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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 #include "sysfloat.h"
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52
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430
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53 /* The code uses emacs_rint, so that it works to undefine HAVE_RINT
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54 if `rint' exists but does not work right. */
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55 #ifdef HAVE_RINT
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56 #define emacs_rint rint
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57 #else
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428
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58 static double
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430
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59 emacs_rint (double x)
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428
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60 {
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61 double r = floor (x + 0.5);
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62 double diff = fabs (r - x);
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63 /* Round to even and correct for any roundoff errors. */
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64 if (diff >= 0.5 && (diff > 0.5 || r != 2.0 * floor (r / 2.0)))
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65 r += r < x ? 1.0 : -1.0;
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66 return r;
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67 }
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68 #endif
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69
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70 /* Nonzero while executing in floating point.
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71 This tells float_error what to do. */
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72 static int in_float;
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73
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74 /* If an argument is out of range for a mathematical function,
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75 here is the actual argument value to use in the error message. */
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76 static Lisp_Object float_error_arg, float_error_arg2;
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442
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77 static const char *float_error_fn_name;
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428
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78
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79 /* Evaluate the floating point expression D, recording NUM
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80 as the original argument for error messages.
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81 D is normally an assignment expression.
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82 Handle errors which may result in signals or may set errno.
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83
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84 Note that float_error may be declared to return void, so you can't
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85 just cast the zero after the colon to (SIGTYPE) to make the types
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86 check properly. */
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87 #ifdef FLOAT_CHECK_ERRNO
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88 #define IN_FLOAT(d, name, num) \
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89 do { \
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90 float_error_arg = num; \
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91 float_error_fn_name = name; \
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92 in_float = 1; errno = 0; (d); in_float = 0; \
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93 if (errno != 0) in_float_error (); \
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94 } while (0)
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95 #define IN_FLOAT2(d, name, num, num2) \
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96 do { \
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97 float_error_arg = num; \
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98 float_error_arg2 = num2; \
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99 float_error_fn_name = name; \
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100 in_float = 2; errno = 0; (d); in_float = 0; \
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101 if (errno != 0) in_float_error (); \
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102 } while (0)
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103 #else
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104 #define IN_FLOAT(d, name, num) (in_float = 1, (d), in_float = 0)
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105 #define IN_FLOAT2(d, name, num, num2) (in_float = 2, (d), in_float = 0)
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106 #endif
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107
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108
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109 #define arith_error(op,arg) \
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771
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110 Fsignal (Qarith_error, list2 (build_msg_string (op), arg))
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428
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111 #define range_error(op,arg) \
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771
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112 Fsignal (Qrange_error, list2 (build_msg_string (op), arg))
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428
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113 #define range_error2(op,a1,a2) \
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771
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114 Fsignal (Qrange_error, list3 (build_msg_string (op), a1, a2))
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428
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115 #define domain_error(op,arg) \
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771
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116 Fsignal (Qdomain_error, list2 (build_msg_string (op), arg))
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428
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117 #define domain_error2(op,a1,a2) \
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771
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118 Fsignal (Qdomain_error, list3 (build_msg_string (op), a1, a2))
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428
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119
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120
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121 /* Convert float to Lisp Integer if it fits, else signal a range
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122 error using the given arguments. */
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123 static Lisp_Object
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442
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124 float_to_int (double x, const char *name, Lisp_Object num, Lisp_Object num2)
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428
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125 {
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126 if (x >= ((EMACS_INT) 1 << (VALBITS-1))
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127 || x <= - ((EMACS_INT) 1 << (VALBITS-1)) - (EMACS_INT) 1)
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128 {
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129 if (!UNBOUNDP (num2))
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130 range_error2 (name, num, num2);
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131 else
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132 range_error (name, num);
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133 }
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134 return (make_int ((EMACS_INT) x));
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135 }
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136
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137
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138 static void
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139 in_float_error (void)
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140 {
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141 switch (errno)
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142 {
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143 case 0:
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144 break;
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145 case EDOM:
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146 if (in_float == 2)
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147 domain_error2 (float_error_fn_name, float_error_arg, float_error_arg2);
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148 else
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149 domain_error (float_error_fn_name, float_error_arg);
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150 break;
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151 case ERANGE:
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152 range_error (float_error_fn_name, float_error_arg);
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153 break;
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154 default:
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155 arith_error (float_error_fn_name, float_error_arg);
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156 break;
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157 }
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158 }
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159
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160
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161 static Lisp_Object
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162 mark_float (Lisp_Object obj)
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163 {
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164 return Qnil;
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165 }
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166
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167 static int
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168 float_equal (Lisp_Object obj1, Lisp_Object obj2, int depth)
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169 {
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170 return (extract_float (obj1) == extract_float (obj2));
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171 }
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172
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665
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173 static Hashcode
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428
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174 float_hash (Lisp_Object obj, int depth)
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175 {
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176 /* mod the value down to 32-bit range */
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177 /* #### change for 64-bit machines */
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178 return (unsigned long) fmod (extract_float (obj), 4e9);
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179 }
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180
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1204
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181 static const struct memory_description float_description[] = {
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428
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182 { XD_END }
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183 };
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184
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934
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185 DEFINE_BASIC_LRECORD_IMPLEMENTATION ("float", float,
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186 1, /*dumpable-flag*/
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187 mark_float, print_float, 0, float_equal,
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188 float_hash, float_description,
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189 Lisp_Float);
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428
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190
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191 /* Extract a Lisp number as a `double', or signal an error. */
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192
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193 double
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194 extract_float (Lisp_Object num)
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195 {
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196 if (FLOATP (num))
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197 return XFLOAT_DATA (num);
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198
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199 if (INTP (num))
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200 return (double) XINT (num);
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201
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202 return extract_float (wrong_type_argument (Qnumberp, num));
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203 }
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204
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205 /* Trig functions. */
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206
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207 DEFUN ("acos", Facos, 1, 1, 0, /*
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444
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208 Return the inverse cosine of NUMBER.
