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428
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1 /* Primitive operations on floating point for XEmacs Lisp interpreter.
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2 Copyright (C) 1988, 1993, 1994 Free Software Foundation, Inc.
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3
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4 This file is part of XEmacs.
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5
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6 XEmacs is free software; you can redistribute it and/or modify it
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7 under the terms of the GNU General Public License as published by the
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8 Free Software Foundation; either version 2, or (at your option) any
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9 later version.
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10
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11 XEmacs is distributed in the hope that it will be useful, but WITHOUT
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12 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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13 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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14 for more details.
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15
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16 You should have received a copy of the GNU General Public License
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17 along with XEmacs; see the file COPYING. If not, write to
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18 the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
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19 Boston, MA 02111-1307, USA. */
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20
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21 /* Synched up with: FSF 19.30. */
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22
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23 /* ANSI C requires only these float functions:
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24 acos, asin, atan, atan2, ceil, cos, cosh, exp, fabs, floor, fmod,
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25 frexp, ldexp, log, log10, modf, pow, sin, sinh, sqrt, tan, tanh.
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26
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27 Define HAVE_INVERSE_HYPERBOLIC if you have acosh, asinh, and atanh.
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28 Define HAVE_CBRT if you have cbrt().
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29 Define HAVE_RINT if you have rint().
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30 If you don't define these, then the appropriate routines will be simulated.
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31
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32 Define HAVE_MATHERR if on a system supporting the SysV matherr() callback.
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33 (This should happen automatically.)
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34
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35 Define FLOAT_CHECK_ERRNO if the float library routines set errno.
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36 This has no effect if HAVE_MATHERR is defined.
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37
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38 Define FLOAT_CATCH_SIGILL if the float library routines signal SIGILL.
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39 (What systems actually do this? Let me know. -jwz)
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40
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41 Define FLOAT_CHECK_DOMAIN if the float library doesn't handle errors by
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42 either setting errno, or signalling SIGFPE/SIGILL. Otherwise, domain and
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43 range checking will happen before calling the float routines. This has
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44 no effect if HAVE_MATHERR is defined (since matherr will be called when
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45 a domain error occurs).
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46 */
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47
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48 #include <config.h>
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49 #include "lisp.h"
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50 #include "syssignal.h"
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51
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52 #ifdef LISP_FLOAT_TYPE
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53
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54 /* Need to define a differentiating symbol -- see sysfloat.h */
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55 #define THIS_FILENAME floatfns
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56 #include "sysfloat.h"
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57
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430
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58 /* The code uses emacs_rint, so that it works to undefine HAVE_RINT
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59 if `rint' exists but does not work right. */
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60 #ifdef HAVE_RINT
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61 #define emacs_rint rint
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62 #else
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428
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63 static double
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430
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64 emacs_rint (double x)
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428
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65 {
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66 double r = floor (x + 0.5);
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67 double diff = fabs (r - x);
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68 /* Round to even and correct for any roundoff errors. */
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69 if (diff >= 0.5 && (diff > 0.5 || r != 2.0 * floor (r / 2.0)))
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70 r += r < x ? 1.0 : -1.0;
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71 return r;
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72 }
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73 #endif
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74
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75 /* Nonzero while executing in floating point.
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76 This tells float_error what to do. */
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77 static int in_float;
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78
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79 /* If an argument is out of range for a mathematical function,
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80 here is the actual argument value to use in the error message. */
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81 static Lisp_Object float_error_arg, float_error_arg2;
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442
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82 static const char *float_error_fn_name;
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428
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83
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84 /* Evaluate the floating point expression D, recording NUM
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85 as the original argument for error messages.
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86 D is normally an assignment expression.
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87 Handle errors which may result in signals or may set errno.
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88
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89 Note that float_error may be declared to return void, so you can't
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90 just cast the zero after the colon to (SIGTYPE) to make the types
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91 check properly. */
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92 #ifdef FLOAT_CHECK_ERRNO
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93 #define IN_FLOAT(d, name, num) \
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94 do { \
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95 float_error_arg = num; \
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96 float_error_fn_name = name; \
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97 in_float = 1; errno = 0; (d); in_float = 0; \
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98 if (errno != 0) in_float_error (); \
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99 } while (0)
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100 #define IN_FLOAT2(d, name, num, num2) \
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101 do { \
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102 float_error_arg = num; \
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103 float_error_arg2 = num2; \
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104 float_error_fn_name = name; \
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105 in_float = 2; errno = 0; (d); in_float = 0; \
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106 if (errno != 0) in_float_error (); \
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107 } while (0)
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108 #else
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109 #define IN_FLOAT(d, name, num) (in_float = 1, (d), in_float = 0)
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110 #define IN_FLOAT2(d, name, num, num2) (in_float = 2, (d), in_float = 0)
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111 #endif
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112
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113
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114 #define arith_error(op,arg) \
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115 Fsignal (Qarith_error, list2 (build_string (op), arg))
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116 #define range_error(op,arg) \
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117 Fsignal (Qrange_error, list2 (build_string (op), arg))
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118 #define range_error2(op,a1,a2) \
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119 Fsignal (Qrange_error, list3 (build_string (op), a1, a2))
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120 #define domain_error(op,arg) \
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121 Fsignal (Qdomain_error, list2 (build_string (op), arg))
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122 #define domain_error2(op,a1,a2) \
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123 Fsignal (Qdomain_error, list3 (build_string (op), a1, a2))
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124
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125
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126 /* Convert float to Lisp Integer if it fits, else signal a range
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127 error using the given arguments. */
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128 static Lisp_Object
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442
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129 float_to_int (double x, const char *name, Lisp_Object num, Lisp_Object num2)
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428
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130 {
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131 if (x >= ((EMACS_INT) 1 << (VALBITS-1))
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132 || x <= - ((EMACS_INT) 1 << (VALBITS-1)) - (EMACS_INT) 1)
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133 {
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134 if (!UNBOUNDP (num2))
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135 range_error2 (name, num, num2);
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136 else
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137 range_error (name, num);
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138 }
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139 return (make_int ((EMACS_INT) x));
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140 }
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141
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142
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143 static void
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144 in_float_error (void)
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145 {
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146 switch (errno)
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147 {
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148 case 0:
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149 break;
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150 case EDOM:
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151 if (in_float == 2)
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152 domain_error2 (float_error_fn_name, float_error_arg, float_error_arg2);
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153 else
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154 domain_error (float_error_fn_name, float_error_arg);
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155 break;
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156 case ERANGE:
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157 range_error (float_error_fn_name, float_error_arg);
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158 break;
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159 default:
