octave-jordi/gnulib-hg: lib/asinl.c annotate

annotate lib/asinl.c @ 18029:e4a13d95b503

mgetgroups: port to strict OS X * doc/glibc-functions/getgrouplist.texi (getgrouplist): Document the getgrouplist problem. * lib/mgetgroups.c (getgrouplist_gids) [HAVE_GETGROUPLIST]: New macro. (mgetgroups): Use it. * m4/mgetgroups.m4 (gl_MGETGROUPS): Check for OS X signature for getgrouplist.

author	Paul Eggert <eggert@cs.ucla.edu>
date	Sun, 28 Jun 2015 23:43:35 -0700
parents	2074f2bf7216
children

rev	line source
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	1 /*
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	2 * ====================================================
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	4 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	5 * Developed at SunPro, a Sun Microsystems, Inc. business.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	6 * Permission to use, copy, modify, and distribute this
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	7 * software is freely granted, provided that this notice
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	8 * is preserved.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	9 * ====================================================
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	10 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	11
8186 c115624bf99a New module 'math'. <math.h> replaces mathl.h. Bruno Haible <bruno@clisp.org> parents: 4652 diff changeset	12 #include <config.h>
c115624bf99a New module 'math'. <math.h> replaces mathl.h. Bruno Haible <bruno@clisp.org> parents: 4652 diff changeset	13
c115624bf99a New module 'math'. <math.h> replaces mathl.h. Bruno Haible <bruno@clisp.org> parents: 4652 diff changeset	14 /* Specification. */
c115624bf99a New module 'math'. <math.h> replaces mathl.h. Bruno Haible <bruno@clisp.org> parents: 4652 diff changeset	15 #include <math.h>
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	16
15942 cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	17 #if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	18
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	19 long double
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	20 asinl (long double x)
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	21 {
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	22 return asin (x);
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	23 }
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	24
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	25 #else
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	26
16511 2074f2bf7216 math code: Add comments. Bruno Haible <bruno@clisp.org> parents: 15942 diff changeset	27 /* Code based on glibc/sysdeps/ieee754/ldbl-128/e_asinl.c. */
2074f2bf7216 math code: Add comments. Bruno Haible <bruno@clisp.org> parents: 15942 diff changeset	28
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	29 /*
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	30 Long double expansions contributed by
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	31 Stephen L. Moshier <moshier@na-net.ornl.gov>
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	32 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	33
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	34 /* asin(x)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	35 * Method :
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	36 * Since asin(x) = x + x^3/6 + x^53/40 + x^715/336 + ...
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	37 * we approximate asin(x) on [0,0.5] by
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	38 * asin(x) = x + xx^2R(x^2)
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	39 * Between .5 and .625 the approximation is
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	40 * asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	41 * For x in [0.625,1]
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	42 * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	43 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	44 * Special cases:
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	45 * if x is NaN, return x itself;
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	46 * if \|x\|>1, return NaN with invalid signal.
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	47 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	48 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	49
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	50
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	51 static const long double
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	52 one = 1.0L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	53 huge = 1.0e+4932L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	54 pio2_hi = 1.5707963267948966192313216916397514420986L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	55 pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	56 pio4_hi = 7.8539816339744830961566084581987569936977E-1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	57
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	58 /* coefficient for R(x^2) */
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	59
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	60 /* asin(x) = x + x^3 pS(x^2) / qS(x^2)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	61 0 <= x <= 0.5
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	62 peak relative error 1.9e-35 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	63 pS0 = -8.358099012470680544198472400254596543711E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	64 pS1 = 3.674973957689619490312782828051860366493E3L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	65 pS2 = -6.730729094812979665807581609853656623219E3L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	66 pS3 = 6.643843795209060298375552684423454077633E3L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	67 pS4 = -3.817341990928606692235481812252049415993E3L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	68 pS5 = 1.284635388402653715636722822195716476156E3L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	69 pS6 = -2.410736125231549204856567737329112037867E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	70 pS7 = 2.219191969382402856557594215833622156220E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	71 pS8 = -7.249056260830627156600112195061001036533E-1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	72 pS9 = 1.055923570937755300061509030361395604448E-3L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	73
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	74 qS0 = -5.014859407482408326519083440151745519205E3L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	75 qS1 = 2.430653047950480068881028451580393430537E4L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	76 qS2 = -4.997904737193653607449250593976069726962E4L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	77 qS3 = 5.675712336110456923807959930107347511086E4L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	78 qS4 = -3.881523118339661268482937768522572588022E4L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	79 qS5 = 1.634202194895541569749717032234510811216E4L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	80 qS6 = -4.151452662440709301601820849901296953752E3L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	81 qS7 = 5.956050864057192019085175976175695342168E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	82 qS8 = -4.175375777334867025769346564600396877176E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	83 /* 1.000000000000000000000000000000000000000E0 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	84
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	85 /* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	86 -0.0625 <= x <= 0.0625
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	87 peak relative error 3.3e-35 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	88 rS0 = -5.619049346208901520945464704848780243887E0L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	89 rS1 = 4.460504162777731472539175700169871920352E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	90 rS2 = -1.317669505315409261479577040530751477488E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	91 rS3 = 1.626532582423661989632442410808596009227E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	92 rS4 = -3.144806644195158614904369445440583873264E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	93 rS5 = -9.806674443470740708765165604769099559553E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	94 rS6 = 5.708468492052010816555762842394927806920E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	95 rS7 = 1.396540499232262112248553357962639431922E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	96 rS8 = -1.126243289311910363001762058295832610344E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	97 rS9 = -4.956179821329901954211277873774472383512E-1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	98 rS10 = 3.313227657082367169241333738391762525780E-1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	99
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	100 sS0 = -4.645814742084009935700221277307007679325E0L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	101 sS1 = 3.879074822457694323970438316317961918430E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	102 sS2 = -1.221986588013474694623973554726201001066E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	103 sS3 = 1.658821150347718105012079876756201905822E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	104 sS4 = -4.804379630977558197953176474426239748977E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	105 sS5 = -1.004296417397316948114344573811562952793E2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	106 sS6 = 7.530281592861320234941101403870010111138E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	107 sS7 = 1.270735595411673647119592092304357226607E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	108 sS8 = -1.815144839646376500705105967064792930282E1L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	109 sS9 = -7.821597334910963922204235247786840828217E-2L,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	110 /* 1.000000000000000000000000000000000000000E0 */
