| 1 | ;;; -*- Mode: Lisp; Package: CCL -*- |
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| 2 | ;;; |
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| 3 | ;;; Copyright (C) 2009 Clozure Associates |
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| 4 | ;;; Copyright (C) 1994-2001 Digitool, Inc |
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| 5 | ;;; This file is part of Clozure CL. |
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| 6 | ;;; |
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| 7 | ;;; Clozure CL is licensed under the terms of the Lisp Lesser GNU Public |
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| 8 | ;;; License , known as the LLGPL and distributed with Clozure CL as the |
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| 9 | ;;; file "LICENSE". The LLGPL consists of a preamble and the LGPL, |
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| 10 | ;;; which is distributed with Clozure CL as the file "LGPL". Where these |
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| 11 | ;;; conflict, the preamble takes precedence. |
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| 12 | ;;; |
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| 13 | ;;; Clozure CL is referenced in the preamble as the "LIBRARY." |
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| 14 | ;;; |
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| 15 | ;;; The LLGPL is also available online at |
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| 16 | ;;; http://opensource.franz.com/preamble.html |
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| 17 | |
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| 18 | ;;; |
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| 19 | ;;; level-0;l0-numbers.lisp |
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| 20 | |
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| 21 | (in-package "CCL") |
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| 22 | |
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| 23 | (eval-when (:compile-toplevel :execute) |
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| 24 | (require "ARCH") |
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| 25 | (require "LISPEQU") |
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| 26 | (require "NUMBER-MACROS") |
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| 27 | (require "NUMBER-CASE-MACRO") |
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| 28 | |
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| 29 | |
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| 30 | |
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| 31 | (defvar *dfloat-dops* '((* . %double-float*-2!)(/ . %double-float/-2!) |
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| 32 | (+ . %double-float+-2!)(- . %double-float--2!))) |
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| 33 | |
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| 34 | (defvar *sfloat-dops* '((* . %short-float*-2!)(/ . %short-float/-2!) |
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| 35 | (+ . %short-float+-2!)(- . %short-float--2!))) |
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| 36 | |
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| 37 | (defmacro dfloat-rat (op x y &optional (destructive-op (cdr (assq op *dfloat-dops*)))) |
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| 38 | (if destructive-op |
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| 39 | (let ((f2 (gensym))) |
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| 40 | `(let ((,f2 (%double-float ,y (%make-dfloat)))) |
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| 41 | (,destructive-op ,x ,f2 ,f2))) |
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| 42 | `(,op (the double-float ,x) (the double-float (%double-float ,y))))) |
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| 43 | |
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| 44 | (defmacro rat-dfloat (op x y &optional (destructive-op (cdr (assq op *dfloat-dops*)))) |
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| 45 | (if destructive-op |
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| 46 | (let ((f1 (gensym))) |
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| 47 | `(let ((,f1 (%double-float ,x (%make-dfloat)))) |
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| 48 | (,destructive-op ,f1 ,y ,f1))) |
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| 49 | `(,op (the double-float (%double-float ,x)) (the double-float ,y)))) |
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| 50 | |
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| 51 | (defmacro sfloat-rat (op x y &optional (destructive-op (cdr (assq op *sfloat-dops*)))) |
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| 52 | (let* ((use-destructive-op |
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| 53 | (target-word-size-case |
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| 54 | (32 destructive-op) |
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| 55 | (64 nil)))) |
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| 56 | (if use-destructive-op |
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| 57 | (let ((f2 (gensym))) |
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| 58 | `(let ((,f2 (%short-float ,y (%make-sfloat)))) |
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| 59 | (,destructive-op ,x ,f2 ,f2))) |
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| 60 | `(,op (the short-float ,x) (the short-float (%short-float ,y)))))) |
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| 61 | |
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| 62 | (defmacro rat-sfloat (op x y &optional (destructive-op (cdr (assq op *sfloat-dops*)))) |
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| 63 | (let* ((use-destructive-op |
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| 64 | (target-word-size-case |
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| 65 | (32 destructive-op) |
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| 66 | (64 nil)))) |
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| 67 | (if use-destructive-op |
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| 68 | (let ((f1 (gensym))) |
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| 69 | `(let ((,f1 (%short-float ,x (%make-sfloat)))) |
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| 70 | (,destructive-op ,f1 ,y ,f1))) |
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| 71 | `(,op (the short-float (%short-float ,x)) (the short-float ,y))))) |
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| 72 | |
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| 73 | |
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| 74 | |
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| 75 | |
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| 76 | |
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| 77 | (declaim (inline %make-complex %make-ratio)) |
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| 78 | (declaim (inline canonical-complex)) |
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| 79 | (declaim (inline build-ratio)) |
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| 80 | (declaim (inline maybe-truncate))) |
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| 81 | |
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| 82 | |
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| 83 | |
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| 84 | (defun %make-complex (realpart imagpart) |
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| 85 | (gvector :complex realpart imagpart)) |
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| 86 | |
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| 87 | (defun %make-ratio (numerator denominator) |
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| 88 | (gvector :ratio numerator denominator)) |
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| 89 | |
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| 90 | |
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| 91 | |
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| 92 | ; this is no longer used |
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| 93 | (defun %integer-signum (num) |
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| 94 | (if (fixnump num) |
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| 95 | (%fixnum-signum num) |
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| 96 | ; there is no such thing as bignum zero we hope |
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| 97 | (if (bignum-minusp num) -1 1))) |
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| 98 | |
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| 99 | |
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| 100 | ; Destructive primitives. |
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| 101 | (macrolet ((defdestructive-df-op (non-destructive-name destructive-name op) |
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| 102 | `(progn |
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| 103 | (defun ,non-destructive-name (x y) |
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| 104 | (,destructive-name x y (%make-dfloat))) |
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| 105 | (defun ,destructive-name (x y result) |
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| 106 | (declare (double-float x y result)) |
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| 107 | (%setf-double-float result (the double-float (,op x y))))))) |
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| 108 | (defdestructive-df-op %double-float+-2 %double-float+-2! +) |
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| 109 | (defdestructive-df-op %double-float--2 %double-float--2! -) |
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| 110 | (defdestructive-df-op %double-float*-2 %double-float*-2! *) |
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| 111 | (defdestructive-df-op %double-float/-2 %double-float/-2! /)) |
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| 112 | |
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| 113 | #-64-bit-target |
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| 114 | (macrolet ((defdestructive-sf-op (non-destructive-name destructive-name op) |
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| 115 | `(progn |
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| 116 | (defun ,non-destructive-name (x y) |
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| 117 | (,destructive-name x y (%make-sfloat))) |
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| 118 | (defun ,destructive-name (x y result) |
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| 119 | (declare (short-float x y result)) |