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428
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209 */
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444
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210 (number))
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428
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211 {
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444
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212 double d = extract_float (number);
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428
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213 #ifdef FLOAT_CHECK_DOMAIN
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214 if (d > 1.0 || d < -1.0)
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444
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215 domain_error ("acos", number);
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428
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216 #endif
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444
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217 IN_FLOAT (d = acos (d), "acos", number);
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428
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218 return make_float (d);
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219 }
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220
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221 DEFUN ("asin", Fasin, 1, 1, 0, /*
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444
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222 Return the inverse sine of NUMBER.
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428
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223 */
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444
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224 (number))
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428
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225 {
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444
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226 double d = extract_float (number);
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428
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227 #ifdef FLOAT_CHECK_DOMAIN
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228 if (d > 1.0 || d < -1.0)
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444
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229 domain_error ("asin", number);
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428
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230 #endif
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444
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231 IN_FLOAT (d = asin (d), "asin", number);
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428
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232 return make_float (d);
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233 }
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234
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235 DEFUN ("atan", Fatan, 1, 2, 0, /*
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444
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236 Return the inverse tangent of NUMBER.
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237 If optional second argument NUMBER2 is provided,
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238 return atan2 (NUMBER, NUMBER2).
|
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428
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239 */
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444
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240 (number, number2))
|
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428
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241 {
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444
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242 double d = extract_float (number);
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428
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243
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444
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244 if (NILP (number2))
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245 IN_FLOAT (d = atan (d), "atan", number);
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428
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246 else
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247 {
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444
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248 double d2 = extract_float (number2);
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428
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249 #ifdef FLOAT_CHECK_DOMAIN
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250 if (d == 0.0 && d2 == 0.0)
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444
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251 domain_error2 ("atan", number, number2);
|
|
428
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252 #endif
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444
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253 IN_FLOAT2 (d = atan2 (d, d2), "atan", number, number2);
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428
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254 }
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255 return make_float (d);
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256 }
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257
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258 DEFUN ("cos", Fcos, 1, 1, 0, /*
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444
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259 Return the cosine of NUMBER.
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428
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260 */
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444
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261 (number))
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428
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262 {
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444
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263 double d = extract_float (number);
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264 IN_FLOAT (d = cos (d), "cos", number);
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428
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265 return make_float (d);
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266 }
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267
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|
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268 DEFUN ("sin", Fsin, 1, 1, 0, /*
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444
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269 Return the sine of NUMBER.
|
|
428
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270 */
|
|
444
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271 (number))
|
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428
|
272 {
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|
444
|
273 double d = extract_float (number);
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274 IN_FLOAT (d = sin (d), "sin", number);
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428
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275 return make_float (d);
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|
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276 }
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277
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|
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278 DEFUN ("tan", Ftan, 1, 1, 0, /*
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|
444
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279 Return the tangent of NUMBER.
|
|
428
|
280 */
|
|
444
|
281 (number))
|
|
428
|
282 {
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|
444
|
283 double d = extract_float (number);
|
|
428
|
284 double c = cos (d);
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|
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285 #ifdef FLOAT_CHECK_DOMAIN
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|
|
286 if (c == 0.0)
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|
444
|
287 domain_error ("tan", number);
|
|
428
|
288 #endif
|
|
444
|
289 IN_FLOAT (d = (sin (d) / c), "tan", number);
|
|
428
|
290 return make_float (d);
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|
|
291 }
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|
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292
|
|
|
293 /* Bessel functions */
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|
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294 #if 0 /* Leave these out unless we find there's a reason for them. */
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295
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|
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296 DEFUN ("bessel-j0", Fbessel_j0, 1, 1, 0, /*
|
|
444
|
297 Return the bessel function j0 of NUMBER.
|
|
428
|
298 */
|
|
444
|
299 (number))
|
|
428
|
300 {
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|
444
|
301 double d = extract_float (number);
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|
|
302 IN_FLOAT (d = j0 (d), "bessel-j0", number);
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|
428
|
303 return make_float (d);
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|
|
304 }
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|
|
305
|
|
|
306 DEFUN ("bessel-j1", Fbessel_j1, 1, 1, 0, /*
|
|
444
|
307 Return the bessel function j1 of NUMBER.
|
|
428
|
308 */
|
|
444
|
309 (number))
|
|
428
|
310 {
|
|
444
|
311 double d = extract_float (number);
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|
|
312 IN_FLOAT (d = j1 (d), "bessel-j1", number);
|
|
428
|
313 return make_float (d);
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|
|
314 }
|
|
|
315
|
|
|
316 DEFUN ("bessel-jn", Fbessel_jn, 2, 2, 0, /*
|
|
444
|
317 Return the order N bessel function output jn of NUMBER.
|
|
|
318 The first number (the order) is truncated to an integer.
|
|
428
|
319 */
|
|
444
|
320 (number1, number2))
|
|
428
|
321 {
|
|
444
|
322 int i1 = extract_float (number1);
|
|
|
323 double f2 = extract_float (number2);
|
|
428
|
324
|
|
444
|
325 IN_FLOAT (f2 = jn (i1, f2), "bessel-jn", number1);
|
|
428
|
326 return make_float (f2);
