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3334
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1 /* Complex math module */
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2
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3 /* much code borrowed from mathmodule.c */
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4
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5 #include "allobjects.h"
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6 #include "complexobject.h"
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7
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8 #include <errno.h>
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9
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10 #include "mymath.h"
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11
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12 #ifdef i860
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13 /* Cray APP has bogus definition of HUGE_VAL in <math.h> */
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14 #undef HUGE_VAL
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15 #endif
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16
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17 #ifdef HUGE_VAL
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18 #define CHECK(x) if (errno != 0) ; \
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19 else if (-HUGE_VAL <= (x) && (x) <= HUGE_VAL) ; \
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20 else errno = ERANGE
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21 #else
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22 #define CHECK(x) /* Don't know how to check */
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23 #endif
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24
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25 #ifndef M_PI
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26 #define M_PI (3.141592653589793239)
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27 #endif
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28
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29 /* First, the C functions that do the real work */
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30
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31 /* constants */
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3771
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32 static Py_complex c_1 = {1., 0.};
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33 static Py_complex c_half = {0.5, 0.};
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34 static Py_complex c_i = {0., 1.};
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35 static Py_complex c_i2 = {0., 0.5};
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36 static Py_complex c_mi = {0., -1.};
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37 static Py_complex c_pi2 = {M_PI/2., 0.};
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3334
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38
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39 /* forward declarations */
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3771
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40 staticforward Py_complex c_log();
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41 staticforward Py_complex c_prodi();
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42 staticforward Py_complex c_sqrt();
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43
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44
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45 static Py_complex c_acos(x)
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46 Py_complex x;
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47 {
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48 return c_neg(c_prodi(c_log(c_sum(x,c_prod(c_i,
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49 c_sqrt(c_diff(c_1,c_prod(x,x))))))));
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50 }
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51
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52 static Py_complex c_acosh(x)
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53 Py_complex x;
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3334
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54 {
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55 return c_log(c_sum(x,c_prod(c_i,
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56 c_sqrt(c_diff(c_1,c_prod(x,x))))));
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57 }
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58
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59 static Py_complex c_asin(x)
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60 Py_complex x;
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3334
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61 {
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62 return c_neg(c_prodi(c_log(c_sum(c_prod(c_i,x),
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63 c_sqrt(c_diff(c_1,c_prod(x,x)))))));
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64 }
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65
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66 static Py_complex c_asinh(x)
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67 Py_complex x;
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68 {
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69 return c_neg(c_log(c_diff(c_sqrt(c_sum(c_1,c_prod(x,x))),x)));
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70 }
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71
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3771
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72 static Py_complex c_atan(x)
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73 Py_complex x;
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74 {
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75 return c_prod(c_i2,c_log(c_quot(c_sum(c_i,x),c_diff(c_i,x))));
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76 }
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77
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78 static Py_complex c_atanh(x)
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79 Py_complex x;
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80 {
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81 return c_prod(c_half,c_log(c_quot(c_sum(c_1,x),c_diff(c_1,x))));
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82 }
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83
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84 static Py_complex c_cos(x)
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85 Py_complex x;
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86 {
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87 Py_complex r;
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88 r.real = cos(x.real)*cosh(x.imag);
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89 r.imag = -sin(x.real)*sinh(x.imag);
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90 return r;
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91 }
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92
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93 static Py_complex c_cosh(x)
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94 Py_complex x;
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95 {
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96 Py_complex r;
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97 r.real = cos(x.imag)*cosh(x.real);
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98 r.imag = sin(x.imag)*sinh(x.real);
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99 return r;
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100 }
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101
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102 static Py_complex c_exp(x)
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103 Py_complex x;
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104 {
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105 Py_complex r;
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3334
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106 double l = exp(x.real);
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107 r.real = l*cos(x.imag);
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108 r.imag = l*sin(x.imag);
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109 return r;
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110 }
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111
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112 static Py_complex c_log(x)
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113 Py_complex x;
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114 {
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115 Py_complex r;
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116 double l = hypot(x.real,x.imag);
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117 r.imag = atan2(x.imag, x.real);
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118 r.real = log(l);
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119 return r;
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120 }
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121
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122 static Py_complex c_log10(x)
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123 Py_complex x;
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124 {
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125 Py_complex r;
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126 double l = hypot(x.real,x.imag);
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127 r.imag = atan2(x.imag, x.real)/log(10.);
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128 r.real = log10(l);
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129 return r;
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130 }
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131
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132 static Py_complex c_prodi(x)
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133 Py_complex x;
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134 {
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135 Py_complex r;
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136 r.real = -x.imag;
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137 r.imag = x.real;
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138 return r;
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139 }
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140
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141 static Py_complex c_sin(x)
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142 Py_complex x;
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143 {
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144 Py_complex r;
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145 r.real = sin(x.real)*cosh(x.imag);
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146 r.imag = cos(x.real)*sinh(x.imag);
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147 return r;
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148 }
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149
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150 static Py_complex c_sinh(x)
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151 Py_complex x;
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152 {
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153 Py_complex r;
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154 r.real = cos(x.imag)*sinh(x.real);
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155 r.imag = sin(x.imag)*cosh(x.real);
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156 return r;
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157 }
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158
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159 static Py_complex c_sqrt(x)
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160 Py_complex x;
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161 {
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162 Py_complex r;
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3334
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163 double s,d;
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164 if (x.real == 0. && x.imag == 0.)
