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<?php
namespace PhpOffice\PhpSpreadsheet\Calculation;
use Complex\Complex;
use Complex\Exception as ComplexException;
use PhpOffice\PhpSpreadsheet\Calculation\Engineering\ConvertUOM;
class Engineering
{
/**
* EULER.
*/
const EULER = 2.71828182845904523536;
/**
* parseComplex.
*
* Parses a complex number into its real and imaginary parts, and an I or J suffix
*
* @deprecated 2.0.0 No longer used by internal code. Please use the Complex\Complex class instead
*
* @param string $complexNumber The complex number
*
* @return mixed[] Indexed on "real", "imaginary" and "suffix"
*/
public static function parseComplex($complexNumber)
{
$complex = new Complex($complexNumber);
return [
'real' => $complex->getReal(),
'imaginary' => $complex->getImaginary(),
'suffix' => $complex->getSuffix(),
];
}
/**
* Formats a number base string value with leading zeroes.
*
* @param string $xVal The "number" to pad
* @param int $places The length that we want to pad this value
*
* @return string The padded "number"
*/
private static function nbrConversionFormat($xVal, $places)
{
if ($places !== null) {
if (is_numeric($places)) {
$places = (int) $places;
} else {
return Functions::VALUE();
}
if ($places < 0) {
return Functions::NAN();
}
if (strlen($xVal) <= $places) {
return substr(str_pad($xVal, $places, '0', STR_PAD_LEFT), -10);
}
return Functions::NAN();
}
return substr($xVal, -10);
}
/**
* BESSELI.
*
* Returns the modified Bessel function In(x), which is equivalent to the Bessel function evaluated
* for purely imaginary arguments
*
* Excel Function:
* BESSELI(x,ord)
*
* @param float $x The value at which to evaluate the function.
* If x is nonnumeric, BESSELI returns the #VALUE! error value.
* @param int $ord The order of the Bessel function.
* If ord is not an integer, it is truncated.
* If $ord is nonnumeric, BESSELI returns the #VALUE! error value.
* If $ord < 0, BESSELI returns the #NUM! error value.
*
* @return float|string Result, or a string containing an error
*/
public static function BESSELI($x, $ord)
{
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
if ((is_numeric($x)) && (is_numeric($ord))) {
$ord = floor($ord);
if ($ord < 0) {
return Functions::NAN();
}
if (abs($x) <= 30) {
$fResult = $fTerm = ($x / 2) ** $ord / MathTrig::FACT($ord);
$ordK = 1;
$fSqrX = ($x * $x) / 4;
do {
$fTerm *= $fSqrX;
$fTerm /= ($ordK * ($ordK + $ord));
$fResult += $fTerm;
} while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
} else {
$f_2_PI = 2 * M_PI;
$fXAbs = abs($x);
$fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs);
if (($ord & 1) && ($x < 0)) {
$fResult = -$fResult;
}
}
return (is_nan($fResult)) ? Functions::NAN() : $fResult;
}
return Functions::VALUE();
}
/**
* BESSELJ.
*
* Returns the Bessel function
*
* Excel Function:
* BESSELJ(x,ord)
*
* @param float $x The value at which to evaluate the function.
* If x is nonnumeric, BESSELJ returns the #VALUE! error value.
* @param int $ord The order of the Bessel function. If n is not an integer, it is truncated.
* If $ord is nonnumeric, BESSELJ returns the #VALUE! error value.
* If $ord < 0, BESSELJ returns the #NUM! error value.
*
* @return float|string Result, or a string containing an error
*/
public static function BESSELJ($x, $ord)
{
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
if ((is_numeric($x)) && (is_numeric($ord))) {
$ord = floor($ord);
if ($ord < 0) {
return Functions::NAN();
}
$fResult = 0;
if (abs($x) <= 30) {
$fResult = $fTerm = ($x / 2) ** $ord / MathTrig::FACT($ord);
$ordK = 1;
$fSqrX = ($x * $x) / -4;
do {
$fTerm *= $fSqrX;
$fTerm /= ($ordK * ($ordK + $ord));
$fResult += $fTerm;
} while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
} else {
$f_PI_DIV_2 = M_PI / 2;
$f_PI_DIV_4 = M_PI / 4;
$fXAbs = abs($x);
$fResult = sqrt(Functions::M_2DIVPI / $fXAbs) * cos($fXAbs - $ord * $f_PI_DIV_2 - $f_PI_DIV_4);
if (($ord & 1) && ($x < 0)) {
$fResult = -$fResult;
}
}
return (is_nan($fResult)) ? Functions::NAN() : $fResult;
}
return Functions::VALUE();
}
private static function besselK0($fNum)
{
if ($fNum <= 2) {
$fNum2 = $fNum * 0.5;
$y = ($fNum2 * $fNum2);
$fRet = -log($fNum2) * self::BESSELI($fNum, 0) +
(-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y *
(0.10750e-3 + $y * 0.74e-5))))));
} else {
$y = 2 / $fNum;
$fRet = exp(-$fNum) / sqrt($fNum) *
(1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y *
(0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3))))));
}
return $fRet;
}
private static function besselK1($fNum)
{
if ($fNum <= 2) {
$fNum2 = $fNum * 0.5;
$y = ($fNum2 * $fNum2);
$fRet = log($fNum2) * self::BESSELI($fNum, 1) +
(1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y *
(-0.110404e-2 + $y * (-0.4686e-4))))))) / $fNum;
} else {
$y = 2 / $fNum;
$fRet = exp(-$fNum) / sqrt($fNum) *
(1.25331414 + $y * (0.23498619 + $y * (-0.3655620e-1 + $y * (0.1504268e-1 + $y * (-0.780353e-2 + $y *
(0.325614e-2 + $y * (-0.68245e-3)))))));
}
return $fRet;
}
/**
* BESSELK.
