diff options
| -rw-r--r-- | AUTHORS | 7 | ||||
| -rw-r--r-- | mpfr.texi | 96 |
2 files changed, 51 insertions, 52 deletions
@@ -9,10 +9,9 @@ Mathieu Dutour asin.c, atan.c and gamma.c Vincent Lefèvre Main author David Daney Hyperbolic and inverse hyperbolic functions, base-2 and base-10 exponential and logarithm, factorial -Patrick Pélissier Working on low-precision optimizations -Laurent Fousse Original version of sum.c. +Patrick Pélissier Main author +Laurent Fousse Original version of sum.c All authors are included in the MPFR mailing-list <mpfr@loria.fr>. This is the preferred way to contact us. For further information, please -look at the MPFR web page <http://www.mpfr.org/> or -<http://www.loria.fr/projets/mpfr/>. +look at the MPFR web page <http://www.mpfr.org/>. @@ -446,7 +446,7 @@ of a floating-point number; the corresponding C data type is @code{mp_prec_t}. The precision can be any integer between @code{MPFR_PREC_MIN} and @code{MPFR_PREC_MAX}. In the current implementation, @code{MPFR_PREC_MIN} -is equal to 2 and @code{MPFR_PREC_MAX} is equal to @code{ULONG_MAX}/2. +is equal to 2. @cindex Rounding Modes @tindex @code{mp_rnd_t} @@ -650,7 +650,7 @@ The precision can be any integer between @code{MPFR_PREC_MIN} and @end deftypefun @deftypefun mp_prec_t mpfr_get_default_prec (void) -Returns the default MPFR precision in bits. +Return the default MPFR precision in bits. @end deftypefun @need 2000 @@ -700,7 +700,7 @@ number of bits used to store its mantissa. These functions assign new values to already initialized floats (@pxref{Initialization Functions}). When using any functions using @code{intmax_t}, you must include @code{<stdint.h>} or @code{<inttypes.h>} -before @file{mpfr.h}, to allow @file{mpfr.h} to define prototypes for +before @file{mpfr.h}, to allow @file{mpfr.h} to define prototypes for these functions. @deftypefun int mpfr_set (mpfr_t @var{rop}, mpfr_t @var{op}, mp_rnd_t @var{rnd}) @@ -716,10 +716,10 @@ these functions. Set the value of @var{rop} from @var{op}, rounded towards the given direction @var{rnd}. Note that the input 0 is converted to +0 by @code{mpfr_set_ui}, -@code{mpfr_set_si}, @code{mpfr_set_sj}, @code{mpfr_set_uj}, +@code{mpfr_set_si}, @code{mpfr_set_sj}, @code{mpfr_set_uj}, @code{mpfr_set_z}, @code{mpfr_set_q} and @code{mpfr_set_f}, regardless of the rounding mode. -If the system doesn't support IEEE 754 standard, @code{mpfr_set_d} and +If the system doesn't support the IEEE-754 standard, @code{mpfr_set_d} and @code{mpfr_set_ld} might not preserve the signed zeros. @end deftypefun @@ -766,18 +766,18 @@ using a third auxiliary variable. Parsing follows the standard C @code{strtod} function. This means optional leading whitespace, an optional @code{+} or @code{-}, mantissa digits, and an - optional exponent consisting of an @code{e} or @code{E} (if - @code{@var{base} <= 10}) or @code{@@}, an optional sign, and digits. + optional exponent consisting of an @code{e} or @code{E} (if + @math{@var{base} @le{} 10}) or @code{@@}, an optional sign, and digits. A hex mantissa can be given with a leading @code{0x} or @code{0}', in which case @code{p} or @code{P} may introduce an optional binary exponent. A binary mantissa can be given with a leading @code{0b} or @code{0B}, in which case - @code{e}, @code{E}, @code{p}, @code{P} or @code{@@} may introduce the + @code{e}, @code{E}, @code{p}, @code{P} or @code{@@} may introduce the binary exponent. - In addition @code{infinity}, @code{inf} (if @code{@var{base} <= 10} ) + In addition @code{infinity}, @code{inf} (if @math{@var{base} @le{} 10}) or @code{@@inf@@} with an optional sign, or @code{nan}, - @code{nan(n-char-sequence)} (if @code{@var{base} <= 10} ), @code{@@nan@@} + @code{nan(n-char-sequence)} (if @math{@var{base} @le{} 10}), @code{@@nan@@} or @code{@@nan@@(n-char-sequence)} all non case significant, can be