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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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1983
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122 error using the given arguments. If bignums are available, range errors
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123 are never signaled. */
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428
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124 static Lisp_Object
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2286
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125 float_to_int (double x,
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126 #ifdef HAVE_BIGNUM
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127 const char *UNUSED (name), Lisp_Object UNUSED (num),
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128 Lisp_Object UNUSED (num2)
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129 #else
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130 const char *name, Lisp_Object num, Lisp_Object num2
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131 #endif
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132 )
|
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428
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133 {
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1983
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134 #ifdef HAVE_BIGNUM
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135 bignum_set_double (scratch_bignum, x);
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136 return Fcanonicalize_number (make_bignum_bg (scratch_bignum));
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137 #else
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2039
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138 REGISTER EMACS_INT result = (EMACS_INT) x;
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139
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140 if (result > EMACS_INT_MAX || result < EMACS_INT_MIN)
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141 {
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142 if (!UNBOUNDP (num2))
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143 range_error2 (name, num, num2);
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144 else
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145 range_error (name, num);
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146 }
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147 return make_int (result);
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1983
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148 #endif /* HAVE_BIGNUM */
|
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428
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149 }
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150
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151
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152 static void
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153 in_float_error (void)
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154 {
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155 switch (errno)
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156 {
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157 case 0:
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158 break;
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159 case EDOM:
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160 if (in_float == 2)
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161 domain_error2 (float_error_fn_name, float_error_arg, float_error_arg2);
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162 else
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163 domain_error (float_error_fn_name, float_error_arg);
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164 break;
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165 case ERANGE:
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166 range_error (float_error_fn_name, float_error_arg);
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167 break;
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168 default:
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169 arith_error (float_error_fn_name, float_error_arg);
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170 break;
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171 }
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172 }
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173
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174
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175 static Lisp_Object
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2286
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176 mark_float (Lisp_Object UNUSED (obj))
|
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428
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177 {
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178 return Qnil;
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179 }
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180
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181 static int
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2286
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182 float_equal (Lisp_Object obj1, Lisp_Object obj2, int UNUSED (depth))
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428
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183 {
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184 return (extract_float (obj1) == extract_float (obj2));
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185 }
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186
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665
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187 static Hashcode
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2286
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188 float_hash (Lisp_Object obj, int UNUSED (depth))
|
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428
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189 {
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|
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190 /* mod the value down to 32-bit range */
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191 /* #### change for 64-bit machines */
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192 return (unsigned long) fmod (extract_float (obj), 4e9);
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193 }
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194
|
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1204
|
195 static const struct memory_description float_description[] = {
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428
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196 { XD_END }
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197 };
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198
|
|
934
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199 DEFINE_BASIC_LRECORD_IMPLEMENTATION ("float", float,
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200 1, /*dumpable-flag*/
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201 mark_float, print_float, 0, float_equal,
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202 float_hash, float_description,
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203 Lisp_Float);
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428
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204
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205 /* Extract a Lisp number as a `double', or signal an error. */
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206
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207 double
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208 extract_float (Lisp_Object num)
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209 {
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210 if (FLOATP (num))
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211 return XFLOAT_DATA (num);
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212
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|
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213 if (INTP (num))
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214 return (double) XINT (num);
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215
|
|
1983
|
216 #ifdef HAVE_BIGNUM
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|
217 if (BIGNUMP (num))
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218 return bignum_to_double (XBIGNUM_DATA (num));
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219 #endif
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220
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221 #ifdef HAVE_RATIO
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222 if (RATIOP (num))
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223 return ratio_to_double (XRATIO_DATA (num));
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224 #endif
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225
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|
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226 #ifdef HAVE_BIGFLOAT
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227 if (BIGFLOATP (num))
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228 return bigfloat_to_double (XBIGFLOAT_DATA (num));
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|
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229 #endif
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|
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230
|
|
428
|
231 return extract_float (wrong_type_argument (Qnumberp, num));
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|
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232 }
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|
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233
|
|
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234 /* Trig functions. */
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235
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236 DEFUN ("acos", Facos, 1, 1, 0, /*
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444
|
237 Return the inverse cosine of NUMBER.
|
|
428
|
238 */
|
|
444
|
239 (number))
|
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428
|
240 {
|
|
444
|
241 double d = extract_float (number);
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|
428
|
242 #ifdef FLOAT_CHECK_DOMAIN
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243 if (d > 1.0 || d < -1.0)
|
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444
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244 domain_error ("acos", number);
|
|
428
|
245 #endif
|
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444
|
246 IN_FLOAT (d = acos (d), "acos", number);
|
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428
|
247 return make_float (d);
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|
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248 }
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|
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249
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|
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250 DEFUN ("asin", Fasin, 1, 1, 0, /*
|
|
444
|
251 Return the inverse sine of NUMBER.
|
|
428
|
252 */
|
|
444
|
253 (number))
|
|
428
|
254 {
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|
444
|
255 double d = extract_float (number);
|
|
428
|
256 #ifdef FLOAT_CHECK_DOMAIN
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|
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257 if (d > 1.0 || d < -1.0)
|
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444
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258 domain_error ("asin", number);
|
|
428
|
259 #endif
|
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444
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260 IN_FLOAT (d = asin (d), "asin", number);
|
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428
|
261 return make_float (d);
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|
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262 }
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263
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|
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264 DEFUN ("atan", Fatan, 1, 2, 0, /*
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|
444
|
265 Return the inverse tangent of NUMBER.
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|
|
266 If optional second argument NUMBER2 is provided,
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|
|
267 return atan2 (NUMBER, NUMBER2).
|
|
428
|
268 */
|
|
444
|
269 (number, number2))
|
|
428
|
270 {
|
|
444
|
271 double d = extract_float (number);
|
|
428
|
272
|
|
444
|
273 if (NILP (number2))
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|
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274 IN_FLOAT (d = atan (d), "atan", number);
|
|
428
|
275 else
|
|
|
276 {
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|
444
|
277 double d2 = extract_float (number2);
|
|
428
|
278 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
279 if (d == 0.0 && d2 == 0.0)
|
|
444
|
280 domain_error2 ("atan", number, number2);
|
|
428
|
281 #endif
|
|
444
|
282 IN_FLOAT2 (d = atan2 (d, d2), "atan", number, number2);
|
|
428
|
283 }
|
|
|
284 return make_float (d);
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|
|
285 }
|
|
|
286
|
|
|
287 DEFUN ("cos", Fcos, 1, 1, 0, /*
|
|
444
|
288 Return the cosine of NUMBER.
|
|
428
|
289 */
|
|
444
|
290 (number))
|
|
428
|
291 {
|
|
444
|
292 double d = extract_float (number);
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|
|
293 IN_FLOAT (d = cos (d), "cos", number);
|
|
428
|
294 return make_float (d);
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|
|
295 }
|
|
|
296
|
|
|
297 DEFUN ("sin", Fsin, 1, 1, 0, /*
|
|
444
|
298 Return the sine of NUMBER.
|
|
428
|
299 */
|
|
444
|
300 (number))
|
|
428
|
301 {
|
|
444
|
302 double d = extract_float (number);
|
|
|
303 IN_FLOAT (d = sin (d), "sin", number);
|
|
428
|
304 return make_float (d);