*
* Returns the modified Bessel function Kn(x), which is equivalent to the Bessel functions evaluated
* for purely imaginary arguments.
*
* Excel Function:
* BESSELK(x,ord)
*
* @param float $x The value at which to evaluate the function.
* If x is nonnumeric, BESSELK returns the #VALUE! error value.
* @param int $ord The order of the Bessel function. If n is not an integer, it is truncated.
* If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
* If $ord < 0, BESSELK returns the #NUM! error value.
*
* @return float|string Result, or a string containing an error
*/
public static function BESSELK($x, $ord)
{
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
if ((is_numeric($x)) && (is_numeric($ord))) {
if (($ord < 0) || ($x == 0.0)) {
return Functions::NAN();
}
switch (floor($ord)) {
case 0:
$fBk = self::besselK0($x);
break;
case 1:
$fBk = self::besselK1($x);
break;
default:
$fTox = 2 / $x;
$fBkm = self::besselK0($x);
$fBk = self::besselK1($x);
for ($n = 1; $n < $ord; ++$n) {
$fBkp = $fBkm + $n * $fTox * $fBk;
$fBkm = $fBk;
$fBk = $fBkp;
}
}
return (is_nan($fBk)) ? Functions::NAN() : $fBk;
}
return Functions::VALUE();
}
private static function besselY0($fNum)
{
if ($fNum < 8.0) {
$y = ($fNum * $fNum);
$f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733))));
$f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y))));
$fRet = $f1 / $f2 + 0.636619772 * self::BESSELJ($fNum, 0) * log($fNum);
} else {
$z = 8.0 / $fNum;
$y = ($z * $z);
$xx = $fNum - 0.785398164;
$f1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
$f2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7))));
$fRet = sqrt(0.636619772 / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
}
return $fRet;
}
private static function besselY1($fNum)
{
if ($fNum < 8.0) {
$y = ($fNum * $fNum);
$f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y *
(-0.4237922726e7 + $y * 0.8511937935e4)))));
$f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
(0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
$fRet = $f1 / $f2 + 0.636619772 * (self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
} else {
$fRet = sqrt(0.636619772 / $fNum) * sin($fNum - 2.356194491);
}
return $fRet;
}
/**
* BESSELY.
*
* Returns the Bessel function, which is also called the Weber function or the Neumann function.
*
* Excel Function:
* BESSELY(x,ord)
*
* @param float $x The value at which to evaluate the function.
* If x is nonnumeric, BESSELK returns the #VALUE! error value.
* @param int $ord The order of the Bessel function. If n is not an integer, it is truncated.
* If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
* If $ord < 0, BESSELK returns the #NUM! error value.
*
* @return float|string Result, or a string containing an error
*/
public static function BESSELY($x, $ord)
{
$x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
$ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
if ((is_numeric($x)) && (is_numeric($ord))) {
if (($ord < 0) || ($x == 0.0)) {
return Functions::NAN();
}
switch (floor($ord)) {
case 0:
$fBy = self::besselY0($x);
break;
case 1:
$fBy = self::besselY1($x);
break;
default:
$fTox = 2 / $x;
$fBym = self::besselY0($x);
$fBy = self::besselY1($x);
for ($n = 1; $n < $ord; ++$n) {
$fByp = $n * $fTox * $fBy - $fBym;
$fBym = $fBy;
$fBy = $fByp;
}
}
return (is_nan($fBy)) ? Functions::NAN() : $fBy;
}
return Functions::VALUE();
}
/**
* BINTODEC.
*
* Return a binary value as decimal.
*
* Excel Function:
* BIN2DEC(x)
*
* @param string $x The binary number (as a string) that you want to convert. The number
* cannot contain more than 10 characters (10 bits). The most significant
* bit of number is the sign bit. The remaining 9 bits are magnitude bits.
* Negative numbers are represented using two's-complement notation.
* If number is not a valid binary number, or if number contains more than
* 10 characters (10 bits), BIN2DEC returns the #NUM! error value.
*
* @return string
*/
public static function BINTODEC($x)
{
$x = Functions::flattenSingleValue($x);
if (is_bool($x)) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return Functions::VALUE();
}
}
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
$x = floor($x);
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
return Functions::NAN();
}
if (strlen($x) > 10) {
return Functions::NAN();
} elseif (strlen($x) == 10) {
// Two's Complement
$x = substr($x, -9);
return '-' . (512 - bindec($x));
}
return bindec($x);
}
/**
* BINTOHEX.
*
* Return a binary value as hex.
*
* Excel Function:
* BIN2HEX(x[,places])
*
* @param string $x The binary number (as a string) that you want to convert. The number
* cannot contain more than 10 characters (10 bits). The most significant
* bit of number is the sign bit. The remaining 9 bits are magnitude bits.
* Negative numbers are represented using two's-complement notation.
* If number is not a valid binary number, or if number contains more than
* 10 characters (10 bits), BIN2HEX returns the #NUM! error value.
* @param int $places The number of characters to use. If places is omitted, BIN2HEX uses the
* minimum number of characters necessary. Places is useful for padding the
* return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, BIN2HEX returns the #VALUE! error value.
* If places is negative, BIN2HEX returns the #NUM! error value.
