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1 #include <float.h> | 1 #include <float.h> |
2 #include "__invtrigl.h" | 2 #include "__invtrigl.h" |
3 | 3 |
4 #if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 | 4 #if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 |
5 static const long double | 5 static const long double pS0 = 1.66666666666666666631e-01L, |
6 pS0 = 1.66666666666666666631e-01L, | 6 pS1 = -4.16313987993683104320e-01L, |
7 pS1 = -4.16313987993683104320e-01L, | 7 pS2 = 3.69068046323246813704e-01L, |
8 pS2 = 3.69068046323246813704e-01L, | 8 pS3 = -1.36213932016738603108e-01L, |
9 pS3 = -1.36213932016738603108e-01L, | 9 pS4 = 1.78324189708471965733e-02L, |
10 pS4 = 1.78324189708471965733e-02L, | 10 pS5 = -2.19216428382605211588e-04L, |
11 pS5 = -2.19216428382605211588e-04L, | 11 pS6 = -7.10526623669075243183e-06L, |
12 pS6 = -7.10526623669075243183e-06L, | 12 qS1 = -2.94788392796209867269e+00L, |
13 qS1 = -2.94788392796209867269e+00L, | 13 qS2 = 3.27309890266528636716e+00L, |
14 qS2 = 3.27309890266528636716e+00L, | 14 qS3 = -1.68285799854822427013e+00L, |
15 qS3 = -1.68285799854822427013e+00L, | 15 qS4 = 3.90699412641738801874e-01L, |
16 qS4 = 3.90699412641738801874e-01L, | 16 qS5 = -3.14365703596053263322e-02L; |
17 qS5 = -3.14365703596053263322e-02L; | |
18 | 17 |
19 const long double pio2_hi = 1.57079632679489661926L; | 18 const long double pio2_hi = 1.57079632679489661926L; |
20 const long double pio2_lo = -2.50827880633416601173e-20L; | 19 const long double pio2_lo = -2.50827880633416601173e-20L; |
21 | 20 |
22 /* used in asinl() and acosl() */ | 21 /* used in asinl() and acosl() */ |
23 /* R(x^2) is a rational approximation of (asin(x)-x)/x^3 with Remez algorithm */ | 22 /* R(x^2) is a rational approximation of (asin(x)-x)/x^3 with Remez algorithm */ |
24 long double __invtrigl_R(long double z) | 23 long double __invtrigl_R(long double z) { |
25 { | 24 long double p, q; |
26 » long double p, q; | 25 p = z * (pS0 + |
27 » p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*(pS5+z*pS6)))))); | 26 z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * (pS5 + z * pS6)))))); |
28 » q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*(qS4+z*qS5)))); | 27 q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * (qS4 + z * qS5)))); |
29 » return p/q; | 28 return p / q; |
30 } | 29 } |
31 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 | 30 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 |
32 static const long double | 31 static const long double pS0 = 1.66666666666666666666666666666700314e-01L, |
33 pS0 = 1.66666666666666666666666666666700314e-01L, | 32 pS1 = -7.32816946414566252574527475428622708e-01L, |
34 pS1 = -7.32816946414566252574527475428622708e-01L, | 33 pS2 = 1.34215708714992334609030036562143589e+00L, |
35 pS2 = 1.34215708714992334609030036562143589e+00L, | 34 pS3 = -1.32483151677116409805070261790752040e+00L, |
36 pS3 = -1.32483151677116409805070261790752040e+00L, | 35 pS4 = 7.61206183613632558824485341162121989e-01L, |
37 pS4 = 7.61206183613632558824485341162121989e-01L, | 36 pS5 = -2.56165783329023486777386833928147375e-01L, |
38 pS5 = -2.56165783329023486777386833928147375e-01L, | 37 pS6 = 4.80718586374448793411019434585413855e-02L, |
39 pS6 = 4.80718586374448793411019434585413855e-02L, | 38 pS7 = -4.42523267167024279410230886239774718e-03L, |
40 pS7 = -4.42523267167024279410230886239774718e-03L, | 39 pS8 = 1.44551535183911458253205638280410064e-04L, |
41 pS8 = 1.44551535183911458253205638280410064e-04L, | 40 pS9 = -2.10558957916600254061591040482706179e-07L, |
42 pS9 = -2.10558957916600254061591040482706179e-07L, | 41 qS1 = -4.84690167848739751544716485245697428e+00L, |
43 qS1 = -4.84690167848739751544716485245697428e+00L, | 42 qS2 = 9.96619113536172610135016921140206980e+00L, |
44 qS2 = 9.96619113536172610135016921140206980e+00L, | 43 qS3 = -1.13177895428973036660836798461641458e+01L, |
45 qS3 = -1.13177895428973036660836798461641458e+01L, | 44 qS4 = 7.74004374389488266169304117714658761e+00L, |
46 qS4 = 7.74004374389488266169304117714658761e+00L, | 45 qS5 = -3.25871986053534084709023539900339905e+00L, |
47 qS5 = -3.25871986053534084709023539900339905e+00L, | 46 qS6 = 8.27830318881232209752469022352928864e-01L, |
48 qS6 = 8.27830318881232209752469022352928864e-01L, | 47 qS7 = -1.18768052702942805423330715206348004e-01L, |
49 qS7 = -1.18768052702942805423330715206348004e-01L, | 48 qS8 = 8.32600764660522313269101537926539470e-03L, |
50 qS8 = 8.32600764660522313269101537926539470e-03L, | 49 qS9 = -1.99407384882605586705979504567947007e-04L; |
51 qS9 = -1.99407384882605586705979504567947007e-04L; | |
52 | 50 |
53 const long double pio2_hi = 1.57079632679489661923132169163975140L; | 51 const long double pio2_hi = 1.57079632679489661923132169163975140L; |
54 const long double pio2_lo = 4.33590506506189051239852201302167613e-35L; | 52 const long double pio2_lo = 4.33590506506189051239852201302167613e-35L; |
55 | 53 |
56 long double __invtrigl_R(long double z) | 54 long double __invtrigl_R(long double z) { |
57 { | 55 long double p, q; |
58 » long double p, q; | 56 p = z * (pS0 + |
59 » p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*(pS5+z*(pS6+z*(pS7+z*(pS8+z*pS9
))))))))); | 57 z * (pS1 + |
60 » q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*(qS4+z*(qS5+z*(pS6+z*(pS7+z*(pS8+z*pS9)))
))))); | 58 z * (pS2 + |
61 » return p/q; | 59 z * (pS3 + |
| 60 z * (pS4 + |
| 61 z * (pS5 + |
| 62 z * (pS6 + |
| 63 z * (pS7 + z * (pS8 + z * pS9))))))))); |
| 64 q = 1.0 + |
| 65 z * (qS1 + |
| 66 z * (qS2 + |
| 67 z * (qS3 + |
| 68 z * (qS4 + |
| 69 z * (qS5 + |
| 70 z * (pS6 + z * (pS7 + z * (pS8 + z * pS9)))))))); |
| 71 return p / q; |
62 } | 72 } |
63 #endif | 73 #endif |
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