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1 //=========================================================================== |
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2 // |
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3 // k_tan.c |
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4 // |
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5 // Part of the standard mathematical function library |
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6 // |
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7 //=========================================================================== |
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8 //####COPYRIGHTBEGIN#### |
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9 // |
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10 // ------------------------------------------- |
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11 // The contents of this file are subject to the Cygnus eCos Public License |
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12 // Version 1.0 (the "License"); you may not use this file except in |
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13 // compliance with the License. You may obtain a copy of the License at |
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14 // http://sourceware.cygnus.com/ecos |
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15 // |
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16 // Software distributed under the License is distributed on an "AS IS" |
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17 // basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See the |
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18 // License for the specific language governing rights and limitations under |
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19 // the License. |
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20 // |
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21 // The Original Code is eCos - Embedded Cygnus Operating System, released |
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22 // September 30, 1998. |
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23 // |
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24 // The Initial Developer of the Original Code is Cygnus. Portions created |
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25 // by Cygnus are Copyright (C) 1998 Cygnus Solutions. All Rights Reserved. |
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26 // ------------------------------------------- |
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27 // |
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28 //####COPYRIGHTEND#### |
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29 //=========================================================================== |
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30 //#####DESCRIPTIONBEGIN#### |
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31 // |
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32 // Author(s): jlarmour@cygnus.co.uk |
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33 // Contributors: jlarmour@cygnus.co.uk |
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34 // Date: 1998-02-13 |
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35 // Purpose: |
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36 // Description: |
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37 // Usage: |
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38 // |
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39 //####DESCRIPTIONEND#### |
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40 // |
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41 //=========================================================================== |
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42 |
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43 // CONFIGURATION |
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44 |
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45 #include <pkgconf/libm.h> // Configuration header |
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46 |
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47 // Include the Math library? |
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48 #ifdef CYGPKG_LIBM |
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49 |
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50 // Derived from code with the following copyright |
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51 |
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52 |
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53 /* @(#)k_tan.c 1.3 95/01/18 */ |
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54 /* |
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55 * ==================================================== |
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56 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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57 * |
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58 * Developed at SunSoft, a Sun Microsystems, Inc. business. |
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59 * Permission to use, copy, modify, and distribute this |
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60 * software is freely granted, provided that this notice |
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61 * is preserved. |
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62 * ==================================================== |
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63 */ |
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64 |
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65 /* __kernel_tan( x, y, k ) |
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66 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 |
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67 * Input x is assumed to be bounded by ~pi/4 in magnitude. |
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68 * Input y is the tail of x. |
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69 * Input k indicates whether tan (if k=1) or |
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70 * -1/tan (if k= -1) is returned. |
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71 * |
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72 * Algorithm |
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73 * 1. Since tan(-x) = -tan(x), we need only to consider positive x. |
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74 * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. |
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75 * 3. tan(x) is approximated by a odd polynomial of degree 27 on |
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76 * [0,0.67434] |
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77 * 3 27 |
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78 * tan(x) ~ x + T1*x + ... + T13*x |
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79 * where |
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80 * |
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81 * |tan(x) 2 4 26 | -59.2 |
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82 * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 |
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83 * | x | |
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84 * |
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85 * Note: tan(x+y) = tan(x) + tan'(x)*y |
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86 * ~ tan(x) + (1+x*x)*y |
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87 * Therefore, for better accuracy in computing tan(x+y), let |
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88 * 3 2 2 2 2 |
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89 * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) |
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90 * then |
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91 * 3 2 |
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92 * tan(x+y) = x + (T1*x + (x *(r+y)+y)) |
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93 * |
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94 * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then |
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95 * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) |
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96 * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) |
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97 */ |
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98 |
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99 #include "mathincl/fdlibm.h" |
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100 static const double |
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101 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
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102 pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ |
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103 pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */ |
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104 T[] = { |
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105 3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */ |
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106 1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */ |
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107 5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */ |
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108 2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */ |
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109 8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */ |
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110 3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */ |
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111 1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */ |
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112 5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */ |
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113 2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */ |
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114 7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */ |
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115 7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */ |
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116 -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */ |
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117 2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */ |
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118 }; |
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119 |
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120 double __kernel_tan(double x, double y, int iy) |
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121 { |
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122 double z,r,v,w,s; |
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123 int ix,hx; |
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124 hx = CYG_LIBM_HI(x); /* high word of x */ |
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125 ix = hx&0x7fffffff; /* high word of |x| */ |
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126 if(ix<0x3e300000) /* x < 2**-28 */ |
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127 {if((int)x==0) { /* generate inexact */ |
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128 if(((ix|CYG_LIBM_LO(x))|(iy+1))==0) return one/fabs(x); |
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129 else return (iy==1)? x: -one/x; |
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130 } |
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131 } |
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132 if(ix>=0x3FE59428) { /* |x|>=0.6744 */ |
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133 if(hx<0) {x = -x; y = -y;} |
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134 z = pio4-x; |
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135 w = pio4lo-y; |
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136 x = z+w; y = 0.0; |
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137 } |
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138 z = x*x; |
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139 w = z*z; |
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140 /* Break x^5*(T[1]+x^2*T[2]+...) into |
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141 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + |
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142 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) |
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143 */ |
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144 r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); |
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145 v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); |
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146 s = z*x; |
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147 r = y + z*(s*(r+v)+y); |
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148 r += T[0]*s; |
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149 w = x+r; |
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150 if(ix>=0x3FE59428) { |
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151 v = (double)iy; |
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152 return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r))); |
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153 } |
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154 if(iy==1) return w; |
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155 else { /* if allow error up to 2 ulp, |
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156 simply return -1.0/(x+r) here */ |
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157 /* compute -1.0/(x+r) accurately */ |
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158 double a,t; |
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159 z = w; |
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160 CYG_LIBM_LO(z) = 0; |
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161 v = r-(z - x); /* z+v = r+x */ |
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162 t = a = -1.0/w; /* a = -1.0/w */ |
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163 CYG_LIBM_LO(t) = 0; |
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164 s = 1.0+t*z; |
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165 return t+a*(s+t*v); |
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166 } |
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167 } |
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168 |
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169 #endif // ifdef CYGPKG_LIBM |
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170 |
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171 // EOF k_tan.c |
