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Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/ldbl-128/e_acosl.c')
| -rw-r--r-- | REORG.TODO/sysdeps/ieee754/ldbl-128/e_acosl.c | 319 |
1 files changed, 319 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_acosl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_acosl.c new file mode 100644 index 0000000000..342ea5f47d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_acosl.c @@ -0,0 +1,319 @@ +/* + * ==================================================== + * 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. + * ==================================================== + */ + +/* + Long double 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, see + <http://www.gnu.org/licenses/>. */ + +/* __ieee754_acosl(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x| <= 0.375 + * acos(x) = pi/2 - asin(x) + * Between .375 and .5 the approximation is + * acos(0.4375 + x) = acos(0.4375) + x P(x) / Q(x) + * Between .5 and .625 the approximation is + * acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x) + * For x > 0.625, + * acos(x) = 2 asin(sqrt((1-x)/2)) + * computed with an extended precision square root in the leading term. + * For x < -0.625 + * acos(x) = pi - 2 asin(sqrt((1-|x|)/2)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Functions needed: __ieee754_sqrtl. + */ + +#include <math.h> +#include <math_private.h> + +static const _Float128 + one = 1, + pio2_hi = L(1.5707963267948966192313216916397514420986), + pio2_lo = L(4.3359050650618905123985220130216759843812E-35), + + /* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x) + -0.0625 <= x <= 0.0625 + peak relative error 3.3e-35 */ + + rS0 = L(5.619049346208901520945464704848780243887E0), + rS1 = L(-4.460504162777731472539175700169871920352E1), + rS2 = L(1.317669505315409261479577040530751477488E2), + rS3 = L(-1.626532582423661989632442410808596009227E2), + rS4 = L(3.144806644195158614904369445440583873264E1), + rS5 = L(9.806674443470740708765165604769099559553E1), + rS6 = L(-5.708468492052010816555762842394927806920E1), + rS7 = L(-1.396540499232262112248553357962639431922E1), + rS8 = L(1.126243289311910363001762058295832610344E1), + rS9 = L(4.956179821329901954211277873774472383512E-1), + rS10 = L(-3.313227657082367169241333738391762525780E-1), + + sS0 = L(-4.645814742084009935700221277307007679325E0), + sS1 = L(3.879074822457694323970438316317961918430E1), + sS2 = L(-1.221986588013474694623973554726201001066E2), + sS3 = L(1.658821150347718105012079876756201905822E2), + sS4 = L(-4.804379630977558197953176474426239748977E1), + sS5 = L(-1.004296417397316948114344573811562952793E2), + sS6 = L(7.530281592861320234941101403870010111138E1), + sS7 = L(1.270735595411673647119592092304357226607E1), + sS8 = L(-1.815144839646376500705105967064792930282E1), + sS9 = L(-7.821597334910963922204235247786840828217E-2), + /* 1.000000000000000000000000000000000000000E0 */ + + acosr5625 = L(9.7338991014954640492751132535550279812151E-1), + pimacosr5625 = L(2.1682027434402468335351320579240000860757E0), + + /* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x) + -0.0625 <= x <= 0.0625 + peak relative error 2.1e-35 */ + + P0 = L(2.177690192235413635229046633751390484892E0), + P1 = L(-2.848698225706605746657192566166142909573E1), + P2 = L(1.040076477655245590871244795403659880304E2), + P3 = L(-1.400087608918906358323551402881238180553E2), + P4 = L(2.221047917671449176051896400503615543757E1), + P5 = L(9.643714856395587663736110523917499638702E1), + P6 = L(-5.158406639829833829027457284942389079196E1), + P7 = L(-1.578651828337585944715290382181219741813E1), + P8 = L(1.093632715903802870546857764647931045906E1), + P9 = L(5.448925479898460003048760932274085300103E-1), + P10 = L(-3.315886001095605268470690485170092986337E-1), + Q0 = L(-1.958219113487162405143608843774587557016E0), + Q1 = L(2.614577866876185080678907676023269360520E1), + Q2 = L(-9.990858606464150981009763389881793660938E1), + Q3 = L(1.443958741356995763628660823395334281596E2), + Q4 = L(-3.206441012484232867657763518369723873129E1), + Q5 = L(-1.048560885341833443564920145642588991492E2), + Q6 = L(6.745883931909770880159915641984874746358E1), + Q7 = L(1.806809656342804436118449982647641392951E1), + Q8 = L(-1.770150690652438294290020775359580915464E1), + Q9 = L(-5.659156469628629327045433069052560211164E-1), + /* 1.000000000000000000000000000000000000000E0 */ + + acosr4375 = L(1.1179797320499710475919903296900511518755E0), + pimacosr4375 = L(2.0236129215398221908706530535894517323217E0), + + /* asin(x) = x + x^3 pS(x^2) / qS(x^2) + 0 <= x <= 0.5 + peak relative error 1.9e-35 */ + pS0 = L(-8.358099012470680544198472400254596543711E2), + pS1 = L(3.674973957689619490312782828051860366493E3), + pS2 = L(-6.730729094812979665807581609853656623219E3), + pS3 = L(6.643843795209060298375552684423454077633E3), + pS4 = L(-3.817341990928606692235481812252049415993E3), + pS5 = L(1.284635388402653715636722822195716476156E3), + pS6 = L(-2.410736125231549204856567737329112037867E2), + pS7 = L(2.219191969382402856557594215833622156220E1), + pS8 = L(-7.249056260830627156600112195061001036533E-1), + pS9 = L(1.055923570937755300061509030361395604448E-3), + + qS0 = L(-5.014859407482408326519083440151745519205E3), + qS1 = L(2.430653047950480068881028451580393430537E4), + qS2 = L(-4.997904737193653607449250593976069726962E4), + qS3 = L(5.675712336110456923807959930107347511086E4), + qS4 = L(-3.881523118339661268482937768522572588022E4), + qS5 = L(1.634202194895541569749717032234510811216E4), + qS6 = L(-4.151452662440709301601820849901296953752E3), + qS7 = L(5.956050864057192019085175976175695342168E2), + qS8 = L(-4.175375777334867025769346564600396877176E1); + /* 1.000000000000000000000000000000000000000E0 */ + +_Float128 +__ieee754_acosl (_Float128 x) +{ + _Float128 z, r, w, p, q, s, t, f2; + int32_t ix, sign; + ieee854_long_double_shape_type u; + + u.value = x; + sign = u.parts32.w0; + ix = sign & 0x7fffffff; + u.parts32.w0 = ix; /* |x| */ + if (ix >= 0x3fff0000) /* |x| >= 1 */ + { + if (ix == 0x3fff0000 + && (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0) + { /* |x| == 1 */ + if ((sign & 0x80000000) == 0) + return 0.0; /* acos(1) = 0 */ + else + return (2.0 * pio2_hi) + (2.0 * pio2_lo); /* acos(-1)= pi */ + } + return (x - x) / (x - x); /* acos(|x| > 1) is NaN */ + } + else if (ix < 0x3ffe0000) /* |x| < 0.5 */ + { + if (ix < 0x3f8e0000) /* |x| < 2**-113 */ + return pio2_hi + pio2_lo; + if (ix < 0x3ffde000) /* |x| < .4375 */ + { + /* Arcsine of x. */ + z = x * x; + p = (((((((((pS9 * z + + pS8) * z + + pS7) * z + + pS6) * z + + pS5) * z + + pS4) * z + + pS3) * z + + pS2) * z + + pS1) * z + + pS0) * z; + q = (((((((( z + + qS8) * z + + qS7) * z + + qS6) * z + + qS5) * z + + qS4) * z + + qS3) * z + + qS2) * z + + qS1) * z + + qS0; + r = x + x * p / q; + z = pio2_hi - (r - pio2_lo); + return z; + } + /* .4375 <= |x| < .5 */ + t = u.value - L(0.4375); + p = ((((((((((P10 * t + + P9) * t + + P8) * t + + P7) * t + + P6) * t + + P5) * t + + P4) * t + + P3) * t + + P2) * t + + P1) * t + + P0) * t; + + q = (((((((((t + + Q9) * t + + Q8) * t + + Q7) * t + + Q6) * t + + Q5) * t + + Q4) * t + + Q3) * t + + Q2) * t + + Q1) * t + + Q0; + r = p / q; + if (sign & 0x80000000) + r = pimacosr4375 - r; + else + r = acosr4375 + r; + return r; + } + else if (ix < 0x3ffe4000) /* |x| < 0.625 */ + { + t = u.value - L(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; + if (sign & 0x80000000) + r = pimacosr5625 - p / q; + else + r = acosr5625 + p / q; + return r; + } + else + { /* |x| >= .625 */ + z = (one - u.value) * 0.5; + s = __ieee754_sqrtl (z); + /* Compute an extended precision square root from + the Newton iteration s -> 0.5 * (s + z / s). + The change w from s to the improved value is + w = 0.5 * (s + z / s) - s = (s^2 + z)/2s - s = (z - s^2)/2s. + Express s = f1 + f2 where f1 * f1 is exactly representable. + w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s . + s + w has extended precision. */ + u.value = s; + u.parts32.w2 = 0; + u.parts32.w3 = 0; + f2 = s - u.value; + w = z - u.value * u.value; + w = w - 2.0 * u.value * f2; + w = w - f2 * f2; + w = w / (2.0 * s); + /* Arcsine of s. */ + p = (((((((((pS9 * z + + pS8) * z + + pS7) * z + + pS6) * z + + pS5) * z + + pS4) * z + + pS3) * z + + pS2) * z + + pS1) * z + + pS0) * z; + q = (((((((( z + + qS8) * z + + qS7) * z + + qS6) * z + + qS5) * z + + qS4) * z + + qS3) * z + + qS2) * z + + qS1) * z + + qS0; + r = s + (w + s * p / q); + + if (sign & 0x80000000) + w = pio2_hi + (pio2_lo - r); + else + w = r; + return 2.0 * w; + } +} +strong_alias (__ieee754_acosl, __acosl_finite) |