|
|
|
305 }
|
|
|
306
|
|
|
307 DEFUN ("tan", Ftan, 1, 1, 0, /*
|
|
444
|
308 Return the tangent of NUMBER.
|
|
428
|
309 */
|
|
444
|
310 (number))
|
|
428
|
311 {
|
|
444
|
312 double d = extract_float (number);
|
|
428
|
313 double c = cos (d);
|
|
|
314 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
315 if (c == 0.0)
|
|
444
|
316 domain_error ("tan", number);
|
|
428
|
317 #endif
|
|
444
|
318 IN_FLOAT (d = (sin (d) / c), "tan", number);
|
|
428
|
319 return make_float (d);
|
|
|
320 }
|
|
|
321
|
|
|
322 /* Bessel functions */
|
|
|
323 #if 0 /* Leave these out unless we find there's a reason for them. */
|
|
|
324
|
|
|
325 DEFUN ("bessel-j0", Fbessel_j0, 1, 1, 0, /*
|
|
444
|
326 Return the bessel function j0 of NUMBER.
|
|
428
|
327 */
|
|
444
|
328 (number))
|
|
428
|
329 {
|
|
444
|
330 double d = extract_float (number);
|
|
|
331 IN_FLOAT (d = j0 (d), "bessel-j0", number);
|
|
428
|
332 return make_float (d);
|
|
|
333 }
|
|
|
334
|
|
|
335 DEFUN ("bessel-j1", Fbessel_j1, 1, 1, 0, /*
|
|
444
|
336 Return the bessel function j1 of NUMBER.
|
|
428
|
337 */
|
|
444
|
338 (number))
|
|
428
|
339 {
|
|
444
|
340 double d = extract_float (number);
|
|
|
341 IN_FLOAT (d = j1 (d), "bessel-j1", number);
|
|
428
|
342 return make_float (d);
|
|
|
343 }
|
|
|
344
|
|
|
345 DEFUN ("bessel-jn", Fbessel_jn, 2, 2, 0, /*
|
|
444
|
346 Return the order N bessel function output jn of NUMBER.
|
|
|
347 The first number (the order) is truncated to an integer.
|
|
428
|
348 */
|
|
444
|
349 (number1, number2))
|
|
428
|
350 {
|
|
444
|
351 int i1 = extract_float (number1);
|
|
|
352 double f2 = extract_float (number2);
|
|
428
|
353
|
|
444
|
354 IN_FLOAT (f2 = jn (i1, f2), "bessel-jn", number1);
|
|
428
|
355 return make_float (f2);
|
|
|
356 }
|
|
|
357
|
|
|
358 DEFUN ("bessel-y0", Fbessel_y0, 1, 1, 0, /*
|
|
444
|
359 Return the bessel function y0 of NUMBER.
|
|
428
|
360 */
|
|
444
|
361 (number))
|
|
428
|
362 {
|
|
444
|
363 double d = extract_float (number);
|
|
|
364 IN_FLOAT (d = y0 (d), "bessel-y0", number);
|
|
428
|
365 return make_float (d);
|
|
|
366 }
|
|
|
367
|
|
|
368 DEFUN ("bessel-y1", Fbessel_y1, 1, 1, 0, /*
|
|
444
|
369 Return the bessel function y1 of NUMBER.
|
|
428
|
370 */
|
|
444
|
371 (number))
|
|
428
|
372 {
|
|
444
|
373 double d = extract_float (number);
|
|
|
374 IN_FLOAT (d = y1 (d), "bessel-y0", number);
|
|
428
|
375 return make_float (d);
|
|
|
376 }
|
|
|
377
|
|
|
378 DEFUN ("bessel-yn", Fbessel_yn, 2, 2, 0, /*
|
|
444
|
379 Return the order N bessel function output yn of NUMBER.
|
|
|
380 The first number (the order) is truncated to an integer.
|
|
428
|
381 */
|
|
444
|
382 (number1, number2))
|
|
428
|
383 {
|
|
444
|
384 int i1 = extract_float (number1);
|
|
|
385 double f2 = extract_float (number2);
|
|
428
|
386
|
|
444
|
387 IN_FLOAT (f2 = yn (i1, f2), "bessel-yn", number1);
|
|
428
|
388 return make_float (f2);
|
|
|
389 }
|
|
|
390
|
|
|
391 #endif /* 0 (bessel functions) */
|
|
|
392
|
|
|
393 /* Error functions. */
|
|
|
394 #if 0 /* Leave these out unless we see they are worth having. */
|
|
|
395
|
|
|
396 DEFUN ("erf", Ferf, 1, 1, 0, /*
|
|
444
|
397 Return the mathematical error function of NUMBER.
|
|
428
|
398 */
|
|
444
|
399 (number))
|
|
428
|
400 {
|
|
444
|
401 double d = extract_float (number);
|
|
|
402 IN_FLOAT (d = erf (d), "erf", number);
|
|
428
|
403 return make_float (d);
|
|
|
404 }
|
|
|
405
|
|
|
406 DEFUN ("erfc", Ferfc, 1, 1, 0, /*
|
|
444
|
407 Return the complementary error function of NUMBER.
|
|
428
|
408 */
|
|
444
|
409 (number))
|
|
428
|
410 {
|
|
444
|
411 double d = extract_float (number);
|
|
|
412 IN_FLOAT (d = erfc (d), "erfc", number);
|
|
428
|
413 return make_float (d);
|
|
|
414 }
|
|
|
415
|
|
|
416 DEFUN ("log-gamma", Flog_gamma, 1, 1, 0, /*
|
|
444
|
417 Return the log gamma of NUMBER.
|
|
428
|
418 */
|
|
444
|
419 (number))
|
|
428
|
420 {
|
|
444
|
421 double d = extract_float (number);
|
|
|
422 IN_FLOAT (d = lgamma (d), "log-gamma", number);
|
|
428
|
423 return make_float (d);
|
|
|
424 }
|
|
|
425
|
|
|
426 #endif /* 0 (error functions) */
|
|
|
427
|
|
|
428
|
|
|
429 /* Root and Log functions. */
|
|
|
430
|
|
|
431 DEFUN ("exp", Fexp, 1, 1, 0, /*
|
|
444
|
432 Return the exponential base e of NUMBER.
|
|
428
|
433 */
|
|
444
|
434 (number))
|
|
428
|
435 {
|
|
444
|
436 double d = extract_float (number);
|
|
428
|
437 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
438 if (d > 709.7827) /* Assume IEEE doubles here */
|
|
444
|
439 range_error ("exp", number);
|
|
428
|
440 else if (d < -709.0)
|
|
|
441 return make_float (0.0);
|
|
|
442 else
|
|
|
443 #endif
|
|
444
|
444 IN_FLOAT (d = exp (d), "exp", number);
|
|
428
|
445 return make_float (d);
