tmp/tmpp7cz_tlc/{from.md → to.md}
RENAMED
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| 1 |
+
### Mathematical constants <a id="math.constants">[[math.constants]]</a>
|
| 2 |
+
|
| 3 |
+
The library-defined partial specializations of mathematical constant
|
| 4 |
+
variable templates are initialized with the nearest representable values
|
| 5 |
+
of e, log₂ e, log₁₀ e, π, $\frac{1}{\pi}$, $\frac{1}{\sqrt{\pi}}$,
|
| 6 |
+
$\ln 2$, $\ln 10$, $\sqrt{2}$, $\sqrt{3}$, $\frac{1}{\sqrt{3}}$, the
|
| 7 |
+
Euler-Mascheroni γ constant, and the golden ratio φ constant
|
| 8 |
+
$\frac{1+\sqrt{5}}{2}$, respectively.
|
| 9 |
+
|
| 10 |
+
Pursuant to [[namespace.std]], a program may partially or explicitly
|
| 11 |
+
specialize a mathematical constant variable template provided that the
|
| 12 |
+
specialization depends on a program-defined type.
|
| 13 |
+
|
| 14 |
+
A program that instantiates a primary template of a mathematical
|
| 15 |
+
constant variable template is ill-formed.
|
| 16 |
+
|
| 17 |
+
<!-- Link reference definitions -->
|
| 18 |
+
[bad.alloc]: support.md#bad.alloc
|
| 19 |
+
[basic.fundamental]: basic.md#basic.fundamental
|
| 20 |
+
[basic.stc.thread]: basic.md#basic.stc.thread
|
| 21 |
+
[basic.types]: basic.md#basic.types
|
| 22 |
+
[bit]: #bit
|
| 23 |
+
[bit.cast]: #bit.cast
|
| 24 |
+
[bit.count]: #bit.count
|
| 25 |
+
[bit.endian]: #bit.endian
|
| 26 |
+
[bit.general]: #bit.general
|
| 27 |
+
[bit.pow.two]: #bit.pow.two
|
| 28 |
+
[bit.rotate]: #bit.rotate
|
| 29 |
+
[bit.syn]: #bit.syn
|
| 30 |
+
[c.math]: #c.math
|
| 31 |
+
[c.math.abs]: #c.math.abs
|
| 32 |
+
[c.math.fpclass]: #c.math.fpclass
|
| 33 |
+
[c.math.hypot3]: #c.math.hypot3
|
| 34 |
+
[c.math.lerp]: #c.math.lerp
|
| 35 |
+
[c.math.rand]: #c.math.rand
|
| 36 |
+
[cfenv]: #cfenv
|
| 37 |
+
[cfenv.syn]: #cfenv.syn
|
| 38 |
+
[class.gslice]: #class.gslice
|
| 39 |
+
[class.gslice.overview]: #class.gslice.overview
|
| 40 |
+
[class.slice]: #class.slice
|
| 41 |
+
[class.slice.overview]: #class.slice.overview
|
| 42 |
+
[cmath.syn]: #cmath.syn
|
| 43 |
+
[cmplx.over]: #cmplx.over
|
| 44 |
+
[complex]: #complex
|
| 45 |
+
[complex.literals]: #complex.literals
|
| 46 |
+
[complex.member.ops]: #complex.member.ops
|
| 47 |
+
[complex.members]: #complex.members
|
| 48 |
+
[complex.numbers]: #complex.numbers
|
| 49 |
+
[complex.ops]: #complex.ops
|
| 50 |
+
[complex.special]: #complex.special
|
| 51 |
+
[complex.syn]: #complex.syn
|
| 52 |
+
[complex.transcendentals]: #complex.transcendentals
|
| 53 |
+
[complex.value.ops]: #complex.value.ops
|
| 54 |
+
[cons.slice]: #cons.slice
|
| 55 |
+
[conv.prom]: expr.md#conv.prom
|
| 56 |
+
[cpp.pragma]: cpp.md#cpp.pragma
|
| 57 |
+
[cpp17.copyassignable]: #cpp17.copyassignable
|
| 58 |
+
[cpp17.copyconstructible]: #cpp17.copyconstructible
|
| 59 |
+
[cpp17.equalitycomparable]: #cpp17.equalitycomparable
|
| 60 |
+
[dcl.init]: dcl.md#dcl.init
|
| 61 |
+
[expr.const]: expr.md#expr.const
|
| 62 |
+
[gslice.access]: #gslice.access
|
| 63 |
+
[gslice.array.assign]: #gslice.array.assign
|
| 64 |
+
[gslice.array.comp.assign]: #gslice.array.comp.assign
|
| 65 |
+
[gslice.array.fill]: #gslice.array.fill
|
| 66 |
+
[gslice.cons]: #gslice.cons
|
| 67 |
+
[implimits]: limits.md#implimits
|
| 68 |
+
[indirect.array.assign]: #indirect.array.assign
|
| 69 |
+
[indirect.array.comp.assign]: #indirect.array.comp.assign
|
| 70 |
+
[indirect.array.fill]: #indirect.array.fill
|
| 71 |
+