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| 120 | (%setf-short-float result (the short-float (,op x y))))))) |
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| 121 | (defdestructive-sf-op %short-float+-2 %short-float+-2! +) |
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| 122 | (defdestructive-sf-op %short-float--2 %short-float--2! -) |
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| 123 | (defdestructive-sf-op %short-float*-2 %short-float*-2! *) |
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| 124 | (defdestructive-sf-op %short-float/-2 %short-float/-2! /)) |
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| 125 | |
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| 126 | |
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| 127 | (defun %negate (x) |
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| 128 | (number-case x |
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| 129 | (fixnum (- (the fixnum x))) |
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| 130 | (double-float (%double-float-negate! x (%make-dfloat))) |
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| 131 | (short-float |
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| 132 | #+32-bit-target (%short-float-negate! x (%make-sfloat)) |
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| 133 | #+64-bit-target (%short-float-negate x)) |
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| 134 | (bignum (negate-bignum x)) |
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| 135 | (ratio (%make-ratio (%negate (%numerator x)) (%denominator x))) |
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| 136 | (complex (%make-complex (%negate (%realpart X))(%negate (%imagpart X))) ))) |
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| 137 | |
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| 138 | (defun %double-float-zerop (n) |
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| 139 | (zerop (the double-float n))) |
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| 140 | |
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| 141 | (defun %short-float-zerop (n) |
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| 142 | (zerop (the single-float n))) |
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| 143 | |
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| 144 | (defun zerop (number) |
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| 145 | "Is this number zero?" |
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| 146 | (number-case number |
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| 147 | (integer (eq number 0)) |
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| 148 | (short-float (%short-float-zerop number)) |
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| 149 | (double-float (%double-float-zerop number)) |
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| 150 | (ratio nil) |
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| 151 | (complex |
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| 152 | (number-case (%realpart number) |
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| 153 | (short-float (and (%short-float-zerop (%realpart number)) |
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| 154 | (%short-float-zerop (%imagpart number)))) |
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| 155 | (double-float (and (%double-float-zerop (%realpart number)) |
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| 156 | (%double-float-zerop (%imagpart number)))) |
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| 157 | (t (and (eql 0 (%realpart number))(eql 0 (%imagpart number)))))))) |
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| 158 | |
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| 159 | (defun %short-float-plusp (x) |
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| 160 | (> (the single-float x) 0.0f0)) |
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| 161 | |
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| 162 | (defun %double-float-plusp (x) |
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| 163 | (> (the double-float x) 0.0d0)) |
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| 164 | |
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| 165 | (defun plusp (number) |
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| 166 | "Is this real number strictly positive?" |
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| 167 | (number-case number |
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| 168 | (fixnum (%i> number 0)) |
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| 169 | (bignum (bignum-plusp number)) |
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| 170 | (short-float (%short-float-plusp number)) |
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| 171 | (double-float (%double-float-plusp number)) |
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| 172 | (ratio (plusp (%numerator number))))) |
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| 173 | |
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| 174 | |
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| 175 | (defun minusp (number) |
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| 176 | "Is this real number strictly negative?" |
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| 177 | (number-case number |
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| 178 | (fixnum (%i< number 0)) |
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| 179 | (bignum (bignum-minusp number)) |
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| 180 | (short-float (%short-float-minusp number)) |
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| 181 | (double-float (%double-float-minusp number)) |
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| 182 | (ratio (minusp (%numerator number))))) |
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| 183 | |
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| 184 | |
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| 185 | (defun oddp (n) |
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| 186 | "Is this integer odd?" |
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| 187 | (case (typecode n) |
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| 188 | (#.target::tag-fixnum (logbitp 0 (the fixnum n))) |
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| 189 | (#.target::subtag-bignum (%bignum-oddp n)) |
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| 190 | (t (report-bad-arg n 'integer)))) |
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| 191 | |
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| 192 | (defun evenp (n) |
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| 193 | "Is this integer even?" |
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| 194 | (case (typecode n) |
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| 195 | (#.target::tag-fixnum (not (logbitp 0 (the fixnum n)))) |
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| 196 | (#.target::subtag-bignum (not (%bignum-oddp n))) |
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| 197 | (t (report-bad-arg n 'integer)))) |
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| 198 | |
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| 199 | ;; expansion slightly changed |
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| 200 | (defun =-2 (x y) |
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| 201 | (number-case x |
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| 202 | (fixnum (number-case y |
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| 203 | (fixnum (eq x y)) |
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| 204 | (double-float (eq 0 (fixnum-dfloat-compare x y))) |
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| 205 | (short-float (eq 0 (fixnum-sfloat-compare x y))) |
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| 206 | ((bignum ratio) nil) |
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| 207 | (complex (and (zerop (%imagpart y)) (= x (%realpart y)))))) |
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| 208 | (double-float (number-case y ; x |
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| 209 | (double-float (= (the double-float x)(the double-float y))) ;x |
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| 210 | (short-float (with-stack-double-floats ((dy y)) |
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| 211 | (= (the double-float x) (the double-float dy)))) |
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| 212 | (fixnum (eq 0 (fixnum-dfloat-compare y x))) |
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| 213 | (bignum (eq 0 (bignum-dfloat-compare y x))) |
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| 214 | (ratio (= (rational x) y)) |
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| 215 | (complex (and (zerop (%imagpart y)) (= x (%realpart y)))))) |
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| 216 | (short-float (number-case y |
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| 217 | (short-float (= (the short-float x) (the short-float y))) |
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| 218 | (double-float (with-stack-double-floats ((dx x)) |
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| 219 | (= (the double-float dx) (the double-float y)))) |
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| 220 | (fixnum (eq 0 (fixnum-sfloat-compare y x))) |
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| 221 | (bignum (eq 0 (bignum-sfloat-compare y x))) |
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| 222 | (ratio (= (rational x) y)) |
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| 223 | (complex (and (zerop (%imagpart y)) (= x (%realpart y)))))) |
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| 224 | (bignum (number-case y |
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| 225 | (bignum (eq 0 (bignum-compare x y))) |
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| 226 | ((fixnum ratio) nil) |
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| 227 | (double-float (eq 0 (bignum-dfloat-compare x y))) |
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| 228 | (short-float (eq 0 (bignum-sfloat-compare x y))) |
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| 229 | (complex (and (zerop (%imagpart y)) (= x (%realpart y)))))) |
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| 230 | (ratio (number-case y |
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| 231 | (integer nil) |
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| 232 | (ratio |
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| 233 | (and (eql (%numerator x) (%numerator y)) |
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| 234 | (eql (%denominator x) (%denominator y)))) |