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160 arith_error (float_error_fn_name, float_error_arg);
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161 break;
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162 }
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163 }
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164
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165
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166 static Lisp_Object
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167 mark_float (Lisp_Object obj)
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168 {
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169 return Qnil;
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170 }
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171
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172 static int
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173 float_equal (Lisp_Object obj1, Lisp_Object obj2, int depth)
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174 {
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175 return (extract_float (obj1) == extract_float (obj2));
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176 }
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177
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178 static unsigned long
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179 float_hash (Lisp_Object obj, int depth)
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180 {
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181 /* mod the value down to 32-bit range */
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182 /* #### change for 64-bit machines */
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183 return (unsigned long) fmod (extract_float (obj), 4e9);
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184 }
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185
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186 static const struct lrecord_description float_description[] = {
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187 { XD_END }
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188 };
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189
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190 DEFINE_BASIC_LRECORD_IMPLEMENTATION ("float", float,
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191 mark_float, print_float, 0, float_equal,
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192 float_hash, float_description,
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440
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193 Lisp_Float);
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428
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194
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195 /* Extract a Lisp number as a `double', or signal an error. */
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196
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197 double
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198 extract_float (Lisp_Object num)
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199 {
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200 if (FLOATP (num))
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201 return XFLOAT_DATA (num);
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202
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203 if (INTP (num))
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204 return (double) XINT (num);
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205
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206 return extract_float (wrong_type_argument (Qnumberp, num));
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207 }
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208 #endif /* LISP_FLOAT_TYPE */
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209
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210
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211 /* Trig functions. */
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212 #ifdef LISP_FLOAT_TYPE
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213
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214 DEFUN ("acos", Facos, 1, 1, 0, /*
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444
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215 Return the inverse cosine of NUMBER.
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428
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216 */
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444
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217 (number))
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428
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218 {
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444
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219 double d = extract_float (number);
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428
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220 #ifdef FLOAT_CHECK_DOMAIN
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221 if (d > 1.0 || d < -1.0)
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444
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222 domain_error ("acos", number);
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428
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223 #endif
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444
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224 IN_FLOAT (d = acos (d), "acos", number);
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428
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225 return make_float (d);
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226 }
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227
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228 DEFUN ("asin", Fasin, 1, 1, 0, /*
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444
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229 Return the inverse sine of NUMBER.
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428
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230 */
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444
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231 (number))
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428
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232 {
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444
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233 double d = extract_float (number);
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428
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234 #ifdef FLOAT_CHECK_DOMAIN
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235 if (d > 1.0 || d < -1.0)
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444
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236 domain_error ("asin", number);
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428
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237 #endif
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444
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238 IN_FLOAT (d = asin (d), "asin", number);
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428
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239 return make_float (d);
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240 }
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241
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242 DEFUN ("atan", Fatan, 1, 2, 0, /*
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444
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243 Return the inverse tangent of NUMBER.
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244 If optional second argument NUMBER2 is provided,
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245 return atan2 (NUMBER, NUMBER2).
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428
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246 */
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444
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247 (number, number2))
|
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428
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248 {
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444
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249 double d = extract_float (number);
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428
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250
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444
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251 if (NILP (number2))
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252 IN_FLOAT (d = atan (d), "atan", number);
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428
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253 else
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254 {
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444
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255 double d2 = extract_float (number2);
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428
|
256 #ifdef FLOAT_CHECK_DOMAIN
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257 if (d == 0.0 && d2 == 0.0)
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444
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258 domain_error2 ("atan", number, number2);
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428
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259 #endif
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444
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260 IN_FLOAT2 (d = atan2 (d, d2), "atan", number, number2);
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428
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261 }
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262 return make_float (d);
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263 }
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264
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265 DEFUN ("cos", Fcos, 1, 1, 0, /*
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444
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266 Return the cosine of NUMBER.
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428
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267 */
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444
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268 (number))
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428
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269 {
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444
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270 double d = extract_float (number);
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271 IN_FLOAT (d = cos (d), "cos", number);
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428
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272 return make_float (d);
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273 }
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274
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|
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275 DEFUN ("sin", Fsin, 1, 1, 0, /*
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444
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276 Return the sine of NUMBER.
|
|
428
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277 */
|
|
444
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278 (number))
|
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428
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279 {
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|
444
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280 double d = extract_float (number);
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281 IN_FLOAT (d = sin (d), "sin", number);
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428
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282 return make_float (d);
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283 }
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284
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|
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285 DEFUN ("tan", Ftan, 1, 1, 0, /*
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444
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286 Return the tangent of NUMBER.
|
|
428
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287 */
|
|
444
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288 (number))
|
|
428
|
289 {
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|
444
|
290 double d = extract_float (number);
|
|
428
|
291 double c = cos (d);
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|
|
292 #ifdef FLOAT_CHECK_DOMAIN
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|
|
293 if (c == 0.0)
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|
444
|
294 domain_error ("tan", number);
|
|
428
|
295 #endif
|
|
444
|
296 IN_FLOAT (d = (sin (d) / c), "tan", number);
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|
428
|
297 return make_float (d);
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|
|
298 }
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|
|
299 #endif /* LISP_FLOAT_TYPE (trig functions) */
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|
|
300
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|
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301
|
|
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302 /* Bessel functions */
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303 #if 0 /* Leave these out unless we find there's a reason for them. */
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|
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304 /* #ifdef LISP_FLOAT_TYPE */
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|
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305
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|
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306 DEFUN ("bessel-j0", Fbessel_j0, 1, 1, 0, /*
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|
444
|
307 Return the bessel function j0 of NUMBER.
|
|
428
|
308 */
|
|
444
|
309 (number))
|
|
428
|
310 {
|
|
444
|
311 double d = extract_float (number);
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|
|
312 IN_FLOAT (d = j0 (d), "bessel-j0", number);
|
|
428
|
313 return make_float (d);