|
|
|
327 }
|
|
|
328
|
|
|
329 DEFUN ("bessel-y0", Fbessel_y0, 1, 1, 0, /*
|
|
444
|
330 Return the bessel function y0 of NUMBER.
|
|
428
|
331 */
|
|
444
|
332 (number))
|
|
428
|
333 {
|
|
444
|
334 double d = extract_float (number);
|
|
|
335 IN_FLOAT (d = y0 (d), "bessel-y0", number);
|
|
428
|
336 return make_float (d);
|
|
|
337 }
|
|
|
338
|
|
|
339 DEFUN ("bessel-y1", Fbessel_y1, 1, 1, 0, /*
|
|
444
|
340 Return the bessel function y1 of NUMBER.
|
|
428
|
341 */
|
|
444
|
342 (number))
|
|
428
|
343 {
|
|
444
|
344 double d = extract_float (number);
|
|
|
345 IN_FLOAT (d = y1 (d), "bessel-y0", number);
|
|
428
|
346 return make_float (d);
|
|
|
347 }
|
|
|
348
|
|
|
349 DEFUN ("bessel-yn", Fbessel_yn, 2, 2, 0, /*
|
|
444
|
350 Return the order N bessel function output yn of NUMBER.
|
|
|
351 The first number (the order) is truncated to an integer.
|
|
428
|
352 */
|
|
444
|
353 (number1, number2))
|
|
428
|
354 {
|
|
444
|
355 int i1 = extract_float (number1);
|
|
|
356 double f2 = extract_float (number2);
|
|
428
|
357
|
|
444
|
358 IN_FLOAT (f2 = yn (i1, f2), "bessel-yn", number1);
|
|
428
|
359 return make_float (f2);
|
|
|
360 }
|
|
|
361
|
|
|
362 #endif /* 0 (bessel functions) */
|
|
|
363
|
|
|
364 /* Error functions. */
|
|
|
365 #if 0 /* Leave these out unless we see they are worth having. */
|
|
|
366
|
|
|
367 DEFUN ("erf", Ferf, 1, 1, 0, /*
|
|
444
|
368 Return the mathematical error function of NUMBER.
|
|
428
|
369 */
|
|
444
|
370 (number))
|
|
428
|
371 {
|
|
444
|
372 double d = extract_float (number);
|
|
|
373 IN_FLOAT (d = erf (d), "erf", number);
|
|
428
|
374 return make_float (d);
|
|
|
375 }
|
|
|
376
|
|
|
377 DEFUN ("erfc", Ferfc, 1, 1, 0, /*
|
|
444
|
378 Return the complementary error function of NUMBER.
|
|
428
|
379 */
|
|
444
|
380 (number))
|
|
428
|
381 {
|
|
444
|
382 double d = extract_float (number);
|
|
|
383 IN_FLOAT (d = erfc (d), "erfc", number);
|
|
428
|
384 return make_float (d);
|
|
|
385 }
|
|
|
386
|
|
|
387 DEFUN ("log-gamma", Flog_gamma, 1, 1, 0, /*
|
|
444
|
388 Return the log gamma of NUMBER.
|
|
428
|
389 */
|
|
444
|
390 (number))
|
|
428
|
391 {
|
|
444
|
392 double d = extract_float (number);
|
|
|
393 IN_FLOAT (d = lgamma (d), "log-gamma", number);
|
|
428
|
394 return make_float (d);
|
|
|
395 }
|
|
|
396
|
|
|
397 #endif /* 0 (error functions) */
|
|
|
398
|
|
|
399
|
|
|
400 /* Root and Log functions. */
|
|
|
401
|
|
|
402 DEFUN ("exp", Fexp, 1, 1, 0, /*
|
|
444
|
403 Return the exponential base e of NUMBER.
|
|
428
|
404 */
|
|
444
|
405 (number))
|
|
428
|
406 {
|
|
444
|
407 double d = extract_float (number);
|
|
428
|
408 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
409 if (d > 709.7827) /* Assume IEEE doubles here */
|
|
444
|
410 range_error ("exp", number);
|
|
428
|
411 else if (d < -709.0)
|
|
|
412 return make_float (0.0);
|
|
|
413 else
|
|
|
414 #endif
|
|
444
|
415 IN_FLOAT (d = exp (d), "exp", number);
|
|
428
|
416 return make_float (d);
