a '.' |
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$i++; |
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$ch = $i < $len ? $value[$i] : '0'; |
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} |
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// split in significant and insignificant part |
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$rounded = substr( $value, 0, $i ); |
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if ( strpos( $rounded, '.' ) === false ) { |
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$suffix = substr( $value, $i ); |
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// strip insignificant digits after the decimal point |
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$ppos = strpos( $suffix, '.' ); |
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if ( $ppos !== false ) { |
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$suffix = substr( $suffix, 0, $ppos ); |
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} |
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// zero out insignificant digits |
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$suffix = strtr( $suffix, '123456789', '000000000' ); |
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} else { |
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// decimal point is in $rounded, so $suffix is insignificant |
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$suffix = ''; |
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} |
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if ( $ch >= '5' ) { |
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$rounded = $this->bumpDigits( $rounded ); |
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} |
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$rounded .= $suffix; |
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if ( $significantDigits > strlen( $rounded ) - 1 ) { |
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if ( strpos( $rounded, '.' ) !== false ) { |
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$rounded = str_pad( $rounded, $significantDigits + 1, '0', STR_PAD_RIGHT ); |
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} |
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} |
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// strip trailing decimal point |
314
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$rounded = rtrim( $rounded, '.' ); |
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return $rounded; |
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} |
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/** |
320
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* Increment the least significant digit by one if it is less than 9, and |
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* set it to zero and continue to the next more significant digit if it is 9. |
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* Exception: bump( 0 ) == 1; |
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* |
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* E.g.: bump( 0.2 ) == 0.3, bump( -0.09 ) == -0.10, bump( 9.99 ) == 10.00 |
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* |
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* This is the inverse of @see slump() |
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* |
328
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* @since 0.1 |
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* |
330
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* @param DecimalValue $decimal |
331
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* |
332
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* @return DecimalValue |
333
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*/ |
334
|
16 |
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public function bump( DecimalValue $decimal ) { |
335
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16 |
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$value = $decimal->getValue(); |
336
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16 |
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$bumped = $this->bumpDigits( $value ); |
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return new DecimalValue( $bumped ); |
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} |
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340
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/** |
341
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* Increment the least significant digit by one if it is less than 9, and |
342
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* set it to zero and continue to the next more significant digit if it is 9. |
343
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* |
344
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* @see bump() |
345
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* |
346
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* @param string $value |
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* @return string |
348
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*/ |
349
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43 |
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private function bumpDigits( $value ) { |
350
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43 |
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if ( $value === '+0' ) { |
351
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return '+1'; |
352
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} |
353
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354
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41 |
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$bumped = ''; |
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356
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for ( $i = strlen( $value ) - 1; $i >= 0; $i-- ) { |
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41 |
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$ch = $value[$i]; |
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359
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41 |
