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1 ;;; -*- mode: lisp -*-
2 ;;; Copyright (c) 2005--2007, by A.J. Rossini <blindglobe@gmail.com>
3 ;;; See COPYRIGHT file for any additional restrictions (BSD license).
4 ;;; Since 1991, ANSI was finally finished. Edited for ANSI Common Lisp.
6 ;;; lsfloat -- Floating point specs and transcendental functions
7 ;;;
8 ;;; Copyright (c) 1991, by Luke Tierney. Permission is granted for
9 ;;; unrestricted use.
10 ;;;
11 ;;; Common Lisp allows for four different floating point types that need
12 ;;; not be distinct. For statistical work, the type I prefer to use is
13 ;;; the one that is closest to a C double. This type is named stat-float.
14 ;;; By setting the variable *read-default-float-format* to this type, you
15 ;;; insure that data entered as floating point data is read in with this
16 ;;; type. The problem arises with data read as integers that is passed to
17 ;;; a transcendental, like sqrt. Floating point contagion rules say these
18 ;;; integers are to be converted to type single-float. Unless single-float
19 ;;; is equivalent to C double, as it is in Mac CL and KCL, this is not
20 ;;; what I want. Hence this file redefines the transcendentals to first
21 ;;; coerce their arguments to stat-float before applying the built-in
22 ;;; functions.
23 ;;;
24 ;;; No actual modifications to the transcendentals are needed if
25 ;;; single-float is the same as stat-float. The feature
26 ;;; :stat-float-is-double-float is used to indicate this.
27 ;;;
28 ;;; KCL NOTE:
29 ;;; In (A)KCL the type short-float corresponds to C float and the types
30 ;;; single-float, double-float and long-float correspond to C double.
31 ;;; But in the implementation of the transcendentals (A)KCL coerces
32 ;;; rationals to short-float, not single-float. CLtL1 is a little vague
33 ;;; on this (it talks about "single precision") but CLtL2 clarifies that
34 ;;; rationals should produce single-float results. So (A)KCL is wrong, at
35 ;;; least relative to the clarification in CLtL2. I therefore decided
36 ;;; to fix (A)KCL in files c/num_sfun.c and lsp/numlib.lsp. If these
37 ;;; fixes are applied, the feature :stat-float-is-double-float should be
38 ;;; defined.
41 ;;; ======== From the CLHS ==========
42 ;;
43 ;; Type SHORT-FLOAT, SINGLE-FLOAT, DOUBLE-FLOAT, LONG-FLOAT
44 ;;
45 ;; Supertypes:
46 ;;
47 ;; short-float: short-float, float, real, number, t
48 ;;
49 ;;
50 ;; single-float: single-float, float, real, number, t
51 ;;
52 ;; double-float: double-float, float, real, number, t
53 ;;
54 ;; long-float: long-float, float, real, number, t
55 ;;
56 ;; Description: For the four defined subtypes of type float, it is true
57 ;; that intermediate between the type short-float and the type long-float
58 ;; are the type single-float and the type double-float. The precise
59 ;; definition of these categories is implementation-defined. The
60 ;; precision (measured in ``bits'', computed as p log 2b) and the
61 ;; exponent size (also measured in ``bits,'' computed as log 2(n+1),
62 ;; where n is the maximum exponent value) is recommended to be at least
63 ;; as great as the values in the next figure. Each of the defined
64 ;; subtypes of type float might or might not have a minus zero.
65 ;;
66 ;;
67 ;; Format Minimum Precision Minimum Exponent Size
68 ;; ----------
69 ;; Short 13 bits 5 bits
70 ;; Single 24 bits 8 bits
71 ;; Double 50 bits 8 bits
72 ;; Long 50 bits 8 bits
73 ;;
74 ;; Figure 12-12. Recommended Minimum Floating-Point Precision and Exponent Size
75 ;;
76 ;; There can be fewer than four internal representations for floats. If
77 ;; there are fewer distinct representations, the following rules apply:
78 ;;
79 ;; If there is only one, it is the type single-float. In this
80 ;; representation, an object is simultaneously of types single-float,
81 ;; double-float, short-float, and long-float.
