| /* |
| * ==================================================== |
| * 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 |
| acosl (long double x) |
| { |
| return acos (x); |
| } |
| |
| #else |
| |
| /* Code based on glibc/sysdeps/ieee754/ldbl-128/e_asinl.c |
| and glibc/sysdeps/ieee754/ldbl-128/e_acosl.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, |
| pi = 3.1415926535897932384626433832795028841972L, |
| 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 |
| acosl (long double x) |
| { |
| long double t, p, q; |
| |
| if (x < 0.0L) |
| { |
| t = pi - acosl (-x); |
| if (huge + x > one) /* return with inexact */ |
| return t; |
| } |
| |
| if (x >= 1.0L) /* |x|>= 1 */ |
| { |
| if (x == 1.0L) |
| return 0.0L; /* return zero */ |
| |
| return (x - x) / (x - x); /* asin(|x|>1) is NaN */ |
| } |
| |
| else if (x < 0.5L) /* |x| < 0.5 */ |
| { |
| if (x < 0.000000000000000006938893903907228377647697925567626953125L) /* |x| < 2**-57 */ |
| /* acos(0)=+-pi/2 with inexact */ |
| return x * pio2_hi + x * pio2_lo; |
| |
| t = x * x; |
| p = (((((((((pS9 * t |
| + pS8) * t |
| + pS7) * t |
| + pS6) * t |
| + pS5) * t |
| + pS4) * t |
| + pS3) * t |
| + pS2) * t |
| + pS1) * t |
| + pS0) * t; |
| |
| q = (((((((( t |
| + qS8) * t |
| + qS7) * t |
| + qS6) * t |
| + qS5) * t |
| + qS4) * t |
| + qS3) * t |
| + qS2) * t |
| + qS1) * t |
| + qS0; |
| |
| return pio2_hi - (x + x * (p / q) - pio2_lo); |
| } |
| |
| else if (x < 0.625) /* 0.625 */ |
| { |
| t = x - 0.5625; |
| p = ((((((((((rS10 * t |
| + rS9) * t |
| + rS8) * t |
| + rS7) * t |
| + rS6) * t |
| + rS5) * t |
| + rS4) * t |
| + rS3) * t |
| + rS2) * t |
| + rS1) * t |
| + rS0) * t; |
| |
| q = ((((((((( t |
| + sS9) * t |
| + sS8) * t |
| + sS7) * t |
| + sS6) * t |
| + sS5) * t |
| + sS4) * t |
| + sS3) * t |
| + sS2) * t |
| + sS1) * t |
| + sS0; |
| |
| return (pio2_hi - asinr5625) - (p / q - pio2_lo); |
| } |
| else |
| return 2 * asinl (sqrtl ((1 - x) / 2)); |
| } |
| |
| #endif |
| |
| #if 0 |
| int |
| main (void) |
| { |
| printf ("%.18Lg %.18Lg\n", |
| acosl (1.0L), |
| 1.5707963267948966192313216916397514420984L - |
| 1.5707963267948966192313216916397514420984L); |
| printf ("%.18Lg %.18Lg\n", |
| acosl (0.7071067811865475244008443621048490392848L), |
| 1.5707963267948966192313216916397514420984L - |
| 0.7853981633974483096156608458198757210492L); |
| printf ("%.18Lg %.18Lg\n", |
| acosl (0.5L), |
| 1.5707963267948966192313216916397514420984L - |
| 0.5235987755982988730771072305465838140328L); |
| printf ("%.18Lg %.18Lg\n", |
| acosl (0.3090169943749474241022934171828190588600L), |
| 1.5707963267948966192313216916397514420984L - |
| 0.3141592653589793238462643383279502884196L); |
| printf ("%.18Lg %.18Lg\n", |
| acosl (-1.0L), |
| 1.5707963267948966192313216916397514420984L - |
| -1.5707963267948966192313216916397514420984L); |
| printf ("%.18Lg %.18Lg\n", |
| acosl (-0.7071067811865475244008443621048490392848L), |
| 1.5707963267948966192313216916397514420984L - |
| -0.7853981633974483096156608458198757210492L); |
| printf ("%.18Lg %.18Lg\n", |
| acosl (-0.5L), |
| 1.5707963267948966192313216916397514420984L - |
| -0.5235987755982988730771072305465838140328L); |
| printf ("%.18Lg %.18Lg\n", |
| acosl (-0.3090169943749474241022934171828190588600L), |
| 1.5707963267948966192313216916397514420984L - |
| -0.3141592653589793238462643383279502884196L); |
| } |
| #endif |
