{"id":601,"date":"2014-12-29T14:45:45","date_gmt":"2014-12-29T13:45:45","guid":{"rendered":"http:\/\/numbercrunch.de\/blog\/?p=601"},"modified":"2023-01-10T12:34:16","modified_gmt":"2023-01-10T11:34:16","slug":"c1114-for-scientific-computing-iii","status":"publish","type":"post","link":"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/","title":{"rendered":"C++11\/14 for scientific computing III"},"content":{"rendered":"

Mathematical functions<\/h2>\n

C++11\/14 introduces several new mathematical functions, which are all overloaded for the types float<\/code>, double<\/code> and long double<\/code> and that are defined in the header file cmath<\/code>. The following table summerizes the new functions.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Basic operations<\/strong><\/td>\n<\/tr>\n
remainder<\/a><\/td>\nsigned remainder of the division operation<\/td>\n<\/tr>\n
remquo<\/a><\/td>\nsigned remainder as well as the three last bits of the division operation<\/td>\n<\/tr>\n
fma<\/a><\/td>\nfused multiply-add operation<\/td>\n<\/tr>\n
fmax<\/a><\/td>\nlarger of two floating point values<\/td>\n<\/tr>\n
fmin<\/a><\/td>\nsmaller of two floating point values<\/td>\n<\/tr>\n
fdim<\/a><\/td>\npositive difference of two floating point values ($\\max(0, x-y)$)<\/td>\n<\/tr>\n
nan, nanf, nanl<\/a><\/td>\nnot-a-number (NaN)<\/td>\n<\/tr>\n
\n
Exponential functions<\/h5>\n<\/td>\n<\/tr>\n
exp2<\/a><\/td>\nreturns $2$ raised to the given power ($2^x$)<\/td>\n<\/tr>\n
expm1<\/a><\/td>\nreturns e<\/i> raised to the given power, minus one ($\\exp x -1$)<\/td>\n<\/tr>\n
log2<\/a><\/td>\nbase 2 logarithm of the given number ($\\log_2x$)<\/td>\n<\/tr>\n
log1p<\/a><\/td>\nnatural logarithm of 1 plus the given number ($\\ln(1+x)$)<\/td>\n<\/tr>\n
\n
Power functions<\/h5>\n<\/td>\n<\/tr>\n
cbrt<\/a><\/td>\ncomputes cubic root ($\\sqrt[3]{x}$)<\/td>\n<\/tr>\n
hypot<\/a><\/td>\ncomputes square root of the sum of the squares of two given numbers ($\\sqrt{x^2+y^2}$)<\/td>\n<\/tr>\n
\n
Hyperbolic functions<\/h5>\n<\/td>\n<\/tr>\n
asinh<\/a><\/td>\ncomputes the inverse hyperbolic sine<\/td>\n<\/tr>\n
acosh<\/a><\/td>\ncomputes the inverse hyperbolic cosine<\/td>\n<\/tr>\n
atanh<\/a><\/td>\ncomputes the inverse hyperbolic tangent<\/td>\n<\/tr>\n
\n
Error and gamma functions<\/h5>\n<\/td>\n<\/tr>\n
erf<\/a><\/td>\nerror function<\/td>\n<\/tr>\n
erfc<\/a><\/td>\ncomplementary error function<\/td>\n<\/tr>\n
tgamma<\/a><\/td>\ngamma function<\/td>\n<\/tr>\n
lgamma<\/a><\/td>\nnatural logarithm of the gamma function<\/td>\n<\/tr>\n
\n
Nearest integer floating point operations<\/h5>\n<\/td>\n<\/tr>\n
trunc<\/a><\/td>\nnearest integer not greater in magnitude than the given value<\/td>\n<\/tr>\n
round, lround, llround<\/a><\/td>\nnearest integer, rounding away from zero in halfway cases<\/td>\n<\/tr>\n
nearbyint<\/a><\/td>\nnearest integer using current rounding mode<\/td>\n<\/tr>\n
rint, lrint, llrint<\/a><\/td>\nnearest integer using current rounding mode with exception if the result differs<\/td>\n<\/tr>\n
\n
Floating point manipulation functions<\/h5>\n<\/td>\n<\/tr>\n
scalbn, scalbln<\/a><\/td>\nmultiplies a number by FLT_RADIX<\/a> raised to a power<\/td>\n<\/tr>\n
ilogb<\/a><\/td>\nextracts exponent of the number<\/td>\n<\/tr>\n
logb<\/a><\/td>\nextracts exponent of the number<\/td>\n<\/tr>\n
nextafter, nexttoward<\/a><\/td>\nnext representable floating point value towards the given value<\/td>\n<\/tr>\n
copysign<\/a><\/td>\ncopies the sign of a floating point value<\/td>\n<\/tr>\n
\n
Classification and comparison <\/span><\/h5>\n<\/td>\n<\/tr>\n
fpclassify<\/a><\/td>\ncategorizes the given floating point value<\/td>\n<\/tr>\n
isfinite<\/a><\/td>\nchecks if the given number has finite value<\/td>\n<\/tr>\n
isinf<\/a><\/td>\nchecks if the given number is infinite<\/td>\n<\/tr>\n
isnan<\/a><\/td>\nchecks if the given number is NaN<\/td>\n<\/tr>\n
isnormal<\/a><\/td>\nchecks if the given number is normal<\/td>\n<\/tr>\n
signbit<\/a><\/td>\nchecks if the given number is negative<\/td>\n<\/tr>\n
isgreater<\/a><\/td>\nchecks if the first floating-point argument is greater than the second<\/td>\n<\/tr>\n
isgreaterequal<\/a><\/td>\nchecks if the first floating-point argument is greater or equal than the second<\/td>\n<\/tr>\n
isless<\/a><\/td>\nchecks if the first floating-point argument is less than the second<\/td>\n<\/tr>\n
islessequal<\/a><\/td>\nchecks if the first floating-point argument is less or equal than the second<\/td>\n<\/tr>\n
islessgreater<\/a><\/td>\nchecks if the first floating-point argument is less or greater than the second<\/td>\n<\/tr>\n
isunordered<\/a><\/td>\nchecks if two floating-point values are unordered<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Minimum maximum functions<\/h2>\n