given. A @code{n-char-sequence} is a string containing only digits (0, 1, 2, ..., 9) and non-digits (_, a, b, ..., z, A, B, ..., Z). @@ -786,7 +786,7 @@ using a third auxiliary variable. be valid. If an exponent has no digits it's ignored and parsing stops after the mantissa. If an @code{0x}, @code{0X}, @code{0b} or @code{0B} is not followed by hexadecimal/binary digits, parsing stops - after the first @code{0}: + after the first @code{0}: the subject sequence is defined as the longest initial subsequence of the input string, starting with the first non-white-space character, that is of the expected form. @@ -797,18 +797,18 @@ using a third auxiliary variable. whereas @code{@@} represents a power of the base (i.e. 16). If the argument @var{base} is different from 0, it must be in the range 2 - to 62. For bases up to 36, + to 62. For bases up to 36, case is ignored; upper-case and lower-case letters have the same - value; for bases 37 to 62, upper-case letter represent the usual + value; for bases 37 to 62, upper-case letter represent the usual 10..35, while lower-case letter represent 36..61. If @code{base} is 0, then it tries to indentify the used base: if the mantissa begins with the '0x' prefix, it assumes that @var{base} is 16. - If it begins with '0b', it assumes that @var{base} is 2. Otherwise, it + If it begins with '0b', it assumes that @var{base} is 2. Otherwise, it assumes it is 10. It returns an usual ternary value. - If @var{endptr} is not @code{NULL}, a pointer to the character after the last + If @var{endptr} is not @code{NULL}, a pointer to the character after the last character used in the conversion is stored in the location referenced by @var{endptr}. @@ -869,7 +869,7 @@ and @m{@var{d}\times 2^{exp}, @var{d} times 2 raised to @var{exp}} equals @deftypefunx {unsigned long} mpfr_get_ui (mpfr_t @var{op}, mp_rnd_t @var{rnd}) @deftypefunx intmax_t mpfr_get_sj (mpfr_t @var{op}, mp_rnd_t @var{rnd}) @deftypefunx uintmax_t mpfr_get_uj (mpfr_t @var{op}, mp_rnd_t @var{rnd}) -Convert @var{op} to a @code{long}, an @code{unsigned long}, +Convert @var{op} to a @code{long}, an @code{unsigned long}, an @code{intmax_t} or an @code{uintmax_t} (respectively) after rounding it with respect to @var{rnd}. If @var{op} is NaN, the result is undefined. @@ -896,7 +896,7 @@ behavior is undefined. @end deftypefun @deftypefun void mpfr_get_z (mpz_t @var{rop}, mpfr_t @var{op}, mp_rnd_t @var{rnd}) -Convert @var{op} to a @code{mpz_t}, after rounding it with respect to +Convert @var{op} to a @code{mpz_t}, after rounding it with respect to @var{rnd}. If @var{op} is NaN or Inf, the result is undefined. @end deftypefun @@ -922,7 +922,7 @@ the current allocation function, and a pointer to the string is returned. To free the returned string, you must use @code{mpfr_free_str}. If @var{str} is not a null pointer, it should point to a block of storage -large enough for the mantissa, i.e., at least @code{max(@var{n} + 2, 7)}. +large enough for the mantissa, i.e., at least @code{max(@var{n} + 2, 7)}. The extra two bytes are for a possible minus sign, and for the terminating null character. @@ -940,7 +940,7 @@ case a null pointer is returned. @deftypefun void mpfr_free_str (char *@var{str}) Free a string allocated by @code{mpfr_get_str} using the current unallocation -function (preliminary interface). +function (preliminary interface). The block is assumed to be @code{strlen(@var{str})+1} bytes. For more information about how it is done: @pxref{Custom Allocation,,, gmp,GNU MP}. @@ -1097,7 +1097,7 @@ Compare @var{op1} and @var{op2}. Return a positive value if @math{@var{op1} > @math{@var{op1} < @var{op2}}. Both @var{op1} and @var{op2} are considered to their full own precision, which may differ. -If one of the operands is NaN (Not-a-Number), return zero and set +If one of the operands is NaN (Not-a-Number), return