|
|
|
446 }
|
|
|
447
|
|
|
448 DEFUN ("expt", Fexpt, 2, 2, 0, /*
|
|
444
|
449 Return the exponential NUMBER1 ** NUMBER2.
|
|
428
|
450 */
|
|
444
|
451 (number1, number2))
|
|
428
|
452 {
|
|
1983
|
453 #ifdef HAVE_BIGNUM
|
|
|
454 if (INTEGERP (number1) && INTP (number2))
|
|
|
455 {
|
|
|
456 if (INTP (number1))
|
|
|
457 {
|
|
|
458 bignum_set_long (scratch_bignum2, XREALINT (number1));
|
|
|
459 bignum_pow (scratch_bignum, scratch_bignum2, XREALINT (number2));
|
|
|
460 }
|
|
|
461 else
|
|
|
462 bignum_pow (scratch_bignum, XBIGNUM_DATA (number1),
|
|
|
463 XREALINT (number2));
|
|
|
464 return Fcanonicalize_number (make_bignum_bg (scratch_bignum));
|
|
|
465 }
|
|
|
466 #endif
|
|
|
467
|
|
444
|
468 if (INTP (number1) && /* common lisp spec */
|
|
|
469 INTP (number2)) /* don't promote, if both are ints */
|
|
428
|
470 {
|
|
|
471 EMACS_INT retval;
|
|
444
|
472 EMACS_INT x = XINT (number1);
|
|
|
473 EMACS_INT y = XINT (number2);
|
|
428
|
474
|
|
|
475 if (y < 0)
|
|
|
476 {
|
|
|
477 if (x == 1)
|
|
|
478 retval = 1;
|
|
|
479 else if (x == -1)
|
|
|
480 retval = (y & 1) ? -1 : 1;
|
|
|
481 else
|
|
|
482 retval = 0;
|
|
|
483 }
|
|
|
484 else
|
|
|
485 {
|
|
|
486 retval = 1;
|
|
|
487 while (y > 0)
|
|
|
488 {
|
|
|
489 if (y & 1)
|
|
|
490 retval *= x;
|
|
|
491 x *= x;
|
|
|
492 y = (EMACS_UINT) y >> 1;
|
|
|
493 }
|
|
|
494 }
|
|
|
495 return make_int (retval);
|
|
|
496 }
|
|
|
497
|
|
1983
|
498 #if defined(HAVE_BIGFLOAT) && defined(bigfloat_pow)
|
|
|
499 if (BIGFLOATP (number1) && INTEGERP (number2))
|
|
|
500 {
|
|
2057
|
501 unsigned long exponent;
|
|
1983
|
502
|
|
|
503 #ifdef HAVE_BIGNUM
|
|
|
504 if (BIGNUMP (number2))
|
|
2057
|
505 exponent = bignum_to_ulong (XBIGNUM_DATA (number2));
|
|
1983
|
506 else
|
|
|
507 #endif
|
|
2057
|
508 exponent = XUINT (number2);
|
|
1983
|
509 bigfloat_set_prec (scratch_bigfloat, XBIGFLOAT_GET_PREC (number1));
|
|
2057
|
510 bigfloat_pow (scratch_bigfloat, XBIGFLOAT_DATA (number1), exponent);
|
|
1983
|
511 return make_bigfloat_bf (scratch_bigfloat);
|
|
|
512 }
|
|
|
513 #endif
|
|
|
514
|
|
428
|
515 {
|
|
444
|
516 double f1 = extract_float (number1);
|
|
|
517 double f2 = extract_float (number2);
|
|
428
|
518 /* Really should check for overflow, too */
|
|
|
519 if (f1 == 0.0 && f2 == 0.0)
|
|
|
520 f1 = 1.0;
|
|
|
521 # ifdef FLOAT_CHECK_DOMAIN
|
|
|
522 else if ((f1 == 0.0 && f2 < 0.0) || (f1 < 0 && f2 != floor(f2)))
|
|
444
|
523 domain_error2 ("expt", number1, number2);
|
|
428
|
524 # endif /* FLOAT_CHECK_DOMAIN */
|
|
444
|
525 IN_FLOAT2 (f1 = pow (f1, f2), "expt", number1, number2);
|
|
428
|
526 return make_float (f1);
|
|
|
527 }
|
|
|
528 }
|
|
|
529
|
|
|
530 DEFUN ("log", Flog, 1, 2, 0, /*
|
|
444
|
531 Return the natural logarithm of NUMBER.
|
|
|
532 If second optional argument BASE is given, return the logarithm of
|
|
|
533 NUMBER using that base.
|
|
428
|
534 */
|
|
444
|
535 (number, base))
|
|
428
|
536 {
|
|
444
|
537 double d = extract_float (number);
|
|
428
|
538 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
539 if (d <= 0.0)
|
|
444
|
540 domain_error2 ("log", number, base);
|
|
428
|
541 #endif
|
|
|
542 if (NILP (base))
|
|
444
|
543 IN_FLOAT (d = log (d), "log", number);
|
|
428
|
544 else
|
|
|
545 {
|
|
|
546 double b = extract_float (base);
|
|
|
547 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
548 if (b <= 0.0 || b == 1.0)
|
|
444
|
549 domain_error2 ("log", number, base);
|
|
428
|
550 #endif
|
|
|
551 if (b == 10.0)
|
|
444
|
552 IN_FLOAT2 (d = log10 (d), "log", number, base);
|
|
428
|
553 else
|
|
444
|
554 IN_FLOAT2 (d = (log (d) / log (b)), "log", number, base);
|
|
428
|
555 }
|
|
|
556 return make_float (d);
|
|
|
557 }
|
|
|
558
|
|
|
559
|
|
|
560 DEFUN ("log10", Flog10, 1, 1, 0, /*
|
|
444
|
561 Return the logarithm base 10 of NUMBER.
|
|
428
|
562 */
|
|
444
|
563 (number))
|
|
428
|
564 {
|
|
444
|
565 double d = extract_float (number);
|
|
428
|
566 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
567 if (d <= 0.0)
|
|
444
|
568 domain_error ("log10", number);
|
|
428
|
569 #endif
|
|
444
|
570 IN_FLOAT (d = log10 (d), "log10", number);
|
|
428
|
571 return make_float (d);
|
|
|
572 }
|
|
|
573
|
|
|
574
|
|
|
575 DEFUN ("sqrt", Fsqrt, 1, 1, 0, /*
|
|
444
|
576 Return the square root of NUMBER.
|
|
428
|
577 */
|
|
444
|
578 (number))
|
|
428
|
579 {
|
|
1983
|
580 double d;
|
|
|
581
|
|
|
582 #if defined(HAVE_BIGFLOAT) && defined(bigfloat_sqrt)
|
|
|
583 if (BIGFLOATP (number))
|
|
|
584 {
|
|
|
585 bigfloat_set_prec (scratch_bigfloat, XBIGFLOAT_GET_PREC (number));
|
|
|
586 bigfloat_sqrt (scratch_bigfloat, XBIGFLOAT_DATA (number));
|
|
|
587 return make_bigfloat_bf (scratch_bigfloat);
|
|
|
588 }
|
|
|
589 #endif /* HAVE_BIGFLOAT */
|
|
|
590 d = extract_float (number);
|
|
428
|
591 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
592 if (d < 0.0)
|
|
444
|
593 domain_error ("sqrt", number);
|
|
428
|
594 #endif
|
|
444
|
595 IN_FLOAT (d = sqrt (d), "sqrt", number);
|
|
428
|
596 return make_float (d);
|
|
|
597 }
|
|
|
598
|
|
|
599
|
|
|
600 DEFUN ("cube-root", Fcube_root, 1, 1, 0, /*
|
|
444
|
601 Return the cube root of NUMBER.
|
|
428
|
602 */
|
|
444
|
603 (number))
|
|
428
|
604 {
|
|
444
|
605 double d = extract_float (number);
|
|
428
|
606 #ifdef HAVE_CBRT
|
|
444
|
607 IN_FLOAT (d = cbrt (d), "cube-root", number);
|
|
428
|
608 #else
|
|
|
609 if (d >= 0.0)
|
|
444
|
610 IN_FLOAT (d = pow (d, 1.0/3.0), "cube-root", number);
|
|
428
|
611 else
|
|
444
|
612 IN_FLOAT (d = -pow (-d, 1.0/3.0), "cube-root", number);
|
|
428
|
613 #endif
|
|
|
614 return make_float (d);
