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diff --git a/winsup/mingw/mingwex/gdtoa/README b/winsup/mingw/mingwex/gdtoa/README deleted file mode 100755 index ce8be5588..000000000 --- a/winsup/mingw/mingwex/gdtoa/README +++ /dev/null @@ -1,357 +0,0 @@ -This directory contains source for a library of binary -> decimal -and decimal -> binary conversion routines, for single-, double-, -and extended-precision IEEE binary floating-point arithmetic, and -other IEEE-like binary floating-point, including "double double", -as in - - T. J. Dekker, "A Floating-Point Technique for Extending the - Available Precision", Numer. Math. 18 (1971), pp. 224-242 - -and - - "Inside Macintosh: PowerPC Numerics", Addison-Wesley, 1994 - -The conversion routines use double-precision floating-point arithmetic -and, where necessary, high precision integer arithmetic. The routines -are generalizations of the strtod and dtoa routines described in - - David M. Gay, "Correctly Rounded Binary-Decimal and - Decimal-Binary Conversions", Numerical Analysis Manuscript - No. 90-10, Bell Labs, Murray Hill, 1990; - http://cm.bell-labs.com/cm/cs/what/ampl/REFS/rounding.ps.gz - -(based in part on papers by Clinger and Steele & White: see the -references in the above paper). - -The present conversion routines should be able to use any of IEEE binary, -VAX, or IBM-mainframe double-precision arithmetic internally, but I (dmg) -have so far only had a chance to test them with IEEE double precision -arithmetic. - -The core conversion routines are strtodg for decimal -> binary conversions -and gdtoa for binary -> decimal conversions. These routines operate -on arrays of unsigned 32-bit integers of type ULong, a signed 32-bit -exponent of type Long, and arithmetic characteristics described in -struct FPI; FPI, Long, and ULong are defined in gdtoa.h. File arith.h -is supposed to provide #defines that cause gdtoa.h to define its -types correctly. File arithchk.c is source for a program that -generates a suitable arith.h on all systems where I've been able to -test it. - -The core conversion routines are meant to be called by helper routines -that know details of the particular binary arithmetic of interest and -convert. The present directory provides helper routines for 5 variants -of IEEE binary floating-point arithmetic, each indicated by one or -two letters: - - f IEEE single precision - d IEEE double precision - x IEEE extended precision, as on Intel 80x87 - and software emulations of Motorola 68xxx chips - that do not pad the way the 68xxx does, but - only store 80 bits - xL IEEE extended precision, as on Motorola 68xxx chips - Q quad precision, as on Sun Sparc chips - dd double double, pairs of IEEE double numbers - whose sum is the desired value - -For decimal -> binary conversions, there are three families of -helper routines: one for round-nearest (or the current rounding -mode on IEEE-arithmetic systems that provide the C99 fegetround() -function, if compiled with -DHonor_FLT_ROUNDS): - - strtof - strtod - strtodd - strtopd - strtopf - strtopx - strtopxL - strtopQ - -one with rounding direction specified: - - strtorf - strtord - strtordd - strtorx - strtorxL - strtorQ - -and one for computing an interval (at most one bit wide) that contains -the decimal number: - - strtoIf - strtoId - strtoIdd - strtoIx - strtoIxL - strtoIQ - -The latter call strtoIg, which makes one call on strtodg and adjusts -the result to provide the desired interval. On systems where native -arithmetic can easily make one-ulp adjustments on values in the -desired floating-point format, it might be more efficient to use the -native arithmetic. Routine strtodI is a variant of strtoId that -illustrates one way to do this for IEEE binary double-precision -arithmetic -- but whether this is more efficient remains to be seen. - -Functions strtod and strtof have "natural" return types, float and -double -- strtod is specified by the C standard, and strtof appears -in the stdlib.h of some systems, such as (at least some) Linux systems. -The other functions write their results to their final argument(s): -to the final two argument for the strtoI... (interval) functions, -and to the final argument for the others (strtop... and strtor...). -Where possible, these arguments have "natural" return types (double* -or float*), to permit at least some type checking. In reality, they -are viewed as arrays of ULong (or, for the "x" functions, UShort) -values. On systems where long double is the appropriate type, one can -pass long double* final argument(s) to these routines. The int value -that these routines return is the return value from the call they make -on strtodg; see the enum of possible return values in gdtoa.h. - -Source files g_ddfmt.c, misc.c, smisc.c, strtod.c, strtodg.c, and ulp.c -should use true IEEE double arithmetic (not, e.g., double extended), -at least for storing (and viewing the bits of) the variables declared -"double" within them. - -One detail indicated in struct FPI is whether the target binary -arithmetic departs from the IEEE standard by flushing denormalized -numbers to 0. On systems that do this, the helper routines for -conversion to double-double format (when compiled with -Sudden_Underflow #defined) penalize the bottom of the exponent -range so that they return a nonzero