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| 235 | (float (= x (rational y))) |
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| 236 | (complex (and (zerop (%imagpart y)) (= x (%realpart y)))))) |
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| 237 | (complex (number-case y |
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| 238 | (complex (and (= (%realpart x) (%realpart y)) |
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| 239 | (= (%imagpart x) (%imagpart y)))) |
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| 240 | ((float rational) |
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| 241 | (and (zerop (%imagpart x)) (= (%realpart x) y))))))) |
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| 242 | |
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| 243 | (defun /=-2 (x y) |
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| 244 | (declare (notinline =-2)) |
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| 245 | (not (= x y))) |
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| 246 | |
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| 247 | |
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| 248 | ; true iff (< x y) is false. |
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| 249 | (defun >=-2 (x y) |
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| 250 | (declare (notinline <-2)) |
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| 251 | (not (< x y))) |
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| 252 | |
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| 253 | |
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| 254 | |
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| 255 | (defun <=-2 (x y) |
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| 256 | (declare (notinline >-2)) |
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| 257 | (not (> x y))) |
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| 258 | |
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| 259 | (defun <-2 (x y) |
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| 260 | (number-case x |
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| 261 | (fixnum (number-case y |
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| 262 | (fixnum (< (the fixnum x) (the fixnum y))) |
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| 263 | (double-float (eq -1 (fixnum-dfloat-compare x y))) |
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| 264 | (short-float (eq -1 (fixnum-sfloat-compare x y))) |
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| 265 | (bignum (bignum-plusp y)) |
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| 266 | (ratio (< x (ceiling (%numerator y)(%denominator y)))))) |
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| 267 | (double-float (number-case y ; x |
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| 268 | (double-float (< (the double-float x)(the double-float y))) ;x |
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| 269 | (short-float (with-stack-double-floats ((dy y)) |
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| 270 | (< (the double-float x) (the double-float dy)))) |
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| 271 | (fixnum (eq 1 (fixnum-dfloat-compare y x))) |
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| 272 | (bignum (eq 1 (bignum-dfloat-compare y x))) |
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| 273 | (ratio (< (rational x) y)))) |
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| 274 | (short-float (number-case y |
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| 275 | (short-float (< (the short-float x) (the short-float y))) |
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| 276 | (double-float (with-stack-double-floats ((dx x)) |
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| 277 | (< (the double-float dx) (the double-float y)))) |
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| 278 | (fixnum (eq 1 (fixnum-sfloat-compare y x))) |
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| 279 | (bignum (eq 1 (bignum-sfloat-compare y x))) |
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| 280 | (ratio (< (rational x) y)))) |
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| 281 | (bignum (number-case y |
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| 282 | (bignum (EQ -1 (bignum-compare x y))) |
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| 283 | (fixnum (not (bignum-plusp x))) |
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| 284 | (ratio (< x (ceiling (%numerator y)(%denominator y)))) |
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| 285 | (double-float (eq -1 (bignum-dfloat-compare x y))) |
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| 286 | (short-float (eq -1 (bignum-sfloat-compare x y))))) |
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| 287 | (ratio (number-case y |
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| 288 | (integer (< (floor (%numerator x)(%denominator x)) y)) |
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| 289 | (ratio |
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| 290 | (< (* (%numerator (the ratio x)) |
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| 291 | (%denominator (the ratio y))) |
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| 292 | (* (%numerator (the ratio y)) |
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| 293 | (%denominator (the ratio x))))) |
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| 294 | (float (< x (rational y))))))) |
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| 295 | |
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| 296 | |
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| 297 | |
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| 298 | (defun >-2 (x y) |
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| 299 | ;(declare (optimize (speed 3)(safety 0))) |
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| 300 | (number-case x |
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| 301 | (fixnum (number-case y |
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| 302 | (fixnum (> (the fixnum x) (the fixnum y))) |
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| 303 | (bignum (not (bignum-plusp y))) |
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| 304 | (double-float (eq 1 (fixnum-dfloat-compare x y))) |
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| 305 | (short-float (eq 1 (fixnum-sfloat-compare x y))) |
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| 306 | ;; or (> (* x denom) num) ? |
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| 307 | (ratio (> x (floor (%numerator y) (%denominator y)))))) |
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| 308 | (double-float (number-case y |
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| 309 | (double-float (> (the double-float x) (the double-float y))) |
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| 310 | (short-float (with-stack-double-floats ((dy y)) |
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| 311 | (> (the double-float x) (the double-float dy)))) |
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| 312 | (fixnum (eq -1 (fixnum-dfloat-compare y x))) |
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| 313 | (bignum (eq -1 (bignum-dfloat-compare y x))) |
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| 314 | (ratio (> (rational x) y)))) |
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| 315 | (short-float (number-case y |
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| 316 | (short-float (> (the short-float x) (the short-float y))) |
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| 317 | (double-float (with-stack-double-floats ((dx x)) |
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| 318 | (> (the double-float dx) (the double-float y)))) |
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| 319 | (fixnum (eq -1 (fixnum-sfloat-compare y x))) |
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| 320 | (bignum (eq -1 (bignum-sfloat-compare y x))) |
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| 321 | (ratio (> (rational x) y)))) |
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| 322 | (bignum (number-case y |
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| 323 | (fixnum (bignum-plusp x)) |
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| 324 | (bignum (eq 1 (bignum-compare x y))) |
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| 325 | ;; or (> (* x demon) num) |
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| 326 | (ratio (> x (floor (%numerator y) (%denominator y)))) |
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| 327 | (double-float (eq 1 (bignum-dfloat-compare x y))) |
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| 328 | (short-float (eq 1 (bignum-sfloat-compare x y))))) |
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| 329 | (ratio (number-case y |
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| 330 | ;; or (> num (* y denom)) |
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| 331 | (integer (> (ceiling (%numerator x) (%denominator x)) y)) |
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| 332 | (ratio |
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| 333 | (> (* (%numerator (the ratio x)) |
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| 334 | (%denominator (the ratio y))) |
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| 335 | (* (%numerator (the ratio y)) |
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| 336 | (%denominator (the ratio x))))) |
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| 337 | (float (> x (rational y))))))) |
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| 338 | |
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| 339 | |
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| 340 | ; t if any bits set after exp (unbiased) |
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| 341 | (defun hi-lo-fraction-p (hi lo exp) |
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| 342 | (declare (fixnum hi lo exp)) |
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| 343 | (if (> exp 24) |
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| 344 | (not (eql 0 (%ilogand lo (%ilsr (- exp 25) #xfffffff)))) |
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| 345 | (or (not (zerop lo))(not (eql 0 (%ilogand hi (%ilsr exp #x1ffffff))))))) |
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| 346 | |
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| 347 | |
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| 348 | |
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| 349 | (defun negate-hi-lo (hi lo) |
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| 350 | (setq hi (%ilogxor hi #x3ffffff)) |
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| 351 | (if (eq 0 lo) |
