annotate lib/asinl.c @ 16366:bb182ee4a09d

maint: replace FSF snail-mail addresses with URLs * config/argz.mk, lib/accept4.c, lib/alignof.h, lib/alloca.in.h: * lib/alphasort.c, lib/arcfour.c, lib/arcfour.h, lib/arctwo.c: * lib/arctwo.h, lib/argz.c, lib/arpa_inet.in.h, lib/asnprintf.c: * lib/asprintf.c, lib/assert.in.h, lib/base32.c, lib/base32.h: * lib/base64.c, lib/base64.h, lib/c-ctype.c, lib/c-ctype.h: * lib/c-strcase.h, lib/c-strcasecmp.c, lib/c-strncasecmp.c: * lib/check-version.c, lib/check-version.h, lib/config.charset: * lib/ctype.in.h, lib/des.c, lib/des.h, lib/dup3.c, lib/errno.in.h: * lib/float+.h, lib/fnmatch.c, lib/fnmatch.in.h, lib/fnmatch_loop.c: * lib/fseeko.c, lib/gai_strerror.c, lib/gc-gnulib.c: * lib/gc-libgcrypt.c, lib/gc-pbkdf2-sha1.c, lib/gc.h: * lib/getaddrinfo.c, lib/getdelim.c, lib/getfilecon.c, lib/getline.c: * lib/getlogin_r.c, lib/getpass.c, lib/getpass.h, lib/gettext.h: * lib/gettimeofday.c, lib/glob.in.h, lib/glthread/cond.c: * lib/glthread/cond.h, lib/glthread/lock.c, lib/glthread/lock.h: * lib/glthread/thread.c, lib/glthread/thread.h: * lib/glthread/threadlib.c, lib/glthread/yield.h, lib/hmac-md5.c: * lib/hmac-sha1.c, lib/hmac.h, lib/iconv.c, lib/iconv.in.h: * lib/iconv_close.c, lib/iconv_open.c, lib/inet_ntop.c, lib/isfinite.c: * lib/isinf.c, lib/iswblank.c, lib/langinfo.in.h, lib/link.c: * lib/localcharset.c, lib/localcharset.h, lib/lseek.c, lib/malloc.c: * lib/malloca.c, lib/malloca.h, lib/md2.c, lib/md2.h, lib/md4.c: * lib/md4.h, lib/md5.c, lib/md5.h, lib/memmem.c, lib/mempcpy.c: * lib/memset.c, lib/memxor.c, lib/memxor.h, lib/minmax.h, lib/mktime.c: * lib/msvc-inval.c, lib/msvc-inval.h, lib/msvc-nothrow.c: * lib/msvc-nothrow.h, lib/netdb.in.h, lib/netinet_in.in.h, lib/nproc.c: * lib/nproc.h, lib/obstack_printf.c, lib/pathmax.h, lib/pipe.c: * lib/pipe2.c, lib/poll.c, lib/poll.in.h, lib/printf-args.c: * lib/printf-args.h, lib/printf-parse.c, lib/printf-parse.h: * lib/pselect.c, lib/pthread.in.h, lib/pty-private.h, lib/pty.in.h: * lib/read-file.c, lib/read-file.h, lib/ref-add.sin, lib/ref-del.sin: * lib/regcomp.c, lib/regex.c, lib/regex.h, lib/regex_internal.c: * lib/regex_internal.h, lib/regexec.c, lib/rijndael-alg-fst.c: * lib/rijndael-alg-fst.h, lib/rijndael-api-fst.c: * lib/rijndael-api-fst.h, lib/rint.c, lib/rintf.c, lib/rintl.c: * lib/round.c, lib/roundf.c, lib/roundl.c, lib/scandir.c, lib/select.c: * lib/sha1.c, lib/sha1.h, lib/size_max.h, lib/snprintf.c: * lib/stdalign.in.h, lib/stdarg.in.h, lib/stdbool.in.h: * lib/stddef.in.h, lib/stdint.in.h, lib/stdio.in.h, lib/str-kmp.h: * lib/str-two-way.h, lib/strcasecmp.c, lib/strcasestr.c, lib/strdup.c: * lib/striconv.c, lib/striconv.h, lib/string.in.h, lib/strings.in.h: * lib/strncasecmp.c, lib/strndup.c, lib/strnlen.c, lib/strpbrk.c: * lib/strptime.c, lib/strsep.c, lib/strstr.c, lib/strverscmp.c: * lib/sys_file.in.h, lib/sys_ioctl.in.h, lib/sys_select.in.h: * lib/sys_socket.in.h, lib/sys_stat.in.h, lib/sys_time.in.h: * lib/sys_times.in.h, lib/sys_types.in.h, lib/sys_uio.in.h: * lib/sys_utsname.in.h, lib/sys_wait.in.h, lib/tcgetsid.c: * lib/termios.in.h, lib/time.in.h, lib/time_r.c, lib/timegm.c: * lib/times.c, lib/unictype/3level.h, lib/unictype/3levelbit.h: * lib/unistd.in.h, lib/vasnprintf.c, lib/vasnprintf.h, lib/vasprintf.c: * lib/vsnprintf.c, lib/waitpid.c, lib/wchar.in.h, lib/wctype.in.h: * lib/xsize.h, tests/test-closein.c, tests/test-des.c: * tests/test-fclose.c, tests/test-fgetc.c, tests/test-filevercmp.c: * tests/test-fputc.c, tests/test-fread.c, tests/test-fwrite.c: * tests/test-gc-arcfour.c, tests/test-gc-arctwo.c, tests/test-gc-des.c: * tests/test-gc-hmac-md5.c, tests/test-gc-hmac-sha1.c: * tests/test-gc-md2.c, tests/test-gc-md4.c, tests/test-gc-md5.c: * tests/test-gc-pbkdf2-sha1.c, tests/test-gc-rijndael.c: * tests/test-gc-sha1.c, tests/test-gc.c, tests/test-getdelim.c: * tests/test-getline.c, tests/test-getndelim2.c, tests/test-md2.c: * tests/test-md4.c, tests/test-parse-datetime.c, tests/test-perror.c: * tests/test-perror2.c, tests/test-pipe.c, tests/test-pipe2.c: * tests/test-poll.c, tests/test-quotearg-simple.c: * tests/test-quotearg.c, tests/test-quotearg.h: * tests/test-round-ieee.c, tests/test-round1.c: * tests/test-roundf-ieee.c, tests/test-roundf1.c: * tests/test-roundl-ieee.c, tests/test-roundl.c: * tests/test-safe-alloc.c, tests/test-sigpipe.c: * tests/test-spawn-pipe-child.c, tests/test-spawn-pipe-main.c: * tests/test-strerror.c, tests/test-strerror_r.c: * tests/test-strsignal.c, tests/test-strverscmp.c: * tests/test-xmemdup0.c: Replace FSF snail mail addresses with URLs, as per GNU coding standards. See glibc bug <http://sourceware.org/bugzilla/show_bug.cgi?id=13673>.