|
|
|
615 }
|
|
|
616
|
|
|
617 /* Inverse trig functions. */
|
|
|
618
|
|
|
619 DEFUN ("acosh", Facosh, 1, 1, 0, /*
|
|
444
|
620 Return the inverse hyperbolic cosine of NUMBER.
|
|
428
|
621 */
|
|
444
|
622 (number))
|
|
428
|
623 {
|
|
444
|
624 double d = extract_float (number);
|
|
428
|
625 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
626 if (d < 1.0)
|
|
444
|
627 domain_error ("acosh", number);
|
|
428
|
628 #endif
|
|
|
629 #ifdef HAVE_INVERSE_HYPERBOLIC
|
|
444
|
630 IN_FLOAT (d = acosh (d), "acosh", number);
|
|
428
|
631 #else
|
|
444
|
632 IN_FLOAT (d = log (d + sqrt (d*d - 1.0)), "acosh", number);
|
|
428
|
633 #endif
|
|
|
634 return make_float (d);
|
|
|
635 }
|
|
|
636
|
|
|
637 DEFUN ("asinh", Fasinh, 1, 1, 0, /*
|
|
444
|
638 Return the inverse hyperbolic sine of NUMBER.
|
|
428
|
639 */
|
|
444
|
640 (number))
|
|
428
|
641 {
|
|
444
|
642 double d = extract_float (number);
|
|
428
|
643 #ifdef HAVE_INVERSE_HYPERBOLIC
|
|
444
|
644 IN_FLOAT (d = asinh (d), "asinh", number);
|
|
428
|
645 #else
|
|
444
|
646 IN_FLOAT (d = log (d + sqrt (d*d + 1.0)), "asinh", number);
|
|
428
|
647 #endif
|
|
|
648 return make_float (d);
|
|
|
649 }
|
|
|
650
|
|
|
651 DEFUN ("atanh", Fatanh, 1, 1, 0, /*
|
|
444
|
652 Return the inverse hyperbolic tangent of NUMBER.
|
|
428
|
653 */
|
|
444
|
654 (number))
|
|
428
|
655 {
|
|
444
|
656 double d = extract_float (number);
|
|
428
|
657 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
658 if (d >= 1.0 || d <= -1.0)
|
|
444
|
659 domain_error ("atanh", number);
|
|
428
|
660 #endif
|
|
|
661 #ifdef HAVE_INVERSE_HYPERBOLIC
|
|
444
|
662 IN_FLOAT (d = atanh (d), "atanh", number);
|
|
428
|
663 #else
|
|
444
|
664 IN_FLOAT (d = 0.5 * log ((1.0 + d) / (1.0 - d)), "atanh", number);
|
|
428
|
665 #endif
|
|
|
666 return make_float (d);
|
|
|
667 }
|
|
|
668
|
|
|
669 DEFUN ("cosh", Fcosh, 1, 1, 0, /*
|
|
444
|
670 Return the hyperbolic cosine of NUMBER.
|
|
428
|
671 */
|
|
444
|
672 (number))
|
|
428
|
673 {
|
|
444
|
674 double d = extract_float (number);
|
|
428
|
675 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
676 if (d > 710.0 || d < -710.0)
|
|
444
|
677 range_error ("cosh", number);
|
|
428
|
678 #endif
|
|
444
|
679 IN_FLOAT (d = cosh (d), "cosh", number);
|
|
428
|
680 return make_float (d);
|
|
|
681 }
|
|
|
682
|
|
|
683 DEFUN ("sinh", Fsinh, 1, 1, 0, /*
|
|
444
|
684 Return the hyperbolic sine of NUMBER.
|
|
428
|
685 */
|
|
444
|
686 (number))
|
|
428
|
687 {
|
|
444
|
688 double d = extract_float (number);
|
|
428
|
689 #ifdef FLOAT_CHECK_DOMAIN
|
|
|
690 if (d > 710.0 || d < -710.0)
|
|
444
|
691 range_error ("sinh", number);
|
|
428
|
692 #endif
|
|
444
|
693 IN_FLOAT (d = sinh (d), "sinh", number);
|
|
428
|
694 return make_float (d);
|
|
|
695 }
|
|
|
696
|
|
|
697 DEFUN ("tanh", Ftanh, 1, 1, 0, /*
|
|
444
|
698 Return the hyperbolic tangent of NUMBER.
|
|
428
|
699 */
|
|
444
|
700 (number))
|
|
428
|
701 {
|
|
444
|
702 double d = extract_float (number);
|
|
|
703 IN_FLOAT (d = tanh (d), "tanh", number);
|
|
428
|
704 return make_float (d);
|
|
|
705 }
|
|
|
706
|
|
|
707 /* Rounding functions */
|
|
|
708
|
|
|
709 DEFUN ("abs", Fabs, 1, 1, 0, /*
|
|
444
|
710 Return the absolute value of NUMBER.
|
|
428
|
711 */
|
|
444
|
712 (number))
|
|
428
|
713 {
|
|
444
|
714 if (FLOATP (number))
|
|
428
|
715 {
|
|
444
|
716 IN_FLOAT (number = make_float (fabs (XFLOAT_DATA (number))),
|
|
|
717 "abs", number);
|
|
|
718 return number;
|
|
428
|
719 }
|
|
|
720
|
|
444
|
721 if (INTP (number))
|
|
1983
|
722 #ifdef HAVE_BIGNUM
|
|
|
723 /* The most negative Lisp fixnum will overflow */
|
|
|
724 return (XINT (number) >= 0) ? number : make_integer (- XINT (number));
|
|
|
725 #else
|
|
444
|
726 return (XINT (number) >= 0) ? number : make_int (- XINT (number));
|
|
1983
|
727 #endif
|
|
|
728
|
|
|
729 #ifdef HAVE_BIGNUM
|
|
|
730 if (BIGNUMP (number))
|
|
|
731 {
|
|
|
732 if (bignum_sign (XBIGNUM_DATA (number)) >= 0)
|
|
|
733 return number;
|
|
|
734 bignum_abs (scratch_bignum, XBIGNUM_DATA (number));
|
|
|
735 return make_bignum_bg (scratch_bignum);
|
|
|
736 }
|
|
|
737 #endif
|
|
|
738
|
|
|
739 #ifdef HAVE_RATIO
|
|
|
740 if (RATIOP (number))
|
|
|
741 {
|
|
|
742 if (ratio_sign (XRATIO_DATA (number)) >= 0)
|
|
|
743 return number;
|
|
|
744 ratio_abs (scratch_ratio, XRATIO_DATA (number));
|
|
|
745 return make_ratio_rt (scratch_ratio);
|
|
|
746 }
|
|
|
747 #endif
|
|
|
748
|
|
|
749 #ifdef HAVE_BIGFLOAT
|
|
|
750 if (BIGFLOATP (number))
|
|
|
751 {
|
|
|
752 if (bigfloat_sign (XBIGFLOAT_DATA (number)) >= 0)
|
|
|
753 return number;
|
|
|
754 bigfloat_set_prec (scratch_bigfloat, XBIGFLOAT_GET_PREC (number));
|
|
|
755 bigfloat_abs (scratch_bigfloat, XBIGFLOAT_DATA (number));
|
|
|
756 return make_bigfloat_bf (scratch_bigfloat);
|
|
|
757 }
|
|
|
758 #endif
|
|
428
|
759
|
|
444
|
760 return Fabs (wrong_type_argument (Qnumberp, number));