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if ( $ch === '.' ) { |
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$bumped = '.' . $bumped; |
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continue; |
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} elseif ( $ch === '9' ) { |
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$bumped = '0' . $bumped; |
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continue; |
365
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41 |
|
} elseif ( $ch === '+' || $ch === '-' ) { |
366
|
14 |
|
$bumped = $ch . '1' . $bumped; |
367
|
14 |
|
break; |
368
|
|
|
} else { |
369
|
27 |
|
$bumped = chr( ord( $ch ) + 1 ) . $bumped; |
370
|
27 |
|
break; |
371
|
|
|
} |
372
|
|
|
} |
373
|
|
|
|
374
|
41 |
|
$bumped = substr( $value, 0, $i ) . $bumped; |
375
|
41 |
|
return $bumped; |
376
|
|
|
} |
377
|
|
|
|
378
|
|
|
/** |
379
|
|
|
* Decrement the least significant digit by one if it is more than 0, and |
380
|
|
|
* set it to 9 and continue to the next more significant digit if it is 0. |
381
|
|
|
* Exception: slump( 0 ) == -1; |
382
|
|
|
* |
383
|
|
|
* E.g.: slump( 0.2 ) == 0.1, slump( -0.10 ) == -0.01, slump( 0.0 ) == -1.0 |
384
|
|
|
* |
385
|
|
|
* This is the inverse of @see bump() |
386
|
|
|
* |
387
|
|
|
* @since 0.1 |
388
|
|
|
* |
389
|
|
|
* @param DecimalValue $decimal |
390
|
|
|
* |
391
|
|
|
* @return DecimalValue |
392
|
|
|
*/ |
393
|
24 |
|
public function slump( DecimalValue $decimal ) { |
394
|
24 |
|
$value = $decimal->getValue(); |
395
|
24 |
|
$slumped = $this->slumpDigits( $value ); |
396
|
24 |
|
return new DecimalValue( $slumped ); |
397
|
|
|
} |
398
|
|
|
|
399
|
|
|
/** |
400
|
|
|
* Decrement the least significant digit by one if it is more than 0, and |
401
|
|
|
* set it to 9 and continue to the next more significant digit if it is 0. |
402
|
|
|
* |
403
|
|
|
* @see slump() |
404
|
|
|
* |
405
|
|
|
* @param string $value |
406
|
|
|
* @return string |
407
|
|
|
*/ |
408
|
24 |
|
private function slumpDigits( $value ) { |
409
|
24 |
|
if ( $value === '+0' ) { |
410
|
2 |
|
return '-1'; |
411
|
|
|
} |
412
|
|
|
|
413
|
|
|
// a "precise zero" will become negative |
414
|
22 |
|
if ( preg_match( '/^\+0\.(0*)0$/', $value, $m ) ) { |
415
|
4 |
|
return '-0.' . $m[1] . '1'; |
416
|
|
|
} |
417
|
|
|
|
418
|
18 |
|
$slumped = ''; |
419
|
|
|
|
420
|
18 |
|
for ( $i = strlen( $value ) - 1; $i >= 0; $i-- ) { |
421
|
18 |
|
$ch = substr( $value, $i, 1 ); |
422
|
|
|
|
423
|
18 |
|
if ( $ch === '.' ) { |
424
|
2 |
|
$slumped = '.' . $slumped; |
425
|
2 |
|
continue; |
426
|
18 |
|
} elseif ( $ch === '0' ) { |
427
|
8 |
|
$slumped = '9' . $slumped; |
428
|
8 |
|
continue; |
429
|
18 |
|
} elseif ( $ch === '+' || $ch === '-' ) { |
430
|
|
|
$slumped = '0'; |
431
|
|
|
break; |
432
|
|
|
} else { |
433
|
18 |
|
$slumped = chr( ord( $ch ) - 1 ) . $slumped; |
434
|
18 |
|
break; |
435
|
|
|
} |
436
|
|
|
} |
437
|
|
|
|
438
|
|
|
// preserve prefix |
439
|
18 |
|
$slumped = substr( $value, 0, $i ) . $slumped; |
440
|
18 |
|
$slumped = $this->stripLeadingZeros( $slumped ); |
441
|
|
|
|
442
|
18 |
|
if ( $slumped === '-0' ) { |
443
|
1 |
|
$slumped = '+0'; |
444
|
|
|
} |
445
|
|
|
|
446
|
18 |
|
return $slumped; |
447
|
|
|
} |
448
|
|
|
|
449
|
|
|
/** |
450
|
|
|
* @param string $digits |
451
|
|
|
* |
452
|
|
|
* @return string |
453
|
|
|
*/ |
454
|
40 |
|
private function stripLeadingZeros( $digits ) { |
455
|
40 |
|
$digits = preg_replace( '/^([-+])0+(?=\d)/', '\1', $digits ); |
456
|
40 |
|
return $digits; |
457
|
|
|
} |
458
|
|
|
|
459
|
|
|
/** |
460
|
|
|
* Shift the decimal point according to the given exponent. |
461
|
|
|
* |
462
|
|
|
* @param DecimalValue $decimal |
463
|
|
|
* @param int $exponent The exponent to apply (digits to shift by). A Positive exponent |
464
|
|
|
* shifts the decimal point to the right, a negative exponent shifts to the left. |
465
|
|
|
* |
466
|
|
|
* @throws InvalidArgumentException |
467
|
|
|
* @return DecimalValue |
468
|
|
|
*/ |
469
|
26 |
|
public function shift( DecimalValue $decimal, $exponent ) { |
470
|
26 |
|
if ( !is_int( $exponent ) ) { |
471
|
|
|
throw new InvalidArgumentException( '$exponent must be an integer' ); |
472
|
|
|
} |
473
|
|
|
|
474
|
26 |
|
if ( $exponent == 0 ) { |
475
|
4 |
|
return $decimal; |
476
|
|
|
} |
477
|
|
|
|
478
|
22 |
|
$sign = $decimal->getSign(); |
479
|
22 |
|
$intPart = $decimal->getIntegerPart(); |
480
|
22 |
|
$fractPart = $decimal->getFractionalPart(); |
481
|
|
|
|
482
|
22 |
|
if ( $exponent < 0 ) { |
483
|
14 |
|
$intPart = $this->shiftLeft( $intPart, $exponent ); |
484
|
|
|
} else { |
485
|
8 |
|
$fractPart = $this->shiftRight( $fractPart, $exponent ); |
486
|
|
|
} |
487
|
|
|
|
488
|
22 |
|
$digits = $sign . $intPart . $fractPart; |
489
|
22 |
|
$digits = $this->stripLeadingZeros( $digits ); |
490
|
|
|
|
491
|
22 |
|
return new DecimalValue( $digits ); |
492
|
|
|
} |
493
|
|
|
|
494
|
|
|
/** |
495
|
|
|
* @param string $intPart |
496
|
|
|
* @param int $exponent must be negative |
497
|
|
|
* |
498
|
|
|
* @return string |
499
|
|
|
*/ |
500
|
14 |
|
private function shiftLeft( $intPart, $exponent ) { |
501
|
|
|
//note: $exponent is negative! |
502
|
14 |
|
if ( -$exponent < strlen( $intPart ) ) { |
503
|
2 |
|
$intPart = substr( $intPart, 0, $exponent ) . '.' . substr( $intPart, $exponent ); |
504
|
|
|
} else { |
505
|
12 |
|
$intPart = '0.' . str_pad( $intPart, -$exponent, '0', STR_PAD_LEFT ); |
506
|
|
|
} |
507
|
|
|
|
508
|
14 |
|
return $intPart; |
509
|
|
|
} |
510
|
|
|
|
511
|
|
|
/** |
512
|
|
|
* @param string $fractPart |
513
|
|
|
* @param int $exponent must be positive |
514
|
|
|
* |
515
|
|
|
* @return string |
516
|
|
|
*/ |
517
|
8 |
|
private function shiftRight( $fractPart, $exponent ) { |
518
|
|
|
//note: $exponent is positive. |
519
|
8 |
|
if ( $exponent < strlen( $fractPart ) ) { |
520
|
|
|
$fractPart = substr( $fractPart, 0, $exponent ) . '.' . substr( $fractPart, $exponent ); |
521
|
|
|
} else { |
522
|
8 |
|
$fractPart = str_pad( $fractPart, $exponent, '0', STR_PAD_RIGHT ); |
523
|
|
|
} |
524
|
|
|
|
525
|
8 |
|
return $fractPart; |
526
|
|
|
} |
527
|
|
|
|
528
|
|
|
} |
529
|
|
|
|