Mathematical functions
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The java.lang.Math class allows the use of many common mathematical functions that can be used while creating programs.
Since it is in the java.lang package, the Math class does not need to be imported. However, in programs extensively utilizing these functions, a static import can be used.
Math constants
There are two constants in the Math class that are fairly accurate approximations of irrational mathematical numbers.
Math.E
The Math.E constant represents the value of Euler's number (e), the base of the natural logarithm.
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Code section 3.20: Math.E
1 public static final double E = 2.718281828459045;
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Math.PI
The Math.PI constant represents the value of pi, the ratio of a circle's circumference to its diameter.
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Code section 3.21: Math.PI
1 public static final double PI = 3.141592653589793;
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Math methods
Exponential methods
There are several methods in the Math class that deal with exponential functions.
Exponentiation
The power method, double Math.pow(double, double), returns the first parameter to the power of the second parameter. For example, a call to Math.pow(2, 10) will return a value of 1024 (210).
The Math.exp(double) method, a special case of pow, returns e to the power of the parameter. In addition, double Math.expm1(double) returns (ex - 1). Both of these methods are more accurate and convenient in these special cases.
Java also provides special cases of the pow function for square roots and cube roots of doubles, double Math.sqrt(double) and double Math.cbrt(double).
Logarithms
Java has no general logarithm function; when needed this can be simulated using the change-of-base theorem.
double Math.log(double)
double Math.log10(double)
double Math.log1p(double)
Trigonometric and hyperbolic methods
The trigonometric methods of the Math class allow users to easily deal with trigonometric functions in programs. All accept only doubles. Please note that all values using these methods are initially passed and returned in radians, not degrees. However, conversions are possible.
Trigonometric functions
The three main trigonometric methods are Math.sin(x), Math.cos(x), and Math.tan(x), which are used to find the sine, cosine, and tangent, respectively, of any given number. So, for example, a call to Math.sin(Math.PI/2) would return a value of about 1. Although methods for finding the cosecant, secant, and cotangent are not available, these values can be found by taking the reciprocal of the sine, cosine, and tangent, respectively. For example, the cosecant of pi/2 could be found using 1/Math.sin(Math.PI/2).
Inverse trigonometric functions
Java provides inverse counterparts to the trigonometric functions: Math.asin(x), and Math.acos(x), Math.atan(x).
Hyperbolic functions
In addition, hyperbolic functions are available: Math.sinh(x), Math.cosh(x), and Math.tanh(x).
Radian/degree conversion
To convert between degree and radian measures of angles, two methods are available, Math.toRadians(x) and Math.toDegrees(x). While using Math.toRadians(x), a degrees value must be passed in, and that value in radians (the degree value multiplied by pi/180) will be returned. The Math.toDegrees(x) method takes in a value in radians and the value in degrees (the radian value multiplied by 180/pi) is returned.
Absolute value: Math.abs
The absolute value method of the Math class is compatible with the int, long, float, and double types. The data returned is the absolute value of parameter (how far away it is from zero) in the same data type. For example:
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Code section 3.22: Math.abs
1 int result = Math.abs(-3);
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In this example, result will contain a value of 3.
Maximum and minimum values
These methods are very simple comparing functions. Instead of using if...else statements, one can use the Math.max(x1, x2) and Math.min(x1, x2) methods. The Math.max(x1, x2) simply returns the greater of the two values, while the Math.min(x1, x2) returns the lesser of the two. Acceptable types for these methods include int, long, float, and double.
Functions dealing with floating-point representation
Java 1.5 and 1.6 introduced several non-mathematical functions specific to the computer floating-point representation of numbers.
Math.ulp( and double)Math.ulp( return an ulp, the smallest value which, when added to the argument, would be recognized as larger than the argument.float)
Math.copySign returns the value of the first argument with the sign of the second argument. It can be used to determine the sign of a zero value.
Math.getExponent returns (as an int) the exponent used to scale the floating-point argument in computer representation.
