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/third_party/boost/libs/math/doc/sf/
Dellint_introduction.qbk3 The main reference for the elliptic integrals is:
32 Elliptic integrals generally cannot be expressed in terms of
34 integrals can be reduced to the following three canonical forms:
61 integrals are expressed in a variety of different ways. In particular,
94 When ['[phi]] = ['[pi]] / 2, the elliptic integrals are called ['complete].
112 Like the other Legendre integrals this comes in both complete and incomplete forms.
162 The Legendre form and Carlson form of elliptic integrals are related
173 There are two functions related to the elliptic integrals which otherwise
182 Both of these functions are easily implemented in terms of Carlson's integrals, and are
187 The conventional methods for computing elliptic integrals are Gauss
[all …]
Dellint_carlson.qbk90 These functions return Carlson's symmetrical elliptic integrals, the functions
193 Numerical computation of real or complex elliptic integrals]]. Numerical Algorithms,
199 There are also sanity checks that use the inter-relations between the integrals
234 expansion to the fifth order. The calculations of the other three integrals
238 the integrals are singular and their
Dellint_legendre.qbk100 These functions are implemented in terms of Carlson's integrals using the relations:
201 These functions are implemented in terms of Carlson's integrals
327 The functions are then implemented in terms of Carlson's integrals using the relations:
401 These functions are trivially computed in terms of other elliptic integrals
424 the Legendre integrals.
489 These functions are trivially computed in terms of other elliptic integrals
500 the Legendre integrals.
563 These functions are trivially computed in terms of other elliptic integrals
574 the Legendre integrals.
578 The function is then implemented in terms of Carlson's integrals R[sub J] and R[sub F]
/third_party/flutter/skia/third_party/externals/icu/source/i18n/
Ddouble-conversion-fast-dtoa.cpp349 uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e()); in DigitGen() local
354 BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()), in DigitGen()
363 int digit = integrals / divisor; in DigitGen()
367 integrals %= divisor; in DigitGen()
372 (static_cast<uint64_t>(integrals) << -one.e()) + fractionals; in DigitGen()
459 uint32_t integrals = static_cast<uint32_t>(w.f() >> -one.e()); in DigitGenCounted() local
464 BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()), in DigitGenCounted()
474 int digit = integrals / divisor; in DigitGenCounted()
479 integrals %= divisor; in DigitGenCounted()
489 (static_cast<uint64_t>(integrals) << -one.e()) + fractionals; in DigitGenCounted()
/third_party/skia/third_party/externals/icu/source/i18n/
Ddouble-conversion-fast-dtoa.cpp349 uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e()); in DigitGen() local
354 BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()), in DigitGen()
363 int digit = integrals / divisor; in DigitGen()
367 integrals %= divisor; in DigitGen()
372 (static_cast<uint64_t>(integrals) << -one.e()) + fractionals; in DigitGen()
459 uint32_t integrals = static_cast<uint32_t>(w.f() >> -one.e()); in DigitGenCounted() local
464 BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()), in DigitGenCounted()
474 int digit = integrals / divisor; in DigitGenCounted()
479 integrals %= divisor; in DigitGenCounted()
489 (static_cast<uint64_t>(integrals) << -one.e()) + fractionals; in DigitGenCounted()
/third_party/node/deps/icu-small/source/i18n/
Ddouble-conversion-fast-dtoa.cpp349 uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e()); in DigitGen() local
354 BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()), in DigitGen()
363 int digit = integrals / divisor; in DigitGen()
367 integrals %= divisor; in DigitGen()
372 (static_cast<uint64_t>(integrals) << -one.e()) + fractionals; in DigitGen()
459 uint32_t integrals = static_cast<uint32_t>(w.f() >> -one.e()); in DigitGenCounted() local
464 BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()), in DigitGenCounted()
474 int digit = integrals / divisor; in DigitGenCounted()
479 integrals %= divisor; in DigitGenCounted()
489 (static_cast<uint64_t>(integrals) << -one.e()) + fractionals; in DigitGenCounted()
/third_party/icu/vendor/double-conversion/upstream/double-conversion/
Dfast-dtoa.cc335 uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e()); in DigitGen() local
340 BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()), in DigitGen()
349 int digit = integrals / divisor; in DigitGen()
353 integrals %= divisor; in DigitGen()
358 (static_cast<uint64_t>(integrals) << -one.e()) + fractionals; in DigitGen()
445 uint32_t integrals = static_cast<uint32_t>(w.f() >> -one.e()); in DigitGenCounted() local
450 BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()), in DigitGenCounted()
460 int digit = integrals / divisor; in DigitGenCounted()
465 integrals %= divisor; in DigitGenCounted()
475 (static_cast<uint64_t>(integrals) << -one.e()) + fractionals; in DigitGenCounted()
Dfixed-dtoa.cc373 uint64_t integrals = significand >> -exponent; in FastFixedDtoa() local
374 uint64_t fractionals = significand - (integrals << -exponent); in FastFixedDtoa()