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|
|
314 }
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|
|
315
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|
|
316 DEFUN ("bessel-j1", Fbessel_j1, 1, 1, 0, /*
|
|
444
|
317 Return the bessel function j1 of NUMBER.
|
|
428
|
318 */
|
|
444
|
319 (number))
|
|
428
|
320 {
|
|
444
|
321 double d = extract_float (number);
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|
|
322 IN_FLOAT (d = j1 (d), "bessel-j1", number);
|
|
428
|
323 return make_float (d);
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|
|
324 }
|
|
|
325
|
|
|
326 DEFUN ("bessel-jn", Fbessel_jn, 2, 2, 0, /*
|
|
444
|
327 Return the order N bessel function output jn of NUMBER.
|
|
|
328 The first number (the order) is truncated to an integer.
|
|
428
|
329 */
|
|
444
|
330 (number1, number2))
|
|
428
|
331 {
|
|
444
|
332 int i1 = extract_float (number1);
|
|
|
333 double f2 = extract_float (number2);
|
|
428
|
334
|
|
444
|
335 IN_FLOAT (f2 = jn (i1, f2), "bessel-jn", number1);
|
|
428
|
336 return make_float (f2);
|
|
|
337 }
|
|
|
338
|
|
|
339 DEFUN ("bessel-y0", Fbessel_y0, 1, 1, 0, /*
|
|
444
|
340 Return the bessel function y0 of NUMBER.
|
|
428
|
341 */
|
|
444
|
342 (number))
|
|
428
|
343 {
|
|
444
|
344 double d = extract_float (number);
|
|
|
345 IN_FLOAT (d = y0 (d), "bessel-y0", number);
|
|
428
|
346 return make_float (d);
|
|
|
347 }
|
|
|
348
|
|
|
349 DEFUN ("bessel-y1", Fbessel_y1, 1, 1, 0, /*
|
|
444
|
350 Return the bessel function y1 of NUMBER.
|
|
428
|
351 */
|
|
444
|
352 (number))
|
|
428
|
353 {
|
|
444
|
354 double d = extract_float (number);
|
|
|
355 IN_FLOAT (d = y1 (d), "bessel-y0", number);
|
|
428
|
356 return make_float (d);
|
|
|
357 }
|
|
|
358
|
|
|
359 DEFUN ("bessel-yn", Fbessel_yn, 2, 2, 0, /*
|
|
444
|
360 Return the order N bessel function output yn of NUMBER.
|
|
|
361 The first number (the order) is truncated to an integer.
|
|
428
|
362 */
|
|
444
|
363 (number1, number2))
|
|
428
|
364 {
|
|
444
|
365 int i1 = extract_float (number1);
|
|
|
366 double f2 = extract_float (number2);
|
|
428
|
367
|
|
444
|
368 IN_FLOAT (f2 = yn (i1, f2), "bessel-yn", number1);
|
|
428
|
369 return make_float (f2);
|
|
|
370 }
|
|
|
371
|
|
|
372 #endif /* 0 (bessel functions) */
|
|
|
373
|
|
|
374 /* Error functions. */
|
|
|
375 #if 0 /* Leave these out unless we see they are worth having. */
|
|
|
376 /* #ifdef LISP_FLOAT_TYPE */
|
|
|
377
|
|
|
378 DEFUN ("erf", Ferf, 1, 1, 0, /*
|
|
444
|
379 Return the mathematical error function of NUMBER.
|
|
428
|
380 */
|
|
444
|
381 (number))
|
|
428
|
382 {
|
|
444
|
383 double d = extract_float (number);
|
|
|
384 IN_FLOAT (d = erf (d), "erf", number);
|
|
428
|
385 return make_float (d);
|
|
|
386 }
|
|
|
387
|
|
|
388 DEFUN ("erfc", Ferfc, 1, 1, 0, /*
|
|
444
|
389 Return the complementary error function of NUMBER.
|
|
428
|
390 */
|
|
444
|
391 (number))
|
|
428
|
392 {
|
|
444
|
393 double d = extract_float (number);
|
|
|
394 IN_FLOAT (d = erfc (d), "erfc", number);
|
|
428
|
395 return make_float (d);
|
|
|
396 }
|
|
|
397
|
|
|
398 DEFUN ("log-gamma", Flog_gamma, 1, 1, 0, /*
|
|
444
|
399 Return the log gamma of NUMBER.
|
|
428
|
400 */
|
|
444
|
401 (number))
|
|
428
|
402 {
|
|
444
|
403 double d = extract_float (number);
|
|
|
404 IN_FLOAT (d = lgamma (d), "log-gamma", number);
|
|
428
|
405 return make_float (d);
|
|
|
406 }
|
|
|
407
|
|
|
408 #endif /* 0 (error functions) */
|
|
|
409
|
|
|
410
|
|
|
411 /* Root and Log functions. */
|
|
|
412
|
|
|
413 #ifdef LISP_FLOAT_TYPE
|
|
|
414 DEFUN ("exp", Fexp, 1, 1, 0, /*
|
|
444
|
415 Return the exponential base e of NUMBER.
|
|
428
|
416 */
|
|
444
|
417 (number))
|
|
428
|
418 {
|
|
444
|
419 double d = extract_float (number);
|
|
428
|
420 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
421 if (d > 709.7827) /* Assume IEEE doubles here */
|
|
444
|
422 range_error ("exp", number);
|
|
428
|
423 else if (d < -709.0)
|
|
|
424 return make_float (0.0);
|
|
|
425 else
|
|
|
426 #endif
|
|
444
|
427 IN_FLOAT (d = exp (d), "exp", number);
|
|
428
|
428 return make_float (d);