*
* @return string
*/
public static function BINTOHEX($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
// Argument X
if (is_bool($x)) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return Functions::VALUE();
}
}
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
$x = floor($x);
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
return Functions::NAN();
}
if (strlen($x) > 10) {
return Functions::NAN();
} elseif (strlen($x) == 10) {
// Two's Complement
return str_repeat('F', 8) . substr(strtoupper(dechex(bindec(substr($x, -9)))), -2);
}
$hexVal = (string) strtoupper(dechex(bindec($x)));
return self::nbrConversionFormat($hexVal, $places);
}
/**
* BINTOOCT.
*
* Return a binary value as octal.
*
* Excel Function:
* BIN2OCT(x[,places])
*
* @param string $x The binary number (as a string) that you want to convert. The number
* cannot contain more than 10 characters (10 bits). The most significant
* bit of number is the sign bit. The remaining 9 bits are magnitude bits.
* Negative numbers are represented using two's-complement notation.
* If number is not a valid binary number, or if number contains more than
* 10 characters (10 bits), BIN2OCT returns the #NUM! error value.
* @param int $places The number of characters to use. If places is omitted, BIN2OCT uses the
* minimum number of characters necessary. Places is useful for padding the
* return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, BIN2OCT returns the #VALUE! error value.
* If places is negative, BIN2OCT returns the #NUM! error value.
*
* @return string
*/
public static function BINTOOCT($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return Functions::VALUE();
}
}
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
$x = floor($x);
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
return Functions::NAN();
}
if (strlen($x) > 10) {
return Functions::NAN();
} elseif (strlen($x) == 10) {
// Two's Complement
return str_repeat('7', 7) . substr(strtoupper(decoct(bindec(substr($x, -9)))), -3);
}
$octVal = (string) decoct(bindec($x));
return self::nbrConversionFormat($octVal, $places);
}
/**
* DECTOBIN.
*
* Return a decimal value as binary.
*
* Excel Function:
* DEC2BIN(x[,places])
*
* @param string $x The decimal integer you want to convert. If number is negative,
* valid place values are ignored and DEC2BIN returns a 10-character
* (10-bit) binary number in which the most significant bit is the sign
* bit. The remaining 9 bits are magnitude bits. Negative numbers are
* represented using two's-complement notation.
* If number < -512 or if number > 511, DEC2BIN returns the #NUM! error
* value.
* If number is nonnumeric, DEC2BIN returns the #VALUE! error value.
* If DEC2BIN requires more than places characters, it returns the #NUM!
* error value.
* @param int $places The number of characters to use. If places is omitted, DEC2BIN uses
* the minimum number of characters necessary. Places is useful for
* padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, DEC2BIN returns the #VALUE! error value.
* If places is zero or negative, DEC2BIN returns the #NUM! error value.
*
* @return string
*/
public static function DECTOBIN($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return Functions::VALUE();
}
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
return Functions::VALUE();
}
$x = (string) floor($x);
if ($x < -512 || $x > 511) {
return Functions::NAN();
}
$r = decbin($x);
// Two's Complement
$r = substr($r, -10);
if (strlen($r) >= 11) {
return Functions::NAN();
}
return self::nbrConversionFormat($r, $places);
}
/**
* DECTOHEX.
*
* Return a decimal value as hex.
*
* Excel Function:
* DEC2HEX(x[,places])
*
* @param string $x The decimal integer you want to convert. If number is negative,
* places is ignored and DEC2HEX returns a 10-character (40-bit)
* hexadecimal number in which the most significant bit is the sign
* bit. The remaining 39 bits are magnitude bits. Negative numbers
* are represented using two's-complement notation.
* If number < -549,755,813,888 or if number > 549,755,813,887,
* DEC2HEX returns the #NUM! error value.
* If number is nonnumeric, DEC2HEX returns the #VALUE! error value.
* If DEC2HEX requires more than places characters, it returns the
* #NUM! error value.
* @param int $places The number of characters to use. If places is omitted, DEC2HEX uses
* the minimum number of characters necessary. Places is useful for
* padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, DEC2HEX returns the #VALUE! error value.
* If places is zero or negative, DEC2HEX returns the #NUM! error value.
*
* @return string
*/
public static function DECTOHEX($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return Functions::VALUE();
}
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
return Functions::VALUE();
}
$x = (string) floor($x);
$r = strtoupper(dechex($x));
if (strlen($r) == 8) {
// Two's Complement
$r = 'FF' . $r;
}
return self::nbrConversionFormat($r, $places);
}
/**
* DECTOOCT.
*
* Return an decimal value as octal.
*
* Excel Function:
* DEC2OCT(x[,places])
*
* @param string $x The decimal integer you want to convert. If number is negative,
* places is ignored and DEC2OCT returns a 10-character (30-bit)
* octal number in which the most significant bit is the sign bit.
* The remaining 29 bits are magnitude bits. Negative numbers are
* represented using two's-complement notation.
* If number < -536,870,912 or if number > 536,870,911, DEC2OCT
* returns the #NUM! error value.
* If number is nonnumeric, DEC2OCT returns the #VALUE! error value.
* If DEC2OCT requires more than places characters, it returns the
* #NUM! error value.
* @param int $places The number of characters to use. If places is omitted, DEC2OCT uses
* the minimum number of characters necessary. Places is useful for
* padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, DEC2OCT returns the #VALUE! error value.
* If places is zero or negative, DEC2OCT returns the #NUM! error value.
*
* @return string
*/
public static function DECTOOCT($x, $places = null)
{
$xorig = $x;
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
$x = (int) $x;
} else {
return Functions::VALUE();
}
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
return Functions::VALUE();
}
$x = (string) floor($x);
$r = decoct($x);
if (strlen($r) == 11) {
// Two's Complement
$r = substr($r, -10);
}
return self::nbrConversionFormat($r, $places);
}
/**
* HEXTOBIN.