Rounding number example
Sometimes, we are not only interested in mathematically correct rounded numbers, but we want that a fixed number of significant digits are always displayed, regardless of the number used. Here is an example program that returns always the correct string. You are invited to modify it such that it does the same and is simpler!
The constant class contains repeating constants that should exist only once in the code so that to avoid inadvertent changes. (If the one constant is changed inadvertently, it is most likely to be seen, as it is used at several locations.)
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Code listing 3.20: StringUtils.java
1 /**
2 * Class that comprises of constant values & string utilities.
3 *
4 * @since 2013-09-05
5 * @version 2014-10-14
6 */
7 public class StringUtils {
8 /** Dash or minus constant */
9 public static final char DASH = '-';
10 /** The exponent sign in a scientific number, or the capital letter E */
11 public static final char EXPONENT = 'E';
12 /** The full stop or period */
13 public static final char PERIOD = '.';
14 /** The zero string constant used at several places */
15 public static final String ZERO = "0";
16
17 /**
18 * Removes all occurrences of the filter character in the text.
19 *
20 * @param text Text to be filtered
21 * @param filter The character to be removed.
22 * @return the string
23 */
24 public static String filter(final String text, final String filter) {
25 final String[] words = text.split("[" + filter + "]");
26
27 switch (words.length) {
28 case 0: return text;
29 case 1: return words[0];
30 default:
31 final StringBuilder filteredText = new StringBuilder();
32
33 for (final String word : words) {
34 filteredText.append(word);
35 }
36
37 return filteredText.toString();
38 }
39 }
40 }
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The MathsUtils class is like an addition to the java.lang.Math class and contains the rounding calculations.
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Code listing 3.21: MathsUtils.java
1 package string;
2
3 /**
4 * Class for special mathematical calculations.<br/>
5 * ATTENTION:<br/>Should depend only on standard Java libraries!
6 *
7 * @since 2013-09-05
8 * @version 2014-10-14
9 */
10 public class MathsUtils {
11
12 // CONSTANTS
13 // ------------------------------------------
14
15 /** The exponent sign in a scientific number, or the capital letter E. */
16 public static final char EXPONENT = 'E';
17
18 /** Value after which the language switches from scientific to double */
19 private static final double E_TO_DOUBLE = 1E-3;
20
21 /** The zero string constant used at several places. */
22 public static final String ZERO = "0";
23
24 /** The string of zeros */
25 private static final String ZEROS = "000000000000000000000000000000000";
26
27 // METHODS
28 // ------------------------------------------
29
30 /**
31 * Determines, if the number uses a scientific representation.
32 *
33 * @param number the number
34 * @return true, if it is a scientific number, false otherwise
35 */
36 private static boolean isScientific(final double number) {
37 return ((new Double(number)).toString().indexOf(EXPONENT) > 0);
38 }
39
40 /**
41 * Determines how many zeros are to be appended after the decimal digits.
42 *
43 * @param significantsAfter Requested significant digits after decimal
44 * @param separator Language-specific decimal separator
45 * @param number Rounded number
46 * @return Requested value
47 */
48 private static byte calculateMissingSignificantZeros(
49 final byte significantsAfter,
50 final char separator,
51 final double number) {
52
53 final byte after = findSignificantsAfterDecimal(separator, number);
54
55 final byte zeros =
56 (byte) (significantsAfter - ((after == 0) ? 1 : after));
57
58 return ((zeros >= 0) ? zeros : 0);
59 }
60
61 /**
62 * Finds the insignificant zeros after the decimal separator.
63 *
64 * @param separator Language-specific decimal separator
65 * @param number the number
66 * @return the byte
67 */
68 private static byte findInsignificantZerosAfterDecimal(
69 final char separator,
70 final double number) {
71
72 if ((Math.abs(number) >= 1) || isScientific(number)) {
73 return 0;
74 } else {
75 final StringBuilder string = new StringBuilder();
76
77 string.append(number);
78 string.delete(0,
79 string.indexOf(new Character(separator).toString()) + 1);
80
81 // Determine what to match:
82 final String regularExpression = "[1-9]";
83
84 final String[] split = string.toString().split(regularExpression);
85
86 return (split.length > 0) ? (byte) split[0].length() : 0;
87 }
88 }
89
90 /**
91 * Calculates the number of all significant digits (without the sign and
92 * the decimal separator).