|
|
|
429 }
|
|
|
430 #endif /* LISP_FLOAT_TYPE */
|
|
|
431
|
|
|
432
|
|
|
433 DEFUN ("expt", Fexpt, 2, 2, 0, /*
|
|
444
|
434 Return the exponential NUMBER1 ** NUMBER2.
|
|
428
|
435 */
|
|
444
|
436 (number1, number2))
|
|
428
|
437 {
|
|
444
|
438 if (INTP (number1) && /* common lisp spec */
|
|
|
439 INTP (number2)) /* don't promote, if both are ints */
|
|
428
|
440 {
|
|
|
441 EMACS_INT retval;
|
|
444
|
442 EMACS_INT x = XINT (number1);
|
|
|
443 EMACS_INT y = XINT (number2);
|
|
428
|
444
|
|
|
445 if (y < 0)
|
|
|
446 {
|
|
|
447 if (x == 1)
|
|
|
448 retval = 1;
|
|
|
449 else if (x == -1)
|
|
|
450 retval = (y & 1) ? -1 : 1;
|
|
|
451 else
|
|
|
452 retval = 0;
|
|
|
453 }
|
|
|
454 else
|
|
|
455 {
|
|
|
456 retval = 1;
|
|
|
457 while (y > 0)
|
|
|
458 {
|
|
|
459 if (y & 1)
|
|
|
460 retval *= x;
|
|
|
461 x *= x;
|
|
|
462 y = (EMACS_UINT) y >> 1;
|
|
|
463 }
|
|
|
464 }
|
|
|
465 return make_int (retval);
|
|
|
466 }
|
|
|
467
|
|
|
468 #ifdef LISP_FLOAT_TYPE
|
|
|
469 {
|
|
444
|
470 double f1 = extract_float (number1);
|
|
|
471 double f2 = extract_float (number2);
|
|
428
|
472 /* Really should check for overflow, too */
|
|
|
473 if (f1 == 0.0 && f2 == 0.0)
|
|
|
474 f1 = 1.0;
|
|
|
475 # ifdef FLOAT_CHECK_DOMAIN
|
|
|
476 else if ((f1 == 0.0 && f2 < 0.0) || (f1 < 0 && f2 != floor(f2)))
|
|
444
|
477 domain_error2 ("expt", number1, number2);
|
|
428
|
478 # endif /* FLOAT_CHECK_DOMAIN */
|
|
444
|
479 IN_FLOAT2 (f1 = pow (f1, f2), "expt", number1, number2);
|
|
428
|
480 return make_float (f1);
|
|
|
481 }
|
|
|
482 #else
|
|
444
|
483 CHECK_INT_OR_FLOAT (number1);
|
|
|
484 CHECK_INT_OR_FLOAT (number2);
|
|
|
485 return Fexpt (number1, number2);
|
|
428
|
486 #endif /* LISP_FLOAT_TYPE */
|
|
|
487 }
|
|
|
488
|
|
|
489 #ifdef LISP_FLOAT_TYPE
|
|
|
490 DEFUN ("log", Flog, 1, 2, 0, /*
|
|
444
|
491 Return the natural logarithm of NUMBER.
|
|
|
492 If second optional argument BASE is given, return the logarithm of
|
|
|
493 NUMBER using that base.
|
|
428
|
494 */
|
|
444
|
495 (number, base))
|
|
428
|
496 {
|
|
444
|
497 double d = extract_float (number);
|
|
428
|
498 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
499 if (d <= 0.0)
|
|
444
|
500 domain_error2 ("log", number, base);
|
|
428
|
501 #endif
|
|
|
502 if (NILP (base))
|
|
444
|
503 IN_FLOAT (d = log (d), "log", number);
|
|
428
|
504 else
|
|
|
505 {
|
|
|
506 double b = extract_float (base);
|
|
|
507 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
508 if (b <= 0.0 || b == 1.0)
|
|
444
|
509 domain_error2 ("log", number, base);
|
|
428
|
510 #endif
|
|
|
511 if (b == 10.0)
|
|
444
|
512 IN_FLOAT2 (d = log10 (d), "log", number, base);
|
|
428
|
513 else
|
|
444
|
514 IN_FLOAT2 (d = (log (d) / log (b)), "log", number, base);
|
|
428
|
515 }
|
|
|
516 return make_float (d);
|
|
|
517 }
|
|
|
518
|
|
|
519
|
|
|
520 DEFUN ("log10", Flog10, 1, 1, 0, /*
|
|
444
|
521 Return the logarithm base 10 of NUMBER.
|
|
428
|
522 */
|
|
444
|
523 (number))
|
|
428
|
524 {
|
|
444
|
525 double d = extract_float (number);
|
|
428
|
526 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
527 if (d <= 0.0)
|
|
444
|
528 domain_error ("log10", number);
|
|
428
|
529 #endif
|
|
444
|
530 IN_FLOAT (d = log10 (d), "log10", number);
|
|
428
|
531 return make_float (d);
|
|
|
532 }
|
|
|
533
|
|
|
534
|
|
|
535 DEFUN ("sqrt", Fsqrt, 1, 1, 0, /*
|
|
444
|
536 Return the square root of NUMBER.
|
|
428
|
537 */
|
|
444
|
538 (number))
|
|
428
|
539 {
|
|
444
|
540 double d = extract_float (number);
|
|
428
|
541 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
542 if (d < 0.0)
|
|
444
|
543 domain_error ("sqrt", number);
|
|
428
|
544 #endif
|
|
444
|
545 IN_FLOAT (d = sqrt (d), "sqrt", number);
|
|
428
|
546 return make_float (d);
|
|
|
547 }
|
|
|
548
|
|
|
549
|
|
|
550 DEFUN ("cube-root", Fcube_root, 1, 1, 0, /*
|
|
444
|
551 Return the cube root of NUMBER.
|
|
428
|
552 */
|
|
444
|
553 (number))
|
|
428
|
554 {
|
|
444
|
555 double d = extract_float (number);
|
|
428
|
556 #ifdef HAVE_CBRT
|
|
444
|
557 IN_FLOAT (d = cbrt (d), "cube-root", number);
|
|
428
|
558 #else
|
|
|
559 if (d >= 0.0)
|
|
444
|
560 IN_FLOAT (d = pow (d, 1.0/3.0), "cube-root", number);
|
|
428
|
561 else
|
|
444
|
562 IN_FLOAT (d = -pow (-d, 1.0/3.0), "cube-root", number);
|
|
428
|
563 #endif
|
|
|
564 return make_float (d);