|
|
|
417 }
|
|
|
418
|
|
|
419 DEFUN ("expt", Fexpt, 2, 2, 0, /*
|
|
444
|
420 Return the exponential NUMBER1 ** NUMBER2.
|
|
428
|
421 */
|
|
444
|
422 (number1, number2))
|
|
428
|
423 {
|
|
444
|
424 if (INTP (number1) && /* common lisp spec */
|
|
|
425 INTP (number2)) /* don't promote, if both are ints */
|
|
428
|
426 {
|
|
|
427 EMACS_INT retval;
|
|
444
|
428 EMACS_INT x = XINT (number1);
|
|
|
429 EMACS_INT y = XINT (number2);
|
|
428
|
430
|
|
|
431 if (y < 0)
|
|
|
432 {
|
|
|
433 if (x == 1)
|
|
|
434 retval = 1;
|
|
|
435 else if (x == -1)
|
|
|
436 retval = (y & 1) ? -1 : 1;
|
|
|
437 else
|
|
|
438 retval = 0;
|
|
|
439 }
|
|
|
440 else
|
|
|
441 {
|
|
|
442 retval = 1;
|
|
|
443 while (y > 0)
|
|
|
444 {
|
|
|
445 if (y & 1)
|
|
|
446 retval *= x;
|
|
|
447 x *= x;
|
|
|
448 y = (EMACS_UINT) y >> 1;
|
|
|
449 }
|
|
|
450 }
|
|
|
451 return make_int (retval);
|
|
|
452 }
|
|
|
453
|
|
|
454 {
|
|
444
|
455 double f1 = extract_float (number1);
|
|
|
456 double f2 = extract_float (number2);
|
|
428
|
457 /* Really should check for overflow, too */
|
|
|
458 if (f1 == 0.0 && f2 == 0.0)
|
|
|
459 f1 = 1.0;
|
|
|
460 # ifdef FLOAT_CHECK_DOMAIN
|
|
|
461 else if ((f1 == 0.0 && f2 < 0.0) || (f1 < 0 && f2 != floor(f2)))
|
|
444
|
462 domain_error2 ("expt", number1, number2);
|
|
428
|
463 # endif /* FLOAT_CHECK_DOMAIN */
|
|
444
|
464 IN_FLOAT2 (f1 = pow (f1, f2), "expt", number1, number2);
|
|
428
|
465 return make_float (f1);
|
|
|
466 }
|
|
|
467 }
|
|
|
468
|
|
|
469 DEFUN ("log", Flog, 1, 2, 0, /*
|
|
444
|
470 Return the natural logarithm of NUMBER.
|
|
|
471 If second optional argument BASE is given, return the logarithm of
|
|
|
472 NUMBER using that base.
|
|
428
|
473 */
|
|
444
|
474 (number, base))
|
|
428
|
475 {
|
|
444
|
476 double d = extract_float (number);
|
|
428
|
477 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
478 if (d <= 0.0)
|
|
444
|
479 domain_error2 ("log", number, base);
|
|
428
|
480 #endif
|
|
|
481 if (NILP (base))
|
|
444
|
482 IN_FLOAT (d = log (d), "log", number);
|
|
428
|
483 else
|
|
|
484 {
|
|
|
485 double b = extract_float (base);
|
|
|
486 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
487 if (b <= 0.0 || b == 1.0)
|
|
444
|
488 domain_error2 ("log", number, base);
|
|
428
|
489 #endif
|
|
|
490 if (b == 10.0)
|
|
444
|
491 IN_FLOAT2 (d = log10 (d), "log", number, base);
|
|
428
|
492 else
|
|
444
|
493 IN_FLOAT2 (d = (log (d) / log (b)), "log", number, base);
|
|
428
|
494 }
|
|
|
495 return make_float (d);
|
|
|
496 }
|
|
|
497
|
|
|
498
|
|
|
499 DEFUN ("log10", Flog10, 1, 1, 0, /*
|
|
444
|
500 Return the logarithm base 10 of NUMBER.
|
|
428
|
501 */
|
|
444
|
502 (number))
|
|
428
|
503 {
|
|
444
|
504 double d = extract_float (number);
|
|
428
|
505 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
506 if (d <= 0.0)
|
|
444
|
507 domain_error ("log10", number);
|
|
428
|
508 #endif
|
|
444
|
509 IN_FLOAT (d = log10 (d), "log10", number);
|
|
428
|
510 return make_float (d);
|
|
|
511 }
|
|
|
512
|
|
|
513
|
|
|
514 DEFUN ("sqrt", Fsqrt, 1, 1, 0, /*
|
|
444
|
515 Return the square root of NUMBER.
|
|
428
|
516 */
|
|
444
|
517 (number))
|
|
428
|
518 {
|
|
444
|
519 double d = extract_float (number);
|
|
428
|
520 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
521 if (d < 0.0)
|
|
444
|
522 domain_error ("sqrt", number);
|
|
428
|
523 #endif
|
|
444
|
524 IN_FLOAT (d = sqrt (d), "sqrt", number);
|
|
428
|
525 return make_float (d);
|
|
|
526 }
|
|
|
527
|
|
|
528
|
|
|
529 DEFUN ("cube-root", Fcube_root, 1, 1, 0, /*
|
|
444
|
530 Return the cube root of NUMBER.
|
|
428
|
531 */
|
|
444
|
532 (number))
|
|
428
|
533 {
|
|
444
|
534 double d = extract_float (number);
|
|
428
|
535 #ifdef HAVE_CBRT
|
|
444
|
536 IN_FLOAT (d = cbrt (d), "cube-root", number);
|
|
428
|
537 #else
|
|
|
538 if (d >= 0.0)
|
|
444
|
539 IN_FLOAT (d = pow (d, 1.0/3.0), "cube-root", number);
|
|
428
|
540 else
|
|
444
|
541 IN_FLOAT (d = -pow (-d, 1.0/3.0), "cube-root", number);
|
|
428
|
542 #endif
|
|
|
543 return make_float (d);
