| /* arcsin (inverse sine) function with 'long double' argument. | |
| Copyright (C) 2003-2026 Free Software Foundation, Inc. | |
| This file is free software: you can redistribute it and/or modify | |
| it under the terms of the GNU Lesser General Public License as | |
| published by the Free Software Foundation, either version 3 of the | |
| License, or (at your option) any later version. | |
| This file is distributed in the hope that it will be useful, | |
| but WITHOUT ANY WARRANTY; without even the implied warranty of | |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
| GNU Lesser General Public License for more details. | |
| You should have received a copy of the GNU Lesser General Public License | |
| along with this program. If not, see <https://www.gnu.org/licenses/>. */ | |
| /* | |
| * ==================================================== | |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |
| * | |
| * Developed at SunPro, a Sun Microsystems, Inc. business. | |
| * Permission to use, copy, modify, and distribute this | |
| * software is freely granted, provided that this notice | |
| * is preserved. | |
| * ==================================================== | |
| */ | |
| #include <config.h> | |
| /* Specification. */ | |
| #include <math.h> | |
| #if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE | |
| long double | |
| asinl (long double x) | |
| { | |
| return asin (x); | |
| } | |
| #else | |
| /* Code based on glibc/sysdeps/ieee754/ldbl-128/e_asinl.c. */ | |
| /* | |
| Long double expansions contributed by | |
| Stephen L. Moshier <moshier@na-net.ornl.gov> | |
| */ | |
| /* asin(x) | |
| * Method : | |
| * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... | |
| * we approximate asin(x) on [0,0.5] by | |
| * asin(x) = x + x*x^2*R(x^2) | |
| * Between .5 and .625 the approximation is | |
| * asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x) | |
| * For x in [0.625,1] | |
| * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) | |
| * | |
| * Special cases: | |
| * if x is NaN, return x itself; | |
| * if |x|>1, return NaN with invalid signal. | |
| * | |
| */ | |
| static const long double | |
| one = 1.0L, | |
| huge = 1.0e+4932L, | |
| pio2_hi = 1.5707963267948966192313216916397514420986L, | |
| pio2_lo = 4.3359050650618905123985220130216759843812E-35L, | |
| pio4_hi = 7.8539816339744830961566084581987569936977E-1L, | |
| /* coefficient for R(x^2) */ | |
| /* asin(x) = x + x^3 pS(x^2) / qS(x^2) | |
| 0 <= x <= 0.5 | |
| peak relative error 1.9e-35 */ | |
| pS0 = -8.358099012470680544198472400254596543711E2L, | |
| pS1 = 3.674973957689619490312782828051860366493E3L, | |
| pS2 = -6.730729094812979665807581609853656623219E3L, | |
| pS3 = 6.643843795209060298375552684423454077633E3L, | |
| pS4 = -3.817341990928606692235481812252049415993E3L, | |
| pS5 = 1.284635388402653715636722822195716476156E3L, | |
| pS6 = -2.410736125231549204856567737329112037867E2L, | |
| pS7 = 2.219191969382402856557594215833622156220E1L, | |
| pS8 = -7.249056260830627156600112195061001036533E-1L, | |
| pS9 = 1.055923570937755300061509030361395604448E-3L, | |
| qS0 = -5.014859407482408326519083440151745519205E3L, | |
| qS1 = 2.430653047950480068881028451580393430537E4L, | |
| qS2 = -4.997904737193653607449250593976069726962E4L, | |
| qS3 = 5.675712336110456923807959930107347511086E4L, | |
| qS4 = -3.881523118339661268482937768522572588022E4L, | |
| qS5 = 1.634202194895541569749717032234510811216E4L, | |
| qS6 = -4.151452662440709301601820849901296953752E3L, | |
| qS7 = 5.956050864057192019085175976175695342168E2L, | |
| qS8 = -4.175375777334867025769346564600396877176E1L, | |
| /* 1.000000000000000000000000000000000000000E0 */ | |
| /* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x) | |
| -0.0625 <= x <= 0.0625 | |
| peak relative error 3.3e-35 */ | |
| rS0 = -5.619049346208901520945464704848780243887E0L, | |
| rS1 = 4.460504162777731472539175700169871920352E1L, | |