|
|
|
565 }
|
|
|
566 #endif /* LISP_FLOAT_TYPE */
|
|
|
567
|
|
|
568
|
|
|
569 /* Inverse trig functions. */
|
|
|
570 #ifdef LISP_FLOAT_TYPE
|
|
|
571 /* #if 0 Not clearly worth adding... */
|
|
|
572
|
|
|
573 DEFUN ("acosh", Facosh, 1, 1, 0, /*
|
|
444
|
574 Return the inverse hyperbolic cosine of NUMBER.
|
|
428
|
575 */
|
|
444
|
576 (number))
|
|
428
|
577 {
|
|
444
|
578 double d = extract_float (number);
|
|
428
|
579 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
580 if (d < 1.0)
|
|
444
|
581 domain_error ("acosh", number);
|
|
428
|
582 #endif
|
|
|
583 #ifdef HAVE_INVERSE_HYPERBOLIC
|
|
444
|
584 IN_FLOAT (d = acosh (d), "acosh", number);
|
|
428
|
585 #else
|
|
444
|
586 IN_FLOAT (d = log (d + sqrt (d*d - 1.0)), "acosh", number);
|
|
428
|
587 #endif
|
|
|
588 return make_float (d);
|
|
|
589 }
|
|
|
590
|
|
|
591 DEFUN ("asinh", Fasinh, 1, 1, 0, /*
|
|
444
|
592 Return the inverse hyperbolic sine of NUMBER.
|
|
428
|
593 */
|
|
444
|
594 (number))
|
|
428
|
595 {
|
|
444
|
596 double d = extract_float (number);
|
|
428
|
597 #ifdef HAVE_INVERSE_HYPERBOLIC
|
|
444
|
598 IN_FLOAT (d = asinh (d), "asinh", number);
|
|
428
|
599 #else
|
|
444
|
600 IN_FLOAT (d = log (d + sqrt (d*d + 1.0)), "asinh", number);
|
|
428
|
601 #endif
|
|
|
602 return make_float (d);
|
|
|
603 }
|
|
|
604
|
|
|
605 DEFUN ("atanh", Fatanh, 1, 1, 0, /*
|
|
444
|
606 Return the inverse hyperbolic tangent of NUMBER.
|
|
428
|
607 */
|
|
444
|
608 (number))
|
|
428
|
609 {
|
|
444
|
610 double d = extract_float (number);
|
|
428
|
611 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
612 if (d >= 1.0 || d <= -1.0)
|
|
444
|
613 domain_error ("atanh", number);
|
|
428
|
614 #endif
|
|
|
615 #ifdef HAVE_INVERSE_HYPERBOLIC
|
|
444
|
616 IN_FLOAT (d = atanh (d), "atanh", number);
|
|
428
|
617 #else
|
|
444
|
618 IN_FLOAT (d = 0.5 * log ((1.0 + d) / (1.0 - d)), "atanh", number);
|
|
428
|
619 #endif
|
|
|
620 return make_float (d);
|
|
|
621 }
|
|
|
622
|
|
|
623 DEFUN ("cosh", Fcosh, 1, 1, 0, /*
|
|
444
|
624 Return the hyperbolic cosine of NUMBER.
|
|
428
|
625 */
|
|
444
|
626 (number))
|
|
428
|
627 {
|
|
444
|
628 double d = extract_float (number);
|
|
428
|
629 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
630 if (d > 710.0 || d < -710.0)
|
|
444
|
631 range_error ("cosh", number);
|
|
428
|
632 #endif
|
|
444
|
633 IN_FLOAT (d = cosh (d), "cosh", number);
|
|
428
|
634 return make_float (d);
|
|
|
635 }
|
|
|
636
|
|
|
637 DEFUN ("sinh", Fsinh, 1, 1, 0, /*
|
|
444
|
638 Return the hyperbolic sine of NUMBER.
|
|
428
|
639 */
|
|
444
|
640 (number))
|
|
428
|
641 {
|
|
444
|
642 double d = extract_float (number);
|
|
428
|
643 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
644 if (d > 710.0 || d < -710.0)
|
|
444
|
645 range_error ("sinh", number);
|
|
428
|
646 #endif
|
|
444
|
647 IN_FLOAT (d = sinh (d), "sinh", number);
|
|
428
|
648 return make_float (d);
|
|
|
649 }
|
|
|
650
|
|
|
651 DEFUN ("tanh", Ftanh, 1, 1, 0, /*
|
|
444
|
652 Return the hyperbolic tangent of NUMBER.
|
|
428
|
653 */
|
|
444
|
654 (number))
|
|
428
|
655 {
|
|
444
|
656 double d = extract_float (number);
|
|
|
657 IN_FLOAT (d = tanh (d), "tanh", number);
|
|
428
|
658 return make_float (d);
|
|
|
659 }
|
|
|
660 #endif /* LISP_FLOAT_TYPE (inverse trig functions) */
|
|
|
661
|
|
|
662 /* Rounding functions */
|
|
|
663
|
|
|
664 DEFUN ("abs", Fabs, 1, 1, 0, /*
|
|
444
|
665 Return the absolute value of NUMBER.
|
|
428
|
666 */
|
|
444
|
667 (number))
|
|
428
|
668 {
|
|
|
669 #ifdef LISP_FLOAT_TYPE
|
|
444
|
670 if (FLOATP (number))
|
|
428
|
671 {
|
|
444
|
672 IN_FLOAT (number = make_float (fabs (XFLOAT_DATA (number))),
|
|
|
673 "abs", number);
|
|
|
674 return number;
|
|
428
|
675 }
|
|
|
676 #endif /* LISP_FLOAT_TYPE */
|
|
|
677
|
|
444
|
678 if (INTP (number))
|
|
|
679 return (XINT (number) >= 0) ? number : make_int (- XINT (number));
|
|
428
|
680
|
|
444
|
681 return Fabs (wrong_type_argument (Qnumberp, number));
|
|
428
|
682 }
|
|
|
683
|
|
|
684 #ifdef LISP_FLOAT_TYPE
|
|
|
685 DEFUN ("float", Ffloat, 1, 1, 0, /*
|
|
444
|
686 Return the floating point number numerically equal to NUMBER.
|
|
428
|
687 */
|
|
444
|
688 (number))
|
|
428
|
689 {
|
|
444
|
690 if (INTP (number))
|
|
|
691 return make_float ((double) XINT (number));
|
|
428
|
692
|
|
444
|
693 if (FLOATP (number)) /* give 'em the same float back */
|
|
|
694 return number;
|
|
428
|
695
|
|
444
|
696 return Ffloat (wrong_type_argument (Qnumberp, number));