|
|
|
544 }
|
|
|
545
|
|
|
546 /* Inverse trig functions. */
|
|
|
547
|
|
|
548 DEFUN ("acosh", Facosh, 1, 1, 0, /*
|
|
444
|
549 Return the inverse hyperbolic cosine of NUMBER.
|
|
428
|
550 */
|
|
444
|
551 (number))
|
|
428
|
552 {
|
|
444
|
553 double d = extract_float (number);
|
|
428
|
554 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
555 if (d < 1.0)
|
|
444
|
556 domain_error ("acosh", number);
|
|
428
|
557 #endif
|
|
|
558 #ifdef HAVE_INVERSE_HYPERBOLIC
|
|
444
|
559 IN_FLOAT (d = acosh (d), "acosh", number);
|
|
428
|
560 #else
|
|
444
|
561 IN_FLOAT (d = log (d + sqrt (d*d - 1.0)), "acosh", number);
|
|
428
|
562 #endif
|
|
|
563 return make_float (d);
|
|
|
564 }
|
|
|
565
|
|
|
566 DEFUN ("asinh", Fasinh, 1, 1, 0, /*
|
|
444
|
567 Return the inverse hyperbolic sine of NUMBER.
|
|
428
|
568 */
|
|
444
|
569 (number))
|
|
428
|
570 {
|
|
444
|
571 double d = extract_float (number);
|
|
428
|
572 #ifdef HAVE_INVERSE_HYPERBOLIC
|
|
444
|
573 IN_FLOAT (d = asinh (d), "asinh", number);
|
|
428
|
574 #else
|
|
444
|
575 IN_FLOAT (d = log (d + sqrt (d*d + 1.0)), "asinh", number);
|
|
428
|
576 #endif
|
|
|
577 return make_float (d);
|
|
|
578 }
|
|
|
579
|
|
|
580 DEFUN ("atanh", Fatanh, 1, 1, 0, /*
|
|
444
|
581 Return the inverse hyperbolic tangent of NUMBER.
|
|
428
|
582 */
|
|
444
|
583 (number))
|
|
428
|
584 {
|
|
444
|
585 double d = extract_float (number);
|
|
428
|
586 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
587 if (d >= 1.0 || d <= -1.0)
|
|
444
|
588 domain_error ("atanh", number);
|
|
428
|
589 #endif
|
|
|
590 #ifdef HAVE_INVERSE_HYPERBOLIC
|
|
444
|
591 IN_FLOAT (d = atanh (d), "atanh", number);
|
|
428
|
592 #else
|
|
444
|
593 IN_FLOAT (d = 0.5 * log ((1.0 + d) / (1.0 - d)), "atanh", number);
|
|
428
|
594 #endif
|
|
|
595 return make_float (d);
|
|
|
596 }
|
|
|
597
|
|
|
598 DEFUN ("cosh", Fcosh, 1, 1, 0, /*
|
|
444
|
599 Return the hyperbolic cosine of NUMBER.
|
|
428
|
600 */
|
|
444
|
601 (number))
|
|
428
|
602 {
|
|
444
|
603 double d = extract_float (number);
|
|
428
|
604 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
605 if (d > 710.0 || d < -710.0)
|
|
444
|
606 range_error ("cosh", number);
|
|
428
|
607 #endif
|
|
444
|
608 IN_FLOAT (d = cosh (d), "cosh", number);
|
|
428
|
609 return make_float (d);
|
|
|
610 }
|
|
|
611
|
|
|
612 DEFUN ("sinh", Fsinh, 1, 1, 0, /*
|
|
444
|
613 Return the hyperbolic sine of NUMBER.
|
|
428
|
614 */
|
|
444
|
615 (number))
|
|
428
|
616 {
|
|
444
|
617 double d = extract_float (number);
|
|
428
|
618 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
619 if (d > 710.0 || d < -710.0)
|
|
444
|
620 range_error ("sinh", number);
|
|
428
|
621 #endif
|
|
444
|
622 IN_FLOAT (d = sinh (d), "sinh", number);
|
|
428
|
623 return make_float (d);
|
|
|
624 }
|
|
|
625
|
|
|
626 DEFUN ("tanh", Ftanh, 1, 1, 0, /*
|
|
444
|
627 Return the hyperbolic tangent of NUMBER.
|
|
428
|
628 */
|
|
444
|
629 (number))
|
|
428
|
630 {
|
|
444
|
631 double d = extract_float (number);
|
|
|
632 IN_FLOAT (d = tanh (d), "tanh", number);
|
|
428
|
633 return make_float (d);
|
|
|
634 }
|
|
|
635
|
|
|
636 /* Rounding functions */
|
|
|
637
|
|
|
638 DEFUN ("abs", Fabs, 1, 1, 0, /*
|
|
444
|
639 Return the absolute value of NUMBER.
|
|
428
|
640 */
|
|
444
|
641 (number))
|
|
428
|
642 {
|
|
444
|
643 if (FLOATP (number))
|
|
428
|
644 {
|
|
444
|
645 IN_FLOAT (number = make_float (fabs (XFLOAT_DATA (number))),
|
|
|
646 "abs", number);
|
|
|
647 return number;
|
|
428
|
648 }
|
|
|
649
|
|
444
|
650 if (INTP (number))
|
|
|
651 return (XINT (number) >= 0) ? number : make_int (- XINT (number));
|
|
428
|
652
|
|
444
|
653 return Fabs (wrong_type_argument (Qnumberp, number));
|
|
428
|
654 }
|
|
|
655
|
|
|
656 DEFUN ("float", Ffloat, 1, 1, 0, /*
|
|
444
|
657 Return the floating point number numerically equal to NUMBER.
|
|
428
|
658 */
|
|
444
|
659 (number))
|
|
428
|
660 {
|
|
444
|
661 if (INTP (number))
|
|
|
662 return make_float ((double) XINT (number));
|
|
428
|
663
|
|
444
|
664 if (FLOATP (number)) /* give 'em the same float back */
|
|
|
665 return number;
|
|
428
|
666
|
|
444
|
667 return Ffloat (wrong_type_argument (Qnumberp, number));