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| 352 | (setq hi (+ hi 1)) |
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| 353 | (setq lo (+ (%ilogxor lo #xfffffff) 1))) |
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| 354 | (values hi lo)) |
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| 355 | |
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| 356 | |
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| 357 | |
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| 358 | (defun fixnum-dfloat-compare (int dfloat) |
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| 359 | (declare (double-float dfloat) (fixnum int)) |
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| 360 | (if (and (eq int 0)(= dfloat 0.0d0)) |
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| 361 | 0 |
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| 362 | (with-stack-double-floats ((d1 int)) |
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| 363 | (locally (declare (double-float d1)) |
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| 364 | (if (eq int (%truncate-double-float->fixnum d1)) |
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| 365 | (cond ((< d1 dfloat) -1) |
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| 366 | ((= d1 dfloat) 0) |
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| 367 | (t 1)) |
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| 368 | ;; Whatever we do here should have the effect |
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| 369 | ;; of comparing the integer to the result of calling |
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| 370 | ;; RATIONAL on the float. We could probably |
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| 371 | ;; skip the call to RATIONAL in more cases, |
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| 372 | ;; but at least check the obvious ones here |
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| 373 | ;; (e.g. different signs) |
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| 374 | (multiple-value-bind (mantissa exponent sign) |
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| 375 | (integer-decode-double-float dfloat) |
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| 376 | (declare (type (integer -1 1) sign) |
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| 377 | (fixnum exponent)) |
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| 378 | (cond ((zerop int) |
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| 379 | (- sign)) |
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| 380 | ((and (< int 0) (eql sign 1)) -1) |
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| 381 | ((and (> int 0) (eql sign -1)) 1) |
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| 382 | (t |
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| 383 | ;; See RATIONAL. Can probably avoid this if |
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| 384 | ;; magnitudes are clearly dissimilar. |
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| 385 | (if (= sign -1) (setq mantissa (- mantissa))) |
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| 386 | (let* ((rat (if (< exponent 0) |
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| 387 | (/ mantissa (ash 1 (the fixnum (- exponent)))) |
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| 388 | (ash mantissa exponent)))) |
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| 389 | (if (< int rat) |
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| 390 | -1 |
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| 391 | (if (eq int rat) |
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| 392 | 0 |
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| 393 | 1))))))))))) |
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| 394 | |
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| 395 | |
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| 396 | |
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| 397 | (defun fixnum-sfloat-compare (int sfloat) |
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| 398 | (declare (short-float sfloat) (fixnum int)) |
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| 399 | (if (and (eq int 0)(= sfloat 0.0s0)) |
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| 400 | 0 |
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| 401 | (#+32-bit-target target::with-stack-short-floats #+32-bit-target ((s1 int)) |
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| 402 | #-32-bit-target let* #-32-bit-target ((s1 (%int-to-sfloat int))) |
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| 403 | (locally |
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| 404 | (declare (short-float s1)) |
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| 405 | (if (eq (%truncate-short-float->fixnum s1) int) |
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| 406 | (cond ((< s1 sfloat) -1) |
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| 407 | ((= s1 sfloat) 0) |
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| 408 | (t 1)) |
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| 409 | ;; Whatever we do here should have the effect |
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| 410 | ;; of comparing the integer to the result of calling |
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| 411 | ;; RATIONAL on the float. We could probably |
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| 412 | ;; skip the call to RATIONAL in more cases, |
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| 413 | ;; but at least check the obvious ones here |
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| 414 | ;; (e.g. different signs) |
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| 415 | (multiple-value-bind (mantissa exponent sign) |
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| 416 | (integer-decode-short-float sfloat) |
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| 417 | (declare (type (integer -1 1) sign) |
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| 418 | (fixnum exponent)) |
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| 419 | (cond ((zerop int) |
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| 420 | (- sign)) |
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| 421 | ((and (< int 0) (eql sign 1)) -1) |
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| 422 | ((and (> int 0) (eql sign -1)) 1) |
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| 423 | (t |
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| 424 | ;; See RATIONAL. Can probably avoid this if |
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| 425 | ;; magnitudes are clearly dissimilar. |
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| 426 | (if (= sign -1) (setq mantissa (- mantissa))) |
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| 427 | (let* ((rat (if (< exponent 0) |
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| 428 | (/ mantissa (ash 1 (the fixnum (- exponent)))) |
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| 429 | (ash mantissa exponent)))) |
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| 430 | (if (< int rat) |
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| 431 | -1 |
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| 432 | (if (eq int rat) |
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| 433 | 0 |
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| 434 | 1))))))))))) |
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| 435 | |
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| 436 | |
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| 437 | |
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| 438 | ;;; lotta stuff to avoid making a rational from a float |
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| 439 | ;;; returns -1 less, 0 equal, 1 greater |
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| 440 | (defun bignum-dfloat-compare (int float) |
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| 441 | (cond |
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| 442 | ((and (eq int 0)(= float 0.0d0)) 0) |
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| 443 | (t |
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| 444 | (let* ((fminus (%double-float-minusp float)) |
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| 445 | (iminus (minusp int)) |
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| 446 | (gt (if iminus -1 1))) |
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| 447 | (declare (fixnum gt)) |
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| 448 | (if (neq fminus iminus) |
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| 449 | gt ; if different signs, done |
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| 450 | (let ((intlen (integer-length int)) |
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| 451 | (exp (- (the fixnum (%double-float-exp float)) 1022))) |
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| 452 | (declare (fixnum intlen exp)) |
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| 453 | (cond |
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| 454 | ((and (not fminus) (< intlen exp)) -1) |
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| 455 | ((> intlen exp) gt) ; if different exp, done |
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| 456 | ((and fminus (or (< (1+ intlen) exp) |
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| 457 | (and (= (1+ intlen) exp) |
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| 458 | (neq (one-bignum-factor-of-two int) intlen)))) |
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| 459 | ;(print 'zow) |
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| 460 | (the fixnum (- gt))) ; ; integer-length is strange for neg powers of 2 |
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| 461 | (t (multiple-value-bind (hi lo)(fixnum-decode-float float) |
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| 462 | (declare (fixnum hi lo)) |
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| 463 | (when fminus (multiple-value-setq (hi lo)(negate-hi-lo hi lo))) |
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| 464 | (let* ((sz 26) ; exp > 28 always |
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| 465 | (pos (- exp 25)) |
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| 466 | (big-bits (%ldb-fixnum-from-bignum int sz pos))) |
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| 467 | (declare (fixnum pos big-bits sz)) |
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| 468 | ;(print (list big-bits hi sz pos)) |
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| 469 | (cond |
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| 470 | ((< big-bits hi) -1) |
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| 471 | ((> big-bits hi) 1) |