|
|
428
|
697 }
|
|
|
698 #endif /* LISP_FLOAT_TYPE */
|
|
|
699
|
|
|
700
|
|
|
701 #ifdef LISP_FLOAT_TYPE
|
|
|
702 DEFUN ("logb", Flogb, 1, 1, 0, /*
|
|
444
|
703 Return largest integer <= the base 2 log of the magnitude of NUMBER.
|
|
428
|
704 This is the same as the exponent of a float.
|
|
|
705 */
|
|
444
|
706 (number))
|
|
428
|
707 {
|
|
444
|
708 double f = extract_float (number);
|
|
428
|
709
|
|
|
710 if (f == 0.0)
|
|
434
|
711 return make_int (- (EMACS_INT)(((EMACS_UINT) 1) << (VALBITS - 1))); /* most-negative-fixnum */
|
|
428
|
712 #ifdef HAVE_LOGB
|
|
|
713 {
|
|
|
714 Lisp_Object val;
|
|
444
|
715 IN_FLOAT (val = make_int ((EMACS_INT) logb (f)), "logb", number);
|
|
434
|
716 return val;
|
|
428
|
717 }
|
|
|
718 #else
|
|
|
719 #ifdef HAVE_FREXP
|
|
|
720 {
|
|
|
721 int exqp;
|
|
444
|
722 IN_FLOAT (frexp (f, &exqp), "logb", number);
|
|
434
|
723 return make_int (exqp - 1);
|
|
428
|
724 }
|
|
|
725 #else
|
|
|
726 {
|
|
|
727 int i;
|
|
|
728 double d;
|
|
|
729 EMACS_INT val;
|
|
|
730 if (f < 0.0)
|
|
|
731 f = -f;
|
|
|
732 val = -1;
|
|
|
733 while (f < 0.5)
|
|
|
734 {
|
|
|
735 for (i = 1, d = 0.5; d * d >= f; i += i)
|
|
|
736 d *= d;
|
|
|
737 f /= d;
|
|
|
738 val -= i;
|
|
|
739 }
|
|
|
740 while (f >= 1.0)
|
|
|
741 {
|
|
|
742 for (i = 1, d = 2.0; d * d <= f; i += i)
|
|
|
743 d *= d;
|
|
|
744 f /= d;
|
|
|
745 val += i;
|
|
|
746 }
|
|
434
|
747 return make_int (val);
|
|
428
|
748 }
|
|
|
749 #endif /* ! HAVE_FREXP */
|
|
|
750 #endif /* ! HAVE_LOGB */
|
|
|
751 }
|
|
|
752 #endif /* LISP_FLOAT_TYPE */
|
|
|
753
|
|
|
754
|
|
|
755 DEFUN ("ceiling", Fceiling, 1, 1, 0, /*
|
|
444
|
756 Return the smallest integer no less than NUMBER. (Round toward +inf.)
|
|
428
|
757 */
|
|
444
|
758 (number))
|
|
428
|
759 {
|
|
|
760 #ifdef LISP_FLOAT_TYPE
|
|
444
|
761 if (FLOATP (number))
|
|
428
|
762 {
|
|
|
763 double d;
|
|
444
|
764 IN_FLOAT ((d = ceil (XFLOAT_DATA (number))), "ceiling", number);
|
|
|
765 return (float_to_int (d, "ceiling", number, Qunbound));
|
|
428
|
766 }
|
|
|
767 #endif /* LISP_FLOAT_TYPE */
|
|
|
768
|
|
444
|
769 if (INTP (number))
|
|
|
770 return number;
|
|
428
|
771
|
|
444
|
772 return Fceiling (wrong_type_argument (Qnumberp, number));
|
|
428
|
773 }
|
|
|
774
|
|
|
775
|
|
|
776 DEFUN ("floor", Ffloor, 1, 2, 0, /*
|
|
444
|
777 Return the largest integer no greater than NUMBER. (Round towards -inf.)
|
|
|
778 With optional second argument DIVISOR, return the largest integer no
|
|
|
779 greater than NUMBER/DIVISOR.
|
|
428
|
780 */
|
|
444
|
781 (number, divisor))
|
|
428
|
782 {
|
|
444
|
783 CHECK_INT_OR_FLOAT (number);
|
|
428
|
784
|
|
|
785 if (! NILP (divisor))
|
|
|
786 {
|
|
|
787 EMACS_INT i1, i2;
|
|
|
788
|
|
|
789 CHECK_INT_OR_FLOAT (divisor);
|
|
|
790
|
|
|
791 #ifdef LISP_FLOAT_TYPE
|
|
444
|
792 if (FLOATP (number) || FLOATP (divisor))
|
|
428
|
793 {
|
|
444
|
794 double f1 = extract_float (number);
|
|
428
|
795 double f2 = extract_float (divisor);
|
|
|
796
|
|
|
797 if (f2 == 0)
|
|
|
798 Fsignal (Qarith_error, Qnil);
|
|
|
799
|
|
444
|
800 IN_FLOAT2 (f1 = floor (f1 / f2), "floor", number, divisor);
|
|
|
801 return float_to_int (f1, "floor", number, divisor);
|
|
428
|
802 }
|
|
|
803 #endif /* LISP_FLOAT_TYPE */
|
|
|
804
|
|
444
|
805 i1 = XINT (number);
|
|
428
|
806 i2 = XINT (divisor);
|
|
|
807
|
|
|
808 if (i2 == 0)
|
|
|
809 Fsignal (Qarith_error, Qnil);
|
|
|
810
|
|
|
811 /* With C's /, the result is implementation-defined if either operand
|
|
|
812 is negative, so use only nonnegative operands. */
|
|
|
813 i1 = (i2 < 0
|
|
|
814 ? (i1 <= 0 ? -i1 / -i2 : -1 - ((i1 - 1) / -i2))
|
|
|
815 : (i1 < 0 ? -1 - ((-1 - i1) / i2) : i1 / i2));
|
|
|
816
|
|
|
817 return (make_int (i1));
|
|
|
818 }
|
|
|
819
|
|
|
820 #ifdef LISP_FLOAT_TYPE
|
|
444
|
821 if (FLOATP (number))
|
|
428
|
822 {
|
|
|
823 double d;
|
|
444
|
824 IN_FLOAT ((d = floor (XFLOAT_DATA (number))), "floor", number);
|
|
|
825 return (float_to_int (d, "floor", number, Qunbound));
|
|
428
|
826 }
|
|
|
827 #endif /* LISP_FLOAT_TYPE */
|
|
|
828
|
|
444
|
829 return number;
