src/math/__invtrigl.c

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