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Diffstat (limited to 'libquadmath/math/asinq.c')
| -rw-r--r-- | libquadmath/math/asinq.c | 254 |
1 files changed, 254 insertions, 0 deletions
diff --git a/libquadmath/math/asinq.c b/libquadmath/math/asinq.c new file mode 100644 index 00000000000..d4321a58e0a --- /dev/null +++ b/libquadmath/math/asinq.c @@ -0,0 +1,254 @@ +/* + * ==================================================== + * 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. + * ==================================================== + */ + +/* + __float128 expansions are + Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> + and are incorporated herein by permission of the author. The author + reserves the right to distribute this material elsewhere under different + copying permissions. These modifications are distributed here under the + following terms: + + This library 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 2.1 of the License, or (at your option) any later version. + + This library 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 library; if not, write to the Free Software + Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ + +/* __ieee754_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)) + * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; + * then for x>0.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + + +#include "quadmath-imp.h" + +static const __float128 + one = 1.0Q, + huge = 1.0e+4932Q, + pio2_hi = 1.5707963267948966192313216916397514420986Q, + pio2_lo = 4.3359050650618905123985220130216759843812E-35Q, + pio4_hi = 7.8539816339744830961566084581987569936977E-1Q, + + /* 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 = -8.358099012470680544198472400254596543711E2Q, + pS1 = 3.674973957689619490312782828051860366493E3Q, + pS2 = -6.730729094812979665807581609853656623219E3Q, + pS3 = 6.643843795209060298375552684423454077633E3Q, + pS4 = -3.817341990928606692235481812252049415993E3Q, + pS5 = 1.284635388402653715636722822195716476156E3Q, + pS6 = -2.410736125231549204856567737329112037867E2Q, + pS7 = 2.219191969382402856557594215833622156220E1Q, + pS8 = -7.249056260830627156600112195061001036533E-1Q, + pS9 = 1.055923570937755300061509030361395604448E-3Q, + + qS0 = -5.014859407482408326519083440151745519205E3Q, + qS1 = 2.430653047950480068881028451580393430537E4Q, + qS2 = -4.997904737193653607449250593976069726962E4Q, + qS3 = 5.675712336110456923807959930107347511086E4Q, + qS4 = -3.881523118339661268482937768522572588022E4Q, + qS5 = 1.634202194895541569749717032234510811216E4Q, + qS6 = -4.151452662440709301601820849901296953752E3Q, + qS7 = 5.956050864057192019085175976175695342168E2Q, + qS8 = -4.175375777334867025769346564600396877176E1Q, + /* 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 = -5.619049346208901520945464704848780243887E0Q, + rS1 = 4.460504162777731472539175700169871920352E1Q, + rS2 = -1.317669505315409261479577040530751477488E2Q, + rS3 = 1.626532582423661989632442410808596009227E2Q, + rS4 = -3.144806644195158614904369445440583873264E1Q, + rS5 = -9.806674443470740708765165604769099559553E1Q, + rS6 = 5.708468492052010816555762842394927806920E1Q, + rS7 = 1.396540499232262112248553357962639431922E1Q, + rS8 = -1.126243289311910363001762058295832610344E1Q, + rS9 = -4.956179821329901954211277873774472383512E-1Q, + rS10 = 3.313227657082367169241333738391762525780E-1Q, + + sS0 = -4.645814742084009935700221277307007679325E0Q, + sS1 = 3.879074822457694323970438316317961918430E1Q, + sS2 = -1.221986588013474694623973554726201001066E2Q, + sS3 = 1.658821150347718105012079876756201905822E2Q, + sS4 = -4.804379630977558197953176474426239748977E1Q, + sS5 = -1.004296417397316948114344573811562952793E2Q, + sS6 = 7.530281592861320234941101403870010111138E1Q, + sS7 = 1.270735595411673647119592092304357226607E1Q, + sS8 = -1.815144839646376500705105967064792930282E1Q, + sS9 = -7.821597334910963922204235247786840828217E-2Q, + /* 1.000000000000000000000000000000000000000E0 */ + + asinr5625 = 5.9740641664535021430381036628424864397707E-1Q; + + + +__float128 +asinq (__float128 x) +{ + __float128 t = 0; + __float128 w, p, q, c, r, s; + int32_t ix, sign, flag; + ieee854_float128 u; + + flag = 0; + u.value = x; + sign = u.words32.w0; + ix = sign & 0x7fffffff; + u.words32.w0 = ix; /* |x| */ + if (ix >= 0x3fff0000) /* |x|>= 1 */ + { + if (ix == 0x3fff0000 + && (u.words32.w1 | u.words32.w2 | u.words32.w3) == 0) + /* asin(1)=+-pi/2 with inexact */ + return x * pio2_hi + x * pio2_lo; + return (x - x) / (x - x); /* asin(|x|>1) is NaN */ + } + else if (ix < 0x3ffe0000) /* |x| < 0.5 */ + { + if (ix < 0x3fc60000) /* |x| < 2**-57 */ + { + if (huge + x > one) + return x; /* return x with inexact if x!=0 */ + } + else + { + t = x * x; + /* Mark to use pS, qS later on. */ + flag = 1; + } + } + else if (ix < 0x3ffe4000) /* 0.625 */ + { + t = u.value - 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; + t = asinr5625 + p / q; + if ((sign & 0x80000000) == 0) + return t; + else + return -t; + } + else + { + /* 1 > |x| >= 0.625 */ + w = one - u.value; + t = w * 0.5; + } + + 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; + + if (flag) /* 2^-57 < |x| < 0.5 */ + { + w = p / q; + return x + x * w; + } + + s = sqrtq (t); + if (ix >= 0x3ffef333) /* |x| > 0.975 */ + { + w = p / q; + t = pio2_hi - (2.0 * (s + s * w) - pio2_lo); + } + else + { + u.value = s; + u.words32.w3 = 0; + u.words32.w2 = 0; + w = u.value; + c = (t - w * w) / (s + w); + r = p / q; + p = 2.0 * s * r - (pio2_lo - 2.0 * c); + q = pio4_hi - 2.0 * w; + t = pio4_hi - (p - q); + } + + if ((sign & 0x80000000) == 0) + return t; + else + return -t; +} |