Forecasting
There’s More Than One Way to Round a Number
October 31, 2017
When we were in school, we all learned the general rule for rounding – if a significant digit is followed by a number that is greater than or equal to 5, we round the number up, otherwise we round the number down. Not surprisingly, this is the behavior we see in Excel, as the ROUND function follows this general rule.
However, this method of rounding tends to create an upward bias. For this reason, another algorithm for rounding numbers has generally become the default when it comes to computer science and software development – section 4 of the IEEE Standard for Floating-Point Arithmetic (IEEE 754) (otherwise known as “rounding to the nearest” or “Bankers’ Rounding”). For example, the Math.Round method in Microsoft’s .NET Framework employs this algorithm.
Developed by the Institute of Electrical and Electronics Engineers (IEEE), this algorithm is designed to minimize rounding bias that results from consistently rounding a midpoint value in a single direction. The way it works is, numbers, which are equidistant from the two nearest integers, are rounded to the nearest even integer. This means that a number like 63.5 would get rounded to 64.0, while a number like 62.5 would get rounded to 62.0. Below is an example generated in VBA Editor.
Essentially, values with an even significant digit (e.g., 61.45) are rounded down, while those with odd significant digits (e.g., 61.55) are rounded up. Other decimal fractions round as you would expect. Only significant digits followed by a 5 get this “special” treatment.
However, this method of rounding tends to create an upward bias. For this reason, another algorithm for rounding numbers has generally become the default when it comes to computer science and software development – section 4 of the IEEE Standard for Floating-Point Arithmetic (IEEE 754) (otherwise known as “rounding to the nearest” or “Bankers’ Rounding”). For example, the Math.Round method in Microsoft’s .NET Framework employs this algorithm.
Developed by the Institute of Electrical and Electronics Engineers (IEEE), this algorithm is designed to minimize rounding bias that results from consistently rounding a midpoint value in a single direction. The way it works is, numbers, which are equidistant from the two nearest integers, are rounded to the nearest even integer. This means that a number like 63.5 would get rounded to 64.0, while a number like 62.5 would get rounded to 62.0. Below is an example generated in VBA Editor.
Essentially, values with an even significant digit (e.g., 61.45) are rounded down, while those with odd significant digits (e.g., 61.55) are rounded up. Other decimal fractions round as you would expect. Only significant digits followed by a 5 get this “special” treatment.
Kesalahan terjadi ketika Memproses Template.
The following has evaluated to null or missing:
==> authorContent.contentFields [in template "44616#44647#114455" at line 9, column 17]
----
Tip: It's the step after the last dot that caused this error, not those before it.
----
Tip: If the failing expression is known to legally refer to something that's sometimes null or missing, either specify a default value like myOptionalVar!myDefault, or use <#if myOptionalVar??>when-present<#else>when-missing</#if>. (These only cover the last step of the expression; to cover the whole expression, use parenthesis: (myOptionalVar.foo)!myDefault, (myOptionalVar.foo)??
----
----
FTL stack trace ("~" means nesting-related):
- Failed at: contentFields = authorContent.content... [in template "44616#44647#114455" at line 9, column 1]
----
1<#assign
2 webContentData = jsonFactoryUtil.createJSONObject(author.getData())
3 classPK = webContentData.classPK
4/>
5
6<#assign
7authorContent = restClient.get("/headless-delivery/v1.0/structured-contents/" + classPK + "?fields=contentFields%2CfriendlyUrlPath%2CtaxonomyCategoryBriefs")
8contentFields = authorContent.contentFields
9categories=authorContent.taxonomyCategoryBriefs
10authorContentData = jsonFactoryUtil.createJSONObject(authorContent)
11friendlyURL = authorContentData.friendlyUrlPath
12authorCategoryId = "0"
13/>
14
15<#list contentFields as contentField >
16 <#assign
17 contentFieldData = jsonFactoryUtil.createJSONObject(contentField)
18 name = contentField.name
19 />
20 <#if name == 'authorImage'>
21 <#if (contentField.contentFieldValue.image)??>