*
* Return a hex value as binary.
*
* Excel Function:
* HEX2BIN(x[,places])
*
* @param string $x the hexadecimal number you want to convert.
* Number cannot contain more than 10 characters.
* The most significant bit of number is the sign bit (40th bit from the right).
* The remaining 9 bits are magnitude bits.
* Negative numbers are represented using two's-complement notation.
* If number is negative, HEX2BIN ignores places and returns a 10-character binary number.
* If number is negative, it cannot be less than FFFFFFFE00,
* and if number is positive, it cannot be greater than 1FF.
* If number is not a valid hexadecimal number, HEX2BIN returns the #NUM! error value.
* If HEX2BIN requires more than places characters, it returns the #NUM! error value.
* @param int $places The number of characters to use. If places is omitted,
* HEX2BIN uses the minimum number of characters necessary. Places
* is useful for padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, HEX2BIN returns the #VALUE! error value.
* If places is negative, HEX2BIN returns the #NUM! error value.
*
* @return string
*/
public static function HEXTOBIN($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
return Functions::VALUE();
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
return Functions::NAN();
}
return self::DECTOBIN(self::HEXTODEC($x), $places);
}
/**
* HEXTODEC.
*
* Return a hex value as decimal.
*
* Excel Function:
* HEX2DEC(x)
*
* @param string $x The hexadecimal number you want to convert. This number cannot
* contain more than 10 characters (40 bits). The most significant
* bit of number is the sign bit. The remaining 39 bits are magnitude
* bits. Negative numbers are represented using two's-complement
* notation.
* If number is not a valid hexadecimal number, HEX2DEC returns the
* #NUM! error value.
*
* @return string
*/
public static function HEXTODEC($x)
{
$x = Functions::flattenSingleValue($x);
if (is_bool($x)) {
return Functions::VALUE();
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
return Functions::NAN();
}
if (strlen($x) > 10) {
return Functions::NAN();
}
$binX = '';
foreach (str_split($x) as $char) {
$binX .= str_pad(base_convert($char, 16, 2), 4, '0', STR_PAD_LEFT);
}
if (strlen($binX) == 40 && $binX[0] == '1') {
for ($i = 0; $i < 40; ++$i) {
$binX[$i] = ($binX[$i] == '1' ? '0' : '1');
}
return (bindec($binX) + 1) * -1;
}
return bindec($binX);
}
/**
* HEXTOOCT.
*
* Return a hex value as octal.
*
* Excel Function:
* HEX2OCT(x[,places])
*
* @param string $x The hexadecimal number you want to convert. Number cannot
* contain more than 10 characters. The most significant bit of
* number is the sign bit. The remaining 39 bits are magnitude
* bits. Negative numbers are represented using two's-complement
* notation.
* If number is negative, HEX2OCT ignores places and returns a
* 10-character octal number.
* If number is negative, it cannot be less than FFE0000000, and
* if number is positive, it cannot be greater than 1FFFFFFF.
* If number is not a valid hexadecimal number, HEX2OCT returns
* the #NUM! error value.
* If HEX2OCT requires more than places characters, it returns
* the #NUM! error value.
* @param int $places The number of characters to use. If places is omitted, HEX2OCT
* uses the minimum number of characters necessary. Places is
* useful for padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, HEX2OCT returns the #VALUE! error
* value.
* If places is negative, HEX2OCT returns the #NUM! error value.
*
* @return string
*/
public static function HEXTOOCT($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
return Functions::VALUE();
}
$x = (string) $x;
if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
return Functions::NAN();
}
$decimal = self::HEXTODEC($x);
if ($decimal < -536870912 || $decimal > 536870911) {
return Functions::NAN();
}
return self::DECTOOCT($decimal, $places);
}
/**
* OCTTOBIN.
*
* Return an octal value as binary.
*
* Excel Function:
* OCT2BIN(x[,places])
*
* @param string $x The octal number you want to convert. Number may not
* contain more than 10 characters. The most significant
* bit of number is the sign bit. The remaining 29 bits
* are magnitude bits. Negative numbers are represented
* using two's-complement notation.
* If number is negative, OCT2BIN ignores places and returns
* a 10-character binary number.
* If number is negative, it cannot be less than 7777777000,
* and if number is positive, it cannot be greater than 777.
* If number is not a valid octal number, OCT2BIN returns
* the #NUM! error value.
* If OCT2BIN requires more than places characters, it
* returns the #NUM! error value.
* @param int $places The number of characters to use. If places is omitted,
* OCT2BIN uses the minimum number of characters necessary.
* Places is useful for padding the return value with
* leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, OCT2BIN returns the #VALUE!
* error value.
* If places is negative, OCT2BIN returns the #NUM! error
* value.
*
* @return string
*/
public static function OCTTOBIN($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
return Functions::VALUE();
}
$x = (string) $x;
if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
return Functions::NAN();
}
return self::DECTOBIN(self::OCTTODEC($x), $places);
}
/**
* OCTTODEC.
*
* Return an octal value as decimal.
*
* Excel Function:
* OCT2DEC(x)
*
* @param string $x The octal number you want to convert. Number may not contain
* more than 10 octal characters (30 bits). The most significant
* bit of number is the sign bit. The remaining 29 bits are
* magnitude bits. Negative numbers are represented using
* two's-complement notation.
* If number is not a valid octal number, OCT2DEC returns the
* #NUM! error value.