|
|
428
|
761 }
|
|
|
762
|
|
|
763 DEFUN ("float", Ffloat, 1, 1, 0, /*
|
|
444
|
764 Return the floating point number numerically equal to NUMBER.
|
|
428
|
765 */
|
|
444
|
766 (number))
|
|
428
|
767 {
|
|
444
|
768 if (INTP (number))
|
|
|
769 return make_float ((double) XINT (number));
|
|
428
|
770
|
|
1983
|
771 #ifdef HAVE_BIGNUM
|
|
|
772 if (BIGFLOATP (number))
|
|
|
773 {
|
|
|
774 #ifdef HAVE_BIGFLOAT
|
|
|
775 if (ZEROP (Vdefault_float_precision))
|
|
|
776 #endif
|
|
|
777 return make_float (bignum_to_double (XBIGNUM_DATA (number)));
|
|
|
778 #ifdef HAVE_BIGFLOAT
|
|
|
779 else
|
|
|
780 {
|
|
|
781 bigfloat_set_prec (scratch_bigfloat, bigfloat_get_default_prec ());
|
|
|
782 bigfloat_set_bignum (scratch_bigfloat, XBIGNUM_DATA (number));
|
|
|
783 return make_bigfloat_bf (scratch_bigfloat);
|
|
|
784 }
|
|
|
785 #endif /* HAVE_BIGFLOAT */
|
|
|
786 }
|
|
|
787 #endif /* HAVE_BIGNUM */
|
|
|
788
|
|
|
789 #ifdef HAVE_RATIO
|
|
|
790 if (RATIOP (number))
|
|
2092
|
791 return make_float (ratio_to_double (XRATIO_DATA (number)));
|
|
1983
|
792 #endif
|
|
|
793
|
|
444
|
794 if (FLOATP (number)) /* give 'em the same float back */
|
|
|
795 return number;
|
|
428
|
796
|
|
444
|
797 return Ffloat (wrong_type_argument (Qnumberp, number));
|
|
428
|
798 }
|
|
|
799
|
|
|
800 DEFUN ("logb", Flogb, 1, 1, 0, /*
|
|
444
|
801 Return largest integer <= the base 2 log of the magnitude of NUMBER.
|
|
428
|
802 This is the same as the exponent of a float.
|
|
|
803 */
|
|
444
|
804 (number))
|
|
428
|
805 {
|
|
444
|
806 double f = extract_float (number);
|
|
428
|
807
|
|
|
808 if (f == 0.0)
|
|
2039
|
809 return make_int (EMACS_INT_MIN);
|
|
428
|
810 #ifdef HAVE_LOGB
|
|
|
811 {
|
|
|
812 Lisp_Object val;
|
|
444
|
813 IN_FLOAT (val = make_int ((EMACS_INT) logb (f)), "logb", number);
|
|
434
|
814 return val;
|
|
428
|
815 }
|
|
|
816 #else
|
|
|
817 #ifdef HAVE_FREXP
|
|
|
818 {
|
|
|
819 int exqp;
|
|
444
|
820 IN_FLOAT (frexp (f, &exqp), "logb", number);
|
|
434
|
821 return make_int (exqp - 1);
|
|
428
|
822 }
|
|
|
823 #else
|
|
|
824 {
|
|
|
825 int i;
|
|
|
826 double d;
|
|
|
827 EMACS_INT val;
|
|
|
828 if (f < 0.0)
|
|
|
829 f = -f;
|
|
|
830 val = -1;
|
|
|
831 while (f < 0.5)
|
|
|
832 {
|
|
|
833 for (i = 1, d = 0.5; d * d >= f; i += i)
|
|
|
834 d *= d;
|
|
|
835 f /= d;
|
|
|
836 val -= i;
|
|
|
837 }
|
|
|
838 while (f >= 1.0)
|
|
|
839 {
|
|
|
840 for (i = 1, d = 2.0; d * d <= f; i += i)
|
|
|
841 d *= d;
|
|
|
842 f /= d;
|
|
|
843 val += i;
|
|
|
844 }
|
|
434
|
845 return make_int (val);
|
|
428
|
846 }
|
|
|
847 #endif /* ! HAVE_FREXP */
|
|
|
848 #endif /* ! HAVE_LOGB */
|
|
|
849 }
|
|
|
850
|
|
|
851 DEFUN ("ceiling", Fceiling, 1, 1, 0, /*
|
|
444
|
852 Return the smallest integer no less than NUMBER. (Round toward +inf.)
|
|
428
|
853 */
|
|
444
|
854 (number))
|
|
428
|
855 {
|
|
444
|
856 if (FLOATP (number))
|
|
428
|
857 {
|
|
|
858 double d;
|
|
444
|
859 IN_FLOAT ((d = ceil (XFLOAT_DATA (number))), "ceiling", number);
|
|
|
860 return (float_to_int (d, "ceiling", number, Qunbound));
|
|
428
|
861 }
|
|
|
862
|
|
1983
|
863 #ifdef HAVE_BIGNUM
|
|
|
864 if (INTEGERP (number))
|
|
|
865 #else
|
|
444
|
866 if (INTP (number))
|
|
1983
|
867 #endif
|
|
444
|
868 return number;
|
|
428
|
869
|
|
1983
|
870 #ifdef HAVE_RATIO
|
|
|
871 if (RATIOP (number))
|
|
|
872 {
|
|
|
873 bignum_ceil (scratch_bignum, XRATIO_NUMERATOR (number),
|
|
|
874 XRATIO_DENOMINATOR (number));
|
|
|
875 return Fcanonicalize_number (make_bignum_bg (scratch_bignum));
|
|
|
876 }
|
|
|
877 #endif
|
|
|
878
|
|
|
879 #ifdef HAVE_BIGFLOAT
|
|
|
880 if (BIGFLOATP (number))
|
|
|
881 {
|
|
|
882 bigfloat_set_prec (scratch_bigfloat, XBIGFLOAT_GET_PREC (number));
|
|
|
883 bigfloat_ceil (scratch_bigfloat, XBIGFLOAT_DATA (number));
|
|
|
884 #ifdef HAVE_BIGNUM
|
|
|
885 bignum_set_bigfloat (scratch_bignum, scratch_bigfloat);
|
|
|
886 return Fcanonicalize_number (make_bignum_bg (scratch_bignum));
|
|
|
887 #else
|
|
|
888 return make_int ((EMACS_INT) bigfloat_to_long (scratch_bigfloat));
|
|
|
889 #endif /* HAVE_BIGNUM */
|
|
|
890 }
|
|
|
891 #endif /* HAVE_BIGFLOAT */
|
|
|
892
|
|
444
|
893 return Fceiling (wrong_type_argument (Qnumberp, number));
|
|
428
|
894 }
|
|
|
895
|
|
|
896
|
|
|
897 DEFUN ("floor", Ffloor, 1, 2, 0, /*
|
|
444
|
898 Return the largest integer no greater than NUMBER. (Round towards -inf.)
|
|
|
899 With optional second argument DIVISOR, return the largest integer no
|
|
|
900 greater than NUMBER/DIVISOR.
