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bigmoney-all.js
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bigmoney-all.js
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/* big.js v2.5.0 https://github.com/MikeMcl/big.js/LICENCE */
;(function ( global ) {
'use strict';
/*
big.js v2.5.0
A small, fast, easy-to-use library for arbitrary-precision decimal arithmetic.
https://github.com/MikeMcl/big.js/
Copyright (c) 2012 Michael Mclaughlin <M8ch88l@gmail.com>
MIT Expat Licence
*/
/****************************** EDITABLE DEFAULTS **********************************/
// The default values below must be integers within the stated ranges (inclusive).
/*
* The maximum number of decimal places of the results of methods involving
* division, i.e. 'div' and 'sqrt', and 'pow' with negative exponents.
*/
Big['DP'] = 20; // 0 to MAX_DP
/*
* The rounding mode used when rounding to the above decimal places.
*
* 0 Round towards zero (i.e. truncate, no rounding). (ROUND_DOWN)
* 1 Round to nearest neighbour. If equidistant, round up. (ROUND_HALF_UP)
* 2 Round to nearest neighbour. If equidistant, to even neighbour. (ROUND_HALF_EVEN)
* 3 Round away from zero. (ROUND_UP)
*/
Big['RM'] = 1; // 0, 1, 2 or 3
// The maximum value of 'Big.DP'.
var MAX_DP = 1E6, // 0 to 1e+6
// The maximum magnitude of the exponent argument to the 'pow' method.
MAX_POWER = 1E6, // 1 to 1e+6
/*
* The exponent value at and beneath which 'toString' returns exponential notation.
* Javascript's Number type: -7
* -1e+6 is the minimum recommended exponent value of a Big.
*/
TO_EXP_NEG = -7, // 0 to -1e+6
/*
* The exponent value at and above which 'toString' returns exponential notation.
* Javascript's Number type: 21
* 1e+6 is the maximum recommended exponent value of a Big, though there is no
* enforcing or checking of a limit.
*/
TO_EXP_POS = 21, // 0 to 1e+6
/***********************************************************************************/
P = Big.prototype,
isValid = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
ONE = new Big(1);
// CONSTRUCTOR
/*
* The exported function.
* Create and return a new instance of a Big object.
*
* n {number|string|Big} A numeric value.
*/
function Big( n ) {
var i, j, nL,
x = this;
// Enable constructor usage without new.
if ( !(x instanceof Big) ) {
return new Big( n )
}
// Duplicate.
if ( n instanceof Big ) {
x['s'] = n['s'];
x['e'] = n['e'];
x['c'] = n['c'].slice();
return
}
// Minus zero?
if ( n === 0 && 1 / n < 0 ) {
n = '-0'
// Ensure 'n' is string and check validity.
} else if ( !isValid.test(n += '') ) {
throwErr( NaN )
}
// Determine sign.
x['s'] = n.charAt(0) == '-' ? ( n = n.slice(1), -1 ) : 1;
// Decimal point?
if ( ( i = n.indexOf('.') ) > -1 ) {
n = n.replace( '.', '' )
}
// Exponential form?
if ( ( j = n.search(/e/i) ) > 0 ) {
// Determine exponent.
if ( i < 0 ) {
i = j
}
i += +n.slice( j + 1 );
n = n.substring( 0, j )
} else if ( i < 0 ) {
// Integer.
i = n.length
}
// Determine leading zeros.
for ( j = 0; n.charAt(j) == '0'; j++ ) {
}
if ( j == ( nL = n.length ) ) {
// Zero.
x['c'] = [ x['e'] = 0 ]
} else {
// Determine trailing zeros.
for ( ; n.charAt(--nL) == '0'; ) {
}
x['e'] = i - j - 1;
x['c'] = [];
// Convert string to array of digits (without leading and trailing zeros).
for ( i = 0; j <= nL; x['c'][i++] = +n.charAt(j++) ) {
}
}
}
// PRIVATE FUNCTIONS
/*
* Round Big 'x' to a maximum of 'dp' decimal places using rounding mode
* 'rm'. (Called by 'div', 'sqrt' and 'round'.)
*
* x {Big} The Big to round.
* dp {number} Integer, 0 to MAX_DP inclusive.
* rm {number} 0, 1, 2 or 3 ( ROUND_DOWN, ROUND_HALF_UP, ROUND_HALF_EVEN, ROUND_UP )
* [more] {boolean} Whether the result of division was truncated.