| rS2 = -1.317669505315409261479577040530751477488E2L, | |
| rS3 = 1.626532582423661989632442410808596009227E2L, | |
| rS4 = -3.144806644195158614904369445440583873264E1L, | |
| rS5 = -9.806674443470740708765165604769099559553E1L, | |
| rS6 = 5.708468492052010816555762842394927806920E1L, | |
| rS7 = 1.396540499232262112248553357962639431922E1L, | |
| rS8 = -1.126243289311910363001762058295832610344E1L, | |
| rS9 = -4.956179821329901954211277873774472383512E-1L, | |
| rS10 = 3.313227657082367169241333738391762525780E-1L, | |
| sS0 = -4.645814742084009935700221277307007679325E0L, | |
| sS1 = 3.879074822457694323970438316317961918430E1L, | |
| sS2 = -1.221986588013474694623973554726201001066E2L, | |
| sS3 = 1.658821150347718105012079876756201905822E2L, | |
| sS4 = -4.804379630977558197953176474426239748977E1L, | |
| sS5 = -1.004296417397316948114344573811562952793E2L, | |
| sS6 = 7.530281592861320234941101403870010111138E1L, | |
| sS7 = 1.270735595411673647119592092304357226607E1L, | |
| sS8 = -1.815144839646376500705105967064792930282E1L, | |
| sS9 = -7.821597334910963922204235247786840828217E-2L, | |
| /* 1.000000000000000000000000000000000000000E0 */ | |
| asinr5625 = 5.9740641664535021430381036628424864397707E-1L; | |
| long double | |
| asinl (long double x) | |
| { | |
| int sign = 1; | |
| long double y = x; | |
| if (x < 0.0L) | |
| { | |
| sign = -1; | |
| y = -x; | |
| } | |
| if (y >= 1.0L) /* |x|>= 1 */ | |
| { | |
| if (y == 1.0L) | |
| /* asin(1)=+-pi/2 with inexact */ | |
| return x * pio2_hi + x * pio2_lo; | |
| return (x - x) / (x - x); /* asin(|x|>1) is NaN */ | |
| } | |
| long double t; | |
| if (y < 0.5L) /* |x| < 0.5 */ | |
| { | |
| if (y < 0.000000000000000006938893903907228377647697925567626953125L) /* |x| < 2**-57 */ | |
| if (huge + y > one) | |
| return y; /* return x with inexact if x!=0 */ | |
| t = x * x; | |
| long double p = (((((((((pS9 * t | |
| + pS8) * t | |
| + pS7) * t | |
| + pS6) * t | |
| + pS5) * t | |
| + pS4) * t | |
| + pS3) * t | |
| + pS2) * t | |
| + pS1) * t | |
| + pS0) * t; | |
| long double q = (((((((( t | |
| + qS8) * t | |
| + qS7) * t | |
| + qS6) * t | |
| + qS5) * t | |
| + qS4) * t | |
| + qS3) * t | |
| + qS2) * t | |
| + qS1) * t | |
| + qS0; | |
| return x + x * (p / q); | |
| } | |
| else if (y < 0.625) /* 0.625 */ | |
| { | |
| t = y - 0.5625; | |
| long double p = ((((((((((rS10 * t | |
| + rS9) * t | |
| + rS8) * t | |
| + rS7) * t | |
| + rS6) * t | |
| + rS5) * t | |
| + rS4) * t | |
| + rS3) * t | |
| + rS2) * t | |
| + rS1) * t | |
| + rS0) * t; | |
| long double q = ((((((((( t | |
| + sS9) * t | |
| + sS8) * t | |
| + sS7) * t | |
| + sS6) * t | |
| + sS5) * t | |
| + sS4) * t | |
| + sS3) * t | |
| + sS2) * t | |
| + sS1) * t | |
| + sS0; | |
| t = asinr5625 + p / q; | |
| } | |
| else | |
| t = pio2_hi + pio2_lo - 2 * asinl (sqrtl ((1 - y) / 2)); | |
| return t * sign; | |
| } | |
| #endif | |
| #if 0 | |
| int | |
| main (void) | |
| { | |
| printf ("%.18Lg %.18Lg\n", | |
| asinl (1.0L), | |
| 1.5707963267948966192313216916397514420984L); | |
| printf ("%.18Lg %.18Lg\n", | |
| asinl (0.7071067811865475244008443621048490392848L), | |
| 0.7853981633974483096156608458198757210492L); | |
| printf ("%.18Lg %.18Lg\n", | |
| asinl (0.5L), | |
| 0.5235987755982988730771072305465838140328L); | |
| printf ("%.18Lg %.18Lg\n", | |
| asinl (0.3090169943749474241022934171828190588600L), | |
| 0.3141592653589793238462643383279502884196L); | |
| printf ("%.18Lg %.18Lg\n", | |
| asinl (-1.0L), | |
| -1.5707963267948966192313216916397514420984L); | |
| printf ("%.18Lg %.18Lg\n", | |
| asinl (-0.7071067811865475244008443621048490392848L), | |
| -0.7853981633974483096156608458198757210492L); | |
| printf ("%.18Lg %.18Lg\n", | |
| asinl (-0.5L), | |
| -0.5235987755982988730771072305465838140328L); | |
| printf ("%.18Lg %.18Lg\n", | |
| asinl (-0.3090169943749474241022934171828190588600L), | |
| -0.3141592653589793238462643383279502884196L); | |
| } | |
| #endif |