|
|
428
|
901 */
|
|
444
|
902 (number, divisor))
|
|
428
|
903 {
|
|
1983
|
904 #ifdef WITH_NUMBER_TYPES
|
|
|
905 CHECK_REAL (number);
|
|
|
906 if (NILP (divisor))
|
|
|
907 {
|
|
|
908 if (FLOATP (number))
|
|
|
909 {
|
|
|
910 double d;
|
|
|
911 IN_FLOAT ((d = floor (XFLOAT_DATA (number))), "floor", number);
|
|
|
912 return (float_to_int (d, "floor", number, Qunbound));
|
|
|
913 }
|
|
|
914 #ifdef HAVE_RATIO
|
|
|
915 else if (RATIOP (number))
|
|
|
916 {
|
|
|
917 bignum_floor (scratch_bignum, XRATIO_NUMERATOR (number),
|
|
|
918 XRATIO_DENOMINATOR (number));
|
|
|
919 return Fcanonicalize_number (make_bignum_bg (scratch_bignum));
|
|
|
920 }
|
|
|
921 #endif
|
|
|
922 #ifdef HAVE_BIGFLOAT
|
|
|
923 else if (BIGFLOATP (number))
|
|
|
924 {
|
|
|
925 bigfloat_set_prec (scratch_bigfloat, XBIGFLOAT_GET_PREC (number));
|
|
|
926 bigfloat_floor (scratch_bigfloat, XBIGFLOAT_DATA (number));
|
|
|
927 return make_bigfloat_bf (scratch_bigfloat);
|
|
|
928 }
|
|
|
929 #endif
|
|
|
930 return number;
|
|
|
931 }
|
|
|
932 else
|
|
|
933 {
|
|
|
934 CHECK_REAL (divisor);
|
|
|
935 switch (promote_args (&number, &divisor))
|
|
|
936 {
|
|
|
937 case FIXNUM_T:
|
|
|
938 {
|
|
|
939 EMACS_INT i1 = XREALINT (number);
|
|
|
940 EMACS_INT i2 = XREALINT (divisor);
|
|
|
941
|
|
|
942 if (i2 == 0)
|
|
|
943 Fsignal (Qarith_error, Qnil);
|
|
|
944
|
|
|
945 /* With C's /, the result is implementation-defined if either
|
|
|
946 operand is negative, so use only nonnegative operands. */
|
|
|
947 i1 = (i2 < 0
|
|
|
948 ? (i1 <= 0 ? -i1 / -i2 : -1 - ((i1 - 1) / -i2))
|
|
|
949 : (i1 < 0 ? -1 - ((-1 - i1) / i2) : i1 / i2));
|
|
|
950
|
|
|
951 return make_int (i1);
|
|
|
952 }
|
|
|
953 #ifdef HAVE_BIGNUM
|
|
|
954 case BIGNUM_T:
|
|
|
955 if (bignum_sign (XBIGNUM_DATA (divisor)) == 0)
|
|
|
956 Fsignal (Qarith_error, Qnil);
|
|
|
957 bignum_floor (scratch_bignum, XBIGNUM_DATA (number),
|
|
|
958 XBIGNUM_DATA (divisor));
|
|
|
959 return Fcanonicalize_number (make_bignum_bg (scratch_bignum));
|
|
|
960 #endif
|
|
|
961 #ifdef HAVE_RATIO
|
|
|
962 case RATIO_T:
|
|
|
963 if (ratio_sign (XRATIO_DATA (divisor)) == 0)
|
|
|
964 Fsignal (Qarith_error, Qnil);
|
|
|
965 ratio_div (scratch_ratio, XRATIO_DATA (number),
|
|
|
966 XRATIO_DATA (divisor));
|
|
|
967 bignum_floor (scratch_bignum, ratio_numerator (scratch_ratio),
|
|
|
968 ratio_denominator (scratch_ratio));
|
|
|
969 return Fcanonicalize_number (make_bignum_bg (scratch_bignum));
|
|
|
970 #endif
|
|
|
971 #ifdef HAVE_BIGFLOAT
|
|
|
972 case BIGFLOAT_T:
|
|
|
973 if (bigfloat_sign (XBIGFLOAT_DATA (divisor)) == 0)
|
|
|
974 Fsignal (Qarith_error, Qnil);
|
|
|
975 bigfloat_set_prec (scratch_bigfloat,
|
|
|
976 max (XBIGFLOAT_GET_PREC (number),
|
|
|
977 XBIGFLOAT_GET_PREC (divisor)));
|
|
|
978 bigfloat_div (scratch_bigfloat, XBIGFLOAT_DATA (number),
|
|
|
979 XBIGFLOAT_DATA (divisor));
|
|
|
980 bigfloat_floor (scratch_bigfloat, scratch_bigfloat);
|
|
|
981 return make_bigfloat_bf (scratch_bigfloat);
|
|
|
982 #endif
|
|
1995
|
983 default: /* FLOAT_T */
|
|
|
984 {
|
|
|
985 double f1 = extract_float (number);
|
|
|
986 double f2 = extract_float (divisor);
|
|
|
987
|
|
|
988 if (f2 == 0.0)
|
|
|
989 Fsignal (Qarith_error, Qnil);
|
|
|
990
|
|
|
991 IN_FLOAT2 (f1 = floor (f1 / f2), "floor", number, divisor);
|
|
|
992 return float_to_int (f1, "floor", number, divisor);
|
|
|
993 }
|
|
1983
|
994 }
|
|
|
995 }
|
|
|
996 #else /* !WITH_NUMBER_TYPES */
|
|
444
|
997 CHECK_INT_OR_FLOAT (number);
|
|
428
|
998
|
|
|
999 if (! NILP (divisor))
|
|
|
1000 {
|
|
|
1001 EMACS_INT i1, i2;
|
|
|
1002
|
|
|
1003 CHECK_INT_OR_FLOAT (divisor);
|
|
|
1004
|
|
444
|
1005 if (FLOATP (number) || FLOATP (divisor))
|
|
428
|
1006 {
|
|
444
|
1007 double f1 = extract_float (number);
|
|
428
|
1008 double f2 = extract_float (divisor);
|
|
|
1009
|
|
|
1010 if (f2 == 0)
|
|
|
1011 Fsignal (Qarith_error, Qnil);
|
|
|
1012
|
|
444
|
1013 IN_FLOAT2 (f1 = floor (f1 / f2), "floor", number, divisor);
|
|
|
1014 return float_to_int (f1, "floor", number, divisor);
|
|
428
|
1015 }
|
|
|
1016
|
|
444
|
1017 i1 = XINT (number);
|
|
428
|
1018 i2 = XINT (divisor);
|
|
|
1019
|
|
|
1020 if (i2 == 0)
|
|
|
1021 Fsignal (Qarith_error, Qnil);
|
|
|
1022
|
|
|
1023 /* With C's /, the result is implementation-defined if either operand
|
|
|
1024 is negative, so use only nonnegative operands. */
|
|
|
1025 i1 = (i2 < 0
|
|
|
1026 ? (i1 <= 0 ? -i1 / -i2 : -1 - ((i1 - 1) / -i2))
|
|
|
1027 : (i1 < 0 ? -1 - ((-1 - i1) / i2) : i1 / i2));
|
|
|
1028
|
|
|
1029 return (make_int (i1));
|
|
|
1030 }
|
|
|
1031
|
|
444
|
1032 if (FLOATP (number))
|
|
428
|
1033 {
|
|
|
1034 double d;
|
|
444
|
1035 IN_FLOAT ((d = floor (XFLOAT_DATA (number))), "floor", number);
|
|
|
1036 return (float_to_int (d, "floor", number, Qunbound));
|
|
428
|
1037 }
|
|
|
1038
|
|
444
|
1039 return number;