result only when the least -significant bit of the less significant member of the pair of -double values returned can be expressed as a normalized double -value. An alternative would be to drop to 53-bit precision near -the bottom of the exponent range. To get correct rounding, this -would (in general) require two calls on strtodg (one specifying -126-bit arithmetic, then, if necessary, one specifying 53-bit -arithmetic). - -By default, the core routine strtodg and strtod set errno to ERANGE -if the result overflows to +Infinity or underflows to 0. Compile -these routines with NO_ERRNO #defined to inhibit errno assignments. - -Routine strtod is based on netlib's "dtoa.c from fp", and -(f = strtod(s,se)) is more efficient for some conversions than, say, -strtord(s,se,1,&f). Parts of strtod require true IEEE double -arithmetic with the default rounding mode (round-to-nearest) and, on -systems with IEEE extended-precision registers, double-precision -(53-bit) rounding precision. If the machine uses (the equivalent of) -Intel 80x87 arithmetic, the call - _control87(PC_53, MCW_PC); -does this with many compilers. Whether this or another call is -appropriate depends on the compiler; for this to work, it may be -necessary to #include "float.h" or another system-dependent header -file. - -Source file strtodnrp.c gives a strtod that does not require 53-bit -rounding precision on systems (such as Intel IA32 systems) that may -suffer double rounding due to use of extended-precision registers. -For some conversions this variant of strtod is less efficient than the -one in strtod.c when the latter is run with 53-bit rounding precision. - -The values that the strto* routines return for NaNs are determined by -gd_qnan.h, which the makefile generates by running the program whose -source is qnan.c. Note that the rules for distinguishing signaling -from quiet NaNs are system-dependent. For cross-compilation, you need -to determine arith.h and gd_qnan.h suitably, e.g., using the -arithmetic of the target machine. - -C99's hexadecimal floating-point constants are recognized by the -strto* routines (but this feature has not yet been heavily tested). -Compiling with NO_HEX_FP #defined disables this feature. - -When compiled with -DINFNAN_CHECK, the strto* routines recognize C99's -NaN and Infinity syntax. Moreover, unless No_Hex_NaN is #defined, the -strto* routines also recognize C99's NaN(...) syntax: they accept -(case insensitively) strings of the form NaN(x), where x is a string -of hexadecimal digits and spaces; if there is only one string of -hexadecimal digits, it is taken for the fraction bits of the resulting -NaN; if there are two or more strings of hexadecimal digits, each -string is assigned to the next available sequence of 32-bit words of -fractions bits (starting with the most significant), right-aligned in -each sequence. - -For binary -> decimal conversions, I've provided just one family -of helper routines: - - g_ffmt - g_dfmt - g_ddfmt - g_xfmt - g_xLfmt - g_Qfmt - -which do a "%g" style conversion either to a specified number of decimal -places (if their ndig argument is positive), or to the shortest -decimal string that rounds to the given binary floating-point value -(if ndig <= 0). They write into a buffer supplied as an argument -and return either a pointer to the end of the string (a null character) -in the buffer, if the buffer was long enough, or 0. Other forms of -conversion are easily done with the help of gdtoa(), such as %e or %f -style and conversions with direction of rounding specified (so that, if -desired, the decimal value is either >= or <= the binary value). -On IEEE-arithmetic systems that provide the C99 fegetround() function, -if compiled with -DHonor_FLT_ROUNDS, these routines honor the current -rounding mode. - -For an example of more general conversions based on dtoa(), see -netlib's "printf.c from ampl/solvers". - -For double-double -> decimal, g_ddfmt() assumes IEEE-like arithmetic -of precision max(126, #bits(input)) bits, where #bits(input) is the -number of mantissa bits needed to represent the sum of the two double -values in the input. - -The makefile creates a library, gdtoa.a. To use the helper -routines, a program only needs to include gdtoa.h. All the -source files for gdtoa.a include a more extensive gdtoaimp.h; -among other things, gdtoaimp.h has #defines that make "internal" -names end in _D2A. To make a "system" library, one could modify -these #defines to make the names start with __. - -Various comments about possible #defines appear in gdtoaimp.h, -but for most purposes, arith.h should set suitable #defines. - -Systems with preemptive scheduling of multiple threads require some -manual intervention. On such systems, it's necessary to compile -dmisc.c, dtoa.c gdota.c, and misc.c with MULTIPLE_THREADS #defined, -and to provide (or suitably #define) two locks, acquired by -ACQUIRE_DTOA_LOCK(n) and freed by FREE_DTOA_LOCK(n) for n = 0 or 1. -(The second lock, accessed in pow5mult, ensures lazy evaluation of -only one copy of high powers of 5; omitting this lock would introduce -a small probability of wasting memory, but would otherwise be harmless.) -Routines that call dtoa or gdtoa directly must also invoke freedtoa(s) -to free the value s returned by dtoa or gdtoa. It's OK to do so whether -or not MULTIPLE_THREADS is #defined, and the helper g_*fmt routines -listed above all do this indirectly (in gfmt_D2A(), which they all call). - -By default, there is a private pool of memory of length 2000 bytes -for intermediate quantities, and MALLOC (see gdtoaimp.h) is called only -if the private pool does not suffice. 