|
|
428
|
668 }
|
|
|
669
|
|
|
670 DEFUN ("logb", Flogb, 1, 1, 0, /*
|
|
444
|
671 Return largest integer <= the base 2 log of the magnitude of NUMBER.
|
|
428
|
672 This is the same as the exponent of a float.
|
|
|
673 */
|
|
444
|
674 (number))
|
|
428
|
675 {
|
|
444
|
676 double f = extract_float (number);
|
|
428
|
677
|
|
|
678 if (f == 0.0)
|
|
434
|
679 return make_int (- (EMACS_INT)(((EMACS_UINT) 1) << (VALBITS - 1))); /* most-negative-fixnum */
|
|
428
|
680 #ifdef HAVE_LOGB
|
|
|
681 {
|
|
|
682 Lisp_Object val;
|
|
444
|
683 IN_FLOAT (val = make_int ((EMACS_INT) logb (f)), "logb", number);
|
|
434
|
684 return val;
|
|
428
|
685 }
|
|
|
686 #else
|
|
|
687 #ifdef HAVE_FREXP
|
|
|
688 {
|
|
|
689 int exqp;
|
|
444
|
690 IN_FLOAT (frexp (f, &exqp), "logb", number);
|
|
434
|
691 return make_int (exqp - 1);
|
|
428
|
692 }
|
|
|
693 #else
|
|
|
694 {
|
|
|
695 int i;
|
|
|
696 double d;
|
|
|
697 EMACS_INT val;
|
|
|
698 if (f < 0.0)
|
|
|
699 f = -f;
|
|
|
700 val = -1;
|
|
|
701 while (f < 0.5)
|
|
|
702 {
|
|
|
703 for (i = 1, d = 0.5; d * d >= f; i += i)
|
|
|
704 d *= d;
|
|
|
705 f /= d;
|
|
|
706 val -= i;
|
|
|
707 }
|
|
|
708 while (f >= 1.0)
|
|
|
709 {
|
|
|
710 for (i = 1, d = 2.0; d * d <= f; i += i)
|
|
|
711 d *= d;
|
|
|
712 f /= d;
|
|
|
713 val += i;
|
|
|
714 }
|
|
434
|
715 return make_int (val);
|
|
428
|
716 }
|
|
|
717 #endif /* ! HAVE_FREXP */
|
|
|
718 #endif /* ! HAVE_LOGB */
|
|
|
719 }
|
|
|
720
|
|
|
721 DEFUN ("ceiling", Fceiling, 1, 1, 0, /*
|
|
444
|
722 Return the smallest integer no less than NUMBER. (Round toward +inf.)
|
|
428
|
723 */
|
|
444
|
724 (number))
|
|
428
|
725 {
|
|
444
|
726 if (FLOATP (number))
|
|
428
|
727 {
|
|
|
728 double d;
|
|
444
|
729 IN_FLOAT ((d = ceil (XFLOAT_DATA (number))), "ceiling", number);
|
|
|
730 return (float_to_int (d, "ceiling", number, Qunbound));
|
|
428
|
731 }
|
|
|
732
|
|
444
|
733 if (INTP (number))
|
|
|
734 return number;
|
|
428
|
735
|
|
444
|
736 return Fceiling (wrong_type_argument (Qnumberp, number));
|
|
428
|
737 }
|
|
|
738
|
|
|
739
|
|
|
740 DEFUN ("floor", Ffloor, 1, 2, 0, /*
|
|
444
|
741 Return the largest integer no greater than NUMBER. (Round towards -inf.)
|
|
|
742 With optional second argument DIVISOR, return the largest integer no
|
|
|
743 greater than NUMBER/DIVISOR.
|
|
428
|
744 */
|
|
444
|
745 (number, divisor))
|
|
428
|
746 {
|
|
444
|
747 CHECK_INT_OR_FLOAT (number);
|
|
428
|
748
|
|
|
749 if (! NILP (divisor))
|
|
|
750 {
|
|
|
751 EMACS_INT i1, i2;
|
|
|
752
|
|
|
753 CHECK_INT_OR_FLOAT (divisor);
|
|
|
754
|
|
444
|
755 if (FLOATP (number) || FLOATP (divisor))
|
|
428
|
756 {
|
|
444
|
757 double f1 = extract_float (number);
|
|
428
|
758 double f2 = extract_float (divisor);
|
|
|
759
|
|
|
760 if (f2 == 0)
|
|
|
761 Fsignal (Qarith_error, Qnil);
|
|
|
762
|
|
444
|
763 IN_FLOAT2 (f1 = floor (f1 / f2), "floor", number, divisor);
|
|
|
764 return float_to_int (f1, "floor", number, divisor);
|
|
428
|
765 }
|
|
|
766
|
|
444
|
767 i1 = XINT (number);
|
|
428
|
768 i2 = XINT (divisor);
|
|
|
769
|
|
|
770 if (i2 == 0)
|
|
|
771 Fsignal (Qarith_error, Qnil);
|
|
|
772
|
|
|
773 /* With C's /, the result is implementation-defined if either operand
|
|
|
774 is negative, so use only nonnegative operands. */
|
|
|
775 i1 = (i2 < 0
|
|
|
776 ? (i1 <= 0 ? -i1 / -i2 : -1 - ((i1 - 1) / -i2))
|
|
|
777 : (i1 < 0 ? -1 - ((-1 - i1) / i2) : i1 / i2));
|
|
|
778
|
|
|
779 return (make_int (i1));
|
|
|
780 }
|
|
|
781
|
|
444
|
782 if (FLOATP (number))
|
|
428
|
783 {
|
|
|
784 double d;
|
|
444
|
785 IN_FLOAT ((d = floor (XFLOAT_DATA (number))), "floor", number);
|
|
|
786 return (float_to_int (d, "floor", number, Qunbound));
|
|
428
|
787 }
|
|
|
788
|
|
444
|
789 return number;