82 ;;
83 ;; Two internal representations can be arranged in either of the
84 ;; following ways:
85 ;;
86 ;; Two types are provided: single-float and short-float. An object is
87 ;; simultaneously of types single-float, double-float, and long-float.
88 ;;
89 ;; Two types are provided: single-float and double-float. An object is
90 ;; simultaneously of types single-float and short-float, or double-float
91 ;; and long-float.
92 ;;
93 ;; Three internal representations can be arranged in either of the
94 ;; following ways:
95 ;;
96 ;; Three types are provided: short-float, single-float, and
97 ;; double-float. An object can simultaneously be of type double-float and
98 ;; long-float.
99 ;;
100 ;; Three types are provided: single-float, double-float, and
101 ;; long-float. An object can simultaneously be of types single-float and
102 ;; short-float.
104 ;;; Package Setup
111 machine-epsilon base-float makedouble
113 make-base-trans-fun-2 make-base-trans-fun
115 BASE-LOG BASE-EXP BASE-EXPT BASE-SQRT BASE-SIN BASE-COS
116 BASE-TAN BASE-ASIN BASE-ACOS BASE-ATAN BASE-SINH
117 BASE-COSH BASE-TANH BASE-ASINH BASE-ACOSH BASE-ATANH
118 BASE-ABS BASE-PHASE BASE-FFLOOR BASE-FCEILING BASE-FTRUNCATE
119 BASE-FROUND BASE-SIGNUM BASE-CIS))
123 ;; This should technically be conditionalized to the Lisp
124 ;; implementation, i.e.
128 ;; etc... the above need to be verified!
130 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
131 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
132 ;;;;
133 ;;;; Constants determining default floating point type for statistical
134 ;;;; operations. This type generally corresponds to a C double.
135 ;;;;
136 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
137 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
139 ;; Why do we do this instead of defparameter? mostly to allow for doc
140 ;; defs as well as to minimize dereferencing mistakes.
149 ;(defparameter +stat-float-typing+ 'long-float)
150 ;(defparameter +stat-cfloat-typing+ '(complex long-float))
151 ;(defparameter +stat-float-template+ 0.d0)
165 ;;; FIX-BASE-DOC adds note about modification to the end of the
166 ;;; documentation string argument.
169 "~a~%Modified to coerce arguments(s) to stat-float or stat-cfloat."
172 ;;; FIX-BASE-FUN-DOC fixes documentation of SYM and installs in BASE-SYM
177 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
178 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
179 ;;;;
180 ;;;; Functions and Macros for modifying functions to coerce to standard
181 ;;;; floating point type.
182 ;;;;
183 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
184 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
186 ;;; FFIX - coerces its arguments to standard real or complex floating
187 ;;; point number if needed.
188 #-stat-float-is-double-float
194 #+stat-float-is-double-float
197 ;;; MAKEDOUBLE coerces its argument to the standard floating point
198 ;;; type specified by +stat-float-template+
202 ;; Why doesn't this optimization work?
203 ;; #+stat-float-is-double-float
204 ;; (eval-when (compile)
205 ;; (proclaim '(function makedouble (t) long-float)))
207 ;;;
208 ;;; MAKE-BASE-TRANS-FUN Macro for re-defining one argument transcendental
209 ;;; functions
210 ;;;
217 ,@doc-list
221 #+:stat-float-is-double-float
228 ;;;
229 ;;; MAKE-BASE-TRANS-FUN-2 Macro for re-defining transcendental functions
230 ;;; with an optional second argument
231 ;;;
238 ,@doc-list
242 #+:stat-float-is-double-float
248 ;;;
249 ;;; Modified base functions to coerce to standard floating point type
250 ;;;
253 ;;; BASE-FLOAT
259 #+:stat-float-is-double-float
262 ;;; BASE-EXPT
271 #+:stat-float-is-double-float
274 ;;; Others