author Paul Eggert <eggert@cs.ucla.edu>
date Thu, 09 Feb 2012 21:39:05 -0800
parents cfc88a2774f7
children 2074f2bf7216
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 /*
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2 * ====================================================
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3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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4 *
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5 * Developed at SunPro, a Sun Microsystems, Inc. business.
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6 * Permission to use, copy, modify, and distribute this
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7 * software is freely granted, provided that this notice
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8 * is preserved.
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9 * ====================================================
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10 */
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11
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12 #include <config.h>
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13
c115624bf99a New module 'math'. <math.h> replaces mathl.h.
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14 /* Specification. */
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15 #include <math.h>
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16
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cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'.
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17 #if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
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18
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'.
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19 long double
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20 asinl (long double x)
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21 {
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22 return asin (x);
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23 }
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24
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'.
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25 #else
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26
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27 /*
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28 Long double expansions contributed by
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29 Stephen L. Moshier <moshier@na-net.ornl.gov>
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30 */
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31
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32 /* asin(x)
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33 * Method :
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34 * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
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35 * we approximate asin(x) on [0,0.5] by
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36 * asin(x) = x + x*x^2*R(x^2)
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37 * Between .5 and .625 the approximation is
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38 * asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
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39 * For x in [0.625,1]
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40 * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
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41 *
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42 * Special cases:
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43 * if x is NaN, return x itself;
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44 * if |x|>1, return NaN with invalid signal.