|
|
428
|
790 }
|
|
|
791
|
|
|
792 DEFUN ("round", Fround, 1, 1, 0, /*
|
|
444
|
793 Return the nearest integer to NUMBER.
|
|
428
|
794 */
|
|
444
|
795 (number))
|
|
428
|
796 {
|
|
444
|
797 if (FLOATP (number))
|
|
428
|
798 {
|
|
|
799 double d;
|
|
|
800 /* Screw the prevailing rounding mode. */
|
|
444
|
801 IN_FLOAT ((d = emacs_rint (XFLOAT_DATA (number))), "round", number);
|
|
|
802 return (float_to_int (d, "round", number, Qunbound));
|
|
428
|
803 }
|
|
|
804
|
|
444
|
805 if (INTP (number))
|
|
|
806 return number;
|
|
428
|
807
|
|
444
|
808 return Fround (wrong_type_argument (Qnumberp, number));
|
|
428
|
809 }
|
|
|
810
|
|
|
811 DEFUN ("truncate", Ftruncate, 1, 1, 0, /*
|
|
|
812 Truncate a floating point number to an integer.
|
|
|
813 Rounds the value toward zero.
|
|
|
814 */
|
|
444
|
815 (number))
|
|
428
|
816 {
|
|
444
|
817 if (FLOATP (number))
|
|
|
818 return float_to_int (XFLOAT_DATA (number), "truncate", number, Qunbound);
|
|
428
|
819
|
|
444
|
820 if (INTP (number))
|
|
|
821 return number;
|
|
428
|
822
|
|
444
|
823 return Ftruncate (wrong_type_argument (Qnumberp, number));
|
|
428
|
824 }
|
|
|
825
|
|
|
826 /* Float-rounding functions. */
|
|
|
827
|
|
|
828 DEFUN ("fceiling", Ffceiling, 1, 1, 0, /*
|
|
444
|
829 Return the smallest integer no less than NUMBER, as a float.
|
|
428
|
830 \(Round toward +inf.\)
|
|
|
831 */
|
|
444
|
832 (number))
|
|
428
|
833 {
|
|
444
|
834 double d = extract_float (number);
|
|
|
835 IN_FLOAT (d = ceil (d), "fceiling", number);
|
|
428
|
836 return make_float (d);
|
|
|
837 }
|
|
|
838
|
|
|
839 DEFUN ("ffloor", Fffloor, 1, 1, 0, /*
|
|
444
|
840 Return the largest integer no greater than NUMBER, as a float.
|
|
428
|
841 \(Round towards -inf.\)
|
|
|
842 */
|
|
444
|
843 (number))
|
|
428
|
844 {
|
|
444
|
845 double d = extract_float (number);
|
|
|
846 IN_FLOAT (d = floor (d), "ffloor", number);
|
|
428
|
847 return make_float (d);
|
|
|
848 }
|
|
|
849
|
|
|
850 DEFUN ("fround", Ffround, 1, 1, 0, /*
|
|
444
|
851 Return the nearest integer to NUMBER, as a float.
|
|
428
|
852 */
|
|
444
|
853 (number))
|
|
428
|
854 {
|
|
444
|
855 double d = extract_float (number);
|
|
|
856 IN_FLOAT (d = emacs_rint (d), "fround", number);
|
|
428
|
857 return make_float (d);
|
|
|
858 }
|
|
|
859
|
|
|
860 DEFUN ("ftruncate", Fftruncate, 1, 1, 0, /*
|
|
|
861 Truncate a floating point number to an integral float value.
|
|
|
862 Rounds the value toward zero.
|
|
|
863 */
|
|
444
|
864 (number))
|
|
428
|
865 {
|
|
444
|
866 double d = extract_float (number);
|
|
428
|
867 if (d >= 0.0)
|
|
444
|
868 IN_FLOAT (d = floor (d), "ftruncate", number);
|
|
428
|
869 else
|
|
444
|
870 IN_FLOAT (d = ceil (d), "ftruncate", number);
|
|
428
|
871 return make_float (d);
|
|
|
872 }
|
|
|
873
|
|
|
874 #ifdef FLOAT_CATCH_SIGILL
|
|
|
875 static SIGTYPE
|
|
|
876 float_error (int signo)
|
|
|
877 {
|
|
|
878 if (! in_float)
|
|
|
879 fatal_error_signal (signo);
|
|
|
880
|
|
|
881 EMACS_REESTABLISH_SIGNAL (signo, arith_error);
|
|
|
882 EMACS_UNBLOCK_SIGNAL (signo);
|
|
|
883
|
|
|
884 in_float = 0;
|
|
|
885
|
|
|
886 /* Was Fsignal(), but it just doesn't make sense for an error
|
|
|
887 occurring inside a signal handler to be restartable, considering
|
|
|
888 that anything could happen when the error is signaled and trapped
|
|
|
889 and considering the asynchronous nature of signal handlers. */
|
|
563
|
890 signal_error (Qarith_error, 0, float_error_arg);
|
|
428
|
891 }
|
|
|
892
|
|
|
893 /* Another idea was to replace the library function `infnan'
|
|
|
894 where SIGILL is signaled. */
|
|
|
895
|
|
|
896 #endif /* FLOAT_CATCH_SIGILL */
|
|
|
897
|
|
|
898 /* In C++, it is impossible to determine what type matherr expects
|
|
|
899 without some more configure magic.