*/
function rnd( x, dp, rm, more ) {
var xc = x['c'],
i = x['e'] + dp + 1;
if ( rm === 1 ) {
// 'xc[i]' is the digit after the digit that may be rounded up.
more = xc[i] >= 5
} else if ( rm === 2 ) {
more = xc[i] > 5 || xc[i] == 5 && ( more || i < 0 || xc[i + 1] != null || xc[i - 1] & 1 )
} else if ( rm === 3 ) {
more = more || xc[i] != null || i < 0
} else if ( more = false, rm !== 0 ) {
throwErr( '!Big.RM!' )
}
if ( i < 1 || !xc[0] ) {
x['c'] = more
// 1, 0.1, 0.01, 0.001, 0.0001 etc.
? ( x['e'] = -dp, [1] )
// Zero.
: [ x['e'] = 0 ];
} else {
// Remove any digits after the required decimal places.
xc.length = i--;
// Round up?
if ( more ) {
// Rounding up may mean the previous digit has to be rounded up and so on.
for ( ; ++xc[i] > 9; ) {
xc[i] = 0;
if ( !i-- ) {
++x['e'];
xc.unshift(1)
}
}
}
// Remove trailing zeros.
for ( i = xc.length; !xc[--i]; xc.pop() ) {
}
}
return x
}
/*
* Throw a BigError.
*
* message {string} The error message.
*/
function throwErr( message ) {
var err = new Error( message );
err['name'] = 'BigError';
throw err
}
// PROTOTYPE/INSTANCE METHODS
/*
* Return a new Big whose value is the absolute value of this Big.
*/
P['abs'] = function () {
var x = new Big(this);
x['s'] = 1;
return x
};
/*
* Return
* 1 if the value of this 'Big' is greater than the value of 'Big' 'y',
* -1 if the value of this 'Big' is less than the value of 'Big' 'y', or
* 0 if they have the same value.
*/
P['cmp'] = function ( y ) {
var xNeg,
x = this,
xc = x['c'],
yc = ( y = new Big( y ) )['c'],
i = x['s'],
j = y['s'],
k = x['e'],
l = y['e'];
// Either zero?
if ( !xc[0] || !yc[0] ) {
return !xc[0] ? !yc[0] ? 0 : -j : i
}
// Signs differ?
if ( i != j ) {
return i
}
xNeg = i < 0;
// Compare exponents.
if ( k != l ) {
return k > l ^ xNeg ? 1 : -1
}
// Compare digit by digit.
for ( i = -1,
j = ( k = xc.length ) < ( l = yc.length ) ? k : l;
++i < j; ) {
if ( xc[i] != yc[i] ) {
return xc[i] > yc[i] ^ xNeg ? 1 : -1
}
}
// Compare lengths.
return k == l ? 0 : k > l ^ xNeg ? 1 : -1
};
/*
* Return a new Big whose value is the value of this Big divided by the
* value of Big 'y', rounded, if necessary, to a maximum of 'Big.DP'
* decimal places using rounding mode 'Big.RM'.
*/
P['div'] = function ( y ) {
var x = this,
dvd = x['c'],
dvs = ( y = new Big(y) )['c'],
s = x['s'] == y['s'] ? 1 : -1,
dp = Big['DP'];
if ( dp !== ~~dp || dp < 0 || dp > MAX_DP ) {
throwErr( '!Big.DP!' )
}
// Either 0?
if ( !dvd[0] || !dvs[0] ) {
// Both 0?
if ( dvd[0] == dvs[0] ) {
throwErr( NaN )
}
// 'dvs' is 0?
if ( !dvs[0] ) {
// Throw +-Infinity.
throwErr( s / 0 )
}
// 'dvd' is 0. Return +-0.
return new Big( s * 0 )
}
var dvsL, dvsT, next, cmp, remI,
dvsZ = dvs.slice(),
dvdI = dvsL = dvs.length,
dvdL = dvd.length,
rem = dvd.slice( 0, dvsL ),
remL = rem.length,
quo = new Big(ONE),
qc = quo['c'] = [],
qi = 0,
digits = dp + ( quo['e'] = x['e'] - y['e'] ) + 1;
quo['s'] = s;
s = digits < 0 ? 0 : digits;
// Create version of divisor with leading zero.