zero and set the erange flag. @end deftypefun @@ -1111,7 +1111,7 @@ the power @var{e}}. Similar as above. Compare @math{|@var{op1}|} and @math{|@var{op2}|}. Return a positive value if @math{|@var{op1}| > |@var{op2}|}, zero if @math{|@var{op1}| = |@var{op2}|}, and a negative value if @math{|@var{op1}| < |@var{op2}|}. -If one of the operands is NaN (Not-a-Number), it returns 0 and set +If one of the operands is NaN (Not-a-Number), return zero and set the erange flag. @end deftypefun @@ -1169,7 +1169,7 @@ compared), zero otherwise. @cindex Special functions All those functions, except explicitly stated, return zero for an -exact return value, a positive value for a return value larger than the +exact return value, a positive value for a return value larger than the exact result, and a negative value otherwise. @deftypefun int mpfr_log (mpfr_t @var{rop}, mpfr_t @var{op}, mp_rnd_t @var{rnd}) @@ -1277,19 +1277,21 @@ If any operand is negative, the return value is NaN. Set @var{rop} to the logarithm of 2, the value of @m{\pi,Pi}, the value of Euler's constant 0.577@dots{}, respectively, rounded in the direction @var{rnd}. These functions cache the computed values to avoid other -calculations if a lower or equal precision is requested. To free theses caches, +calculations if a lower or equal precision is requested. To free these caches, use @code{mpfr_free_cache}. @end deftypefun @deftypefun void mpfr_free_cache (void) Free the cache used by the functions computing constants if needed -(currently +(currently @code{mpfr_const_log2}, @code{mpfr_const_pi} and @code{mpfr_const_euler}). @end deftypefun @deftypefun int mpfr_sum (mpfr_t @var{rop}, const mpfr_t* const @var{tab}[], unsigned long @var{n}, mp_rnd_t @var{rnd}) -Set @var{ret} to the sum of all elements of @var{tab} whose size is @var{n}, rounded in the direction @var{rnd}. Warning, @var{tab} is a table of pointer to mpfr_t, not a table of mpfr_t (priliminary interface). +Set @var{ret} to the sum of all elements of @var{tab} whose size is @var{n}, +rounded in the direction @var{rnd}. Warning, @var{tab} is a table of pointers +to mpfr_t, not a table of mpfr_t (preliminary interface). @end deftypefun @node Input and Output Functions, Integer Related Functions, Special Functions, MPFR Interface @@ -1494,7 +1496,7 @@ Return the MPFR version, as a null-terminated string. @defmacx MPFR_VERSION_MINOR @defmacx MPFR_VERSION_PATCHLEVEL @code{MPFR_VERSION} is the version of MPFR as a preprocessing constant. -@code{MPFR_VERSION_MAJOR}, @code{MPFR_VERSION_MINOR} and +@code{MPFR_VERSION_MAJOR}, @code{MPFR_VERSION_MINOR} and @code{MPFR_VERSION_PATCHLEVEL} are respectively the major, minor and patch level of MPFR version, as preprocessing constants. @end defmac @@ -1502,7 +1504,7 @@ level of MPFR version, as preprocessing constants. @deftypefn Macro long MPFR_VERSION_NUM (@var{major}, @var{minor}, @var{patchlevel}) Create an integer in the same format as used by @code{MPFR_VERSION} from the given @var{major}, @var{minor} and @var{patchlevel}. -Here is an example of how to check the MPFR version at compiled time: +Here is an example of how to check the MPFR version at compile time: @example #if (!defined(MPFR_VERSION) || (MPFR_VERSION<MPFR_VERSION_NUM(2,1,0))) # error "Wrong MPFR version." @@ -1515,16 +1517,16 @@ Here is an example of how to check the MPFR version at compiled time: @cindex Rounding Modes @deftypefun void mpfr_set_default_rounding_mode (mp_rnd_t @var{rnd}) -Sets the default rounding mode to @var{rnd}. +Set the default rounding mode to @var{rnd}. The default rounding mode is to nearest initially. @end deftypefun @deftypefun mp_rnd_t mpfr_get_default_rounding_mode (void) -Gets the default rounding mode. +Get the default rounding mode. @end deftypefun @deftypefun int mpfr_prec_round (mpfr_t @var{x}, mp_prec_t @var{prec}, mp_rnd_t @var{rnd}) -Rounds @var{x} according to @var{rnd} with precision @var{prec}, which +Round @var{x} according to @var{rnd} with precision @var{prec}, which must be an integer between @code{MPFR_PREC_MIN} and @code{MPFR_PREC_MAX} (otherwise the behavior is undefined). If @var{prec} is greater or equal to the precision of @var{x}, then new @@ -1538,7 +1540,7 @@ direction. In both cases, the precision of @var{x} is changed to @var{prec}. @end deftypefun @deftypefun {const char *} mpfr_print_rnd_mode (mp_rnd_t @var{rnd}) -Returns the input string (GMP_RNDD, GMP_RNDU, GMP_RNDN, GMP_RNDZ) +Return the input string (GMP_RNDD, GMP_RNDU, GMP_RNDN, GMP_RNDZ) corresponding to the rounding mode @var{rnd} or a null pointer if @var{rnd} is an invalid rounding mode. @end deftypefun @@ -1580,7 +1582,7 @@ behavior will be undefined, in the sense of the ISO C standard. @deftypefunx mp_exp_t mpfr_get_emax_min (void) @deftypefunx mp_exp_t mpfr_get_emax_max (void) Return the minimum and maximum of the smallest and largest exponents -allowed for @code{mpfr_set_emin} and @code{mpfr_set_emax}. Theses values +allowed for @code{mpfr_set_emin} and @code{mpfr_set_emax}. These values are implementation dependent; it is possible to create a non portable program by writting @code{mpfr_set_emax(mpfr_get_emax_max())} and @code{mpfr_set_emin(mpfr_get_emin_min())} since the values @@ -1619,7 +1621,7 @@ Clear all global flags (underflow, overflow, inexact, invalid, erange). @deftypefunx int mpfr_nanflag_p (void) @deftypefunx int mpfr_inexflag_p (void) @deftypefunx int mpfr_erangeflag_p (void) -Return the corresponding (underflow, overflow, invalid, inexact, erange) +Return the corresponding (underflow, overflow, invalid, inexact, erange) flag, which is non-zero iff the flag is set. @end deftypefun @@ -1637,7 +1639,8 @@ flag, which is non-zero iff the flag is set. @section Advanced Functions @cindex Advanced Functions -All the given interface are preliminary. It might change incompatibly in future revisions. +All the given interfaces are preliminary. They might change incompatibly in +future revisions. @defmac MPFR_DECL_INIT (@var{name}, @var{prec}) This macro declares @var{name} as an automatic variable of type @code{mpfr_t}, @@ -1647,22 +1650,22 @@ You must use this macro in the declaration section. This macro is much faster th drawbacks: @itemize @bullet -@item You @strong{must not} call @code{mpfr_clear} with variables +@item You @strong{must not} call @code{mpfr_clear} with variables created with this macro (The storage is allocated at the point of declaration and deallocated when the brace-level is exited.). @item You @strong{can not} change their precision. @item You @strong{should not} create variables with huge precision with this macro. @item Your compiler must support @samp{Non-Constant Initializers} (standard -in C++ and ISO C99) and @samp{Tokken Pasting} +in C++ and ISO C99) and @samp{Token Pasting} (standard in ISO C89). If @var{prec} is not a compiler constant, your compiler must support @samp{Variable-length automatic arrays} (standard in ISO C99). -@samp{GCC 2.95.3} supports all theses features. +@samp{GCC 2.95.3} supports all these features. @end itemize @end defmac @deftypefun void mpfr_inits (mpfr_t @var{x}, ...) Initialize all the @code{mpfr_t} variables of the given @code{va_list}, -set their precision to be the default precision and their value to NaN. +set their precision to be the default precision and their value to NaN. See @code{mpfr_init} for more details. The @code{va_list} is assumed to be composed only of type @code{mpfr_t}. It begins from @var{x}. It ends when it encounters a @code{NULL} pointer. @@ -1672,7 +1675,7 @@ It begins from @var{x}. It ends when it encounters a @code{NULL} pointer. @deftypefun void mpfr_inits2 (mp_prec_t @var{prec}, mpfr_t @var{x}, ...) Initialize all the @code{mpfr_t} variables