*
* @return string
*/
public static function OCTTODEC($x)
{
$x = Functions::flattenSingleValue($x);
if (is_bool($x)) {
return Functions::VALUE();
}
$x = (string) $x;
if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
return Functions::NAN();
}
$binX = '';
foreach (str_split($x) as $char) {
$binX .= str_pad(decbin((int) $char), 3, '0', STR_PAD_LEFT);
}
if (strlen($binX) == 30 && $binX[0] == '1') {
for ($i = 0; $i < 30; ++$i) {
$binX[$i] = ($binX[$i] == '1' ? '0' : '1');
}
return (bindec($binX) + 1) * -1;
}
return bindec($binX);
}
/**
* OCTTOHEX.
*
* Return an octal value as hex.
*
* Excel Function:
* OCT2HEX(x[,places])
*
* @param string $x The octal number you want to convert. Number may not contain
* more than 10 octal characters (30 bits). The most significant
* bit of number is the sign bit. The remaining 29 bits are
* magnitude bits. Negative numbers are represented using
* two's-complement notation.
* If number is negative, OCT2HEX ignores places and returns a
* 10-character hexadecimal number.
* If number is not a valid octal number, OCT2HEX returns the
* #NUM! error value.
* If OCT2HEX requires more than places characters, it returns
* the #NUM! error value.
* @param int $places The number of characters to use. If places is omitted, OCT2HEX
* uses the minimum number of characters necessary. Places is useful
* for padding the return value with leading 0s (zeros).
* If places is not an integer, it is truncated.
* If places is nonnumeric, OCT2HEX returns the #VALUE! error value.
* If places is negative, OCT2HEX returns the #NUM! error value.
*
* @return string
*/
public static function OCTTOHEX($x, $places = null)
{
$x = Functions::flattenSingleValue($x);
$places = Functions::flattenSingleValue($places);
if (is_bool($x)) {
return Functions::VALUE();
}
$x = (string) $x;
if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
return Functions::NAN();
}
$hexVal = strtoupper(dechex(self::OCTTODEC($x)));
return self::nbrConversionFormat($hexVal, $places);
}
/**
* COMPLEX.
*
* Converts real and imaginary coefficients into a complex number of the form x +/- yi or x +/- yj.
*
* Excel Function:
* COMPLEX(realNumber,imaginary[,suffix])
*
* @param float $realNumber the real coefficient of the complex number
* @param float $imaginary the imaginary coefficient of the complex number
* @param string $suffix The suffix for the imaginary component of the complex number.
* If omitted, the suffix is assumed to be "i".
*
* @return string
*/
public static function COMPLEX($realNumber = 0.0, $imaginary = 0.0, $suffix = 'i')
{
$realNumber = ($realNumber === null) ? 0.0 : Functions::flattenSingleValue($realNumber);
$imaginary = ($imaginary === null) ? 0.0 : Functions::flattenSingleValue($imaginary);
$suffix = ($suffix === null) ? 'i' : Functions::flattenSingleValue($suffix);
if (
((is_numeric($realNumber)) && (is_numeric($imaginary))) &&
(($suffix == 'i') || ($suffix == 'j') || ($suffix == ''))
) {
$complex = new Complex($realNumber, $imaginary, $suffix);
return (string) $complex;
}
return Functions::VALUE();
}
/**
* IMAGINARY.
*
* Returns the imaginary coefficient of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMAGINARY(complexNumber)
*
* @param string $complexNumber the complex number for which you want the imaginary
* coefficient
*
* @return float
*/
public static function IMAGINARY($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (new Complex($complexNumber))->getImaginary();
}
/**
* IMREAL.
*
* Returns the real coefficient of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMREAL(complexNumber)
*
* @param string $complexNumber the complex number for which you want the real coefficient
*
* @return float
*/
public static function IMREAL($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (new Complex($complexNumber))->getReal();
}
/**
* IMABS.
*
* Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMABS(complexNumber)
*
* @param string $complexNumber the complex number for which you want the absolute value
*
* @return float
*/
public static function IMABS($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (new Complex($complexNumber))->abs();
}
/**
* IMARGUMENT.
*
* Returns the argument theta of a complex number, i.e. the angle in radians from the real
* axis to the representation of the number in polar coordinates.
*
* Excel Function:
* IMARGUMENT(complexNumber)
*
* @param string $complexNumber the complex number for which you want the argument theta
*
* @return float|string
*/
public static function IMARGUMENT($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
$complex = new Complex($complexNumber);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return Functions::DIV0();
}
return $complex->argument();
}
/**
* IMCONJUGATE.
*
* Returns the complex conjugate of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCONJUGATE(complexNumber)
*
* @param string $complexNumber the complex number for which you want the conjugate
*
* @return string
*/
public static function IMCONJUGATE($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->conjugate();
}
/**
* IMCOS.
*
* Returns the cosine of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCOS(complexNumber)
*
* @param string $complexNumber the complex number for which you want the cosine
*
* @return float|string
*/
public static function IMCOS($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->cos();
}
/**
* IMCOSH.
*
* Returns the hyperbolic cosine of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCOSH(complexNumber)
*
* @param string $complexNumber the complex number for which you want the hyperbolic cosine
*
* @return float|string
*/
public static function IMCOSH($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->cosh();
}
/**
* IMCOT.
*
* Returns the cotangent of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCOT(complexNumber)
*
* @param string $complexNumber the complex number for which you want the cotangent
*
* @return float|string
*/
public static function IMCOT($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->cot();
}
/**
* IMCSC.
*
* Returns the cosecant of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCSC(complexNumber)
*
* @param string $complexNumber the complex number for which you want the cosecant
*
* @return float|string
*/
public static function IMCSC($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->csc();
}
/**
* IMCSCH.