dvsZ.unshift(0);
// Add zeros to make remainder as long as divisor.
for ( ; remL++ < dvsL; rem.push(0) ) {
}
do {
// 'next' is how many times the divisor goes into the current remainder.
for ( next = 0; next < 10; next++ ) {
// Compare divisor and remainder.
if ( dvsL != ( remL = rem.length ) ) {
cmp = dvsL > remL ? 1 : -1
} else {
for ( remI = -1, cmp = 0; ++remI < dvsL; ) {
if ( dvs[remI] != rem[remI] ) {
cmp = dvs[remI] > rem[remI] ? 1 : -1;
break
}
}
}
// Subtract divisor from remainder (if divisor < remainder).
if ( cmp < 0 ) {
// Remainder cannot be more than one digit longer than divisor.
// Equalise lengths using divisor with extra leading zero?
for ( dvsT = remL == dvsL ? dvs : dvsZ; remL; ) {
if ( rem[--remL] < dvsT[remL] ) {
for ( remI = remL;
remI && !rem[--remI];
rem[remI] = 9 ) {
}
--rem[remI];
rem[remL] += 10
}
rem[remL] -= dvsT[remL]
}
for ( ; !rem[0]; rem.shift() ) {
}
} else {
break
}
}
// Add the 'next' digit to the result array.
qc[qi++] = cmp ? next : ++next;
// Update the remainder.
rem[0] && cmp
? ( rem[remL] = dvd[dvdI] || 0 )
: ( rem = [ dvd[dvdI] ] )
} while ( ( dvdI++ < dvdL || rem[0] != null ) && s-- );
// Leading zero? Do not remove if result is simply zero (qi == 1).
if ( !qc[0] && qi != 1) {
// There can't be more than one zero.
qc.shift();
quo['e']--;
}
// Round?
if ( qi > digits ) {
rnd( quo, dp, Big['RM'], rem[0] != null )
}
return quo
}
/*
* Return true if the value of this Big is equal to the value of Big 'y',
* otherwise returns false.
*/
P['eq'] = function ( y ) {
return !this.cmp( y )
};
/*
* Return true if the value of this Big is greater than the value of Big 'y',
* otherwise returns false.
*/
P['gt'] = function ( y ) {
return this.cmp( y ) > 0
};
/*
* Return true if the value of this Big is greater than or equal to the
* value of Big 'y', otherwise returns false.
*/
P['gte'] = function ( y ) {
return this.cmp( y ) > -1
};
/*
* Return true if the value of this Big is less than the value of Big 'y',
* otherwise returns false.
*/
P['lt'] = function ( y ) {
return this.cmp( y ) < 0
};
/*
* Return true if the value of this Big is less than or equal to the value
* of Big 'y', otherwise returns false.
*/
P['lte'] = function ( y ) {
return this.cmp( y ) < 1
};
/*
* Return a new Big whose value is the value of this Big minus the value
* of Big 'y'.
*/
P['minus'] = function ( y ) {
var d, i, j, xLTy,
x = this,
a = x['s'],
b = ( y = new Big( y ) )['s'];
// Signs differ?
if ( a != b ) {
return y['s'] = -b, x['plus'](y)
}
var xc = x['c'].slice(),
xe = x['e'],
yc = y['c'],
ye = y['e'];
// Either zero?
if ( !xc[0] || !yc[0] ) {
// 'y' is non-zero?
return yc[0]
? ( y['s'] = -b, y )
// 'x' is non-zero?
: new Big( xc[0]
? x
// Both are zero.
: 0 )
}
// Determine which is the bigger number.
// Prepend zeros to equalise exponents.
if ( a = xe - ye ) {
d = ( xLTy = a < 0 ) ? ( a = -a, xc ) : ( ye = xe, yc );
for ( d.reverse(), b = a; b--; d.push(0) ) {
}
d.reverse()
} else {
// Exponents equal. Check digit by digit.
j = ( ( xLTy = xc.length < yc.length ) ? xc : yc ).length;
for ( a = b = 0; b < j; b++ ) {
if ( xc[b] != yc[b] ) {
xLTy = xc[b] < yc[b];
break
}
}
}
// 'x' < 'y'? Point 'xc' to the array of the bigger number.
if ( xLTy ) {
d = xc, xc = yc, yc = d;
y['s'] = -y['s']
}
/*
* Append zeros to 'xc' if shorter. No need to add zeros to 'yc' if shorter
* as subtraction only needs to start at 'yc.length'.