375 if (integrals > kMaxUInt32) { in FastFixedDtoa()
376 FillDigits64(integrals, buffer, length); in FastFixedDtoa()
378 FillDigits32(static_cast<uint32_t>(integrals), buffer, length); in FastFixedDtoa()
/third_party/icu/icu4c/source/i18n/
Ddouble-conversion-fast-dtoa.cpp349 uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e()); in DigitGen() local
354 BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()), in DigitGen()
363 int digit = integrals / divisor; in DigitGen()
367 integrals %= divisor; in DigitGen()
372 (static_cast<uint64_t>(integrals) << -one.e()) + fractionals; in DigitGen()
459 uint32_t integrals = static_cast<uint32_t>(w.f() >> -one.e()); in DigitGenCounted() local
464 BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()), in DigitGenCounted()
474 int digit = integrals / divisor; in DigitGenCounted()
479 integrals %= divisor; in DigitGenCounted()
489 (static_cast<uint64_t>(integrals) << -one.e()) + fractionals; in DigitGenCounted()
/third_party/boost/boost/math/statistics/
Danderson_darling.hpp91 Real integrals = 0; in anderson_darling_normality_statistic() local
103 integrals += term; in anderson_darling_normality_statistic()
107 integrals -= log(erfcs0); in anderson_darling_normality_statistic()
108 return v.size()*(left_tail + right_tail + integrals); in anderson_darling_normality_statistic()
/third_party/boost/libs/math/doc/quadrature/
Dooura_fourier_integrals.qbk45 Ooura's method for Fourier integrals computes
54 These integrals arise when computing continuous Fourier transform of odd and even functions, respec…
55 Oscillatory integrals are known to cause trouble for standard quadrature methods, so these routines…
135 …d Masatake Mori, ['A robust double exponential formula for Fourier-type integrals.] Journal of com…
Ddouble_exponential.qbk150 Most well-behaved integrals should converge to full machine precision with this termination conditi…
192 It is the absolute difference between the last two approximations, and for well behaved integrals, …
193 The following table illustrates how the errors and conditioning vary for few sample integrals, in e…
216 [h4 Complex integrals]
238 Tanh-sinh quadrature has a unique feature which makes it well suited to handling integrals with eit…
247 However, there are some integrals which may have all of their area near ['both] endpoints, or else …
424 so that for example, many integrals can achieve 100 decimal digit precision after just 7 levels. T…
443 of integrals - even at quad precision - and means that integrators for these types are relatively c…
472 Oscillatory integrals, such as the sinc integral, are poorly approximated by double-exponential qua…
473 …e error estimates and L1 norm are massive for these integrals, but nonetheless, oscillatory integr…
Dtrapezoidal.qbk45 …s://en.wikipedia.org/wiki/Bump_function bump functions] and bell-shaped integrals over the infinit…
56 This is useful for contour integrals (which are manifestly periodic) and high-order numerical diffe…
Dgauss_kronrod.qbk113 …se routines work well with end-point singularities or other "difficult" integrals. In such cases …
/third_party/boost/libs/math/doc/overview/
Dissues.qbk46 * There are a several other integrals: Bulirsch's ['el] functions that could
47 be implemented using Carlson's integrals (Low Priority).
48 * The integrals K(k) and E(k) could be implemented using rational
Doverview.qbk54 Bessel functions, elliptic integrals, sinus cardinals (along with their
87 …all usable for functions returning complex results - and as a result for contour integrals as well.
Droadmap.qbk49 * Domain of elliptic integrals extended.
53 * Ooura's method for evaluation of Fourier integrals.
75 * Update integration routines to support complex valued integrands and contour integrals.
92 …nue to improve numerical integration routines, and in particular add support for contour integrals.
189 …of spurious under/overflow in the incomplete beta and gamma functions, plus the elliptic integrals,
197 * Added __ellint_d, __jacobi_zeta and __heuman_lambda elliptic integrals.
262 * Improve consistency of argument reduction in the elliptic integrals [@https://svn.boost.org/trac/…
Dcredits.qbk25 Xiaogang Zhang worked on the Bessel functions and elliptic integrals for his
/third_party/boost/libs/math/
DREADME.md32 …us the digamma, various factorial functions, Bessel functions, elliptic integrals, hypergeometrics…
56 … functions returning complex results - and hence can be used for computation of contour integrals.
/third_party/boost/libs/math/test/
Dtest_lambert_w_integrals_quad.cpp175 BOOST_AUTO_TEST_CASE( integrals ) in BOOST_AUTO_TEST_CASE() argument
Dtest_lambert_w_integrals_long_double.cpp172 BOOST_AUTO_TEST_CASE( integrals ) in BOOST_AUTO_TEST_CASE() argument
Dtest_lambert_w_integrals_float.cpp172 BOOST_AUTO_TEST_CASE( integrals ) in BOOST_AUTO_TEST_CASE() argument
Dtest_lambert_w_integrals_double.cpp172 BOOST_AUTO_TEST_CASE( integrals ) in BOOST_AUTO_TEST_CASE() argument
Dtest_lambert_w_integrals_float128.cpp176 BOOST_AUTO_TEST_CASE( integrals ) in BOOST_AUTO_TEST_CASE() argument
/third_party/boost/libs/icl/doc/
Dprojects.qbk37 Bitsets are just sets. Sets of unsigned integrals,
110 we will use `nat`[^['k]] for unsigned integrals

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