The header file algorithm<\/code><\/a> defines template functions for determining the minimum or the maximum of two comparable objects of the same type, e.g., numbers. In C++11 overloaded versions of these functions have been introduced that allow to determine the minimum or the maximum of an arbitrary number of objects, which are passed via an initializer list<\/a>. Furthermore, <\/code><\/code>minmax<\/a> determines both the minimum and the maximum in a single scan. The following code gives an illustrative example.<\/p>\n

#include <iostream>\n#include <algorithm>\n\nint main() {\n  int i0(0), i1(1), i2(2), i3(3), i4(4);\n  \/\/ determine minimum and maximum seperately\n  std::cout << \"min : \" << std::min({i3, i1, i2, i0, i4}) << '\\n'\n        << \"max : \" << std::max({i3, i1, i2, i0, i4}) << '\\n';\n  \/\/ determine minimum and maximum in a single scan\n  auto min_max=std::minmax({i3, i1, i2, i0, i4});\n  std::cout << \"min : \" << min_max.first << '\\n'\n        << \"max : \" << min_max.second << '\\n';\n}\n\n\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
Mathematical functions C++11\/14 introduces several new mathematical functions, which are all overloaded for the types float, double and long double and that are defined in the header file cmath. The following table summerizes the new functions. Basic operations remainder signed remainder of the division operation remquo signed remainder as well as the three last bits… Continue reading C++11\/14 for scientific computing III<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-601","post","type-post","status-publish","format-standard","hentry","category-c"],"yoast_head":"\nC++11\/14 for scientific computing III - Number Crunch<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"C++11\/14 for scientific computing III - Number Crunch\" \/>\n<meta property=\"og:description\" content=\"Mathematical functions C++11\/14 introduces several new mathematical functions, which are all overloaded for the types float, double and long double and that are defined in the header file cmath. The following table summerizes the new functions. Basic operations remainder signed remainder of the division operation remquo signed remainder as well as the three last bits… Continue reading C++11\/14 for scientific computing III\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/\" \/>\n<meta property=\"og:site_name\" content=\"Number Crunch\" \/>\n<meta property=\"article:published_time\" content=\"2014-12-29T13:45:45+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-01-10T11:34:16+00:00\" \/>\n<meta name=\"author\" content=\"Heiko Bauke\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Heiko Bauke\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/\"},\"author\":{\"name\":\"Heiko Bauke\",\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/#\/schema\/person\/e73eab65b1721dd0c3d408edb887e413\"},\"headline\":\"C++11\/14 for scientific computing III\",\"datePublished\":\"2014-12-29T13:45:45+00:00\",\"dateModified\":\"2023-01-10T11:34:16+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/\"},\"wordCount\":503,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/#\/schema\/person\/e73eab65b1721dd0c3d408edb887e413\"},\"articleSection\":[\"C++\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/\",\"url\":\"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/\",\"name\":\"C++11\/14 for scientific computing III - Number Crunch\",\"isPartOf\":{\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/#website\"},\"datePublished\":\"2014-12-29T13:45:45+00:00\",\"dateModified\":\"2023-01-10T11:34:16+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.numbercrunch.de\/blog\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"C++11\/14 for scientific computing III\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/#website\",\"url\":\"https:\/\/www.numbercrunch.de\/blog\/\",\"name\":\"Number Crunch\",\"description\":\"A computational science blog.\",\"publisher\":{\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/#\/schema\/person\/e73eab65b1721dd0c3d408edb887e413\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.numbercrunch.de\/blog\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":[\"Person\",\"Organization\"],\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/#\/schema\/person\/e73eab65b1721dd0c3d408edb887e413\",\"name\":\"Heiko Bauke\",\"logo\":{\"@id\":\"https:\/\/www.numbercrunch.de\/blog\/#\/schema\/person\/image\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"C++11\/14 for scientific computing III - Number Crunch","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.numbercrunch.de\/blog\/2014\/12\/c1114-for-scientific-computing-iii\/","og_locale":"en_US","og_type":"article","og_title":"C++11\/14 for scientific computing III - Number Crunch","og_description":"Mathematical functions C++11\/14 introduces several new mathematical functions, which are all overloaded for the types float, double and long double and that are defined in the header file cmath. The following table summerizes the new functions. 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