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45 *
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46 */
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47
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48
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49 static const long double
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50 one = 1.0L,
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51 huge = 1.0e+4932L,
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52 pio2_hi = 1.5707963267948966192313216916397514420986L,
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53 pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
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54 pio4_hi = 7.8539816339744830961566084581987569936977E-1L,
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55
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56 /* coefficient for R(x^2) */
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57
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58 /* asin(x) = x + x^3 pS(x^2) / qS(x^2)
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59 0 <= x <= 0.5
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60 peak relative error 1.9e-35 */
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61 pS0 = -8.358099012470680544198472400254596543711E2L,
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62 pS1 = 3.674973957689619490312782828051860366493E3L,
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63 pS2 = -6.730729094812979665807581609853656623219E3L,
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64 pS3 = 6.643843795209060298375552684423454077633E3L,
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65 pS4 = -3.817341990928606692235481812252049415993E3L,
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66 pS5 = 1.284635388402653715636722822195716476156E3L,
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67 pS6 = -2.410736125231549204856567737329112037867E2L,
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68 pS7 = 2.219191969382402856557594215833622156220E1L,
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69 pS8 = -7.249056260830627156600112195061001036533E-1L,
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70 pS9 = 1.055923570937755300061509030361395604448E-3L,
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71
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72 qS0 = -5.014859407482408326519083440151745519205E3L,
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73 qS1 = 2.430653047950480068881028451580393430537E4L,
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74 qS2 = -4.997904737193653607449250593976069726962E4L,
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75 qS3 = 5.675712336110456923807959930107347511086E4L,
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76 qS4 = -3.881523118339661268482937768522572588022E4L,
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77 qS5 = 1.634202194895541569749717032234510811216E4L,
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78 qS6 = -4.151452662440709301601820849901296953752E3L,
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79 qS7 = 5.956050864057192019085175976175695342168E2L,
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80 qS8 = -4.175375777334867025769346564600396877176E1L,
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81 /* 1.000000000000000000000000000000000000000E0 */
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82
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83 /* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
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84 -0.0625 <= x <= 0.0625
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85 peak relative error 3.3e-35 */
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86 rS0 = -5.619049346208901520945464704848780243887E0L,
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87 rS1 = 4.460504162777731472539175700169871920352E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
88 rS2 = -1.317669505315409261479577040530751477488E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
89 rS3 = 1.626532582423661989632442410808596009227E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
90 rS4 = -3.144806644195158614904369445440583873264E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
91 rS5 = -9.806674443470740708765165604769099559553E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
92 rS6 = 5.708468492052010816555762842394927806920E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
93 rS7 = 1.396540499232262112248553357962639431922E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
94 rS8 = -1.126243289311910363001762058295832610344E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
95 rS9 = -4.956179821329901954211277873774472383512E-1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
96 rS10 = 3.313227657082367169241333738391762525780E-1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
97
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
98 sS0 = -4.645814742084009935700221277307007679325E0L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
99 sS1 = 3.879074822457694323970438316317961918430E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
100 sS2 = -1.221986588013474694623973554726201001066E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
101 sS3 = 1.658821150347718105012079876756201905822E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
102 sS4 = -4.804379630977558197953176474426239748977E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
103 sS5 = -1.004296417397316948114344573811562952793E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
104 sS6 = 7.530281592861320234941101403870010111138E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
105 sS7 = 1.270735595411673647119592092304357226607E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
106 sS8 = -1.815144839646376500705105967064792930282E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
107 sS9 = -7.821597334910963922204235247786840828217E-2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
108 /* 1.000000000000000000000000000000000000000E0 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
109
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
110 asinr5625 = 5.9740641664535021430381036628424864397707E-1L;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
111
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
112
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
113 long double
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
114 asinl (long double x)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
115 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
116 long double y, t, p, q;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
117 int sign;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
118
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
119 sign = 1;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
120 y = x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
121 if (x < 0.0L)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
122 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
123 sign = -1;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
124 y = -x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
125 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
126
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
127 if (y >= 1.0L) /* |x|>= 1 */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
128 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
129 if (y == 1.0L)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
130 /* asin(1)=+-pi/2 with inexact */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
131 return x * pio2_hi + x * pio2_lo;
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
132
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
133 return (x - x) / (x - x); /* asin(|x|>1) is NaN */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
134 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
135 else if (y < 0.5L) /* |x| < 0.5 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
136 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
137 if (y < 0.000000000000000006938893903907228377647697925567626953125L) /* |x| < 2**-57 */
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
138 if (huge + y > one)
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
139 return y; /* return x with inexact if x!=0 */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
140
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
141 t = x * x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
142 p = (((((((((pS9 * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
143 + pS8) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
144 + pS7) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
145 + pS6) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
146 + pS5) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
147 + pS4) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
148 + pS3) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
149 + pS2) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
150 + pS1) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
151 + pS0) * t;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
152
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
153 q = (((((((( t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
154 + qS8) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
155 + qS7) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
156 + qS6) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
157 + qS5) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
158 + qS4) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
159 + qS3) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
160 + qS2) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
161 + qS1) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
162 + qS0;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
163
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
164 return x + x * (p / q);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
165 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
166
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
167 else if (y < 0.625) /* 0.625 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
168 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
169 t = y - 0.5625;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
170 p = ((((((((((rS10 * t
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
171 + rS9) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
172 + rS8) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
173 + rS7) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
174 + rS6) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
175 + rS5) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
176 + rS4) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
177 + rS3) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
178 + rS2) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
179 + rS1) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
180 + rS0) * t;
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
181
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
182 q = ((((((((( t
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
183 + sS9) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
184 + sS8) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
185 + sS7) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
186 + sS6) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
187 + sS5) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
188 + sS4) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
189 + sS3) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
190 + sS2) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
191 + sS1) * t
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
192 + sS0;
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
193 t = asinr5625 + p / q;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
194 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
195 else
13051
094f6cfdb5c3 Minor formatting changes.
