1*f504f610SAugustin Cavalier #include <float.h>
2*f504f610SAugustin Cavalier #include "__invtrigl.h"
3*f504f610SAugustin Cavalier
4*f504f610SAugustin Cavalier #if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
5*f504f610SAugustin Cavalier static const long double
6*f504f610SAugustin Cavalier pS0 = 1.66666666666666666631e-01L,
7*f504f610SAugustin Cavalier pS1 = -4.16313987993683104320e-01L,
8*f504f610SAugustin Cavalier pS2 = 3.69068046323246813704e-01L,
9*f504f610SAugustin Cavalier pS3 = -1.36213932016738603108e-01L,
10*f504f610SAugustin Cavalier pS4 = 1.78324189708471965733e-02L,
11*f504f610SAugustin Cavalier pS5 = -2.19216428382605211588e-04L,
12*f504f610SAugustin Cavalier pS6 = -7.10526623669075243183e-06L,
13*f504f610SAugustin Cavalier qS1 = -2.94788392796209867269e+00L,
14*f504f610SAugustin Cavalier qS2 = 3.27309890266528636716e+00L,
15*f504f610SAugustin Cavalier qS3 = -1.68285799854822427013e+00L,
16*f504f610SAugustin Cavalier qS4 = 3.90699412641738801874e-01L,
17*f504f610SAugustin Cavalier qS5 = -3.14365703596053263322e-02L;
18*f504f610SAugustin Cavalier
19*f504f610SAugustin Cavalier const long double pio2_hi = 1.57079632679489661926L;
20*f504f610SAugustin Cavalier const long double pio2_lo = -2.50827880633416601173e-20L;
21*f504f610SAugustin Cavalier
22*f504f610SAugustin Cavalier /* used in asinl() and acosl() */
23*f504f610SAugustin Cavalier /* R(x^2) is a rational approximation of (asin(x)-x)/x^3 with Remez algorithm */
__invtrigl_R(long double z)24*f504f610SAugustin Cavalier long double __invtrigl_R(long double z)
25*f504f610SAugustin Cavalier {
26*f504f610SAugustin Cavalier long double p, q;
27*f504f610SAugustin Cavalier p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*(pS5+z*pS6))))));
28*f504f610SAugustin Cavalier q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*(qS4+z*qS5))));
29*f504f610SAugustin Cavalier return p/q;
30*f504f610SAugustin Cavalier }
31*f504f610SAugustin Cavalier #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
32*f504f610SAugustin Cavalier static const long double
33*f504f610SAugustin Cavalier pS0 = 1.66666666666666666666666666666700314e-01L,
34*f504f610SAugustin Cavalier pS1 = -7.32816946414566252574527475428622708e-01L,
35*f504f610SAugustin Cavalier pS2 = 1.34215708714992334609030036562143589e+00L,
36*f504f610SAugustin Cavalier pS3 = -1.32483151677116409805070261790752040e+00L,
37*f504f610SAugustin Cavalier pS4 = 7.61206183613632558824485341162121989e-01L,
38*f504f610SAugustin Cavalier pS5 = -2.56165783329023486777386833928147375e-01L,
39*f504f610SAugustin Cavalier pS6 = 4.80718586374448793411019434585413855e-02L,
40*f504f610SAugustin Cavalier pS7 = -4.42523267167024279410230886239774718e-03L,
41*f504f610SAugustin Cavalier pS8 = 1.44551535183911458253205638280410064e-04L,
42*f504f610SAugustin Cavalier pS9 = -2.10558957916600254061591040482706179e-07L,
43*f504f610SAugustin Cavalier qS1 = -4.84690167848739751544716485245697428e+00L,
44*f504f610SAugustin Cavalier qS2 = 9.96619113536172610135016921140206980e+00L,
45*f504f610SAugustin Cavalier qS3 = -1.13177895428973036660836798461641458e+01L,
46*f504f610SAugustin Cavalier qS4 = 7.74004374389488266169304117714658761e+00L,
47*f504f610SAugustin Cavalier qS5 = -3.25871986053534084709023539900339905e+00L,
48*f504f610SAugustin Cavalier qS6 = 8.27830318881232209752469022352928864e-01L,
49*f504f610SAugustin Cavalier qS7 = -1.18768052702942805423330715206348004e-01L,
50*f504f610SAugustin Cavalier qS8 = 8.32600764660522313269101537926539470e-03L,
51*f504f610SAugustin Cavalier qS9 = -1.99407384882605586705979504567947007e-04L;
52*f504f610SAugustin Cavalier
53*f504f610SAugustin Cavalier const long double pio2_hi = 1.57079632679489661923132169163975140L;
54*f504f610SAugustin Cavalier const long double pio2_lo = 4.33590506506189051239852201302167613e-35L;
55*f504f610SAugustin Cavalier
__invtrigl_R(long double z)56*f504f610SAugustin Cavalier long double __invtrigl_R(long double z)
57*f504f610SAugustin Cavalier {
58*f504f610SAugustin Cavalier long double p, q;
59*f504f610SAugustin Cavalier p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*(pS5+z*(pS6+z*(pS7+z*(pS8+z*pS9)))))))));
60*f504f610SAugustin Cavalier q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*(qS4+z*(qS5+z*(qS6+z*(qS7+z*(qS8+z*qS9))))))));
61*f504f610SAugustin Cavalier return p/q;
62*f504f610SAugustin Cavalier }
63*f504f610SAugustin Cavalier #endif
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