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| 472 | (t (let* ((sz (min (- exp 25) 28)) |
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| 473 | (pos (- exp 25 sz)) ; ? |
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| 474 | (ilo (if (< exp 53) (ash lo (- exp 53)) lo)) |
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| 475 | (big-bits (%ldb-fixnum-from-bignum int sz pos))) |
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| 476 | (declare (fixnum pos sz ilo big-bits)) |
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| 477 | ;(PRINT (list big-bits ilo)) |
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| 478 | (cond |
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| 479 | ((< big-bits ilo) -1) |
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| 480 | ((> big-bits ilo) 1) |
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| 481 | ((eq exp 53) 0) |
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| 482 | ((< exp 53) |
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| 483 | (if (not (hi-lo-fraction-p hi lo exp)) 0 -1)) ; -1 if pos |
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| 484 | (t (if (%i< (one-bignum-factor-of-two int) (- exp 53)) 1 0))))))) |
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| 485 | ))))))))) |
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| 486 | |
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| 487 | |
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| 488 | |
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| 489 | ;;; I don't know if it's worth doing a more "real" version of this. |
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| 490 | (defun bignum-sfloat-compare (int float) |
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| 491 | (with-stack-double-floats ((df float)) |
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| 492 | (bignum-dfloat-compare int df))) |
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| 493 | |
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| 494 | ;;;; Canonicalization utilities: |
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| 495 | |
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| 496 | ;;; CANONICAL-COMPLEX -- Internal |
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| 497 | ;;; |
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| 498 | ;;; If imagpart is 0, return realpart, otherwise make a complex. This is |
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| 499 | ;;; used when we know that realpart and imagpart are the same type, but |
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| 500 | ;;; rational canonicalization might still need to be done. |
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| 501 | ;;; |
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| 502 | |
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| 503 | (defun canonical-complex (realpart imagpart) |
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| 504 | (if (eql imagpart 0) |
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| 505 | realpart |
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| 506 | (%make-complex realpart imagpart))) |
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| 507 | |
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| 508 | |
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| 509 | |
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| 510 | |
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| 511 | (defun +-2 (x y) |
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| 512 | (number-case x |
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| 513 | (fixnum (number-case y |
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| 514 | (fixnum (+ (the fixnum x) (the fixnum y))) |
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| 515 | (double-float (rat-dfloat + x y)) |
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| 516 | (short-float (rat-sfloat + x y)) |
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| 517 | (bignum (add-bignum-and-fixnum y x)) |
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| 518 | (complex (complex (+ x (%realpart y)) |
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| 519 | (%imagpart y))) |
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| 520 | (ratio (let* ((dy (%denominator y)) |
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| 521 | (n (+ (* x dy) (%numerator y)))) |
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| 522 | (%make-ratio n dy))))) |
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| 523 | (double-float (number-case y |
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| 524 | (double-float (+ (the double-float x) (the double-float y))) |
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| 525 | (short-float (with-stack-double-floats ((dy y)) |
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| 526 | (+ (the double-float x) (the double-float dy)))) |
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| 527 | (rational (dfloat-rat + x y)) |
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| 528 | (complex (complex (+ x (%realpart y)) |
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| 529 | (%imagpart y))))) |
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| 530 | (short-float (number-case y |
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| 531 | (short-float (+ (the short-float x) (the short-float y))) |
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| 532 | (double-float (with-stack-double-floats ((dx x)) |
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| 533 | (+ (the double-float dx) (the double-float y)))) |
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| 534 | (rational (sfloat-rat + x y)) |
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| 535 | (complex (complex (+ x (%realpart y)) |
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| 536 | (%imagpart y))))) |
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| 537 | (bignum (number-case y |
|---|
| 538 | (bignum (add-bignums x y)) |
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| 539 | (fixnum (add-bignum-and-fixnum x y)) |
|---|
| 540 | (double-float (rat-dfloat + x y)) |
|---|
| 541 | (short-float (rat-sfloat + x y)) |
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| 542 | (complex (complex (+ x (realpart y)) |
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| 543 | (%imagpart y))) |
|---|
| 544 | (ratio |
|---|
| 545 | (let* ((dy (%denominator y)) |
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| 546 | (n (+ (* x dy) (%numerator y)))) |
|---|
| 547 | (%make-ratio n dy))))) |
|---|
| 548 | (complex (number-case y |
|---|
| 549 | (complex (canonical-complex (+ (%realpart x) (%realpart y)) |
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| 550 | (+ (%imagpart x) (%imagpart y)))) |
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| 551 | ((rational float) (complex (+ (%realpart x) y) (%imagpart x))))) |
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| 552 | (ratio (number-case y |
|---|
| 553 | (ratio |
|---|
| 554 | (let* ((nx (%numerator x)) |
|---|
| 555 | (dx (%denominator x)) |
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| 556 | (ny (%numerator y)) |
|---|
| 557 | (dy (%denominator y)) |
|---|
| 558 | (g1 (gcd dx dy))) |
|---|
| 559 | (if (eql g1 1) |
|---|
| 560 | (%make-ratio (+ (* nx dy) (* dx ny)) (* dx dy)) |
|---|
| 561 | (let* ((t1 (+ (* nx (truncate dy g1)) (* (truncate dx g1) ny))) |
|---|
| 562 | (g2 (gcd t1 g1)) |
|---|
| 563 | (t2 (truncate dx g1))) |
|---|
| 564 | (cond ((eql t1 0) 0) |
|---|
| 565 | ((eql g2 1) (%make-ratio t1 (* t2 dy))) |
|---|
| 566 | (t |
|---|
| 567 | (let* ((nn (truncate t1 g2)) |
|---|
| 568 | (t3 (truncate dy g2)) |
|---|
| 569 | (nd (if (eql t2 1) t3 (* t2 t3)))) |
|---|
| 570 | (if (eql nd 1) nn (%make-ratio nn nd))))))))) |
|---|
| 571 | (integer |
|---|
| 572 | (let* ((dx (%denominator x)) (n (+ (%numerator x) (* y dx)))) |
|---|
| 573 | (%make-ratio n dx))) |
|---|
| 574 | (double-float (rat-dfloat + x y)) |
|---|
| 575 | (short-float (rat-sfloat + x y)) |
|---|
| 576 | (complex (complex (+ x (%realpart y)) |
|---|
| 577 | (%imagpart y))))))) |
|---|
| 578 | |
|---|
| 579 | (defun --2 (x y) |
|---|
| 580 | (number-case x |
|---|
| 581 | (fixnum (number-case y |
|---|
| 582 | (fixnum (- (the fixnum x) (the fixnum y))) |
|---|
| 583 | (double-float (rat-dfloat - x y)) |
|---|
| 584 | (short-float (rat-sfloat - x y)) |
|---|
| 585 | (bignum |
|---|
| 586 | (with-small-bignum-buffers ((bx x)) |
|---|
| 587 | (subtract-bignum bx y))) |
|---|
| 588 | (complex (complex (- x (%realpart y)) |
|---|
| 589 | (- (%imagpart y)))) |
|---|
| 590 | (ratio (let* ((dy (%denominator y)) |
|---|
| 591 | (n (- (* x dy) (%numerator y)))) |
|---|
| 592 | (%make-ratio n dy))))) |
|---|
| 593 | (double-float (number-case y |
|---|
| 594 | (double-float (- (the double-float x) (the double-float y))) |
|---|
| 595 | (short-float (with-stack-double-floats ((dy y)) |
|---|
| 596 | (- (the double-float x) (the double-float dy)))) |
|---|
| 597 | (rational (dfloat-rat - x y)) |
|---|
| 598 | (complex (complex (- x (%realpart y)) |
|---|
| 599 | (- (%imagpart y)))))) |
|---|
| 600 | (short-float (number-case y |
|---|
| 601 | (short-float (- (the short-float x) (the short-float y))) |
|---|
| 602 | (double-float (with-stack-double-floats ((dx x)) |
|---|
| 603 | (- (the double-float dx) (the double-float y)))) |
|---|
| 604 | (rational (sfloat-rat - x y)) |
|---|
| 605 | (complex (complex (- x (%realpart y)) |
|---|
| 606 | (- (%imagpart y)))))) |
|---|
| 607 | (bignum (number-case y |
|---|
| 608 | (bignum (subtract-bignum x y)) |
|---|
| 609 | (fixnum (if (eql y target::target-most-negative-fixnum) |
|---|
| 610 | (with-small-bignum-buffers ((by y)) |
|---|
| 611 | (subtract-bignum x by)) |
|---|
| 612 | (add-bignum-and-fixnum x (- y)))) |
|---|
| 613 | (double-float (rat-dfloat - x y)) |
|---|
| 614 | (short-float (rat-sfloat - x y)) |
|---|
| 615 | (complex (complex (- x (realpart y)) |
|---|
| 616 | (- (%imagpart y)))) |
|---|
| 617 | (ratio |
|---|
| 618 | (let* ((dy (%denominator y)) |
|---|
| 619 | (n (- (* x dy) (%numerator y)))) |
|---|
| 620 | (%make-ratio n dy))))) |
|---|
| 621 | (complex (number-case y |
|---|
| 622 | (complex (canonical-complex (- (%realpart x) (%realpart y)) |
|---|
| 623 | (- (%imagpart x) (%imagpart y)))) |
|---|
| 624 | ((rational float) (complex (- (%realpart x) y) (%imagpart x))))) |
|---|
| 625 | (ratio (number-case y |
|---|
| 626 | (ratio |
|---|
| 627 | (let* ((nx (%numerator x)) |
|---|
| 628 | (dx (%denominator x)) |
|---|
| 629 | (ny (%numerator y)) |
|---|
| 630 | (dy (%denominator y)) |
|---|
| 631 | (g1 (gcd dx dy))) |
|---|
| 632 | (if (eql g1 1) |
|---|
| 633 | (%make-ratio (- (* nx dy) (* dx ny)) (* dx dy)) |
|---|
| 634 | (let* ((t1 (- (* nx (truncate dy g1)) (* (truncate dx g1) ny))) |