93 *
94 * @param significantsAfter Requested significant digits after decimal
95 * @param separator Language-specific decimal separator
96 * @param number Value where the digits are to be counted
97 * @return Number of significant digits
98 */
99 private static byte findSignificantDigits(final byte significantsAfter,
100 final char separator,
101 final double number) {
102
103 if (number == 0) { return 0; }
104 else {
105 String mantissa =
106 findMantissa(separator, new Double(number).toString());
107
108 if (number == (long)number) {
109 mantissa = mantissa.substring(0, mantissa.length() - 1);
110 }
111
112 mantissa = retrieveDigits(separator, mantissa);
113 // Find the position of the first non-zero digit:
114 short nonZeroAt = 0;
115
116 for (; (nonZeroAt < mantissa.length())
117 && (mantissa.charAt(nonZeroAt) == '0'); nonZeroAt++) ;
118
119 return (byte)mantissa.substring(nonZeroAt).length();
120 }
121 }
122
123 /**
124 * Determines the number of significant digits after the decimal separator
125 * knowing the total number of significant digits and the number before the
126 * decimal separator.
127 *
128 * @param significantsBefore Number of significant digits before separator
129 * @param significantDigits Number of all significant digits
130 * @return Number of significant decimals after the separator
131 */
132 private static byte findSignificantsAfterDecimal(
133 final byte significantsBefore,
134 final byte significantDigits) {
135
136 final byte afterDecimal =
137 (byte) (significantDigits - significantsBefore);
138
139 return (byte) ((afterDecimal > 0) ? afterDecimal : 0);
140 }
141
142 /**
143 * Determines the number of digits before the decimal point.
144 *
145 * @param separator Language-specific decimal separator
146 * @param number Value to be scrutinised
147 * @return Number of digits before the decimal separator
148 */
149 private static byte findSignificantsBeforeDecimal(final char separator,
150 final double number) {
151
152 final String value = new Double(number).toString();
153
154 // Return immediately, if result is clear: Special handling at
155 // crossroads of floating point and exponential numbers:
156 if ((number == 0) || (Math.abs(number) >= E_TO_DOUBLE)
157 && (Math.abs(number) < 1)) {
158
159 return 0;
160 } else if ((Math.abs(number) > 0) && (Math.abs(number) < E_TO_DOUBLE)) {
161 return 1;
162 } else {
163 byte significants = 0;
164 // Significant digits to the right of decimal separator:
165 for (byte b = 0; b < value.length(); b++) {
166 if (value.charAt(b) == separator) {
167 break;
168 } else if (value.charAt(b) != StringUtils.DASH) {
169 significants++;
170 }
171 }
172
173 return significants;
174 }
175 }
176
177 /**
178 * Returns the exponent part of the double number.
179 *
180 * @param number Value of which the exponent is of interest
181 * @return Exponent of the number or zero.
182 */
183 private static short findExponent(final double number) {
184 return new Short(findExponent((new Double(number)).toString()));
185 }
186
187 /**
188 * Finds the exponent of a number.
189 *
190 * @param value Value where an exponent is to be searched
191 * @return Exponent, if it exists, or "0".
192 */
193 private static String findExponent(final String value) {
194 final short exponentAt = (short) value.indexOf(EXPONENT);
195
196 if (exponentAt < 0) { return ZERO; }
197 else {
198 return value.substring(exponentAt + 1);
199 }
200 }
201
202 /**
203 * Finds the mantissa of a number.