|
|
|
900 We shouldn't be using matherr anyways - it's a non-standard SYSVism. */
|
|
|
901 #if defined (HAVE_MATHERR) && !defined(__cplusplus)
|
|
|
902 int
|
|
|
903 matherr (struct exception *x)
|
|
|
904 {
|
|
|
905 Lisp_Object args;
|
|
|
906 if (! in_float)
|
|
|
907 /* Not called from emacs-lisp float routines; do the default thing. */
|
|
|
908 return 0;
|
|
|
909
|
|
|
910 /* if (!strcmp (x->name, "pow")) x->name = "expt"; */
|
|
|
911
|
|
|
912 args = Fcons (build_string (x->name),
|
|
|
913 Fcons (make_float (x->arg1),
|
|
|
914 ((in_float == 2)
|
|
|
915 ? Fcons (make_float (x->arg2), Qnil)
|
|
|
916 : Qnil)));
|
|
|
917 switch (x->type)
|
|
|
918 {
|
|
|
919 case DOMAIN: Fsignal (Qdomain_error, args); break;
|
|
|
920 case SING: Fsignal (Qsingularity_error, args); break;
|
|
|
921 case OVERFLOW: Fsignal (Qoverflow_error, args); break;
|
|
|
922 case UNDERFLOW: Fsignal (Qunderflow_error, args); break;
|
|
|
923 default: Fsignal (Qarith_error, args); break;
|
|
|
924 }
|
|
|
925 return 1; /* don't set errno or print a message */
|
|
|
926 }
|
|
|
927 #endif /* HAVE_MATHERR */
|
|
|
928
|
|
|
929 void
|
|
|
930 init_floatfns_very_early (void)
|
|
|
931 {
|
|
|
932 # ifdef FLOAT_CATCH_SIGILL
|
|
613
|
933 EMACS_SIGNAL (SIGILL, float_error);
|
|
428
|
934 # endif
|
|
|
935 in_float = 0;
|
|
|
936 }
|
|
|
937
|
|
|
938 void
|
|
|
939 syms_of_floatfns (void)
|
|
|
940 {
|
|
442
|
941 INIT_LRECORD_IMPLEMENTATION (float);
|
|
428
|
942
|
|
|
943 /* Trig functions. */
|
|
|
944
|
|
|
945 DEFSUBR (Facos);
|
|
|
946 DEFSUBR (Fasin);
|
|
|
947 DEFSUBR (Fatan);
|
|
|
948 DEFSUBR (Fcos);
|
|
|
949 DEFSUBR (Fsin);
|
|
|
950 DEFSUBR (Ftan);
|
|
|
951
|
|
|
952 /* Bessel functions */
|
|
|
953
|
|
|
954 #if 0
|
|
|
955 DEFSUBR (Fbessel_y0);
|
|
|
956 DEFSUBR (Fbessel_y1);
|
|
|
957 DEFSUBR (Fbessel_yn);
|
|
|
958 DEFSUBR (Fbessel_j0);
|
|
|
959 DEFSUBR (Fbessel_j1);
|
|
|
960 DEFSUBR (Fbessel_jn);
|
|
|
961 #endif /* 0 */
|
|
|
962
|
|
|
963 /* Error functions. */
|
|
|
964
|
|
|
965 #if 0
|
|
|
966 DEFSUBR (Ferf);
|
|
|
967 DEFSUBR (Ferfc);
|
|
|
968 DEFSUBR (Flog_gamma);
|
|
|
969 #endif /* 0 */
|
|
|
970
|
|
|
971 /* Root and Log functions. */
|
|
|
972
|
|
|
973 DEFSUBR (Fexp);
|
|
|
974 DEFSUBR (Fexpt);
|
|
|
975 DEFSUBR (Flog);
|
|
|
976 DEFSUBR (Flog10);
|
|
|
977 DEFSUBR (Fsqrt);
|
|
|
978 DEFSUBR (Fcube_root);
|
|
|
979
|
|
|
980 /* Inverse trig functions. */
|
|
|
981
|
|
|
982 DEFSUBR (Facosh);
|
|
|
983 DEFSUBR (Fasinh);
|
|
|
984 DEFSUBR (Fatanh);
|
|
|
985 DEFSUBR (Fcosh);
|
|
|
986 DEFSUBR (Fsinh);
|
|
|
987 DEFSUBR (Ftanh);
|
|
|
988
|
|
|
989 /* Rounding functions */
|
|
|
990
|
|
|
991 DEFSUBR (Fabs);
|
|
|
992 DEFSUBR (Ffloat);
|
|
|
993 DEFSUBR (Flogb);
|
|
|
994 DEFSUBR (Fceiling);
|
|
|
995 DEFSUBR (Ffloor);
|
|
|
996 DEFSUBR (Fround);
|
|
|
997 DEFSUBR (Ftruncate);
|
|
|
998
|
|
|
999 /* Float-rounding functions. */
|
|
|
1000
|
|
|
1001 DEFSUBR (Ffceiling);
|
|
|
1002 DEFSUBR (Fffloor);
|
|
|
1003 DEFSUBR (Ffround);
|
|
|
1004 DEFSUBR (Fftruncate);
|
|
|
1005 }
|
|
|
1006
|
|
|
1007 void
|
|
|
1008 vars_of_floatfns (void)
|
|
|
1009 {
|
|
|
1010 Fprovide (intern ("lisp-float-type"));
|
|
|
1011 }
|