|---|
| 635 | (g2 (gcd t1 g1)) |
|---|
| 636 | (t2 (truncate dx g1))) |
|---|
| 637 | (cond ((eql t1 0) 0) |
|---|
| 638 | ((eql g2 1) (%make-ratio t1 (* t2 dy))) |
|---|
| 639 | (t |
|---|
| 640 | (let* ((nn (truncate t1 g2)) |
|---|
| 641 | (t3 (truncate dy g2)) |
|---|
| 642 | (nd (if (eql t2 1) t3 (* t2 t3)))) |
|---|
| 643 | (if (eql nd 1) nn (%make-ratio nn nd))))))))) |
|---|
| 644 | (integer |
|---|
| 645 | (let* ((dx (%denominator x)) (n (- (%numerator x) (* y dx)))) |
|---|
| 646 | (%make-ratio n dx))) |
|---|
| 647 | (double-float (rat-dfloat - x y)) |
|---|
| 648 | (short-float (rat-sfloat - x y)) |
|---|
| 649 | (complex (complex (- x (%realpart y)) |
|---|
| 650 | (- (%imagpart y)))))))) |
|---|
| 651 | |
|---|
| 652 | |
|---|
| 653 | ;;; BUILD-RATIO -- Internal |
|---|
| 654 | ;;; |
|---|
| 655 | ;;; Given a numerator and denominator with the GCD already divided out, make |
|---|
| 656 | ;;; a canonical rational. We make the denominator positive, and check whether |
|---|
| 657 | ;;; it is 1. |
|---|
| 658 | ;;; |
|---|
| 659 | |
|---|
| 660 | (defun build-ratio (num den) |
|---|
| 661 | (if (minusp den) (setq num (- num) den (- den))) |
|---|
| 662 | (case den |
|---|
| 663 | (0 (divide-by-zero-error 'build-ratio num den)) |
|---|
| 664 | (1 num) |
|---|
| 665 | (t (%make-ratio num den)))) |
|---|
| 666 | |
|---|
| 667 | |
|---|
| 668 | |
|---|
| 669 | |
|---|
| 670 | ;;; MAYBE-TRUNCATE -- Internal |
|---|
| 671 | ;;; |
|---|
| 672 | ;;; Truncate X and Y, but bum the case where Y is 1. |
|---|
| 673 | ;;; |
|---|
| 674 | |
|---|
| 675 | |
|---|
| 676 | (defun maybe-truncate (x y) |
|---|
| 677 | (if (eql y 1) |
|---|
| 678 | x |
|---|
| 679 | (truncate x y))) |
|---|
| 680 | |
|---|
| 681 | |
|---|
| 682 | (defun *-2 (x y) |
|---|
| 683 | ;(declare (optimize (speed 3)(safety 0))) |
|---|
| 684 | (flet ((integer*ratio (x y) |
|---|
| 685 | (if (eql x 0) 0 |
|---|
| 686 | (let* ((ny (%numerator y)) |
|---|
| 687 | (dy (%denominator y)) |
|---|
| 688 | (gcd (gcd x dy))) |
|---|
| 689 | (if (eql gcd 1) |
|---|
| 690 | (%make-ratio (* x ny) dy) |
|---|
| 691 | (let ((nn (* (truncate x gcd) ny)) |
|---|
| 692 | (nd (truncate dy gcd))) |
|---|
| 693 | (if (eql nd 1) |
|---|
| 694 | nn |
|---|
| 695 | (%make-ratio nn nd))))))) |
|---|
| 696 | (complex*real (x y) |
|---|
| 697 | (canonical-complex (* (%realpart x) y) (* (%imagpart x) y)))) |
|---|
| 698 | (number-case x |
|---|
| 699 | (double-float (number-case y |
|---|
| 700 | (double-float (* (the double-float x)(the double-float y))) |
|---|
| 701 | (short-float (with-stack-double-floats ((dy y)) |
|---|
| 702 | (* (the double-float x) (the double-float dy)))) |
|---|
| 703 | (rational (dfloat-rat * x y)) |
|---|
| 704 | (complex (complex*real y x)))) |
|---|
| 705 | (short-float (number-case y |
|---|
| 706 | (double-float (with-stack-double-floats ((dx x)) |
|---|
| 707 | (* (the double-float dx) (the double-float y)))) |
|---|
| 708 | (short-float (* (the short-float x) (the short-float y))) |
|---|
| 709 | (rational (sfloat-rat * x y)) |
|---|
| 710 | (complex (complex*real y x)))) |
|---|
| 711 | (bignum (number-case y |
|---|
| 712 | (fixnum |
|---|
| 713 | (if (eql y target::target-most-negative-fixnum) |
|---|
| 714 | (with-small-bignum-buffers ((by y)) |
|---|
| 715 | (multiply-bignums x by)) |
|---|
| 716 | (multiply-bignum-and-fixnum x y))) |
|---|
| 717 | (bignum (multiply-bignums x y)) |
|---|
| 718 | (double-float (dfloat-rat * y x)) |
|---|
| 719 | (short-float (sfloat-rat * y x)) |
|---|
| 720 | (ratio (integer*ratio x y)) |
|---|
| 721 | (complex (complex*real y x)))) |
|---|
| 722 | (fixnum (number-case y |
|---|
| 723 | (bignum (if (eql x target::target-most-negative-fixnum) |
|---|
| 724 | (with-small-bignum-buffers ((bx x)) |
|---|
| 725 | (multiply-bignums y bx)) |
|---|
| 726 | (multiply-bignum-and-fixnum y x))) |
|---|
| 727 | (fixnum (multiply-fixnums (the fixnum x) (the fixnum y))) |
|---|
| 728 | (short-float (sfloat-rat * y x)) |
|---|
| 729 | (double-float (dfloat-rat * y x)) |
|---|
| 730 | (ratio (integer*ratio x y)) |
|---|
| 731 | (complex (complex*real y x)))) |
|---|
| 732 | (complex (number-case y |
|---|
| 733 | (complex (let* ((rx (%realpart x)) |
|---|
| 734 | (ix (%imagpart x)) |
|---|
| 735 | (ry (%realpart y)) |
|---|
| 736 | (iy (%imagpart y))) |
|---|
| 737 | (canonical-complex (- (* rx ry) (* ix iy)) (+ (* rx iy) (* ix ry))))) |
|---|
| 738 | (real (complex*real x y)))) |
|---|
| 739 | (ratio (number-case y |
|---|
| 740 | (ratio (let* ((nx (%numerator x)) |
|---|
| 741 | (dx (%denominator x)) |
|---|
| 742 | (ny (%numerator y)) |
|---|
| 743 | (dy (%denominator y)) |
|---|
| 744 | (g1 (gcd nx dy)) |
|---|
| 745 | (g2 (gcd dx ny))) |
|---|
| 746 | (build-ratio (* (maybe-truncate nx g1) |
|---|
| 747 | (maybe-truncate ny g2)) |
|---|
| 748 | (* (maybe-truncate dx g2) |
|---|
| 749 | (maybe-truncate dy g1))))) |
|---|
| 750 | (integer (integer*ratio y x)) |
|---|
| 751 | (double-float (rat-dfloat * x y)) |
|---|
| 752 | (short-float (rat-sfloat * x y)) |
|---|
| 753 | (complex (complex*real y x))))))) |
|---|
| 754 | |
|---|
| 755 | |
|---|
| 756 | |
|---|
| 757 | (defun integer*integer (x y &optional res) |
|---|
| 758 | (declare (ignore res)) |
|---|
| 759 | (number-case x |
|---|
| 760 | (fixnum (number-case y |
|---|
| 761 | (fixnum (* (the fixnum x) (the fixnum y))) |
|---|
| 762 | (t (multiply-bignum-and-fixnum y x)))) |
|---|
| 763 | (bignum (number-case y |
|---|
| 764 | (fixnum (multiply-bignum-and-fixnum x y)) |
|---|
| 765 | (t (multiply-bignums x y)))))) |
|---|
| 766 | |
|---|
| 767 | |
|---|
| 768 | |
|---|
| 769 | |
|---|
| 770 | |
|---|
| 771 | ;;; INTEGER-/-INTEGER -- Internal |
|---|
| 772 | ;;; |
|---|
| 773 | ;;; Divide two integers, producing a canonical rational. If a fixnum, we |
|---|
| 774 | ;;; see if they divide evenly before trying the GCD. In the bignum case, we |
|---|
| 775 | ;;; don't bother, since bignum division is expensive, and the test is not very |
|---|
| 776 | ;;; likely to suceed. |
|---|
| 777 | ;;; |
|---|
| 778 | (defun integer-/-integer (x y) |
|---|
| 779 | (if (and (typep x 'fixnum) (typep y 'fixnum)) |
|---|
| 780 | (multiple-value-bind (quo rem) (%fixnum-truncate x y) |
|---|
| 781 | (if (eql 0 rem) |
|---|
| 782 | quo |
|---|
| 783 | (let ((gcd (gcd x y))) |
|---|
| 784 | (declare (fixnum gcd)) |
|---|
| 785 | (if (eql gcd 1) |
|---|
| 786 | (build-ratio x y) |
|---|
| 787 | (build-ratio (%fixnum-truncate x gcd) (%fixnum-truncate y gcd)))))) |
|---|
| 788 | (let ((gcd (gcd x y))) |
|---|
| 789 | (if (eql gcd 1) |
|---|
| 790 | (build-ratio x y) |
|---|
| 791 | (build-ratio (truncate x gcd) (truncate y gcd)))))) |
|---|
| 792 | |
|---|
| 793 | |
|---|
| 794 | |
|---|
| 795 | (defun /-2 (x y) |
|---|
| 796 | (macrolet ((real-complex-/ (x y) |
|---|
| 797 | (let ((ry (gensym)) |
|---|
| 798 | (iy (gensym)) |
|---|
| 799 | (r (gensym)) |
|---|
| 800 | (dn (gensym))) |
|---|
| 801 | `(let* ((,ry (%realpart ,y)) |
|---|
| 802 | (,iy (%imagpart ,y))) |
|---|
| 803 | (if (> (abs ,ry) (abs ,iy)) |
|---|
| 804 | (let* ((,r (/ ,iy ,ry)) |
|---|
| 805 | (,dn (* ,ry (+ 1 (* ,r ,r))))) |
|---|
| 806 | (canonical-complex (/ ,x ,dn) |
|---|
| 807 | (/ (- (* ,x ,r)) ,dn))) |
|---|
| 808 | (let* ((,r (/ ,ry ,iy)) |
|---|
| 809 | (,dn (* ,iy (+ 1 (* ,r ,r))))) |
|---|
| 810 | (canonical-complex (/ (* ,x ,r) ,dn) |
|---|
| 811 | (/ (- ,x) ,dn)))))))) |
|---|
| 812 | (number-case x |
|---|
| 813 | (double-float (number-case y |
|---|
| 814 | (double-float (/ (the double-float x) (the double-float y))) |
|---|
| 815 | (short-float (with-stack-double-floats ((dy y)) |
|---|
| 816 | (/ (the double-float x) |
|---|
| 817 | (the double-float dy)))) |
|---|
| 818 | (rational (dfloat-rat / x y)) |
|---|
| 819 | (complex (real-complex-/ x y)))) |
|---|
| 820 | (short-float (number-case y |
|---|
| 821 | (short-float (/ (the short-float x) (the short-float y))) |
|---|
| 822 | (double-float (with-stack-double-floats ((dx x)) |
|---|
| 823 | (/ (the double-float dx) |
|---|
| 824 | (the double-float y)))) |
|---|
| 825 | (rational (sfloat-rat / x y)) |
|---|
| 826 | (complex (real-complex-/ x y)))) |
|---|
| 827 | (integer (number-case y |
|---|
| 828 | (double-float (rat-dfloat / x y)) |
|---|
| 829 | (short-float (rat-sfloat / x y)) |
|---|
| 830 | (integer (integer-/-integer x y)) |
|---|
| 831 | (complex (real-complex-/ x y)) |
|---|
| 832 | (ratio |
|---|
| 833 | (if (eql 0 x) |
|---|
| 834 | 0 |
|---|
| 835 | (let* ((ny (%numerator y)) |
|---|
| 836 | (dy (%denominator y)) |
|---|
| 837 | (gcd (gcd x ny))) |
|---|
| 838 | (build-ratio (* (maybe-truncate x gcd) dy) |
|---|
| 839 | (maybe-truncate ny gcd))))))) |
|---|
| 840 | (complex (number-case y |
|---|
| 841 | (complex (let* ((rx (%realpart x)) |
|---|
| 842 | (ix (%imagpart x)) |
|---|
| 843 | (ry (%realpart y)) |
|---|
| 844 | (iy (%imagpart y))) |
|---|
| 845 | (if (> (abs ry) (abs iy)) |
|---|
| 846 | (let* ((r (/ iy ry)) |
|---|
| 847 | (dn (+ ry (* r iy)))) |
|---|
| 848 | (canonical-complex (/ (+ rx (* ix r)) dn) |
|---|
| 849 | (/ (- ix (* rx r)) dn))) |
|---|
| 850 | (let* ((r (/ ry iy)) |
|---|
| 851 | (dn (+ iy (* r ry)))) |
|---|
| 852 | (canonical-complex (/ (+ (* rx r) ix) dn) |
|---|
| 853 | (/ (- (* ix r) rx) dn)))))) |
|---|
| 854 | ((rational float) |
|---|
| 855 | (canonical-complex (/ (%realpart x) y) (/ (%imagpart x) y))))) |
|---|
| 856 | (ratio (number-case y |
|---|
| 857 | (double-float (rat-dfloat / x y)) |
|---|
| 858 | (short-float (rat-sfloat / x y)) |
|---|
| 859 | (integer |
|---|
| 860 | (when (eql y 0) |
|---|
| 861 | (divide-by-zero-error '/ x y)) |
|---|
| 862 | (let* ((nx (%numerator x)) (gcd (gcd nx y))) |
|---|
| 863 | (build-ratio (maybe-truncate nx gcd) |
|---|
| 864 | (* (maybe-truncate y gcd) (%denominator x))))) |
|---|
| 865 | (complex (real-complex-/ x y)) |
|---|
| 866 | (ratio |
|---|
| 867 | (let* ((nx (%numerator x)) |
|---|
| 868 | (dx (%denominator x)) |
|---|
| 869 | (ny (%numerator y)) |
|---|
| 870 | (dy (%denominator y)) |
|---|
| 871 | (g1 (gcd nx ny)) |
|---|
| 872 | (g2 (gcd dx dy))) |
|---|
| 873 | (build-ratio (* (maybe-truncate nx g1) |
|---|
| 874 | (maybe-truncate dy g2)) |
|---|
| 875 | (* (maybe-truncate dx g2) |
|---|
| 876 | (maybe-truncate ny g1)))))))))) |
|---|
| 877 | |
|---|
| 878 | |
|---|
| 879 | |
|---|
| 880 | (defun divide-by-zero-error (operation &rest operands) |
|---|
| 881 | (error (make-condition 'division-by-zero |
|---|
| 882 | :operation operation |
|---|
| 883 | :operands operands))) |
|---|
| 884 | |
|---|
| 885 | |
|---|
| 886 | (defun 1+ (number) |
|---|
| 887 | "Returns NUMBER + 1." |
|---|
| 888 | (+-2 number 1)) |
|---|
| 889 | |
|---|
| 890 | (defun 1- (number) |
|---|
| 891 | "Returns NUMBER - 1." |
|---|
| 892 | (--2 number 1)) |
|---|
| 893 | |
|---|
| 894 | |
|---|
| 895 | |
|---|
| 896 | |
|---|
| 897 | (defun conjugate (number) |
|---|