[input.iterators]: iterators.md#input.iterators
|
| 72 |
+
[input.output]: input.md#input.output
|
| 73 |
+
[intro.object]: basic.md#intro.object
|
| 74 |
+
[iostate.flags]: input.md#iostate.flags
|
| 75 |
+
[istream.formatted]: input.md#istream.formatted
|
| 76 |
+
[iterator.concept.contiguous]: iterators.md#iterator.concept.contiguous
|
| 77 |
+
[iterator.requirements.general]: iterators.md#iterator.requirements.general
|
| 78 |
+
[library.c]: library.md#library.c
|
| 79 |
+
[mask.array.assign]: #mask.array.assign
|
| 80 |
+
[mask.array.comp.assign]: #mask.array.comp.assign
|
| 81 |
+
[mask.array.fill]: #mask.array.fill
|
| 82 |
+
[math.constants]: #math.constants
|
| 83 |
+
[namespace.std]: library.md#namespace.std
|
| 84 |
+
[numarray]: #numarray
|
| 85 |
+
[numbers]: #numbers
|
| 86 |
+
[numbers.syn]: #numbers.syn
|
| 87 |
+
[numeric.requirements]: #numeric.requirements
|
| 88 |
+
[numerics]: #numerics
|
| 89 |
+
[numerics.general]: #numerics.general
|
| 90 |
+
[numerics.summary]: #numerics.summary
|
| 91 |
+
[output.iterators]: iterators.md#output.iterators
|
| 92 |
+
[rand]: #rand
|
| 93 |
+
[rand.adapt]: #rand.adapt
|
| 94 |
+
[rand.adapt.disc]: #rand.adapt.disc
|
| 95 |
+
[rand.adapt.general]: #rand.adapt.general
|
| 96 |
+
[rand.adapt.ibits]: #rand.adapt.ibits
|
| 97 |
+
[rand.adapt.shuf]: #rand.adapt.shuf
|
| 98 |
+
[rand.device]: #rand.device
|
| 99 |
+
[rand.dist]: #rand.dist
|
| 100 |
+
[rand.dist.bern]: #rand.dist.bern
|
| 101 |
+
[rand.dist.bern.bernoulli]: #rand.dist.bern.bernoulli
|
| 102 |
+
[rand.dist.bern.bin]: #rand.dist.bern.bin
|
| 103 |
+
[rand.dist.bern.geo]: #rand.dist.bern.geo
|
| 104 |
+
[rand.dist.bern.negbin]: #rand.dist.bern.negbin
|
| 105 |
+
[rand.dist.general]: #rand.dist.general
|
| 106 |
+
[rand.dist.norm]: #rand.dist.norm
|
| 107 |
+
[rand.dist.norm.cauchy]: #rand.dist.norm.cauchy
|
| 108 |
+
[rand.dist.norm.chisq]: #rand.dist.norm.chisq
|
| 109 |
+
[rand.dist.norm.f]: #rand.dist.norm.f
|
| 110 |
+
[rand.dist.norm.lognormal]: #rand.dist.norm.lognormal
|
| 111 |
+
[rand.dist.norm.normal]: #rand.dist.norm.normal
|
| 112 |
+
[rand.dist.norm.t]: #rand.dist.norm.t
|
| 113 |
+
[rand.dist.pois]: #rand.dist.pois
|
| 114 |
+
[rand.dist.pois.exp]: #rand.dist.pois.exp
|
| 115 |
+
[rand.dist.pois.extreme]: #rand.dist.pois.extreme
|
| 116 |
+
[rand.dist.pois.gamma]: #rand.dist.pois.gamma
|
| 117 |
+
[rand.dist.pois.poisson]: #rand.dist.pois.poisson
|
| 118 |
+
[rand.dist.pois.weibull]: #rand.dist.pois.weibull
|
| 119 |
+
[rand.dist.samp]: #rand.dist.samp
|
| 120 |
+
[rand.dist.samp.discrete]: #rand.dist.samp.discrete
|
| 121 |
+
[rand.dist.samp.pconst]: #rand.dist.samp.pconst
|
| 122 |
+
[rand.dist.samp.plinear]: #rand.dist.samp.plinear
|
| 123 |
+
[rand.dist.uni]: #rand.dist.uni
|
| 124 |
+
[rand.dist.uni.int]: #rand.dist.uni.int
|
| 125 |
+
[rand.dist.uni.real]: #rand.dist.uni.real
|
| 126 |
+
[rand.eng]: #rand.eng
|
| 127 |
+
[rand.eng.lcong]: #rand.eng.lcong
|
| 128 |
+
[rand.eng.mers]: #rand.eng.mers
|
| 129 |
+
[rand.eng.sub]: #rand.eng.sub
|
| 130 |
+
[rand.predef]: #rand.predef
|
| 131 |
+
[rand.req]: #rand.req
|
| 132 |
+
[rand.req.adapt]: #rand.req.adapt
|
| 133 |
+
[rand.req.dist]: #rand.req.dist
|
| 134 |
+
[rand.req.eng]: #rand.req.eng
|
| 135 |
+
[rand.req.genl]: #rand.req.genl
|
| 136 |
+
[rand.req.seedseq]: #rand.req.seedseq
|
| 137 |
+
[rand.req.urng]: #rand.req.urng
|
| 138 |
+
[rand.synopsis]: #rand.synopsis
|
| 139 |
+
[rand.util]: #rand.util
|
| 140 |
+
[rand.util.canonical]: #rand.util.canonical