2000 is large enough that MALLOC -is called only under very unusual circumstances (decimal -> binary -conversion of very long strings) for conversions to and from double -precision. For systems with preemptively scheduled multiple threads -or for conversions to extended or quad, it may be appropriate to -#define PRIVATE_MEM nnnn, where nnnn is a suitable value > 2000. -For extended and quad precisions, -DPRIVATE_MEM=20000 is probably -plenty even for many digits at the ends of the exponent range. -Use of the private pool avoids some overhead. - -Directory test provides some test routines. See its README. -I've also tested this stuff (except double double conversions) -with Vern Paxson's testbase program: see - - V. Paxson and W. Kahan, "A Program for Testing IEEE Binary-Decimal - Conversion", manuscript, May 1991, - ftp://ftp.ee.lbl.gov/testbase-report.ps.Z . - -(The same ftp directory has source for testbase.) - -Some system-dependent additions to CFLAGS in the makefile: - - HU-UX: -Aa -Ae - OSF (DEC Unix): -ieee_with_no_inexact - SunOS 4.1x: -DKR_headers -DBad_float_h - -If you want to put this stuff into a shared library and your -operating system requires export lists for shared libraries, -the following would be an appropriate export list: - - dtoa - freedtoa - g_Qfmt - g_ddfmt - g_dfmt - g_ffmt - g_xLfmt - g_xfmt - gdtoa - strtoIQ - strtoId - strtoIdd - strtoIf - strtoIx - strtoIxL - strtod - strtodI - strtodg - strtof - strtopQ - strtopd - strtopdd - strtopf - strtopx - strtopxL - strtorQ - strtord - strtordd - strtorf - strtorx - strtorxL - -When time permits, I (dmg) hope to write in more detail about the -present conversion routines; for now, this README file must suffice. -Meanwhile, if you wish to write helper functions for other kinds of -IEEE-like arithmetic, some explanation of struct FPI and the bits -array may be helpful. Both gdtoa and strtodg operate on a bits array -described by FPI *fpi. The bits array is of type ULong, a 32-bit -unsigned integer type. Floating-point numbers have fpi->nbits bits, -with the least significant 32 bits in bits[0], the next 32 bits in -bits[1], etc. These numbers are regarded as integers multiplied by -2^e (i.e., 2 to the power of the exponent e), where e is the second -argument (be) to gdtoa and is stored in *exp by strtodg. The minimum -and maximum exponent values fpi->emin and fpi->emax for normalized -floating-point numbers reflect this arrangement. For example, the -P754 standard for binary IEEE arithmetic specifies doubles as having -53 bits, with normalized values of the form 1.xxxxx... times 2^(b-1023), -with 52 bits (the x's) and the biased exponent b represented explicitly; -b is an unsigned integer in the range 1 <= b <= 2046 for normalized -finite doubles, b = 0 for denormals, and b = 2047 for Infinities and NaNs. -To turn an IEEE double into the representation used by strtodg and gdtoa, -we multiply 1.xxxx... by 2^52 (to make it an integer) and reduce the -exponent e = (b-1023) by 52: - - fpi->emin = 1 - 1023 - 52 - fpi->emax = 1046 - 1023 - 52 - -In various wrappers for IEEE double, we actually write -53 + 1 rather -than -52, to emphasize that there are 53 bits including one implicit bit. -Field fpi->rounding indicates the desired rounding direction, with -possible values - FPI_Round_zero = toward 0, - FPI_Round_near = unbiased rounding -- the IEEE default, - FPI_Round_up = toward +Infinity, and - FPI_Round_down = toward -Infinity -given in gdtoa.h. - -Field fpi->sudden_underflow indicates whether strtodg should return -denormals or flush them to zero. Normal floating-point numbers have -bit fpi->nbits in the bits array on. Denormals have it off, with -exponent = fpi->emin. Strtodg provides distinct return values for normals -and denormals; see gdtoa.h. - -Compiling g__fmt.c, strtod.c, and strtodg.c with -DUSE_LOCALE causes -the decimal-point character to be taken from the current locale; otherwise -it is '.'. - -Source files dtoa.c and strtod.c in this directory are derived from -netlib's "dtoa.c from fp" and are meant to function equivalently. -When compiled with Honor_FLT_ROUNDS #defined (on systems that provide -FLT_ROUNDS and fegetround() as specified in the C99 standard), they -honor the current rounding mode. Because FLT_ROUNDS is buggy on some -(Linux) systems -- not reflecting calls on fesetround(), as the C99 -standard says it should -- when Honor_FLT_ROUNDS is #defined, the -current rounding mode is obtained from fegetround() rather than from -FLT_ROUNDS, unless Trust_FLT_ROUNDS is also #defined. - -Compile with -DUSE_LOCALE to use the current locale; otherwise -decimal points are assumed to be '.'. With -DUSE_LOCALE, unless -you also compile with -DNO_LOCALE_CACHE, the details about the -current "decimal point" character string are cached and assumed not -to change during the program's execution. - -Please send comments to David M. Gay (dmg at acm dot org, with " at " -changed at "@" and " dot " changed to "."). |