*/
if ( ( b = -( ( j = xc.length ) - yc.length ) ) > 0 ) {
for ( ; b--; xc[j++] = 0 ) {
}
}
// Subtract 'yc' from 'xc'.
for ( b = yc.length; b > a; ){
if ( xc[--b] < yc[b] ) {
for ( i = b; i && !xc[--i]; xc[i] = 9 ) {
}
--xc[i];
xc[b] += 10
}
xc[b] -= yc[b]
}
// Remove trailing zeros.
for ( ; xc[--j] == 0; xc.pop() ) {
}
// Remove leading zeros and adjust exponent accordingly.
for ( ; xc[0] == 0; xc.shift(), --ye ) {
}
if ( !xc[0] ) {
// n - n = +0
y['s'] = 1;
// Result must be zero.
xc = [ye = 0]
}
return y['c'] = xc, y['e'] = ye, y
};
/*
* Return a new Big whose value is the value of this Big modulo the
* value of Big 'y'.
*/
P['mod'] = function ( y ) {
y = new Big( y );
var c,
x = this,
i = x['s'],
j = y['s'];
if ( !y['c'][0] ) {
throwErr( NaN )
}
x['s'] = y['s'] = 1;
c = y.cmp( x ) == 1;
x['s'] = i, y['s'] = j;
return c
? new Big(x)
: ( i = Big['DP'], j = Big['RM'],
Big['DP'] = Big['RM'] = 0,
x = x['div'](y),
Big['DP'] = i, Big['RM'] = j,
this['minus']( x['times'](y) ) )
};
/*
* Return a new Big whose value is the value of this Big plus the value
* of Big 'y'.
*/
P['plus'] = function ( y ) {
var d,
x = this,
a = x['s'],
b = ( y = new Big( y ) )['s'];
// Signs differ?
if ( a != b ) {
return y['s'] = -b, x['minus'](y)
}
var xe = x['e'],
xc = x['c'],
ye = y['e'],
yc = y['c'];
// Either zero?
if ( !xc[0] || !yc[0] ) {
// 'y' is non-zero?
return yc[0]
? y
: new Big( xc[0]
// 'x' is non-zero?
? x
// Both are zero. Return zero.
: a * 0 )
}
// Prepend zeros to equalise exponents.
// Note: Faster to use reverse then do unshifts.
if ( xc = xc.slice(), a = xe - ye ) {
d = a > 0 ? ( ye = xe, yc ) : ( a = -a, xc );
for ( d.reverse(); a--; d.push(0) ) {
}
d.reverse()
}
// Point 'xc' to the longer array.
if ( xc.length - yc.length < 0 ) {
d = yc, yc = xc, xc = d
}
/*
* Only start adding at 'yc.length - 1' as the
* further digits of 'xc' can be left as they are.
*/
for ( a = yc.length, b = 0; a;
b = ( xc[--a] = xc[a] + yc[a] + b ) / 10 ^ 0, xc[a] %= 10 ) {
}
// No need to check for zero, as +x + +y != 0 && -x + -y != 0
if ( b ) {
xc.unshift(b);
++ye
}
// Remove trailing zeros.
for ( a = xc.length; xc[--a] == 0; xc.pop() ) {
}
return y['c'] = xc, y['e'] = ye, y
};
/*
* Return a Big whose value is the value of this Big raised to the power
* 'e'. If 'e' is negative, round, if necessary, to a maximum of 'Big.DP'
* decimal places using rounding mode 'Big.RM'.
*
* e {number} Integer, -MAX_POWER to MAX_POWER inclusive.
*/
P['pow'] = function ( e ) {
var isNeg = e < 0,
x = new Big(this),
y = ONE;
if ( e !== ~~e || e < -MAX_POWER || e > MAX_POWER ) {
throwErr( '!pow!' )
}
for ( e = isNeg ? -e : e; ; ) {
if ( e & 1 ) {
y = y['times'](x)
}
e >>= 1;
if ( !e ) {
break
}
x = x['times'](x)
}
return isNeg ? ONE['div'](y) : y
};
/*
* Return a new Big whose value is the value of this Big rounded, if
* necessary, to a maximum of 'dp' decimal places using rounding mode 'rm'.