204 *
205 * @param separator Language-specific decimal separator
206 * @param value Value where the mantissa is to be found
207 * @return Mantissa of the number
208 */
209 private static String findMantissa(final char separator,
210 final String value) {
211
212 String strValue = value;
213
214 final short exponentAt = (short) strValue.indexOf(EXPONENT);
215
216 if (exponentAt > -1) {
217 strValue = strValue.substring(0, exponentAt);
218 }
219 return strValue;
220 }
221
222 /**
223 * Retrieves the digits of the value without decimal separator or sign.
224 *
225 * @param separator
226 * @param number Mantissa to be scrutinised
227 * @return The digits only
228 */
229 private static String retrieveDigits(final char separator, String number) {
230 // Strip off exponent part, if it exists:
231 short eAt = (short)number.indexOf(EXPONENT);
232
233 if (eAt > -1) {
234 number = number.substring(0, eAt);
235 }
236
237 return number.replace((new Character(StringUtils.DASH)).toString(), "").
238 replace((new Character(separator)).toString(), "");
239 }
240
241
242 // ---- Public methods ----------------------
243
244 /**
245 * Returns the number of digits in the long value.
246 *
247 * @param value the value
248 * @return the byte
249 */
250 public static byte digits(final long value) {
251 return (byte) StringUtils.filter(Long.toString(value), ".,").length();
252 }
253
254 /**
255 * Finds the significant digits after the decimal separator of a mantissa.
256 *
257 * @param separator Language-specific decimal separator
258 * @param number Value to be scrutinised
259 * @return Number of significant zeros after decimal separator.
260 */
261 public static byte findSignificantsAfterDecimal(final char separator,
262 final double number) {
263
264 if (number == 0) { return 1; }
265 else {
266 String value = (new Double(number)).toString();
267
268 final short separatorAt = (short) value.indexOf(separator);
269
270 if (separatorAt > -1) {
271 value = value.substring(separatorAt + 1);
272 }
273
274 final short exponentAt = (short) value.indexOf(EXPONENT);
275
276 if (exponentAt > 0) {
277 value = value.substring(0, exponentAt);
278 }
279
280 final Long longValue = new Long(value).longValue();
281
282 if (Math.abs(number) < 1) {
283 return (byte) longValue.toString().length();
284 } else if (longValue == 0) {
285 return 0;
286 } else {
287 return (byte) (("0." + value).length() - 2);
288 }
289 }
290 }
291
292 /**
293 * Calculates the power of the base to the exponent without changing the
294 * least-significant digits of a number.
295 *
296 * @param basis
297 * @param exponent
298 * @return basis to power of exponent
299 */
300 public static double power(final int basis, final short exponent) {
301 return power((short) basis, exponent);
302 }
303
304 /**
305 * Calculates the power of the base to the exponent without changing the
306 * least-significant digits of a number.
307 *
308 * @param basis the basis
309 * @param exponent the exponent
310 * @return basis to power of exponent
311 */
312 public static double power(final short basis, final short exponent) {
313 if (basis == 0) {
314 return (exponent != 0) ? 1 : 0;
315 } else {
316 if (exponent == 0) {
317 return 1;
318 } else {
319 // The Math method power does change the least significant
320 // digits after the decimal separator and is therefore useless.
321 double result = 1;
322 short s = 0;
323
324 if (exponent > 0) {
325 for (; s < exponent; s++) {
326 result *= basis;
327 }
328 } else if (exponent < 0) {
329 for (s = exponent; s < 0; s++) {
330 result /= basis;
331 }
332 }
333
334 return result;
335 }
336 }
337 }
338
339 /**
340 * Rounds a number to the decimal places.