|
|
1983
|
1040 #endif /* WITH_NUMBER_TYPES */
|
|
428
|
1041 }
|
|
|
1042
|
|
|
1043 DEFUN ("round", Fround, 1, 1, 0, /*
|
|
444
|
1044 Return the nearest integer to NUMBER.
|
|
428
|
1045 */
|
|
444
|
1046 (number))
|
|
428
|
1047 {
|
|
444
|
1048 if (FLOATP (number))
|
|
428
|
1049 {
|
|
|
1050 double d;
|
|
|
1051 /* Screw the prevailing rounding mode. */
|
|
444
|
1052 IN_FLOAT ((d = emacs_rint (XFLOAT_DATA (number))), "round", number);
|
|
|
1053 return (float_to_int (d, "round", number, Qunbound));
|
|
428
|
1054 }
|
|
|
1055
|
|
1983
|
1056 #ifdef HAVE_BIGNUM
|
|
|
1057 if (INTEGERP (number))
|
|
|
1058 #else
|
|
444
|
1059 if (INTP (number))
|
|
1983
|
1060 #endif
|
|
444
|
1061 return number;
|
|
428
|
1062
|
|
1983
|
1063 #ifdef HAVE_RATIO
|
|
|
1064 if (RATIOP (number))
|
|
|
1065 {
|
|
|
1066 if (bignum_divisible_p (XRATIO_NUMERATOR (number),
|
|
|
1067 XRATIO_DENOMINATOR (number)))
|
|
|
1068 {
|
|
|
1069 bignum_div (scratch_bignum, XRATIO_NUMERATOR (number),
|
|
|
1070 XRATIO_DENOMINATOR (number));
|
|
|
1071 }
|
|
|
1072 else
|
|
|
1073 {
|
|
|
1074 bignum_add (scratch_bignum2, XRATIO_NUMERATOR (number),
|
|
|
1075 XRATIO_DENOMINATOR (number));
|
|
|
1076 bignum_div (scratch_bignum, scratch_bignum2,
|
|
|
1077 XRATIO_DENOMINATOR (number));
|
|
|
1078 }
|
|
|
1079 return Fcanonicalize_number (make_bignum_bg (scratch_bignum));
|
|
|
1080 }
|
|
|
1081 #endif
|
|
|
1082
|
|
|
1083 #ifdef HAVE_BIGFLOAT
|
|
|
1084 if (BIGFLOATP (number))
|
|
|
1085 {
|
|
|
1086 unsigned long prec = XBIGFLOAT_GET_PREC (number);
|
|
|
1087 bigfloat_set_prec (scratch_bigfloat, prec);
|
|
|
1088 bigfloat_set_prec (scratch_bigfloat2, prec);
|
|
|
1089 bigfloat_set_double (scratch_bigfloat2,
|
|
|
1090 bigfloat_sign (XBIGFLOAT_DATA (number)) * 0.5);
|
|
|
1091 bigfloat_floor (scratch_bigfloat, scratch_bigfloat2);
|
|
|
1092 #ifdef HAVE_BIGNUM
|
|
|
1093 bignum_set_bigfloat (scratch_bignum, scratch_bigfloat);
|
|
|
1094 return Fcanonicalize_number (make_bignum_bg (scratch_bignum));
|
|
|
1095 #else
|
|
|
1096 return make_int ((EMACS_INT) bigfloat_to_long (scratch_bigfloat));
|
|
|
1097 #endif /* HAVE_BIGNUM */
|
|
|
1098 }
|
|
|
1099 #endif /* HAVE_BIGFLOAT */
|
|
|
1100
|
|
444
|
1101 return Fround (wrong_type_argument (Qnumberp, number));
|
|
428
|
1102 }
|
|
|
1103
|
|
|
1104 DEFUN ("truncate", Ftruncate, 1, 1, 0, /*
|
|
|
1105 Truncate a floating point number to an integer.
|
|
|
1106 Rounds the value toward zero.
|
|
|
1107 */
|
|
444
|
1108 (number))
|
|
428
|
1109 {
|
|
444
|
1110 if (FLOATP (number))
|
|
|
1111 return float_to_int (XFLOAT_DATA (number), "truncate", number, Qunbound);
|
|
428
|
1112
|
|
1983
|
1113 #ifdef HAVE_BIGNUM
|
|
|
1114 if (INTEGERP (number))
|
|
|
1115 #else
|
|
444
|
1116 if (INTP (number))
|
|
1983
|
1117 #endif
|
|
444
|
1118 return number;
|
|
428
|
1119
|
|
1983
|
1120 #ifdef HAVE_RATIO
|
|
|
1121 if (RATIOP (number))
|
|
|
1122 {
|
|
|
1123 bignum_div (scratch_bignum, XRATIO_NUMERATOR (number),
|
|
|
1124 XRATIO_DENOMINATOR (number));
|
|
|
1125 return Fcanonicalize_number (make_bignum_bg (scratch_bignum));
|
|
|
1126 }
|
|
|
1127 #endif
|
|
|
1128
|
|
|
1129 #ifdef HAVE_BIGFLOAT
|
|
|
1130 if (BIGFLOATP (number))
|
|
|
1131 {
|
|
|
1132 bigfloat_set_prec (scratch_bigfloat, XBIGFLOAT_GET_PREC (number));
|
|
|
1133 bigfloat_trunc (scratch_bigfloat, XBIGFLOAT_DATA (number));
|
|
|
1134 #ifdef HAVE_BIGNUM
|
|
|
1135 bignum_set_bigfloat (scratch_bignum, scratch_bigfloat);
|
|
|
1136 return Fcanonicalize_number (make_bignum_bg (scratch_bignum));
|
|
|
1137 #else
|
|
|
1138 return make_int ((EMACS_INT) bigfloat_to_long (scratch_bigfloat));
|
|
|
1139 #endif /* HAVE_BIGNUM */
|
|
|
1140 }
|
|
|
1141 #endif /* HAVE_BIGFLOAT */
|
|
|
1142
|
|
444
|
1143 return Ftruncate (wrong_type_argument (Qnumberp, number));
|
|
428
|
1144 }
|
|
|
1145
|
|
|
1146 /* Float-rounding functions. */
|
|
|
1147
|
|
|
1148 DEFUN ("fceiling", Ffceiling, 1, 1, 0, /*
|
|
444
|
1149 Return the smallest integer no less than NUMBER, as a float.
|
|
428
|
1150 \(Round toward +inf.\)
|
|
|
1151 */
|
|
444
|
1152 (number))
|
|
428
|
1153 {
|
|
444
|
1154 double d = extract_float (number);
|
|
|
1155 IN_FLOAT (d = ceil (d), "fceiling", number);
|
|
428
|
1156 return make_float (d);
|
|
|
1157 }
|
|
|
1158
|
|
|
1159 DEFUN ("ffloor", Fffloor, 1, 1, 0, /*
|
|
444
|
1160 Return the largest integer no greater than NUMBER, as a float.
|
|
428
|
1161 \(Round towards -inf.\)
|
|
|
1162 */
|
|
444
|
1163 (number))
|
|
428
|
1164 {
|
|
444
|
1165 double d = extract_float (number);
|
|
|
1166 IN_FLOAT (d = floor (d), "ffloor", number);
|
|
428
|
1167 return make_float (d);
|
|
|
1168 }
|
|
|
1169
|
|
|
1170 DEFUN ("fround", Ffround, 1, 1, 0, /*
|
|
444
|
1171 Return the nearest integer to NUMBER, as a float.
|
|
428
|
1172 */
|
|
444
|
1173 (number))
|
|
428
|
1174 {
|
|
444
|
1175 double d = extract_float (number);
|
|
|
1176 IN_FLOAT (d = emacs_rint (d), "fround", number);
|
|
428
|
1177 return make_float (d);