|
|
428
|
830 }
|
|
|
831
|
|
|
832 DEFUN ("round", Fround, 1, 1, 0, /*
|
|
444
|
833 Return the nearest integer to NUMBER.
|
|
428
|
834 */
|
|
444
|
835 (number))
|
|
428
|
836 {
|
|
|
837 #ifdef LISP_FLOAT_TYPE
|
|
444
|
838 if (FLOATP (number))
|
|
428
|
839 {
|
|
|
840 double d;
|
|
|
841 /* Screw the prevailing rounding mode. */
|
|
444
|
842 IN_FLOAT ((d = emacs_rint (XFLOAT_DATA (number))), "round", number);
|
|
|
843 return (float_to_int (d, "round", number, Qunbound));
|
|
428
|
844 }
|
|
|
845 #endif /* LISP_FLOAT_TYPE */
|
|
|
846
|
|
444
|
847 if (INTP (number))
|
|
|
848 return number;
|
|
428
|
849
|
|
444
|
850 return Fround (wrong_type_argument (Qnumberp, number));
|
|
428
|
851 }
|
|
|
852
|
|
|
853 DEFUN ("truncate", Ftruncate, 1, 1, 0, /*
|
|
|
854 Truncate a floating point number to an integer.
|
|
|
855 Rounds the value toward zero.
|
|
|
856 */
|
|
444
|
857 (number))
|
|
428
|
858 {
|
|
|
859 #ifdef LISP_FLOAT_TYPE
|
|
444
|
860 if (FLOATP (number))
|
|
|
861 return float_to_int (XFLOAT_DATA (number), "truncate", number, Qunbound);
|
|
428
|
862 #endif /* LISP_FLOAT_TYPE */
|
|
|
863
|
|
444
|
864 if (INTP (number))
|
|
|
865 return number;
|
|
428
|
866
|
|
444
|
867 return Ftruncate (wrong_type_argument (Qnumberp, number));
|
|
428
|
868 }
|
|
|
869
|
|
|
870 /* Float-rounding functions. */
|
|
|
871 #ifdef LISP_FLOAT_TYPE
|
|
|
872 /* #if 1 It's not clear these are worth adding... */
|
|
|
873
|
|
|
874 DEFUN ("fceiling", Ffceiling, 1, 1, 0, /*
|
|
444
|
875 Return the smallest integer no less than NUMBER, as a float.
|
|
428
|
876 \(Round toward +inf.\)
|
|
|
877 */
|
|
444
|
878 (number))
|
|
428
|
879 {
|
|
444
|
880 double d = extract_float (number);
|
|
|
881 IN_FLOAT (d = ceil (d), "fceiling", number);
|
|
428
|
882 return make_float (d);
|
|
|
883 }
|
|
|
884
|
|
|
885 DEFUN ("ffloor", Fffloor, 1, 1, 0, /*
|
|
444
|
886 Return the largest integer no greater than NUMBER, as a float.
|
|
428
|
887 \(Round towards -inf.\)
|
|
|
888 */
|
|
444
|
889 (number))
|
|
428
|
890 {
|
|
444
|
891 double d = extract_float (number);
|
|
|
892 IN_FLOAT (d = floor (d), "ffloor", number);
|
|
428
|
893 return make_float (d);
|
|
|
894 }
|
|
|
895
|
|
|
896 DEFUN ("fround", Ffround, 1, 1, 0, /*
|
|
444
|
897 Return the nearest integer to NUMBER, as a float.
|
|
428
|
898 */
|
|
444
|
899 (number))
|
|
428
|
900 {
|
|
444
|
901 double d = extract_float (number);
|
|
|
902 IN_FLOAT (d = emacs_rint (d), "fround", number);
|
|
428
|
903 return make_float (d);
|
|
|
904 }
|
|
|
905
|
|
|
906 DEFUN ("ftruncate", Fftruncate, 1, 1, 0, /*
|
|
|
907 Truncate a floating point number to an integral float value.
|
|
|
908 Rounds the value toward zero.
|
|
|
909 */
|
|
444
|
910 (number))
|
|
428
|
911 {
|
|
444
|
912 double d = extract_float (number);
|
|
428
|
913 if (d >= 0.0)
|
|
444
|
914 IN_FLOAT (d = floor (d), "ftruncate", number);
|
|
428
|
915 else
|
|
444
|
916 IN_FLOAT (d = ceil (d), "ftruncate", number);
|
|
428
|
917 return make_float (d);
|
|
|
918 }
|
|
|
919
|
|
|
920 #endif /* LISP_FLOAT_TYPE (float-rounding functions) */
|
|
|
921
|
|
|
922
|
|
|
923 #ifdef LISP_FLOAT_TYPE
|
|
|
924 #ifdef FLOAT_CATCH_SIGILL
|
|
|
925 static SIGTYPE
|
|
|
926 float_error (int signo)
|
|
|
927 {
|
|
|
928 if (! in_float)
|
|
|
929 fatal_error_signal (signo);
|
|
|
930
|
|
|
931 EMACS_REESTABLISH_SIGNAL (signo, arith_error);
|
|
|
932 EMACS_UNBLOCK_SIGNAL (signo);
|
|
|
933
|
|
|
934 in_float = 0;
|
|
|
935
|
|
|
936 /* Was Fsignal(), but it just doesn't make sense for an error
|
|
|
937 occurring inside a signal handler to be restartable, considering
|
|
|
938 that anything could happen when the error is signaled and trapped
|
|
|
939 and considering the asynchronous nature of signal handlers. */
|
|
|
940 signal_error (Qarith_error, list1 (float_error_arg));
|
|
|
941 }
|
|
|
942
|
|
|
943 /* Another idea was to replace the library function `infnan'
|
|
|
944 where SIGILL is signaled. */
|
|
|
945
|
|
|
946 #endif /* FLOAT_CATCH_SIGILL */
|
|
|
947
|
|
|
948 /* In C++, it is impossible to determine what type matherr expects
|
|
|
949 without some more configure magic.