Bruno Haible <bruno@clisp.org>
parents: 12421
diff changeset
196 t = pio2_hi + pio2_lo - 2 * asinl (sqrtl ((1 - y) / 2));
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
197
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
198 return t * sign;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
199 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
200
15942
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'.
Bruno Haible <bruno@clisp.org>
parents: 13051
diff changeset
201 #endif
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'.
Bruno Haible <bruno@clisp.org>
parents: 13051
diff changeset
202
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
203 #if 0
4652
b09c3f1225b6 Remove K&R cruft.
Paul Eggert <eggert@cs.ucla.edu>
parents: 4239
diff changeset
204 int
b09c3f1225b6 Remove K&R cruft.
Paul Eggert <eggert@cs.ucla.edu>
parents: 4239
diff changeset
205 main (void)
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
206 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
207 printf ("%.18Lg %.18Lg\n",
13051
094f6cfdb5c3 Minor formatting changes.
Bruno Haible <bruno@clisp.org>
parents: 12421
diff changeset
208 asinl (1.0L),
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
209 1.5707963267948966192313216916397514420984L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
210 printf ("%.18Lg %.18Lg\n",
13051
094f6cfdb5c3 Minor formatting changes.
Bruno Haible <bruno@clisp.org>
parents: 12421
diff changeset
211 asinl (0.7071067811865475244008443621048490392848L),
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
212 0.7853981633974483096156608458198757210492L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
213 printf ("%.18Lg %.18Lg\n",
13051
094f6cfdb5c3 Minor formatting changes.
Bruno Haible <bruno@clisp.org>
parents: 12421
diff changeset
214 asinl (0.5L),
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
215 0.5235987755982988730771072305465838140328L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
216 printf ("%.18Lg %.18Lg\n",
13051
094f6cfdb5c3 Minor formatting changes.
Bruno Haible <bruno@clisp.org>
parents: 12421
diff changeset
217 asinl (0.3090169943749474241022934171828190588600L),
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
218 0.3141592653589793238462643383279502884196L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
219 printf ("%.18Lg %.18Lg\n",
13051
094f6cfdb5c3 Minor formatting changes.
Bruno Haible <bruno@clisp.org>
parents: 12421
diff changeset
220 asinl (-1.0L),
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
221 -1.5707963267948966192313216916397514420984L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
222 printf ("%.18Lg %.18Lg\n",
13051
094f6cfdb5c3 Minor formatting changes.
Bruno Haible <bruno@clisp.org>
parents: 12421
diff changeset
223 asinl (-0.7071067811865475244008443621048490392848L),
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
224 -0.7853981633974483096156608458198757210492L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
225 printf ("%.18Lg %.18Lg\n",
13051
094f6cfdb5c3 Minor formatting changes.
Bruno Haible <bruno@clisp.org>
parents: 12421
diff changeset
226 asinl (-0.5L),
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
227 -0.5235987755982988730771072305465838140328L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
228 printf ("%.18Lg %.18Lg\n",
13051
094f6cfdb5c3 Minor formatting changes.
Bruno Haible <bruno@clisp.org>
parents: 12421
diff changeset
229 asinl (-0.3090169943749474241022934171828190588600L),
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
230 -0.3141592653589793238462643383279502884196L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
231 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
232 #endif