| 898 | "Return the complex conjugate of NUMBER. For non-complex numbers, this is |
|---|
| 899 | an identity." |
|---|
| 900 | (number-case number |
|---|
| 901 | (complex (complex (%realpart number) (- (%imagpart number)))) |
|---|
| 902 | (number number))) |
|---|
| 903 | |
|---|
| 904 | (defun numerator (rational) |
|---|
| 905 | "Return the numerator of NUMBER, which must be rational." |
|---|
| 906 | (number-case rational |
|---|
| 907 | (ratio (%numerator rational)) |
|---|
| 908 | (integer rational))) |
|---|
| 909 | |
|---|
| 910 | (defun denominator (rational) |
|---|
| 911 | "Return the denominator of NUMBER, which must be rational." |
|---|
| 912 | (number-case rational |
|---|
| 913 | (ratio (%denominator rational)) |
|---|
| 914 | (integer 1))) |
|---|
| 915 | |
|---|
| 916 | |
|---|
| 917 | |
|---|
| 918 | (defun abs (number) |
|---|
| 919 | "Return the absolute value of the number." |
|---|
| 920 | (number-case number |
|---|
| 921 | (fixnum |
|---|
| 922 | (locally (declare (fixnum number)) |
|---|
| 923 | (if (minusp number) (- number) number))) |
|---|
| 924 | (double-float |
|---|
| 925 | (%double-float-abs number)) |
|---|
| 926 | (short-float |
|---|
| 927 | (%short-float-abs number)) |
|---|
| 928 | (bignum |
|---|
| 929 | (if (bignum-minusp number)(negate-bignum number) number)) |
|---|
| 930 | (ratio |
|---|
| 931 | (if (minusp number) (- number) number)) |
|---|
| 932 | (complex |
|---|
| 933 | (let ((rx (%realpart number)) |
|---|
| 934 | (ix (%imagpart number))) |
|---|
| 935 | (number-case rx |
|---|
| 936 | (rational |
|---|
| 937 | (sqrt (+ (* rx rx) (* ix ix)))) |
|---|
| 938 | (short-float |
|---|
| 939 | (%short-float (%double-float-hypot (%double-float rx) |
|---|
| 940 | (%double-float ix)))) |
|---|
| 941 | (double-float |
|---|
| 942 | (%double-float-hypot rx ix))))))) |
|---|
| 943 | |
|---|
| 944 | |
|---|
| 945 | |
|---|
| 946 | (defun phase (number) |
|---|
| 947 | "Return the angle part of the polar representation of a complex number. |
|---|
| 948 | For complex numbers, this is (atan (imagpart number) (realpart number)). |
|---|
| 949 | For non-complex positive numbers, this is 0. For non-complex negative |
|---|
| 950 | numbers this is PI." |
|---|
| 951 | (number-case number |
|---|
| 952 | (rational |
|---|
| 953 | (if (minusp number) |
|---|
| 954 | (%short-float pi) |
|---|
| 955 | 0.0f0)) |
|---|
| 956 | (double-float |
|---|
| 957 | (if (minusp number) |
|---|
| 958 | (%double-float pi) |
|---|
| 959 | 0.0d0)) |
|---|
| 960 | (complex |
|---|
| 961 | (atan (%imagpart number) (%realpart number))) |
|---|
| 962 | (short-float |
|---|
| 963 | (if (minusp number) |
|---|
| 964 | (%short-float pi) |
|---|
| 965 | 0.0s0)))) |
|---|
| 966 | |
|---|
| 967 | |
|---|
| 968 | |
|---|
| 969 | ; from Lib;numbers.lisp, sort of |
|---|
| 970 | (defun float (number &optional other) |
|---|
| 971 | "Converts any REAL to a float. If OTHER is not provided, it returns a |
|---|
| 972 | SINGLE-FLOAT if NUMBER is not already a FLOAT. If OTHER is provided, the |
|---|
| 973 | result is the same float format as OTHER." |
|---|
| 974 | (if (null other) |
|---|
| 975 | (if (typep number 'float) |
|---|
| 976 | number |
|---|
| 977 | (%short-float number)) |
|---|
| 978 | (if (typep other 'double-float) |
|---|
| 979 | (%double-float number) |
|---|
| 980 | (if (typep other 'short-float) |
|---|
| 981 | (%short-float number) |
|---|
| 982 | (float number (require-type other 'float)))))) |
|---|
| 983 | |
|---|
| 984 | |
|---|
| 985 | |
|---|
| 986 | |
|---|
| 987 | |
|---|
| 988 | ;;; If the numbers do not divide exactly and the result of (/ number divisor) |
|---|
| 989 | ;;; would be negative then decrement the quotient and augment the remainder by |
|---|
| 990 | ;;; the divisor. |
|---|
| 991 | ;;; |
|---|
| 992 | (defun floor (number &optional divisor) |
|---|
| 993 | "Return the greatest integer not greater than number, or number/divisor. |
|---|
| 994 | The second returned value is (mod number divisor)." |
|---|
| 995 | (if (null divisor)(setq divisor 1)) |
|---|
| 996 | (multiple-value-bind (tru rem) (truncate number divisor) |
|---|
| 997 | (if (and (not (zerop rem)) |
|---|
| 998 | (if (minusp divisor) |
|---|
| 999 | (plusp number) |
|---|
| 1000 | (minusp number))) |
|---|
| 1001 | (if (called-for-mv-p) |
|---|
| 1002 | (values (1- tru) (+ rem divisor)) |
|---|
| 1003 | (1- tru)) |
|---|
| 1004 | (values tru rem)))) |
|---|
| 1005 | |
|---|
| 1006 | |
|---|
| 1007 | |
|---|
| 1008 | (defun %fixnum-floor (number divisor) |
|---|
| 1009 | (declare (fixnum number divisor)) |
|---|
| 1010 | (if (eq divisor 1) |
|---|
| 1011 | (values number 0) |
|---|
| 1012 | (multiple-value-bind (tru rem) (truncate number divisor) |
|---|
| 1013 | (if (eq rem 0) |
|---|
| 1014 | (values tru 0) |
|---|
| 1015 | (locally (declare (fixnum tru rem)) |
|---|
| 1016 | (if (and ;(not (zerop rem)) |
|---|
| 1017 | (if (minusp divisor) |
|---|
| 1018 | (plusp number) |
|---|
| 1019 | (minusp number))) |
|---|
| 1020 | (values (the fixnum (1- tru)) (the fixnum (+ rem divisor))) |
|---|
| 1021 | (values tru rem))))))) |
|---|
| 1022 | |
|---|
| 1023 | |
|---|
| 1024 | |
|---|
| 1025 | ;;; If the numbers do not divide exactly and the result of (/ number divisor) |
|---|
| 1026 | ;;; would be positive then increment the quotient and decrement the remainder by |
|---|
| 1027 | ;;; the divisor. |
|---|
| 1028 | ;;; |
|---|
| 1029 | (defun ceiling (number &optional divisor) |
|---|
| 1030 | "Return the smallest integer not less than number, or number/divisor. |
|---|
| 1031 | The second returned value is the remainder." |
|---|
| 1032 | (if (null divisor)(setq divisor 1)) |
|---|
| 1033 | (multiple-value-bind (tru rem) (truncate number divisor) |
|---|
| 1034 | (if (and (not (zerop rem)) |
|---|
| 1035 | (if (minusp divisor) |
|---|
| 1036 | (minusp number) |
|---|
| 1037 | (plusp number))) |
|---|
| 1038 | (if (called-for-mv-p) |
|---|
| 1039 | (values (+ tru 1) (- rem divisor)) |
|---|
| 1040 | (+ tru 1)) |
|---|
| 1041 | (values tru rem)))) |
|---|
| 1042 | |
|---|
| 1043 | |
|---|
| 1044 | |
|---|
| 1045 | (defun %fixnum-ceiling (number divisor) |
|---|
| 1046 | "Returns the smallest integer not less than number, or number/divisor. |
|---|
| 1047 | The second returned value is the remainder." |
|---|
| 1048 | (declare (fixnum number divisor)) |
|---|
| 1049 | (multiple-value-bind (tru rem) (%fixnum-truncate number divisor) |
|---|
| 1050 | (if (eq 0 rem) |
|---|
| 1051 | (values tru 0) |
|---|
| 1052 | (locally (declare (fixnum tru rem)) |
|---|
| 1053 | (if (and ;(not (zerop rem)) |
|---|
| 1054 | (if (minusp divisor) |
|---|
| 1055 | (minusp number) |
|---|
| 1056 | (plusp number))) |
|---|
| 1057 | (values (the fixnum (+ tru 1))(the fixnum (- rem divisor))) |
|---|
| 1058 | (values tru rem)))))) |
|---|
| 1059 | |
|---|
| 1060 | |
|---|
| 1061 | |
|---|
| 1062 | (defun integer-decode-denorm-short-float (mantissa sign) |
|---|
| 1063 | (declare (fixnum mantissa sign)) |
|---|
| 1064 | (do* ((bias 0 (1+ bias)) |
|---|
| 1065 | (sig mantissa (ash sig 1))) |
|---|
| 1066 | ((logbitp 23 sig) |
|---|
| 1067 | (values sig |
|---|
| 1068 | (- (- IEEE-single-float-bias) |
|---|
| 1069 | IEEE-single-float-digits |
|---|
| 1070 | bias) |
|---|
| 1071 | sign)))) |
|---|
| 1072 | |
|---|
| 1073 | |
|---|
| 1074 | (defun integer-decode-short-float (sfloat) |
|---|
| 1075 | (multiple-value-bind (mantissa exp sign)(fixnum-decode-short-float sfloat) |
|---|
| 1076 | (let* ((biased (- exp IEEE-single-float-bias IEEE-single-float-digits))) |
|---|
| 1077 | (setq sign (if (eql 0 sign) 1 -1)) |
|---|
| 1078 | (if (eq exp 255) |
|---|
| 1079 | (error "Can't decode NAN/Inf: ~s" sfloat)) |
|---|
| 1080 | (if (eql 0 exp) |
|---|
| 1081 | (if (eql 0 mantissa) |
|---|
| 1082 | (values 0 biased sign) |
|---|
| 1083 | (integer-decode-denorm-short-float (ash mantissa 1) sign)) |
|---|
| 1084 | (values (logior #x800000 mantissa) biased sign))))) |
|---|
| 1085 | |
|---|
| 1086 | |
|---|
| 1087 | |
|---|
| 1088 | |
|---|
| 1089 | ;;; INTEGER-DECODE-FLOAT -- Public |
|---|
| 1090 | ;;; |
|---|
| 1091 | ;;; Dispatch to the correct type-specific i-d-f function. |
|---|
| 1092 | ;;; |
|---|
| 1093 | (defun integer-decode-float (x) |
|---|
| 1094 | "Returns three values: |
|---|
| 1095 | 1) an integer representation of the significand. |
|---|
| 1096 | 2) the exponent for the power of 2 that the significand must be multiplied |
|---|
| 1097 | by to get the actual value. This differs from the DECODE-FLOAT exponent |
|---|
| 1098 | by FLOAT-DIGITS, since the significand has been scaled to have all its |
|---|
| 1099 | digits before the radix point. |
|---|
| 1100 | 3) -1 or 1 (i.e. the sign of the argument.)" |
|---|
| 1101 | (number-case x |
|---|
| 1102 | (short-float |
|---|
| 1103 | (integer-decode-short-float x)) |
|---|
| 1104 | (double-float |
|---|
| 1105 | (integer-decode-double-float x)))) |
|---|
| 1106 | |
|---|
| 1107 | |
|---|
| 1108 | ;;; %UNARY-TRUNCATE -- Interface |
|---|
| 1109 | ;;; |
|---|
| 1110 | ;;; This function is called when we are doing a truncate without any funky |
|---|
| 1111 | ;;; divisor, i.e. converting a float or ratio to an integer. Note that we do |
|---|
| 1112 | ;;; *not* return the second value of truncate, so it must be computed by the |
|---|
| 1113 | ;;; caller if needed. |
|---|
| 1114 | ;;; |
|---|
| 1115 | ;;; In the float case, we pick off small arguments so that compiler can use |
|---|
| 1116 | ;;; special-case operations. We use an exclusive test, since (due to round-off |
|---|
| 1117 | ;;; error), (float most-positive-fixnum) may be greater than |
|---|
| 1118 | ;;; most-positive-fixnum. |
|---|
| 1119 | ;;; |
|---|
| 1120 | (defun %unary-truncate (number) |
|---|
| 1121 | (number-case number |
|---|
| 1122 | (integer number) |
|---|
| 1123 | (ratio (truncate-no-rem (%numerator number) (%denominator number))) |
|---|
| 1124 | (double-float |
|---|
| 1125 | (if (and (< (the double-float number) |
|---|
| 1126 | (float (1- (ash 1 (- (1- target::nbits-in-word) target::fixnumshift))) 0.0d0)) |
|---|
| 1127 | (< (float (ash -1 (- (1- target::nbits-in-word) target::fixnumshift)) 0.0d0) |
|---|
| 1128 | (the double-float number))) |
|---|
| 1129 | (%truncate-double-float->fixnum number) |
|---|
| 1130 | (%truncate-double-float number))) |
|---|
| 1131 | (short-float |
|---|
| 1132 | (if (and (< (the short-float number) |
|---|
| 1133 | (float (1- (ash 1 (- (1- target::nbits-in-word) target::fixnumshift))) 0.0s0)) |
|---|
| 1134 | (< (float (ash -1 (- (1- target::nbits-in-word) target::fixnumshift)) 0.0s0) |
|---|
| 1135 | (the short-float number))) |
|---|
| 1136 | (%truncate-short-float->fixnum number) |
|---|
| 1137 | (%truncate-short-float number))))) |
|---|
| 1138 | |
|---|
| 1139 | |
|---|
| 1140 | |
|---|
| 1141 | ; cmucl:compiler:float-tran.lisp |
|---|
| 1142 | (defun xform-truncate (x) |
|---|
| 1143 | (let ((res (%unary-truncate x))) |
|---|
| 1144 | (values res (- x res)))) |
|---|