*
* Returns the hyperbolic cosecant of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMCSCH(complexNumber)
*
* @param string $complexNumber the complex number for which you want the hyperbolic cosecant
*
* @return float|string
*/
public static function IMCSCH($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->csch();
}
/**
* IMSIN.
*
* Returns the sine of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMSIN(complexNumber)
*
* @param string $complexNumber the complex number for which you want the sine
*
* @return float|string
*/
public static function IMSIN($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->sin();
}
/**
* IMSINH.
*
* Returns the hyperbolic sine of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMSINH(complexNumber)
*
* @param string $complexNumber the complex number for which you want the hyperbolic sine
*
* @return float|string
*/
public static function IMSINH($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->sinh();
}
/**
* IMSEC.
*
* Returns the secant of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMSEC(complexNumber)
*
* @param string $complexNumber the complex number for which you want the secant
*
* @return float|string
*/
public static function IMSEC($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->sec();
}
/**
* IMSECH.
*
* Returns the hyperbolic secant of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMSECH(complexNumber)
*
* @param string $complexNumber the complex number for which you want the hyperbolic secant
*
* @return float|string
*/
public static function IMSECH($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->sech();
}
/**
* IMTAN.
*
* Returns the tangent of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMTAN(complexNumber)
*
* @param string $complexNumber the complex number for which you want the tangent
*
* @return float|string
*/
public static function IMTAN($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->tan();
}
/**
* IMSQRT.
*
* Returns the square root of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMSQRT(complexNumber)
*
* @param string $complexNumber the complex number for which you want the square root
*
* @return string
*/
public static function IMSQRT($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
$theta = self::IMARGUMENT($complexNumber);
if ($theta === Functions::DIV0()) {
return '0';
}
return (string) (new Complex($complexNumber))->sqrt();
}
/**
* IMLN.
*
* Returns the natural logarithm of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMLN(complexNumber)
*
* @param string $complexNumber the complex number for which you want the natural logarithm
*
* @return string
*/
public static function IMLN($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
$complex = new Complex($complexNumber);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return Functions::NAN();
}
return (string) (new Complex($complexNumber))->ln();
}
/**
* IMLOG10.
*
* Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMLOG10(complexNumber)
*
* @param string $complexNumber the complex number for which you want the common logarithm
*
* @return string
*/
public static function IMLOG10($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
$complex = new Complex($complexNumber);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return Functions::NAN();
}
return (string) (new Complex($complexNumber))->log10();
}
/**
* IMLOG2.
*
* Returns the base-2 logarithm of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMLOG2(complexNumber)
*
* @param string $complexNumber the complex number for which you want the base-2 logarithm
*
* @return string
*/
public static function IMLOG2($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
$complex = new Complex($complexNumber);
if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
return Functions::NAN();
}
return (string) (new Complex($complexNumber))->log2();
}
/**
* IMEXP.
*
* Returns the exponential of a complex number in x + yi or x + yj text format.
*
* Excel Function:
* IMEXP(complexNumber)
*
* @param string $complexNumber the complex number for which you want the exponential
*
* @return string
*/
public static function IMEXP($complexNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
return (string) (new Complex($complexNumber))->exp();
}
/**
* IMPOWER.
*
* Returns a complex number in x + yi or x + yj text format raised to a power.
*
* Excel Function:
* IMPOWER(complexNumber,realNumber)
*
* @param string $complexNumber the complex number you want to raise to a power
* @param float $realNumber the power to which you want to raise the complex number
*
* @return string
*/
public static function IMPOWER($complexNumber, $realNumber)
{
$complexNumber = Functions::flattenSingleValue($complexNumber);
$realNumber = Functions::flattenSingleValue($realNumber);
if (!is_numeric($realNumber)) {
return Functions::VALUE();
}
return (string) (new Complex($complexNumber))->pow($realNumber);
}
/**
* IMDIV.
*
* Returns the quotient of two complex numbers in x + yi or x + yj text format.
*
* Excel Function:
* IMDIV(complexDividend,complexDivisor)
*
* @param string $complexDividend the complex numerator or dividend
* @param string $complexDivisor the complex denominator or divisor
*
* @return string
*/
public static function IMDIV($complexDividend, $complexDivisor)
{
$complexDividend = Functions::flattenSingleValue($complexDividend);
$complexDivisor = Functions::flattenSingleValue($complexDivisor);
try {
return (string) (new Complex($complexDividend))->divideby(new Complex($complexDivisor));
} catch (ComplexException $e) {
return Functions::NAN();
}
}
/**
* IMSUB.
*
* Returns the difference of two complex numbers in x + yi or x + yj text format.
*
* Excel Function:
* IMSUB(complexNumber1,complexNumber2)
*
* @param string $complexNumber1 the complex number from which to subtract complexNumber2
* @param string $complexNumber2 the complex number to subtract from complexNumber1
*
* @return string
*/
public static function IMSUB($complexNumber1, $complexNumber2)
{
$complexNumber1 = Functions::flattenSingleValue($complexNumber1);
$complexNumber2 = Functions::flattenSingleValue($complexNumber2);
try {
return (string) (new Complex($complexNumber1))->subtract(new Complex($complexNumber2));
} catch (ComplexException $e) {
return Functions::NAN();
}
}
/**
* IMSUM.
*
* Returns the sum of two or more complex numbers in x + yi or x + yj text format.
*
* Excel Function:
* IMSUM(complexNumber[,complexNumber[,...]])