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165 r = x;
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166 else {
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167 s = sqrt(0.5*(fabs(x.real) + hypot(x.real,x.imag)));
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168 d = 0.5*x.imag/s;
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169 if (x.real > 0.) {
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170 r.real = s;
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171 r.imag = d;
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172 }
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173 else if (x.imag >= 0.) {
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174 r.real = d;
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175 r.imag = s;
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176 }
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177 else {
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178 r.real = -d;
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179 r.imag = -s;
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180 }
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181 }
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182 return r;
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183 }
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184
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185 static Py_complex c_tan(x)
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186 Py_complex x;
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187 {
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188 Py_complex r;
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3334
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189 double sr,cr,shi,chi;
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190 double rs,is,rc,ic;
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191 double d;
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192 sr = sin(x.real);
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193 cr = cos(x.real);
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194 shi = sinh(x.imag);
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195 chi = cosh(x.imag);
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196 rs = sr*chi;
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197 is = cr*shi;
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198 rc = cr*chi;
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199 ic = -sr*shi;
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200 d = rc*rc + ic*ic;
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201 r.real = (rs*rc+is*ic)/d;
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202 r.imag = (is*rc-rs*ic)/d;
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203 return r;
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204 }
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205
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206 static Py_complex c_tanh(x)
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207 Py_complex x;
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208 {
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209 Py_complex r;
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210 double si,ci,shr,chr;
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211 double rs,is,rc,ic;
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212 double d;
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213 si = sin(x.imag);
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214 ci = cos(x.imag);
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215 shr = sinh(x.real);
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216 chr = cosh(x.real);
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217 rs = ci*shr;
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218 is = si*chr;
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219 rc = ci*chr;
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220 ic = si*shr;
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221 d = rc*rc + ic*ic;
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222 r.real = (rs*rc+is*ic)/d;
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223 r.imag = (is*rc-rs*ic)/d;
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224 return r;
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225 }
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226
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227
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228 /* And now the glue to make them available from Python: */
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229
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230 static object *
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231 math_error()
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232 {
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233 if (errno == EDOM)
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234 err_setstr(ValueError, "math domain error");
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235 else if (errno == ERANGE)
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236 err_setstr(OverflowError, "math range error");
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237 else
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238 err_errno(ValueError); /* Unexpected math error */
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239 return NULL;
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240 }
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241
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242 static object *
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243 math_1(args, func)
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244 object *args;
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245 Py_complex (*func) FPROTO((Py_complex));
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246 {
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247 Py_complex x;
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248 if (!PyArg_ParseTuple(args, "D", &x))
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249 return NULL;
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250 errno = 0;
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251 x = (*func)(x);
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252 CHECK(x.real);
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253 CHECK(x.imag);
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254 if (errno != 0)
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255 return math_error();
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256 else
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257 return newcomplexobject(x);
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258 }
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259
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260 #define FUNC1(stubname, func) \
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261 static object * stubname(self, args) object *self, *args; { \
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262 return math_1(args, func); \
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263 }
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264
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265 FUNC1(cmath_acos, c_acos)
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266 FUNC1(cmath_acosh, c_acosh)
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267 FUNC1(cmath_asin, c_asin)
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268 FUNC1(cmath_asinh, c_asinh)
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269 FUNC1(cmath_atan, c_atan)
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270 FUNC1(cmath_atanh, c_atanh)
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271 FUNC1(cmath_cos, c_cos)
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272 FUNC1(cmath_cosh, c_cosh)
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273 FUNC1(cmath_exp, c_exp)
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274 FUNC1(cmath_log, c_log)
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275 FUNC1(cmath_log10, c_log10)
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276 FUNC1(cmath_sin, c_sin)
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277 FUNC1(cmath_sinh, c_sinh)
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278 FUNC1(cmath_sqrt, c_sqrt)
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279 FUNC1(cmath_tan, c_tan)
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280 FUNC1(cmath_tanh, c_tanh)
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281
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282
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283 static struct methodlist cmath_methods[] = {
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284 {"acos", cmath_acos, 1},
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285 {"acosh", cmath_acosh, 1},
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286 {"asin", cmath_asin, 1},
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287 {"asinh", cmath_asinh, 1},
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288 {"atan", cmath_atan, 1},
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289 {"atanh", cmath_atanh, 1},
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290 {"cos", cmath_cos, 1},
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291 {"cosh", cmath_cosh, 1},
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292 {"exp", cmath_exp, 1},
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293 {"log", cmath_log, 1},
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294 {"log10", cmath_log10, 1},
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295 {"sin", cmath_sin, 1},
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296 {"sinh", cmath_sinh, 1},
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297 {"sqrt", cmath_sqrt, 1},
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298 {"tan", cmath_tan, 1},
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299 {"tanh", cmath_tanh, 1},
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300 {NULL, NULL} /* sentinel */
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301 };
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302
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303 void
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304 initcmath()
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305 {
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306 object *m, *d, *v;
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307
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308 m = Py_InitModule("cmath", cmath_methods);
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309 d = getmoduledict(m);
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310 dictinsert(d, "pi", v = newfloatobject(atan(1.0) * 4.0));
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311 DECREF(v);
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312 dictinsert(d, "e", v = newfloatobject(exp(1.0)));
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313 DECREF(v);
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314 }
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