* If 'dp' is not specified, round to 0 decimal places.
* If 'rm' is not specified, use 'Big.RM'.
*
* [dp] {number} Integer, 0 to MAX_DP inclusive.
* [rm] 0, 1, 2 or 3 ( ROUND_DOWN, ROUND_HALF_UP, ROUND_HALF_EVEN, ROUND_UP )
*/
P['round'] = function ( dp, rm ) {
var x = new Big(this);
if ( dp == null ) {
dp = 0
} else if ( dp !== ~~dp || dp < 0 || dp > MAX_DP ) {
throwErr( '!round!' )
}
rnd( x, dp, rm == null ? Big['RM'] : rm );
return x
};
/*
* Return a new Big whose value is the square root of the value of this
* Big, rounded, if necessary, to a maximum of 'Big.DP' decimal places
* using rounding mode 'Big.RM'.
*/
P['sqrt'] = function () {
var estimate, r, approx,
x = this,
xc = x['c'],
i = x['s'],
e = x['e'],
half = new Big('0.5');
// Zero?
if ( !xc[0] ) {
return new Big(x)
}
// Negative?
if ( i < 0 ) {
throwErr( NaN )
}
// Estimate.
i = Math.sqrt( x.toString() );
// Math.sqrt underflow/overflow?
// Pass 'x' to Math.sqrt as integer, then adjust the exponent of the result.
if ( i == 0 || i == 1 / 0 ) {
estimate = xc.join('');
if ( !( estimate.length + e & 1 ) ) {
estimate += '0'
}
r = new Big( Math.sqrt(estimate).toString() );
r['e'] = ( ( ( e + 1 ) / 2 ) | 0 ) - ( e < 0 || e & 1 )
} else {
r = new Big( i.toString() )
}
i = r['e'] + ( Big['DP'] += 4 );
// Newton-Raphson loop.
do {
approx = r;
r = half['times']( approx['plus']( x['div'](approx) ) )
} while ( approx['c'].slice( 0, i ).join('') !==
r['c'].slice( 0, i ).join('') );
rnd( r, Big['DP'] -= 4, Big['RM'] );
return r
};
/*
* Return a new Big whose value is the value of this Big times the value
* of Big 'y'.
*/
P['times'] = function ( y ) {
var c,
x = this,
xc = x['c'],
yc = ( y = new Big( y ) )['c'],
a = xc.length,
b = yc.length,
i = x['e'],
j = y['e'];
y['s'] = x['s'] == y['s'] ? 1 : -1;
// Either 0?
if ( !xc[0] || !yc[0] ) {
return new Big( y['s'] * 0 )
}
y['e'] = i + j;
if ( a < b ) {
c = xc, xc = yc, yc = c, j = a, a = b, b = j
}
for ( j = a + b, c = []; j--; c.push(0) ) {
}
// Multiply!
for ( i = b - 1; i > -1; i-- ) {
for ( b = 0, j = a + i;
j > i;
b = c[j] + yc[i] * xc[j - i - 1] + b,
c[j--] = b % 10 | 0,
b = b / 10 | 0 ) {
}
if ( b ) {
c[j] = ( c[j] + b ) % 10
}
}
b && ++y['e'];
// Remove any leading zero.
!c[0] && c.shift();
// Remove trailing zeros.
for ( j = c.length; !c[--j]; c.pop() ) {
}
return y['c'] = c, y
};
/*
* Return a string representing the value of this Big.
* Return exponential notation if this Big has a positive exponent equal
* to or greater than 'TO_EXP_POS', or a negative exponent equal to or less
* than 'TO_EXP_NEG'.
*/
P['toString'] = P['valueOf'] = P['toJSON'] = function () {
var x = this,
e = x['e'],
str = x['c'].join(''),
strL = str.length;
// Exponential notation?
if ( e <= TO_EXP_NEG || e >= TO_EXP_POS ) {
str = str.charAt(0) + ( strL > 1 ? '.' + str.slice(1) : '' ) +
( e < 0 ? 'e' : 'e+' ) + e
// Negative exponent?
} else if ( e < 0 ) {
// Prepend zeros.
for ( ; ++e; str = '0' + str ) {
}
str = '0.' + str
// Positive exponent?