341 *
342 * @param significantsAfter Requested significant digits after decimal
343 * @param separator Language-specific decimal separator
344 * @param number Number to be rounded
345 * @return Rounded number to the requested decimal places
346 */
347 public static double round(final byte significantsAfter,
348 final char separator,
349 final double number) {
350
351 if (number == 0) { return 0; }
352 else {
353 final double constant = power(10, (short)
354 (findInsignificantZerosAfterDecimal(separator, number)
355 + significantsAfter));
356 final short dExponent = findExponent(number);
357
358 short exponent = dExponent;
359
360 double value = number*constant*Math.pow(10, -exponent);
361 final String exponentSign =
362 (exponent < 0) ? String.valueOf(StringUtils.DASH) : "";
363
364 if (exponent != 0) {
365 exponent = (short) Math.abs(exponent);
366
367 value = round(value);
368 } else {
369 value = round(value)/constant;
370 }
371
372 // Power method cannot be used, as the exponentiated number may
373 // exceed the maximal long value.
374 exponent -= Math.signum(dExponent)*(findSignificantDigits
375 (significantsAfter, separator, value) - 1);
376
377 if (dExponent != 0) {
378 String strValue = Double.toString(value);
379
380 strValue = strValue.substring(0, strValue.indexOf(separator))
381 + EXPONENT + exponentSign + Short.toString(exponent);
382
383 value = new Double(strValue);
384 }
385
386 return value;
387 }
388 }
389
390 /**
391 * Rounds a number according to mathematical rules.
392 *
393 * @param value the value
394 * @return the double
395 */
396 public static double round(final double value) {
397 return (long) (value + .5);
398 }
399
400 /**
401 * Rounds to a fixed number of significant digits.
402 *
403 * @param significantDigits Requested number of significant digits
404 * @param separator Language-specific decimal separator
405 * @param dNumber Number to be rounded
406 * @return Rounded number
407 */
408 public static String roundToString(final byte significantDigits,
409 final char separator,
410 double dNumber) {
411
412 // Number of significants that *are* before the decimal separator:
413 final byte significantsBefore =
414 findSignificantsBeforeDecimal(separator, dNumber);
415 // Number of decimals that *should* be after the decimal separator:
416 final byte significantsAfter = findSignificantsAfterDecimal(
417 significantsBefore, significantDigits);
418 // Round to the specified number of digits after decimal separator:
419 final double rounded = MathsUtils.round(significantsAfter, separator, dNumber);
420
421 final String exponent = findExponent((new Double(rounded)).toString());
422 final String mantissa = findMantissa(separator,
423 (new Double(rounded)).toString());
424
425 final double dMantissa = new Double(mantissa).doubleValue();
426 final StringBuilder result = new StringBuilder(mantissa);
427 // Determine the significant digits in this number:
428 final byte significants = findSignificantDigits(significantsAfter,
429 separator, dMantissa);
430 // Add lagging zeros, if necessary:
431 if (significants <= significantDigits) {
432 if (significantsAfter != 0) {
433 result.append(ZEROS.substring(0,
434 calculateMissingSignificantZeros(significantsAfter,
435 separator, dMantissa)));
436 } else {
437 // Cut off the decimal separator & after decimal digits:
438 final short decimal = (short) result.indexOf(
439 new Character(separator).toString());
440
441 if (decimal > -1) {
442 result.setLength(decimal);
443 }
444 }
445 } else if (significantsBefore > significantDigits) {
446 dNumber /= power(10, (short) (significantsBefore - significantDigits));
447
448 dNumber = round(dNumber);
449
450 final short digits =
451 (short) (significantDigits + ((dNumber < 0) ? 1 : 0));
452
453 final String strDouble = (new Double(dNumber)).toString().substring(0, digits);
454
455 result.setLength(0);
456 result.append(strDouble + ZEROS.substring(0,
457 significantsBefore - significantDigits));
458 }
459
460 if (new Short(exponent) != 0) {
461 result.append(EXPONENT + exponent);
462 }
463
464 return result.toString();
465 } // public static String roundToString(…)
466
467 /**
468 * Rounds to a fixed number of significant digits.