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 asinr5625 = 5.9740641664535021430381036628424864397707E-1L;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	113
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	114
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	115 long double
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	116 asinl (long double x)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	117 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	118 long double y, t, p, q;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	119 int sign;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	120
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	121 sign = 1;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	122 y = x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	123 if (x < 0.0L)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	124 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	125 sign = -1;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	126 y = -x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	127 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	128
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	129 if (y >= 1.0L) /* \|x\|>= 1 */
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	130 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	131 if (y == 1.0L)
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	132 /* asin(1)=+-pi/2 with inexact */
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	133 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	134
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	135 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	136 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	137 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	138 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	139 if (y < 0.000000000000000006938893903907228377647697925567626953125L) /* \|x\| < 2*-57 /
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	140 if (huge + y > one)
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	141 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	142
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	143 t = x * x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	144 p = (((((((((pS9 * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	145 + pS8) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	146 + pS7) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	147 + pS6) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	148 + pS5) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	149 + pS4) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	150 + pS3) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	151 + pS2) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	152 + pS1) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	153 + pS0) * t;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	154
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	155 q = (((((((( t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	156 + qS8) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	157 + qS7) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	158 + qS6) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	159 + qS5) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	160 + qS4) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	161 + qS3) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	162 + qS2) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	163 + qS1) * t
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	164 + qS0;
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 return x + x * (p / q);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	167 }
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 else if (y < 0.625) /* 0.625 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	170 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	171 t = y - 0.5625;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	172 p = ((((((((((rS10 * t
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	173 + rS9) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	174 + rS8) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	175 + rS7) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	176 + rS6) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	177 + rS5) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	178 + rS4) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	179 + rS3) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	180 + rS2) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	181 + rS1) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	182 + rS0) * t;
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	183
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	184 q = ((((((((( t
12421 e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	185 + sS9) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	186 + sS8) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	187 + sS7) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	188 + sS6) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	189 + sS5) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	190 + sS4) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	191 + sS3) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	192 + sS2) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	193 + sS1) * t
e8d2c6fc33ad Use spaces for indentation, not tabs. Bruno Haible <bruno@clisp.org> parents: 8186 diff changeset	194 + sS0;
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	195 t = asinr5625 + p / q;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	196 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	197 else
13051 094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12421 diff changeset	198 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	199
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	200 return t * sign;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	201 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	202
15942 cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	203 #endif
cfc88a2774f7 asinl: Simplify for platforms where 'long double' == 'double'. Bruno Haible <bruno@clisp.org> parents: 13051 diff changeset	204
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	205 #if 0
4652 b09c3f1225b6 Remove K&R cruft. Paul Eggert <eggert@cs.ucla.edu> parents: 4239 diff changeset	206 int
b09c3f1225b6 Remove K&R cruft. Paul Eggert <eggert@cs.ucla.edu> parents: 4239 diff changeset	207 main (void)
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	208 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	209 printf ("%.18Lg %.18Lg\n",
13051 094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12421 diff changeset	210 asinl (1.0L),
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	211 1.5707963267948966192313216916397514420984L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	212 printf ("%.18Lg %.18Lg\n",
13051 094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12421 diff changeset	213 asinl (0.7071067811865475244008443621048490392848L),
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	214 0.7853981633974483096156608458198757210492L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	215 printf ("%.18Lg %.18Lg\n",
13051 094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12421 diff changeset	216 asinl (0.5L),
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	217 0.5235987755982988730771072305465838140328L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	218 printf ("%.18Lg %.18Lg\n",
13051 094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12421 diff changeset	219 asinl (0.3090169943749474241022934171828190588600L),
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	220 0.3141592653589793238462643383279502884196L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	221 printf ("%.18Lg %.18Lg\n",
13051 094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12421 diff changeset	222 asinl (-1.0L),
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	223 -1.5707963267948966192313216916397514420984L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	224 printf ("%.18Lg %.18Lg\n",
13051 094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12421 diff changeset	225 asinl (-0.7071067811865475244008443621048490392848L),
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	226 -0.7853981633974483096156608458198757210492L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	227 printf ("%.18Lg %.18Lg\n",
13051 094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12421 diff changeset	228 asinl (-0.5L),
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	229 -0.5235987755982988730771072305465838140328L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	230 printf ("%.18Lg %.18Lg\n",
13051 094f6cfdb5c3 Minor formatting changes. Bruno Haible <bruno@clisp.org> parents: 12421 diff changeset	231 asinl (-0.3090169943749474241022934171828190588600L),
4239 b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	232 -0.3141592653589793238462643383279502884196L);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	233 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini. Bruno Haible <bruno@clisp.org> parents: diff changeset	234 #endif

Mercurial > hg > octave-jordi > gnulib-hg

annotate lib/asinl.c @ 18029:e4a13d95b503