} else if ( e > 0 ) {
if ( ++e > strL ) {
// Append zeros.
for ( e -= strL; e-- ; str += '0' ) {
}
} else if ( e < strL ) {
str = str.slice( 0, e ) + '.' + str.slice(e)
}
// Exponent zero.
} else if ( strL > 1 ) {
str = str.charAt(0) + '.' + str.slice(1)
}
// Avoid '-0'
return x['s'] < 0 && x['c'][0] ? '-' + str : str
};
/*
***************************************************************************
* If 'toExponential', 'toFixed', 'toPrecision' and 'format' are not
* required they can safely be commented-out or deleted. No redundant code
* will be left. 'format' is used only by 'toExponential', 'toFixed' and
* 'toPrecision'.
***************************************************************************
*/
/*
* PRIVATE FUNCTION
*
* Return a string representing the value of Big 'x' in normal or
* exponential notation to a fixed number of decimal places or significant
* digits 'dp'.
* (Called by toString, toExponential, toFixed and toPrecision.)
*
* x {Big} The Big to format.
* dp {number} Integer, 0 to MAX_DP inclusive.
* toE {number} undefined (toFixed), 1 (toExponential) or 2 (toPrecision).
*/
function format( x, dp, toE ) {
// The index (in normal notation) of the digit that may be rounded up.
var i = dp - ( x = new Big(x) )['e'],
c = x['c'];
// Round?
if ( c.length > ++dp ) {
rnd( x, i, Big['RM'] )
}
// Recalculate 'i' if toFixed as 'x.e' may have changed if value rounded up.
i = !c[0] ? i + 1 : toE ? dp : ( c = x['c'], x['e'] + i + 1 );
// Append zeros?
for ( ; c.length < i; c.push(0) ) {
}
i = x['e'];
/*
* 'toPrecision' returns exponential notation if the number of
* significant digits specified is less than the number of digits
* necessary to represent the integer part of the value in normal
* notation.
*/
return toE == 1 || toE == 2 && ( dp <= i || i <= TO_EXP_NEG )
// Exponential notation.
? ( x['s'] < 0 && c[0] ? '-' : '' ) + ( c.length > 1
? ( c.splice( 1, 0, '.' ), c.join('') )
: c[0] ) + ( i < 0 ? 'e' : 'e+' ) + i
// Normal notation.
: x.toString()
}
/*
* Return a string representing the value of this Big in exponential
* notation to 'dp' fixed decimal places and rounded, if necessary, using
* 'Big.RM'.
*
* [dp] {number} Integer, 0 to MAX_DP inclusive.
*/
P['toExponential'] = function ( dp ) {
if ( dp == null ) {
dp = this['c'].length - 1
} else if ( dp !== ~~dp || dp < 0 || dp > MAX_DP ) {
throwErr( '!toExp!' )
}
return format( this, dp, 1 )
};
/*
* Return a string representing the value of this Big in normal notation
* to 'dp' fixed decimal places and rounded, if necessary, using 'Big.RM'.
*
* [dp] {number} Integer, 0 to MAX_DP inclusive.
*/
P['toFixed'] = function ( dp ) {
var str,
x = this,
neg = TO_EXP_NEG,
pos = TO_EXP_POS;
TO_EXP_NEG = -( TO_EXP_POS = 1 / 0 );
if ( dp == null ) {
str = x.toString()
} else if ( dp === ~~dp && dp >= 0 && dp <= MAX_DP ) {
str = format( x, x['e'] + dp );
// (-0).toFixed() is '0', but (-0.1).toFixed() is '-0'.
// (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
if ( x['s'] < 0 && x['c'][0] && str.indexOf('-') < 0 ) {
// As e.g. -0.5 if rounded to -0 will cause toString to omit the minus sign.
str = '-' + str
}
}
TO_EXP_NEG = neg, TO_EXP_POS = pos;
if ( !str ) {
throwErr( '!toFix!' )
}
return str
};
/*
* Return a string representing the value of this Big to 'sd' significant
* digits and rounded, if necessary, using 'Big.RM'. If 'sd' is less than
* the number of digits necessary to represent the integer part of the value
* in normal notation, then use exponential notation.
*
* sd {number} Integer, 1 to MAX_DP inclusive.
*/
P['toPrecision'] = function ( sd ) {
if ( sd == null ) {
return this.toString()
} else if ( sd !== ~~sd || sd < 1 || sd > MAX_DP ) {