|
| 141 |
+
[rand.util.seedseq]: #rand.util.seedseq
|
| 142 |
+
[random.access.iterators]: iterators.md#random.access.iterators
|
| 143 |
+
[res.on.data.races]: library.md#res.on.data.races
|
| 144 |
+
[sf.cmath]: #sf.cmath
|
| 145 |
+
[sf.cmath.assoc.laguerre]: #sf.cmath.assoc.laguerre
|
| 146 |
+
[sf.cmath.assoc.legendre]: #sf.cmath.assoc.legendre
|
| 147 |
+
[sf.cmath.beta]: #sf.cmath.beta
|
| 148 |
+
[sf.cmath.comp.ellint.1]: #sf.cmath.comp.ellint.1
|
| 149 |
+
[sf.cmath.comp.ellint.2]: #sf.cmath.comp.ellint.2
|
| 150 |
+
[sf.cmath.comp.ellint.3]: #sf.cmath.comp.ellint.3
|
| 151 |
+
[sf.cmath.cyl.bessel.i]: #sf.cmath.cyl.bessel.i
|
| 152 |
+
[sf.cmath.cyl.bessel.j]: #sf.cmath.cyl.bessel.j
|
| 153 |
+
[sf.cmath.cyl.bessel.k]: #sf.cmath.cyl.bessel.k
|
| 154 |
+
[sf.cmath.cyl.neumann]: #sf.cmath.cyl.neumann
|
| 155 |
+
[sf.cmath.ellint.1]: #sf.cmath.ellint.1
|
| 156 |
+
[sf.cmath.ellint.2]: #sf.cmath.ellint.2
|
| 157 |
+
[sf.cmath.ellint.3]: #sf.cmath.ellint.3
|
| 158 |
+
[sf.cmath.expint]: #sf.cmath.expint
|
| 159 |
+
[sf.cmath.hermite]: #sf.cmath.hermite
|
| 160 |
+
[sf.cmath.laguerre]: #sf.cmath.laguerre
|
| 161 |
+
[sf.cmath.legendre]: #sf.cmath.legendre
|
| 162 |
+
[sf.cmath.riemann.zeta]: #sf.cmath.riemann.zeta
|
| 163 |
+
[sf.cmath.sph.bessel]: #sf.cmath.sph.bessel
|
| 164 |
+
[sf.cmath.sph.legendre]: #sf.cmath.sph.legendre
|
| 165 |
+
[sf.cmath.sph.neumann]: #sf.cmath.sph.neumann
|
| 166 |
+
[slice.access]: #slice.access
|
| 167 |
+
[slice.arr.assign]: #slice.arr.assign
|
| 168 |
+
[slice.arr.comp.assign]: #slice.arr.comp.assign
|
| 169 |
+
[slice.arr.fill]: #slice.arr.fill
|
| 170 |
+
[slice.ops]: #slice.ops
|
| 171 |
+
[strings]: strings.md#strings
|
| 172 |
+
[template.gslice.array]: #template.gslice.array
|
| 173 |
+
[template.gslice.array.overview]: #template.gslice.array.overview
|
| 174 |
+
[template.indirect.array]: #template.indirect.array
|
| 175 |
+
[template.indirect.array.overview]: #template.indirect.array.overview
|
| 176 |
+
[template.mask.array]: #template.mask.array
|
| 177 |
+
[template.mask.array.overview]: #template.mask.array.overview
|
| 178 |
+
[template.slice.array]: #template.slice.array
|
| 179 |
+
[template.slice.array.overview]: #template.slice.array.overview
|
| 180 |
+
[template.valarray]: #template.valarray
|
| 181 |
+
[template.valarray.overview]: #template.valarray.overview
|
| 182 |
+
[thread.jthread.class]: thread.md#thread.jthread.class
|
| 183 |
+
[thread.thread.class]: thread.md#thread.thread.class
|
| 184 |
+
[utility.arg.requirements]: library.md#utility.arg.requirements
|
| 185 |
+
[valarray.access]: #valarray.access
|
| 186 |
+
[valarray.assign]: #valarray.assign
|
| 187 |
+
[valarray.binary]: #valarray.binary
|
| 188 |
+
[valarray.cassign]: #valarray.cassign
|
| 189 |
+
[valarray.comparison]: #valarray.comparison
|
| 190 |
+
[valarray.cons]: #valarray.cons
|
| 191 |
+
[valarray.members]: #valarray.members
|
| 192 |
+
[valarray.nonmembers]: #valarray.nonmembers
|
| 193 |
+
[valarray.range]: #valarray.range
|
| 194 |
+
[valarray.special]: #valarray.special
|
| 195 |
+
[valarray.sub]: #valarray.sub
|
| 196 |
+
[valarray.syn]: #valarray.syn
|
| 197 |
+
[valarray.transcend]: #valarray.transcend
|
| 198 |
+
[valarray.unary]: #valarray.unary
|
| 199 |
+
|
| 200 |
+
[^1]: In other words, value types. These include arithmetic types,
|
| 201 |
+
pointers, the library class `complex`, and instantiations of
|
| 202 |
+
`valarray` for value types.