*
* @param string ...$complexNumbers Series of complex numbers to add
*
* @return string
*/
public static function IMSUM(...$complexNumbers)
{
// Return value
$returnValue = new Complex(0.0);
$aArgs = Functions::flattenArray($complexNumbers);
try {
// Loop through the arguments
foreach ($aArgs as $complex) {
$returnValue = $returnValue->add(new Complex($complex));
}
} catch (ComplexException $e) {
return Functions::NAN();
}
return (string) $returnValue;
}
/**
* IMPRODUCT.
*
* Returns the product of two or more complex numbers in x + yi or x + yj text format.
*
* Excel Function:
* IMPRODUCT(complexNumber[,complexNumber[,...]])
*
* @param string ...$complexNumbers Series of complex numbers to multiply
*
* @return string
*/
public static function IMPRODUCT(...$complexNumbers)
{
// Return value
$returnValue = new Complex(1.0);
$aArgs = Functions::flattenArray($complexNumbers);
try {
// Loop through the arguments
foreach ($aArgs as $complex) {
$returnValue = $returnValue->multiply(new Complex($complex));
}
} catch (ComplexException $e) {
return Functions::NAN();
}
return (string) $returnValue;
}
/**
* DELTA.
*
* Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise.
* Use this function to filter a set of values. For example, by summing several DELTA
* functions you calculate the count of equal pairs. This function is also known as the
* Kronecker Delta function.
*
* Excel Function:
* DELTA(a[,b])
*
* @param float $a the first number
* @param float $b The second number. If omitted, b is assumed to be zero.
*
* @return int
*/
public static function DELTA($a, $b = 0)
{
$a = Functions::flattenSingleValue($a);
$b = Functions::flattenSingleValue($b);
return (int) ($a == $b);
}
/**
* GESTEP.
*
* Excel Function:
* GESTEP(number[,step])
*
* Returns 1 if number >= step; returns 0 (zero) otherwise
* Use this function to filter a set of values. For example, by summing several GESTEP
* functions you calculate the count of values that exceed a threshold.
*
* @param float $number the value to test against step
* @param float $step The threshold value.
* If you omit a value for step, GESTEP uses zero.
*
* @return int
*/
public static function GESTEP($number, $step = 0)
{
$number = Functions::flattenSingleValue($number);
$step = Functions::flattenSingleValue($step);
return (int) ($number >= $step);
}
//
// Private method to calculate the erf value
//
private static $twoSqrtPi = 1.128379167095512574;
public static function erfVal($x)
{
if (abs($x) > 2.2) {
return 1 - self::erfcVal($x);
}
$sum = $term = $x;
$xsqr = ($x * $x);
$j = 1;
do {
$term *= $xsqr / $j;
$sum -= $term / (2 * $j + 1);
++$j;
$term *= $xsqr / $j;
$sum += $term / (2 * $j + 1);
++$j;
if ($sum == 0.0) {
break;
}
} while (abs($term / $sum) > Functions::PRECISION);
return self::$twoSqrtPi * $sum;
}
/**
* Validate arguments passed to the bitwise functions.
*
* @param mixed $value
*
* @return int
*/
private static function validateBitwiseArgument($value)
{
$value = Functions::flattenSingleValue($value);
if (is_int($value)) {
return $value;
} elseif (is_numeric($value)) {
if ($value == (int) ($value)) {
$value = (int) ($value);
if (($value > 2 ** 48 - 1) || ($value < 0)) {
throw new Exception(Functions::NAN());
}
return $value;
}
throw new Exception(Functions::NAN());
}
throw new Exception(Functions::VALUE());
}
/**
* BITAND.
*
* Returns the bitwise AND of two integer values.
*
* Excel Function:
* BITAND(number1, number2)
*
* @param int $number1
* @param int $number2
*
* @return int|string
*/
public static function BITAND($number1, $number2)
{
try {
$number1 = self::validateBitwiseArgument($number1);
$number2 = self::validateBitwiseArgument($number2);
} catch (Exception $e) {
return $e->getMessage();
}
return $number1 & $number2;
}
/**
* BITOR.
*
* Returns the bitwise OR of two integer values.
*
* Excel Function:
* BITOR(number1, number2)
*
* @param int $number1
* @param int $number2
*
* @return int|string
*/
public static function BITOR($number1, $number2)
{
try {
$number1 = self::validateBitwiseArgument($number1);
$number2 = self::validateBitwiseArgument($number2);
} catch (Exception $e) {
return $e->getMessage();
}
return $number1 | $number2;
}
/**
* BITXOR.
*
* Returns the bitwise XOR of two integer values.
*
* Excel Function:
* BITXOR(number1, number2)
*
* @param int $number1
* @param int $number2
*
* @return int|string
*/
public static function BITXOR($number1, $number2)
{
try {
$number1 = self::validateBitwiseArgument($number1);
$number2 = self::validateBitwiseArgument($number2);
} catch (Exception $e) {
return $e->getMessage();
}
return $number1 ^ $number2;
}
/**
* BITLSHIFT.
*
* Returns the number value shifted left by shift_amount bits.
*
* Excel Function:
* BITLSHIFT(number, shift_amount)
*
* @param int $number
* @param int $shiftAmount
*
* @return int|string
*/
public static function BITLSHIFT($number, $shiftAmount)
{
try {
$number = self::validateBitwiseArgument($number);
} catch (Exception $e) {
return $e->getMessage();
}
$shiftAmount = Functions::flattenSingleValue($shiftAmount);
$result = $number << $shiftAmount;
if ($result > 2 ** 48 - 1) {
return Functions::NAN();
}
return $result;
}
/**
* BITRSHIFT.
*
* Returns the number value shifted right by shift_amount bits.
