ceph/src/boost/libs/math/doc/sf/pow.qbk

   1 [section:ct_pow Compile Time Power of a Runtime Base]
   2
   3 The `pow` function effectively computes the compile-time integral
   4 power of a run-time base.
   5
   6 [h4 Synopsis]
   7
   8 [@../../../../boost/math/special_functions/pow.hpp `#include <boost/math/special_functions/pow.hpp>`]
   9
  10     namespace boost { namespace math {
  11
  12     template <int N, typename T>
  13     ``__sf_result`` pow(T base);
  14
  15     template <int N, typename T, class Policy>
  16     ``__sf_result`` pow(T base, const Policy& policy);
  17
  18     }}
  19
  20 [h4 Rationale and Usage]
  21
  22 Computing the power of a number with an exponent that is known
  23 at compile time is a common need for programmers. In such cases,
  24 the usual method is to avoid the overhead implied by
  25 the `pow`, `powf` and `powl` C functions by hardcoding an expression
  26 such as:
  27
  28     // Hand-written 8th power of a 'base' variable
  29     double result = base*base*base*base*base*base*base*base;
  30
  31 However, this kind of expression is not really readable (knowing the
  32 value of the exponent involves counting the number of occurrences of /base/),
  33 error-prone (it's easy to forget an occurrence), syntactically bulky, and
  34 non-optimal in terms of performance.
  35
  36 The pow function of Boost.Math helps writing this kind expression along
  37 with solving all the problems listed above:
  38
  39     // 8th power of a 'base' variable using math::pow
  40     double result = pow<8>(base);
  41
  42 The expression is now shorter, easier to read, safer, and even faster.
  43 Indeed, `pow` will compute the expression such that only log2(N)
  44 products are made for a power of N. For instance in the
  45 example above, the resulting expression will be the same as if we had
  46 written this, with only one computation of each identical subexpression:
  47
  48     // Internal effect of pow<8>(base)
  49     double result = ((base*base)*(base*base))*((base*base)*(base*base));
  50
  51 Only 3 different products were actually computed.
  52
  53
  54 [h4 Return Type]
  55
  56 The return type of these functions is computed using the __arg_promotion_rules.
  57 For example:
  58
  59 * If T is a `float`, the return type is a `float`.
  60 * If T is a `long double`, the return type is a `long double`.
  61 * Otherwise, the return type is a `double`.
  62
  63 [h4 Policies]
  64
  65 [optional_policy]
  66
  67 [h4 Error Handling]
  68
  69 Two cases of errors can occur when using `pow`:
  70
  71 * In case of null base and negative exponent, an __overflow_error occurs since
  72 this operation is a division by 0 (it equals to 1/0).
  73 * In case of null base and null exponent, an __indeterminate_result_error
  74 occurs since the result of this operation is indeterminate.
  75 Those errors follow the
  76 [link math_toolkit.error_handling
  77 general policies of error handling in Boost.Math].
  78
  79 The default overflow error policy is `throw_on_error`. A call like `pow<-2>(0)`
  80 will thus throw a `std::overflow_error` exception. As shown in the
  81 link given above, other error handling policies can be used:
  82
  83 * `errno_on_error`: Sets `::errno`  to `ERANGE` and returns `std::numeric_limits<T>::infinity()`.
  84 * `ignore_error`: Returns `std::numeric_limits<T>::infinity()`.
  85 * `user_error`: Returns the result of `boost::math::policies::user_overflow_error`:
  86    this function must be defined by the user.
  87
  88 The default indeterminate result error policy is `ignore_error`, which for this
  89 function returns 1 since it's the most commonly chosen result for a power of 0.
  90 Here again, other error handling policies can be used:
  91
  92 * `throw_on_error`: Throws `std::domain_error`
  93 * `errno_on_error`: Sets `::errno`  to `EDOM` and returns 1.
  94 * `user_error`: Returns the result of `boost::math::policies::user_indeterminate_result_error`:
  95    this function must be defined by the user.
  96
  97 Here is an example of error handling customization where we want to
  98 specify the result that has to be returned in case of error. We will
  99 thus use the `user_error` policy, by passing as second argument an
 100 instance of an overflow_error policy templated with `user_error`:
 101
 102     // First we open the boost::math::policies namespace and define the `user_overflow_error`
 103     // by making it return the value we want in case of error (-1 here)
 104
 105     namespace boost { namespace math { namespace policies {
 106     template <class T>
 107     T user_overflow_error(const char*, const char*, const T&)
 108     { return -1; }
 109     }}}
 110
 111
 112     // Then we invoke pow and indicate that we want to use the user_error policy
 113     using boost::math::policies;
 114     double result = pow<-5>(base, policy<overflow_error<user_error> >());
 115
 116     // We can now test the returned value and treat the special case if needed:
 117     if (result == -1)
 118     {
 119         // there was an error, do something...
 120     }
 121
 122 Another way is to redefine the default `overflow_error` policy by using the
 123 BOOST_MATH_OVERFLOW_ERROR_POLICY macro. Once the `user_overflow_error` function
 124 is defined as above, we can achieve the same result like this:
 125
 126     // Redefine the default error_overflow policy
 127     #define BOOST_MATH_OVERFLOW_ERROR_POLICY user_error
 128     #include <boost/math/special_functions/pow.hpp>
 129
 130     // From this point, passing a policy in argument is no longer needed, a call like this one
 131     // will return -1 in case of error:
 132
 133     double result = pow<-5>(base);
 134
 135
 136 [h4 Acknowledgements]
 137
 138 Bruno Lalande submitted this addition to Boost.Math.
 139
 140 '''
 141 Thanks to Joaqu&#xed;n L&#xf3;pez Mu&#xf1;oz and Scott McMurray for their help in
 142 improving the implementation.
 143 '''
 144
 145 [h4 References]
 146
 147 D.E. Knuth, ['The Art of Computer Programming, Vol. 2: Seminumerical Algorithms], 2nd ed., Addison-Wesley, Reading, MA, 1981
 148
 149 [endsect]
 150
 151 [/
 152   Copyright 2008 Bruno Lalande.
 153   Distributed under the Boost Software License, Version 1.0.
 154   (See accompanying file LICENSE_1_0.txt or copy at
 155   http://www.boost.org/LICENSE_1_0.txt).
 156 ]
 157