|
| 203 |
+
|
| 204 |
+
[^2]: The name of this engine refers, in part, to a property of its
|
| 205 |
+
period: For properly-selected values of the parameters, the period
|
| 206 |
+
is closely related to a large Mersenne prime number.
|
| 207 |
+
|
| 208 |
+
[^3]: The parameter is intended to allow an implementation to
|
| 209 |
+
differentiate between different sources of randomness.
|
| 210 |
+
|
| 211 |
+
[^4]: If a device has n states whose respective probabilities are
|
| 212 |
+
P₀, …, Pₙ₋₁, the device entropy S is defined as
|
| 213 |
+
$S = - \sum_{i=0}^{n-1} P_i \cdot \log P_i$.
|
| 214 |
+
|
| 215 |
+
[^5]: b is introduced to avoid any attempt to produce more bits of
|
| 216 |
+
randomness than can be held in `RealType`.
|
| 217 |
+
|
| 218 |
+
[^6]: The distribution corresponding to this probability density
|
| 219 |
+
function is also known (with a possible change of variable) as the
|
| 220 |
+
Gumbel Type I, the log-Weibull, or the Fisher-Tippett Type I
|
| 221 |
+
distribution.
|
| 222 |
+
|
| 223 |
+
[^7]: [[implimits]] recommends a minimum number of recursively nested
|
| 224 |
+
template instantiations. This requirement thus indirectly suggests a
|
| 225 |
+
minimum allowable complexity for valarray expressions.
|
| 226 |
+
|
| 227 |
+
[^8]: The intent is to specify an array template that has the minimum
|
| 228 |
+
functionality necessary to address aliasing ambiguities and the
|
| 229 |
+
proliferation of temporary objects. Thus, the `valarray` template is
|
| 230 |
+
neither a matrix class nor a field class. However, it is a very
|
| 231 |
+
useful building block for designing such classes.
|
| 232 |
+
|
| 233 |
+
[^9]: This default constructor is essential, since arrays of `valarray`
|
| 234 |
+
may be useful. After initialization, the length of an empty array
|
| 235 |
+
can be increased with the `resize` member function.
|
| 236 |
+
|
| 237 |
+
[^10]: This constructor is the preferred method for converting a C array
|
| 238 |
+
to a `valarray` object.
|
| 239 |
+
|
| 240 |
+
[^11]: This copy constructor creates a distinct array rather than an
|
| 241 |
+
alias. Implementations in which arrays share storage are permitted,
|
| 242 |
+
but they would need to implement a copy-on-reference mechanism to
|
| 243 |
+
ensure that arrays are conceptually distinct.
|
| 244 |
+
|
| 245 |
+
[^12]: BLAS stands for *Basic Linear Algebra Subprograms.* C++ programs
|
| 246 |
+
may instantiate this class. See, for example, Dongarra, Du Croz,
|
| 247 |
+
Duff, and Hammerling: *A set of Level 3 Basic Linear Algebra
|
| 248 |
+
Subprograms*; Technical Report MCS-P1-0888, Argonne National
|
| 249 |
+
Laboratory (USA), Mathematics and Computer Science Division, August,
|
| 250 |
+
1988.
|
| 251 |
+
|
| 252 |
+
[^13]: A mathematical function is mathematically defined for a given set
|
| 253 |
+
of argument values (a) if it is explicitly defined for that set of
|
| 254 |
+
argument values, or (b) if its limiting value exists and does not
|
| 255 |
+
depend on the direction of approach.
|