|
|
|
950 We shouldn't be using matherr anyways - it's a non-standard SYSVism. */
|
|
|
951 #if defined (HAVE_MATHERR) && !defined(__cplusplus)
|
|
|
952 int
|
|
|
953 matherr (struct exception *x)
|
|
|
954 {
|
|
|
955 Lisp_Object args;
|
|
|
956 if (! in_float)
|
|
|
957 /* Not called from emacs-lisp float routines; do the default thing. */
|
|
|
958 return 0;
|
|
|
959
|
|
|
960 /* if (!strcmp (x->name, "pow")) x->name = "expt"; */
|
|
|
961
|
|
|
962 args = Fcons (build_string (x->name),
|
|
|
963 Fcons (make_float (x->arg1),
|
|
|
964 ((in_float == 2)
|
|
|
965 ? Fcons (make_float (x->arg2), Qnil)
|
|
|
966 : Qnil)));
|
|
|
967 switch (x->type)
|
|
|
968 {
|
|
|
969 case DOMAIN: Fsignal (Qdomain_error, args); break;
|
|
|
970 case SING: Fsignal (Qsingularity_error, args); break;
|
|
|
971 case OVERFLOW: Fsignal (Qoverflow_error, args); break;
|
|
|
972 case UNDERFLOW: Fsignal (Qunderflow_error, args); break;
|
|
|
973 default: Fsignal (Qarith_error, args); break;
|
|
|
974 }
|
|
|
975 return 1; /* don't set errno or print a message */
|
|
|
976 }
|
|
|
977 #endif /* HAVE_MATHERR */
|
|
|
978 #endif /* LISP_FLOAT_TYPE */
|
|
|
979
|
|
|
980
|
|
|
981 void
|
|
|
982 init_floatfns_very_early (void)
|
|
|
983 {
|
|
|
984 #ifdef LISP_FLOAT_TYPE
|
|
|
985 # ifdef FLOAT_CATCH_SIGILL
|
|
|
986 signal (SIGILL, float_error);
|
|
|
987 # endif
|
|
|
988 in_float = 0;
|
|
|
989 #endif /* LISP_FLOAT_TYPE */
|
|
|
990 }
|
|
|
991
|
|
|
992 void
|
|
|
993 syms_of_floatfns (void)
|
|
|
994 {
|
|
442
|
995 INIT_LRECORD_IMPLEMENTATION (float);
|
|
428
|
996
|
|
|
997 /* Trig functions. */
|
|
|
998
|
|
|
999 #ifdef LISP_FLOAT_TYPE
|
|
|
1000 DEFSUBR (Facos);
|
|
|
1001 DEFSUBR (Fasin);
|
|
|
1002 DEFSUBR (Fatan);
|
|
|
1003 DEFSUBR (Fcos);
|
|
|
1004 DEFSUBR (Fsin);
|
|
|
1005 DEFSUBR (Ftan);
|
|
|
1006 #endif /* LISP_FLOAT_TYPE */
|
|
|
1007
|
|
|
1008 /* Bessel functions */
|
|
|
1009
|
|
|
1010 #if 0
|
|
|
1011 DEFSUBR (Fbessel_y0);
|
|
|
1012 DEFSUBR (Fbessel_y1);
|
|
|
1013 DEFSUBR (Fbessel_yn);
|
|
|
1014 DEFSUBR (Fbessel_j0);
|
|
|
1015 DEFSUBR (Fbessel_j1);
|
|
|
1016 DEFSUBR (Fbessel_jn);
|
|
|
1017 #endif /* 0 */
|
|
|
1018
|
|
|
1019 /* Error functions. */
|
|
|
1020
|
|
|
1021 #if 0
|
|
|
1022 DEFSUBR (Ferf);
|
|
|
1023 DEFSUBR (Ferfc);
|
|
|
1024 DEFSUBR (Flog_gamma);
|
|
|
1025 #endif /* 0 */
|
|
|
1026
|
|
|
1027 /* Root and Log functions. */
|
|
|
1028
|
|
|
1029 #ifdef LISP_FLOAT_TYPE
|
|
|
1030 DEFSUBR (Fexp);
|
|
|
1031 #endif /* LISP_FLOAT_TYPE */
|
|
|
1032 DEFSUBR (Fexpt);
|
|
|
1033 #ifdef LISP_FLOAT_TYPE
|
|
|
1034 DEFSUBR (Flog);
|
|
|
1035 DEFSUBR (Flog10);
|
|
|
1036 DEFSUBR (Fsqrt);
|
|
|
1037 DEFSUBR (Fcube_root);
|
|
|
1038 #endif /* LISP_FLOAT_TYPE */
|
|
|
1039
|
|
|
1040 /* Inverse trig functions. */
|
|
|
1041
|
|
|
1042 #ifdef LISP_FLOAT_TYPE
|
|
|
1043 DEFSUBR (Facosh);
|
|
|
1044 DEFSUBR (Fasinh);
|
|
|
1045 DEFSUBR (Fatanh);
|
|
|
1046 DEFSUBR (Fcosh);
|
|
|
1047 DEFSUBR (Fsinh);
|
|
|
1048 DEFSUBR (Ftanh);
|
|
|
1049 #endif /* LISP_FLOAT_TYPE */
|
|
|
1050
|
|
|
1051 /* Rounding functions */
|
|
|
1052
|
|
|
1053 DEFSUBR (Fabs);
|
|
|
1054 #ifdef LISP_FLOAT_TYPE
|
|
|
1055 DEFSUBR (Ffloat);
|
|
|
1056 DEFSUBR (Flogb);
|
|
|
1057 #endif /* LISP_FLOAT_TYPE */
|
|
|
1058 DEFSUBR (Fceiling);
|
|
|
1059 DEFSUBR (Ffloor);
|
|
|
1060 DEFSUBR (Fround);
|
|
|
1061 DEFSUBR (Ftruncate);
|
|
|
1062
|
|
|
1063 /* Float-rounding functions. */
|
|
|
1064
|
|
|
1065 #ifdef LISP_FLOAT_TYPE
|
|
|
1066 DEFSUBR (Ffceiling);
|
|
|
1067 DEFSUBR (Fffloor);
|
|
|
1068 DEFSUBR (Ffround);
|
|
|
1069 DEFSUBR (Fftruncate);
|
|
|
1070 #endif /* LISP_FLOAT_TYPE */
|
|
|
1071 }
|
|
|
1072
|
|
|
1073 void
|
|
|
1074 vars_of_floatfns (void)
|
|
|
1075 {
|
|
|
1076 #ifdef LISP_FLOAT_TYPE
|
|
|
1077 Fprovide (intern ("lisp-float-type"));
|
|
|
1078 #endif
|
|
|
1079 }
|