|
|
|
1178 }
|
|
|
1179
|
|
|
1180 DEFUN ("ftruncate", Fftruncate, 1, 1, 0, /*
|
|
|
1181 Truncate a floating point number to an integral float value.
|
|
|
1182 Rounds the value toward zero.
|
|
|
1183 */
|
|
444
|
1184 (number))
|
|
428
|
1185 {
|
|
444
|
1186 double d = extract_float (number);
|
|
428
|
1187 if (d >= 0.0)
|
|
444
|
1188 IN_FLOAT (d = floor (d), "ftruncate", number);
|
|
428
|
1189 else
|
|
444
|
1190 IN_FLOAT (d = ceil (d), "ftruncate", number);
|
|
428
|
1191 return make_float (d);
|
|
|
1192 }
|
|
|
1193
|
|
|
1194 #ifdef FLOAT_CATCH_SIGILL
|
|
|
1195 static SIGTYPE
|
|
|
1196 float_error (int signo)
|
|
|
1197 {
|
|
|
1198 if (! in_float)
|
|
|
1199 fatal_error_signal (signo);
|
|
|
1200
|
|
|
1201 EMACS_REESTABLISH_SIGNAL (signo, arith_error);
|
|
|
1202 EMACS_UNBLOCK_SIGNAL (signo);
|
|
|
1203
|
|
|
1204 in_float = 0;
|
|
|
1205
|
|
|
1206 /* Was Fsignal(), but it just doesn't make sense for an error
|
|
|
1207 occurring inside a signal handler to be restartable, considering
|
|
|
1208 that anything could happen when the error is signaled and trapped
|
|
|
1209 and considering the asynchronous nature of signal handlers. */
|
|
563
|
1210 signal_error (Qarith_error, 0, float_error_arg);
|
|
428
|
1211 }
|
|
|
1212
|
|
|
1213 /* Another idea was to replace the library function `infnan'
|
|
|
1214 where SIGILL is signaled. */
|
|
|
1215
|
|
|
1216 #endif /* FLOAT_CATCH_SIGILL */
|
|
|
1217
|
|
|
1218 /* In C++, it is impossible to determine what type matherr expects
|
|
|
1219 without some more configure magic.
|
|
|
1220 We shouldn't be using matherr anyways - it's a non-standard SYSVism. */
|
|
|
1221 #if defined (HAVE_MATHERR) && !defined(__cplusplus)
|
|
|
1222 int
|
|
|
1223 matherr (struct exception *x)
|
|
|
1224 {
|
|
|
1225 Lisp_Object args;
|
|
|
1226 if (! in_float)
|
|
|
1227 /* Not called from emacs-lisp float routines; do the default thing. */
|
|
|
1228 return 0;
|
|
|
1229
|
|
|
1230 /* if (!strcmp (x->name, "pow")) x->name = "expt"; */
|
|
|
1231
|
|
|
1232 args = Fcons (build_string (x->name),
|
|
|
1233 Fcons (make_float (x->arg1),
|
|
|
1234 ((in_float == 2)
|
|
|
1235 ? Fcons (make_float (x->arg2), Qnil)
|
|
|
1236 : Qnil)));
|
|
|
1237 switch (x->type)
|
|
|
1238 {
|
|
|
1239 case DOMAIN: Fsignal (Qdomain_error, args); break;
|
|
|
1240 case SING: Fsignal (Qsingularity_error, args); break;
|
|
|
1241 case OVERFLOW: Fsignal (Qoverflow_error, args); break;
|
|
|
1242 case UNDERFLOW: Fsignal (Qunderflow_error, args); break;
|
|
|
1243 default: Fsignal (Qarith_error, args); break;
|
|
|
1244 }
|
|
|
1245 return 1; /* don't set errno or print a message */
|
|
|
1246 }
|
|
|
1247 #endif /* HAVE_MATHERR */
|
|
|
1248
|
|
|
1249 void
|
|
|
1250 init_floatfns_very_early (void)
|
|
|
1251 {
|
|
|
1252 # ifdef FLOAT_CATCH_SIGILL
|
|
613
|
1253 EMACS_SIGNAL (SIGILL, float_error);
|
|
428
|
1254 # endif
|
|
|
1255 in_float = 0;
|
|
|
1256 }
|
|
|
1257
|
|
|
1258 void
|
|
|
1259 syms_of_floatfns (void)
|
|
|
1260 {
|
|
442
|
1261 INIT_LRECORD_IMPLEMENTATION (float);
|
|
428
|
1262
|
|
|
1263 /* Trig functions. */
|
|
|
1264
|
|
|
1265 DEFSUBR (Facos);
|
|
|
1266 DEFSUBR (Fasin);
|
|
|
1267 DEFSUBR (Fatan);
|
|
|
1268 DEFSUBR (Fcos);
|
|
|
1269 DEFSUBR (Fsin);
|
|
|
1270 DEFSUBR (Ftan);
|
|
|
1271
|
|
|
1272 /* Bessel functions */
|
|
|
1273
|
|
|
1274 #if 0
|
|
|
1275 DEFSUBR (Fbessel_y0);
|
|
|
1276 DEFSUBR (Fbessel_y1);
|
|
|
1277 DEFSUBR (Fbessel_yn);
|
|
|
1278 DEFSUBR (Fbessel_j0);
|
|
|
1279 DEFSUBR (Fbessel_j1);
|
|
|
1280 DEFSUBR (Fbessel_jn);
|
|
|
1281 #endif /* 0 */
|
|
|
1282
|
|
|
1283 /* Error functions. */
|
|
|
1284
|
|
|
1285 #if 0
|
|
|
1286 DEFSUBR (Ferf);
|
|
|
1287 DEFSUBR (Ferfc);
|
|
|
1288 DEFSUBR (Flog_gamma);
|
|
|
1289 #endif /* 0 */
|
|
|
1290
|
|
|
1291 /* Root and Log functions. */
|
|
|
1292
|
|
|
1293 DEFSUBR (Fexp);
|
|
|
1294 DEFSUBR (Fexpt);
|
|
|
1295 DEFSUBR (Flog);
|
|
|
1296 DEFSUBR (Flog10);
|
|
|
1297 DEFSUBR (Fsqrt);
|
|
|
1298 DEFSUBR (Fcube_root);
|
|
|
1299
|
|
|
1300 /* Inverse trig functions. */
|
|
|
1301
|
|
|
1302 DEFSUBR (Facosh);
|
|
|
1303 DEFSUBR (Fasinh);
|
|
|
1304 DEFSUBR (Fatanh);
|
|
|
1305 DEFSUBR (Fcosh);
|
|
|
1306 DEFSUBR (Fsinh);
|
|
|
1307 DEFSUBR (Ftanh);
|
|
|
1308
|
|
|
1309 /* Rounding functions */
|
|
|
1310
|
|
|
1311 DEFSUBR (Fabs);
|
|
|
1312 DEFSUBR (Ffloat);
|
|
|
1313 DEFSUBR (Flogb);
|
|
|
1314 DEFSUBR (Fceiling);
|
|
|
1315 DEFSUBR (Ffloor);
|
|
|
1316 DEFSUBR (Fround);
|
|
|
1317 DEFSUBR (Ftruncate);
|
|
|
1318
|
|
|
1319 /* Float-rounding functions. */
|
|
|
1320
|
|
|
1321 DEFSUBR (Ffceiling);
|
|
|
1322 DEFSUBR (Fffloor);
|
|
|
1323 DEFSUBR (Ffround);
|
|
|
1324 DEFSUBR (Fftruncate);
|
|
|
1325 }
|
|
|
1326
|
|
|
1327 void
|
|
|
1328 vars_of_floatfns (void)
|
|
|
1329 {
|
|
|
1330 Fprovide (intern ("lisp-float-type"));
|
|
|
1331 }
|