*
* Excel Function:
* BITRSHIFT(number, shift_amount)
*
* @param int $number
* @param int $shiftAmount
*
* @return int|string
*/
public static function BITRSHIFT($number, $shiftAmount)
{
try {
$number = self::validateBitwiseArgument($number);
} catch (Exception $e) {
return $e->getMessage();
}
$shiftAmount = Functions::flattenSingleValue($shiftAmount);
return $number >> $shiftAmount;
}
/**
* ERF.
*
* Returns the error function integrated between the lower and upper bound arguments.
*
* Note: In Excel 2007 or earlier, if you input a negative value for the upper or lower bound arguments,
* the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
* improved, so that it can now calculate the function for both positive and negative ranges.
* PhpSpreadsheet follows Excel 2010 behaviour, and accepts negative arguments.
*
* Excel Function:
* ERF(lower[,upper])
*
* @param float $lower lower bound for integrating ERF
* @param float $upper upper bound for integrating ERF.
* If omitted, ERF integrates between zero and lower_limit
*
* @return float|string
*/
public static function ERF($lower, $upper = null)
{
$lower = Functions::flattenSingleValue($lower);
$upper = Functions::flattenSingleValue($upper);
if (is_numeric($lower)) {
if ($upper === null) {
return self::erfVal($lower);
}
if (is_numeric($upper)) {
return self::erfVal($upper) - self::erfVal($lower);
}
}
return Functions::VALUE();
}
/**
* ERFPRECISE.
*
* Returns the error function integrated between the lower and upper bound arguments.
*
* Excel Function:
* ERF.PRECISE(limit)
*
* @param float $limit bound for integrating ERF
*
* @return float|string
*/
public static function ERFPRECISE($limit)
{
$limit = Functions::flattenSingleValue($limit);
return self::ERF($limit);
}
//
// Private method to calculate the erfc value
//
private static $oneSqrtPi = 0.564189583547756287;
private static function erfcVal($x)
{
if (abs($x) < 2.2) {
return 1 - self::erfVal($x);
}
if ($x < 0) {
return 2 - self::ERFC(-$x);
}
$a = $n = 1;
$b = $c = $x;
$d = ($x * $x) + 0.5;
$q1 = $q2 = $b / $d;
$t = 0;
do {
$t = $a * $n + $b * $x;
$a = $b;
$b = $t;
$t = $c * $n + $d * $x;
$c = $d;
$d = $t;
$n += 0.5;
$q1 = $q2;
$q2 = $b / $d;
} while ((abs($q1 - $q2) / $q2) > Functions::PRECISION);
return self::$oneSqrtPi * exp(-$x * $x) * $q2;
}
/**
* ERFC.
*
* Returns the complementary ERF function integrated between x and infinity
*
* Note: In Excel 2007 or earlier, if you input a negative value for the lower bound argument,
* the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
* improved, so that it can now calculate the function for both positive and negative x values.
* PhpSpreadsheet follows Excel 2010 behaviour, and accepts nagative arguments.
*
* Excel Function:
* ERFC(x)
*
* @param float $x The lower bound for integrating ERFC
*
* @return float|string
*/
public static function ERFC($x)
{
$x = Functions::flattenSingleValue($x);
if (is_numeric($x)) {
return self::erfcVal($x);
}
return Functions::VALUE();
}
/**
* getConversionGroups
* Returns a list of the different conversion groups for UOM conversions.
*
* @Deprecated Use the getConversionCategories() method in the ConvertUOM class instead
*
* @return array
*/
public static function getConversionGroups()
{
return Engineering\ConvertUOM::getConversionCategories();
}
/**
* getConversionGroupUnits
* Returns an array of units of measure, for a specified conversion group, or for all groups.
*
* @Deprecated Use the getConversionCategoryUnits() method in the ConvertUOM class instead
*
* @param null|mixed $category
*
* @return array
*/
public static function getConversionGroupUnits($category = null)
{
return Engineering\ConvertUOM::getConversionCategoryUnits($category);
}
/**
* getConversionGroupUnitDetails.
*
* @Deprecated Use the getConversionCategoryUnitDetails() method in the ConvertUOM class instead
*
* @param null|mixed $category
*
* @return array
*/
public static function getConversionGroupUnitDetails($category = null)
{
return Engineering\ConvertUOM::getConversionCategoryUnitDetails($category);
}
/**
* getConversionMultipliers
* Returns an array of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM().
*
* @Deprecated Use the getConversionMultipliers() method in the ConvertUOM class instead
*
* @return array of mixed
*/
public static function getConversionMultipliers()
{
return Engineering\ConvertUOM::getConversionMultipliers();
}
/**
* getBinaryConversionMultipliers
* Returns an array of the additional Multiplier prefixes that can be used with Information Units of Measure in CONVERTUOM().
*
* @Deprecated Use the getBinaryConversionMultipliers() method in the ConvertUOM class instead
*
* @return array of mixed
*/
public static function getBinaryConversionMultipliers()
{
return Engineering\ConvertUOM::getBinaryConversionMultipliers();
}
/**
* CONVERTUOM.
*
* Converts a number from one measurement system to another.
* For example, CONVERT can translate a table of distances in miles to a table of distances
* in kilometers.
*
* Excel Function:
* CONVERT(value,fromUOM,toUOM)
*
* @Deprecated Use the CONVERT() method in the ConvertUOM class instead
*
* @param float|int $value the value in fromUOM to convert
* @param string $fromUOM the units for value
* @param string $toUOM the units for the result
*
* @return float|string
*/
public static function CONVERTUOM($value, $fromUOM, $toUOM)
{
return Engineering\ConvertUOM::CONVERT($value, $fromUOM, $toUOM);
}
}
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