of the given @code{va_list}, set their precision to be @strong{exactly} -@var{prec} bits and their value to NaN. +@var{prec} bits and their value to NaN. See @code{mpfr_init2} for more details. The @code{va_list} is assumed to be composed only of type @code{mpfr_t}. It begins from @var{x}. It ends when it encounters a @code{NULL} pointer. @@ -1745,7 +1748,7 @@ rounding mode @var{rnd} for all operations and the precision of @var{rop}. @deftypefun int mpfr_mul_2exp (mpfr_t @var{rop}, mpfr_t @var{op1}, unsigned long int @var{op2}, mp_rnd_t @var{rnd}) @deftypefunx int mpfr_div_2exp (mpfr_t @var{rop}, mpfr_t @var{op1}, unsigned long int @var{op2}, mp_rnd_t @var{rnd}) -See @code{mpfr_mul_2ui} and @code{mpfr_div_2ui}. Theses functions are only kept +See @code{mpfr_mul_2ui} and @code{mpfr_div_2ui}. These functions are only kept for compatibility with MPF. @end deftypefun @@ -1767,7 +1770,7 @@ The @code{mpfr_t} type consists of four fields. @item The @code{_mpfr_prec} field is used to store the precision of the variable (in bits); this is not less than @code{MPFR_PREC_MIN}. -@item The @code{_mpfr_sign} field is used to store the sign of the variable. +@item The @code{_mpfr_sign} field is used to store the sign of the variable. @item The @code{_mpfr_exp} field stores the exponent. An exponent of 0 means a radix point just above the most significant @@ -1778,7 +1781,7 @@ A NaN, an Infinity and a Zero are indicated by a special value of the exponent. @item Finally, the @code{_mpfr_d} is a pointer to the limbs, least significant limbs stored first. The number of limbs in use is controlled by @code{_mpfr_prec}, namely -ceil(@code{_mpfr_prec}/@code{BITS_PER_MP_LIMB}). +ceil(@code{_mpfr_prec}/@code{mp_bits_per_limb}). Non-singular values always have the most significant bit of the most significant limb set to 1. When the precision does not correspond to a whole number of limbs, the excess bits at the low end of the data are zero. @@ -1803,7 +1806,7 @@ whole number of limbs, the excess bits at the low end of the data are zero. @deftypefun int mpfr_can_round (mpfr_t @var{b}, mp_exp_t @var{err}, mp_rnd_t @var{rnd1}, mp_rnd_t @var{rnd2}, mp_prec_t @var{prec}) Assuming @var{b} is an approximation of an unknown number @var{x} in direction @var{rnd1} with error at most two to the power -E(b)-@var{err} where E(b) is the exponent of @var{b}, returns a non-zero +E(b)-@var{err} where E(b) is the exponent of @var{b}, return a non-zero value if one is able to round exactly @var{x} to precision @var{prec} with direction @var{rnd2}, and 0 otherwise (including for NaN and Inf). @@ -1832,7 +1835,7 @@ This function @strong{does not modify} its arguments. @unnumbered Contributors The main developers consist of Guillaume Hanrot, Vincent Lef@`evre, -Kevin Ryde and Paul Zimmermann. +Patrick P@'elissier and Paul Zimmermann. We would like to thank Jean-Michel Muller and Joris van der Hoeven for very fruitful discussions at the beginning of that project, Torbj@"orn Granlund @@ -1857,13 +1860,10 @@ contributed the original version of @file{mul_ui.c}, the @file{gmp_op.c} file, and helped to the Windows porting. Jean-Luc R@'emy contributed the @code{mpfr_zeta} code. Ludovic Meunier helped in the design of the @code{mpfr_erf} code. -Patrick P@'elissier has worked on low-precision optimizations -(new internal format), on debugging (specially the file @file{gmp_op.c}) -and on some other functions (@code{MPFR_DECL_INIT}, @code{mpfr_set_sj}, etc.). The development of the MPFR library would not have been possible without the continuous support of LORIA, INRIA and INRIA Lorraine. -The development of MPFR was also supported by a grant +The development of MPFR was also supported by a grant (202F0659 00 MPN 121) from the Conseil R@'egional de Lorraine in 2002. @node References, GNU Free Documentation License, Contributors, Top |