469 *
470 * @param separator Language-specific decimal separator
471 * @param significantDigits Requested number of significant digits
472 * @param value Number to be rounded
473 * @return Rounded number
474 */
475 public static String roundToString(final char separator,
476 final int significantDigits,
477 float value) {
478
479 return roundToString((byte)significantDigits, separator,
480 (double)value);
481 }
482 } // class MathsUtils
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The code is tested with the following JUnit test:
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Code listing 3.22: MathsUtilsTest.java
1 package string;
2
3 import static org.junit.Assert.assertEquals;
4 import static org.junit.Assert.assertFalse;
5 import static org.junit.Assert.assertTrue;
6
7 import java.util.Vector;
8
9 import org.junit.Test;
10
11 /**
12 * The JUnit test for the <code>MathsUtils</code> class.
13 *
14 * @since 2013-03-26
15 * @version 2014-10-14
16 */
17 public class MathsUtilsTest {
18
19 /**
20 * Method that adds a negative and a positive value to values.
21 *
22 * @param d the double value
23 * @param values the values
24 */
25 private static void addValue(final double d, Vector<Double> values) {
26 values.add(-d);
27 values.add(d);
28 }
29
30 // Public methods ------
31
32 /**
33 * Tests the round method with a double parameter.
34 */
35 @Test
36 public void testRoundToStringDoubleByteCharDouble() {
37 // Test rounding
38 final Vector<Double> values = new Vector<Double>();
39 final Vector<String> strValues = new Vector<String>();
40
41 values.add(0.0);
42 strValues.add("0.00000");
43 addValue(1.4012984643248202e-45, values);
44 strValues.add("-1.4012E-45");
45 strValues.add("1.4013E-45");
46 addValue(1.999999757e-5, values);
47 strValues.add("-1.9999E-5");
48 strValues.add("2.0000E-5");
49 addValue(1.999999757e-4, values);
50 strValues.add("-1.9999E-4");
51 strValues.add("2.0000E-4");
52 addValue(1.999999757e-3, values);
53 strValues.add("-0.0019999");
54 strValues.add("0.0020000");
55 addValue(0.000640589, values);
56 strValues.add("-6.4058E-4");
57 strValues.add("6.4059E-4");
58 addValue(0.3396899998188019, values);
59 strValues.add("-0.33968");
60 strValues.add("0.33969");
61 addValue(0.34, values);
62 strValues.add("-0.33999");
63 strValues.add("0.34000");
64 addValue(7.07, values);
65 strValues.add("-7.0699");
66 strValues.add("7.0700");
67 addValue(118.188, values);
68 strValues.add("-118.18");
69 strValues.add("118.19");
70 addValue(118.2, values);
71 strValues.add("-118.19");
72 strValues.add("118.20");
73 addValue(123.405009, values);
74 strValues.add("-123.40");
75 strValues.add("123.41");
76 addValue(30.76994323730469, values);
77 strValues.add("-30.769");
78 strValues.add("30.770");
79 addValue(130.76994323730469, values);
80 strValues.add("-130.76");
81 strValues.add("130.77");
82 addValue(540, values);
83 strValues.add("-539.99");
84 strValues.add("540.00");
85 addValue(12345, values);
86 strValues.add("-12344");
87 strValues.add("12345");
88 addValue(123456, values);
89 strValues.add("-123450");
90 strValues.add("123460");
91 addValue(540911, values);
92 strValues.add("-540900");
93 strValues.add("540910");
94 addValue(9.223372036854776e56, values);
95 strValues.add("-9.2233E56");
96 strValues.add("9.2234E56");
97
98 byte i = 0;
99 final byte significants = 5;
100
101 for (final double element : values) {