22 <#assign authorImageURL = contentField.contentFieldValue.image.contentUrl />
23 </#if>
24 </#if>
25 <#if name == 'authorName'>
26 <#assign authorName = contentField.contentFieldValue.data />
27 <#list categories as category >
28 <#if authorName == category.taxonomyCategoryName>
29 <#assign authorCategoryId = category.taxonomyCategoryId />
30 </#if>
31 </#list>
32 </#if>
33 <#if name == 'authorDescription'>
34 <#assign authorDescription = contentField.contentFieldValue.data />
35
36 </#if>
37
38 <#if name == 'authorJobTitle'>
39 <#assign authorJobTitle = contentField.contentFieldValue.data />
40
41 </#if>
42
43</#list>
44
45<div class="blog-author-info">
46 <#if authorImageURL??>
47 <img class="blog-author-img" id="author-image" src="${authorImageURL}" alt="" />
48 </#if>
49 <#if authorName??>
50 <#if authorName != "">
51 <p class="blog-author-name">By <a id="author-detail-page" href="/w/${friendlyURL}?filter_category_552298=${authorCategoryId}"><span id="author-full-name">${authorName}</span></a></p>
52 <hr />
53 </#if>
54 </#if>
55 <#if authorJobTitle??>
56 <#if authorJobTitle != "">
57 <p class="blog-author-title" id="author-job-title" >${authorJobTitle}</p>
58 <hr />
59 </#if>
60 </#if>
61 <#if authorDescription??>
62 <#if authorDescription != "" && authorDescription != "null" >
63 <p class="blog-author-desc" id="author-job-desc">${authorDescription}</p>
64 <hr />
65 </#if>
66 </#if>
67</div>
The following has evaluated to null or missing:
==> authorContent.contentFields [in template "44616#44647#114455" at line 9, column 17]
----
Tip: It's the step after the last dot that caused this error, not those before it.
----
Tip: If the failing expression is known to legally refer to something that's sometimes null or missing, either specify a default value like myOptionalVar!myDefault, or use <#if myOptionalVar??>when-present<#else>when-missing</#if>. (These only cover the last step of the expression; to cover the whole expression, use parenthesis: (myOptionalVar.foo)!myDefault, (myOptionalVar.foo)??
----
----
FTL stack trace ("~" means nesting-related):
- Failed at: contentFields = authorContent.content... [in template "44616#44647#114455" at line 9, column 1]
----
1<#assign
2 webContentData = jsonFactoryUtil.createJSONObject(author.getData())
3 classPK = webContentData.classPK
4/>
5
6<#assign
7authorContent = restClient.get("/headless-delivery/v1.0/structured-contents/" + classPK + "?fields=contentFields%2CfriendlyUrlPath%2CtaxonomyCategoryBriefs")
8contentFields = authorContent.contentFields
9categories=authorContent.taxonomyCategoryBriefs
10authorContentData = jsonFactoryUtil.createJSONObject(authorContent)
11friendlyURL = authorContentData.friendlyUrlPath
12authorCategoryId = "0"
13/>
14
15<#list contentFields as contentField >
16 <#assign
17 contentFieldData = jsonFactoryUtil.createJSONObject(contentField)
18 name = contentField.name
19 />
20 <#if name == 'authorImage'>
21 <#if (contentField.contentFieldValue.image)??>
22 <#assign authorImageURL = contentField.contentFieldValue.image.contentUrl />
23 </#if>
24 </#if>
25 <#if name == 'authorName'>
26 <#assign authorName = contentField.contentFieldValue.data />
27 <#list categories as category >
28 <#if authorName == category.taxonomyCategoryName>
29 <#assign authorCategoryId = category.taxonomyCategoryId />
30 </#if>
31 </#list>
32 </#if>
33 <#if name == 'authorDescription'>
34 <#assign authorDescription = contentField.contentFieldValue.data />
35
36 </#if>
37
38 <#if name == 'authorJobTitle'>
39 <#assign authorJobTitle = contentField.contentFieldValue.data />
40
41 </#if>
42
43</#list>
44
45<div class="blog-author-info">
46 <#if authorImageURL??>
47 <img class="blog-author-img" id="author-image" src="${authorImageURL}" alt="" />
48 </#if>
49 <#if authorName??>
50 <#if authorName != "">
51 <p class="blog-author-name">By <a id="author-detail-page" href="/w/${friendlyURL}?filter_category_552298=${authorCategoryId}"><span id="author-full-name">${authorName}</span></a></p>
52 <hr />
53 </#if>
54 </#if>
55 <#if authorJobTitle??>
56 <#if authorJobTitle != "">
57 <p class="blog-author-title" id="author-job-title" >${authorJobTitle}</p>
58 <hr />
59 </#if>
60 </#if>
61 <#if authorDescription??>
62 <#if authorDescription != "" && authorDescription != "null" >
63 <p class="blog-author-desc" id="author-job-desc">${authorDescription}</p>
64 <hr />
65 </#if>
66 </#if>
67</div>