102 final String strValue;
103
104 try {
105 strValue = MathsUtils.roundToString(significants, StringUtils.PERIOD, element);
106
107 System.out.println(" MathsUtils.round(" + significants + ", '"
108 + StringUtils.PERIOD + "', " + element + ") ==> "
109 + strValue + " = " + strValues.get(i));
110 assertEquals("Testing roundToString", strValue, strValues.get(i++));
111 } catch (final Exception e) {
112 // TODO Auto-generated catch block
113 e.printStackTrace();
114 }
115 }
116 }
117
118 } // class MathsUtilsTest
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The output of the JUnit test follows:
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Output for code listing 3.22
MathsUtils.round(5, '.', 0.0) ==> 0.00000 = 0.00000 MathsUtils.round(5, '.', -1.4012984643248202E-45) ==> -1.4012E-45 = -1.4012E-45 MathsUtils.round(5, '.', 1.4012984643248202E-45) ==> 1.4013E-45 = 1.4013E-45 MathsUtils.round(5, '.', -1.999999757E-5) ==> -1.9999E-5 = -1.9999E-5 MathsUtils.round(5, '.', 1.999999757E-5) ==> 2.0000E-5 = 2.0000E-5 MathsUtils.round(5, '.', -1.999999757E-4) ==> -1.9999E-4 = -1.9999E-4 MathsUtils.round(5, '.', 1.999999757E-4) ==> 2.0000E-4 = 2.0000E-4 MathsUtils.round(5, '.', -0.001999999757) ==> -0.0019999 = -0.0019999 MathsUtils.round(5, '.', 0.001999999757) ==> 0.0020000 = 0.0020000 MathsUtils.round(5, '.', -6.40589E-4) ==> -6.4058E-4 = -6.4058E-4 MathsUtils.round(5, '.', 6.40589E-4) ==> 6.4059E-4 = 6.4059E-4 MathsUtils.round(5, '.', -0.3396899998188019) ==> -0.33968 = -0.33968 MathsUtils.round(5, '.', 0.3396899998188019) ==> 0.33969 = 0.33969 MathsUtils.round(5, '.', -0.34) ==> -0.33999 = -0.33999 MathsUtils.round(5, '.', 0.34) ==> 0.34000 = 0.34000 MathsUtils.round(5, '.', -7.07) ==> -7.0699 = -7.0699 MathsUtils.round(5, '.', 7.07) ==> 7.0700 = 7.0700 MathsUtils.round(5, '.', -118.188) ==> -118.18 = -118.18 MathsUtils.round(5, '.', 118.188) ==> 118.19 = 118.19 MathsUtils.round(5, '.', -118.2) ==> -118.19 = -118.19 MathsUtils.round(5, '.', 118.2) ==> 118.20 = 118.20 MathsUtils.round(5, '.', -123.405009) ==> -123.40 = -123.40 MathsUtils.round(5, '.', 123.405009) ==> 123.41 = 123.41 MathsUtils.round(5, '.', -30.76994323730469) ==> -30.769 = -30.769 MathsUtils.round(5, '.', 30.76994323730469) ==> 30.770 = 30.770 MathsUtils.round(5, '.', -130.7699432373047) ==> -130.76 = -130.76 MathsUtils.round(5, '.', 130.7699432373047) ==> 130.77 = 130.77 MathsUtils.round(5, '.', -540.0) ==> -539.99 = -539.99 MathsUtils.round(5, '.', 540.0) ==> 540.00 = 540.00 MathsUtils.round(5, '.', -12345.0) ==> -12344 = -12344 MathsUtils.round(5, '.', 12345.0) ==> 12345 = 12345 MathsUtils.round(5, '.', -123456.0) ==> -123450 = -123450 MathsUtils.round(5, '.', 123456.0) ==> 123460 = 123460 MathsUtils.round(5, '.', -540911.0) ==> -540900 = -540900 MathsUtils.round(5, '.', 540911.0) ==> 540910 = 540910 MathsUtils.round(5, '.', -9.223372036854776E56) ==> -9.2233E56 = -9.2233E56 MathsUtils.round(5, '.', 9.223372036854776E56) ==> 9.2234E56 = 9.2234E56 |
If you are interested in a comparison with C#, take a look at the rounding number example there. If you are interested in a comparison with C++, you can compare this code here with the same example over there.
Notice that in the expression starting with if ((D == 0), I have to use OR instead of the || because of a bug in the source template.
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