| 1145 | |
|---|
| 1146 | |
|---|
| 1147 | |
|---|
| 1148 | (defun truncate (number &optional divisor) |
|---|
| 1149 | "Returns number (or number/divisor) as an integer, rounded toward 0. |
|---|
| 1150 | The second returned value is the remainder." |
|---|
| 1151 | (if (null divisor)(setq divisor 1)) |
|---|
| 1152 | (when (not (called-for-mv-p)) |
|---|
| 1153 | (return-from truncate (truncate-no-rem number divisor))) |
|---|
| 1154 | (macrolet |
|---|
| 1155 | ((truncate-rat-dfloat (number divisor) |
|---|
| 1156 | `(with-stack-double-floats ((fnum ,number) |
|---|
| 1157 | (f2)) |
|---|
| 1158 | (let ((res (%unary-truncate (%double-float/-2! fnum ,divisor f2)))) |
|---|
| 1159 | (values res |
|---|
| 1160 | (%double-float--2 fnum (%double-float*-2! (%double-float res f2) ,divisor f2)))))) |
|---|
| 1161 | (truncate-rat-sfloat (number divisor) |
|---|
| 1162 | #+32-bit-target |
|---|
| 1163 | `(target::with-stack-short-floats ((fnum ,number) |
|---|
| 1164 | (f2)) |
|---|
| 1165 | (let ((res (%unary-truncate (%short-float/-2! fnum ,divisor f2)))) |
|---|
| 1166 | (values res |
|---|
| 1167 | (%short-float--2 fnum (%short-float*-2! (%short-float res f2) ,divisor f2))))) |
|---|
| 1168 | #+64-bit-target |
|---|
| 1169 | `(let* ((temp (%short-float ,number)) |
|---|
| 1170 | (res (%unary-truncate (/ (the short-float temp) |
|---|
| 1171 | (the short-float ,divisor))))) |
|---|
| 1172 | (values res |
|---|
| 1173 | (- (the short-float temp) |
|---|
| 1174 | (the short-float (* (the short-float (%short-float res)) |
|---|
| 1175 | (the short-float ,divisor))))))) |
|---|
| 1176 | ) |
|---|
| 1177 | (number-case number |
|---|
| 1178 | (fixnum |
|---|
| 1179 | (number-case divisor |
|---|
| 1180 | (fixnum (if (eq divisor 1) (values number 0) (%fixnum-truncate number divisor))) |
|---|
| 1181 | (bignum (if (eq number target::target-most-negative-fixnum) |
|---|
| 1182 | (with-small-bignum-buffers ((bn number)) |
|---|
| 1183 | (multiple-value-bind (q r) (bignum-truncate bn divisor) |
|---|
| 1184 | (if (eq r bn) |
|---|
| 1185 | (values q number) |
|---|
| 1186 | (values q r)))) |
|---|
| 1187 | (values 0 number))) |
|---|
| 1188 | (double-float (truncate-rat-dfloat number divisor)) |
|---|
| 1189 | (short-float (truncate-rat-sfloat number divisor)) |
|---|
| 1190 | (ratio (let ((q (truncate (* number (%denominator divisor)) ; this was wrong |
|---|
| 1191 | (%numerator divisor)))) |
|---|
| 1192 | (values q (- number (* q divisor))))))) |
|---|
| 1193 | (bignum (number-case divisor |
|---|
| 1194 | (fixnum (if (eq divisor 1) |
|---|
| 1195 | (values number 0) |
|---|
| 1196 | (if (eq divisor target::target-most-negative-fixnum);; << aargh |
|---|
| 1197 | (with-small-bignum-buffers ((bd divisor)) |
|---|
| 1198 | (bignum-truncate number bd)) |
|---|
| 1199 | (bignum-truncate-by-fixnum number divisor)))) |
|---|
| 1200 | (bignum (bignum-truncate number divisor)) |
|---|
| 1201 | (double-float (truncate-rat-dfloat number divisor)) |
|---|
| 1202 | (short-float (truncate-rat-sfloat number divisor)) |
|---|
| 1203 | (ratio (let ((q (truncate (* number (%denominator divisor)) ; so was this |
|---|
| 1204 | (%numerator divisor)))) |
|---|
| 1205 | (values q (- number (* q divisor))))))) |
|---|
| 1206 | (short-float (if (eql divisor 1) |
|---|
| 1207 | (let* ((res (%unary-truncate number))) |
|---|
| 1208 | (values res (- number res))) |
|---|
| 1209 | (number-case divisor |
|---|
| 1210 | (short-float |
|---|
| 1211 | #+32-bit-target |
|---|
| 1212 | (target::with-stack-short-floats ((f2)) |
|---|
| 1213 | (let ((res (%unary-truncate (%short-float/-2! number divisor f2)))) |
|---|
| 1214 | (values res |
|---|
| 1215 | (%short-float--2 |
|---|
| 1216 | number |
|---|
| 1217 | (%short-float*-2! (%short-float res f2) divisor f2))))) |
|---|
| 1218 | #+64-bit-target |
|---|
| 1219 | (let ((res (%unary-truncate |
|---|
| 1220 | (/ (the short-float number) |
|---|
| 1221 | (the short-float divisor))))) |
|---|
| 1222 | (values res |
|---|
| 1223 | (- (the short-float number) |
|---|
| 1224 | (* (the short-float (%short-float res)) |
|---|
| 1225 | (the short-float divisor)))))) |
|---|
| 1226 | ((fixnum bignum ratio) |
|---|
| 1227 | #+32-bit-target |
|---|
| 1228 | (target::with-stack-short-floats ((fdiv divisor) |
|---|
| 1229 | (f2)) |
|---|
| 1230 | (let ((res (%unary-truncate (%short-float/-2! number fdiv f2)))) |
|---|
| 1231 | (values res |
|---|
| 1232 | (%short-float--2 |
|---|
| 1233 | number |
|---|
| 1234 | (%short-float*-2! (%short-float res f2) fdiv f2))))) |
|---|
| 1235 | #+64-bit-target |
|---|
| 1236 | (let* ((fdiv (%short-float divisor)) |
|---|
| 1237 | (res (%unary-truncate |
|---|
| 1238 | (/ (the short-float number) |
|---|
| 1239 | (the short-float fdiv))))) |
|---|
| 1240 | (values res (- number (* res fdiv)))) |
|---|
| 1241 | |
|---|
| 1242 | ) |
|---|
| 1243 | (double-float |
|---|
| 1244 | (with-stack-double-floats ((fnum number) |
|---|
| 1245 | (f2)) |
|---|
| 1246 | (let* ((res (%unary-truncate (%double-float/-2! fnum divisor f2)))) |
|---|
| 1247 | (values res |
|---|
| 1248 | (%double-float--2 |
|---|
| 1249 | fnum |
|---|
| 1250 | (%double-float*-2! (%double-float res f2) divisor f2))))))))) |
|---|
| 1251 | (double-float (if (eql divisor 1) |
|---|
| 1252 | (let ((res (%unary-truncate number))) |
|---|
| 1253 | (values res (- number res))) |
|---|
| 1254 | (number-case divisor |
|---|
| 1255 | ((fixnum bignum ratio short-float) |
|---|
| 1256 | (with-stack-double-floats ((fdiv divisor) |
|---|
| 1257 | (f2)) |
|---|
| 1258 | (let ((res (%unary-truncate (%double-float/-2! number fdiv f2)))) |
|---|
| 1259 | (values res |
|---|
| 1260 | (%double-float--2 |
|---|
| 1261 | number |
|---|
| 1262 | (%double-float*-2! (%double-float res f2) fdiv f2)))))) |
|---|
| 1263 | (double-float |
|---|
| 1264 | (with-stack-double-floats ((f2)) |
|---|
| 1265 | (let ((res (%unary-truncate (%double-float/-2! number divisor f2)))) |
|---|
| 1266 | (values res |
|---|
| 1267 | (%double-float--2 |
|---|
| 1268 | number |
|---|
| 1269 | (%double-float*-2! (%double-float res f2) divisor f2))))))))) |
|---|
| 1270 | (ratio (number-case divisor |
|---|
| 1271 | (double-float (truncate-rat-dfloat number divisor)) |
|---|
| 1272 | (short-float (truncate-rat-sfloat number divisor)) |
|---|
| 1273 | (rational |
|---|
| 1274 | (let ((q (truncate (%numerator number) |
|---|
| 1275 | (* (%denominator number) divisor)))) |
|---|
| 1276 | (values q (- number (* q divisor)))))))))) |
|---|
| 1277 | |
|---|
| 1278 | (defun truncate-no-rem (number divisor) |
|---|
| 1279 | "Returns number (or number/divisor) as an integer, rounded toward 0." |
|---|
| 1280 | (macrolet |
|---|
| 1281 | ((truncate-rat-dfloat (number divisor) |
|---|
| 1282 | `(with-stack-double-floats ((fnum ,number) |
|---|
| 1283 | (f2)) |
|---|
| 1284 | (%unary-truncate (%double-float/-2! fnum ,divisor f2)))) |
|---|
| 1285 | (truncate-rat-sfloat (number divisor) |
|---|
| 1286 | #+32-bit-target |
|---|
| 1287 | `(target::with-stack-short-floats ((fnum ,number) |
|---|
| 1288 | (f2)) |
|---|
| 1289 | (%unary-truncate (%short-float/-2! fnum ,divisor f2))) |
|---|
| 1290 | #+64-bit-target |
|---|
| 1291 | `(let ((fnum (%short-float ,number))) |
|---|
| 1292 | (%unary-truncate (/ (the short-float fnum) |
|---|
| 1293 | (the short-float ,divisor)))))) |
|---|
| 1294 | (number-case number |
|---|
| 1295 | (fixnum |
|---|
| 1296 | (if (eql number target::target-most-negative-fixnum) |
|---|
| 1297 | (if (zerop divisor) |
|---|
| 1298 | (error 'division-by-zero :operation 'truncate :operands (list number divisor)) |
|---|
| 1299 | (with-small-bignum-buffers ((bn number)) |
|---|
| 1300 | (let* ((result (truncate-no-rem bn divisor))) |
|---|
| 1301 | (if (eq result bn) |
|---|
| 1302 | number |
|---|
| 1303 | result)))) |
|---|
| 1304 | (number-case divisor |
|---|
| 1305 | (fixnum (if (eq divisor 1) number (values (%fixnum-truncate number divisor)))) |
|---|
| 1306 | (bignum 0) |
|---|
| 1307 | (double-float (truncate-rat-dfloat number divisor)) |
|---|
| 1308 | (short-float (truncate-rat-sfloat number divisor)) |
|---|
| 1309 | (ratio (let ((q (truncate (* number (%denominator divisor)) |
|---|
| 1310 | (%numerator divisor)))) |
|---|
| 1311 | q))))) |
|---|
| 1312 | (bignum (number-case divisor |
|---|
| 1313 | (fixnum (if (eq divisor 1) number |
|---|
| 1314 | (if (eq divisor target::target-most-negative-fixnum) |
|---|
| 1315 | (with-small-bignum-buffers ((bd divisor)) |
|---|
| 1316 | (bignum-truncate number bd :no-rem)) |
|---|
| 1317 | (bignum-truncate-by-fixnum number divisor)))) |
|---|
| 1318 | (bignum (bignum-truncate number divisor :no-rem)) |
|---|
| 1319 | (double-float (truncate-rat-dfloat number divisor)) |
|---|
| 1320 | (short-float (truncate-rat-sfloat number divisor)) |
|---|
| 1321 | (ratio (let ((q (truncate (* number (%denominator divisor)) |
|---|
| 1322 | (%numerator divisor)))) |
|---|
| 1323 | Q)))) |
|---|
| 1324 | (double-float (if (eql divisor 1) |
|---|
| 1325 | (let ((res (%unary-truncate number))) |
|---|
| 1326 | RES) |
|---|
| 1327 | (number-case divisor |
|---|
| 1328 | ((fixnum bignum ratio) |
|---|
| 1329 | (with-stack-double-floats ((fdiv divisor) |
|---|
| 1330 | (f2)) |
|---|
| 1331 | (let ((res (%unary-truncate (%double-float/-2! number fdiv f2)))) |
|---|
| 1332 | RES))) |
|---|
| 1333 | (short-float |
|---|
| 1334 | (with-stack-double-floats ((ddiv divisor) |
|---|
| 1335 | (f2)) |
|---|
| 1336 | (%unary-truncate (%double-float/-2! number ddiv f2)))) |
|---|
| 1337 | (double-float |
|---|
| 1338 | (with-stack-double-floats ((f2)) |
|---|
| 1339 | (%unary-truncate (%double-float/-2! number divisor f2))))))) |
|---|
| 1340 | (short-float (if (eql divisor 1) |
|---|
| 1341 | (let ((res (%unary-truncate number))) |
|---|
| 1342 | RES) |
|---|
| 1343 | (number-case divisor |
|---|
| 1344 | ((fixnum bignum ratio) |
|---|
| 1345 | #+32-bit-target |
|---|
| 1346 | (target::with-stack-short-floats ((fdiv divisor) |
|---|
| 1347 | (f2)) |
|---|
| 1348 | (let ((res (%unary-truncate (%short-float/-2! number fdiv f2)))) |
|---|
| 1349 | RES)) |
|---|
| 1350 | #+64-bit-target |
|---|
| 1351 | (%unary-truncate (/ (the short-float number) |
|---|
| 1352 | (the short-float (%short-float divisor))))) |
|---|
| 1353 | (short-float |
|---|
| 1354 | #+32-bit-target |
|---|
| 1355 | (target::with-stack-short-floats ((ddiv divisor) |
|---|
| 1356 | (f2)) |
|---|
| 1357 | (%unary-truncate (%short-float/-2! number ddiv f2))) |
|---|
| 1358 | #+64-bit-target |
|---|
| 1359 | (%unary-truncate (/ (the short-float number) |
|---|
| 1360 | (the short-float (%short-float divisor))))) |
|---|
| 1361 | (double-float |
|---|
| 1362 | (with-stack-double-floats ((n2 number) |
|---|
| 1363 | (f2)) |
|---|
| 1364 | (%unary-truncate (%double-float/-2! n2 divisor f2))))))) |
|---|
| 1365 | (ratio (number-case divisor |
|---|
| 1366 | (double-float (truncate-rat-dfloat number divisor)) |
|---|
| 1367 | (short-float (truncate-rat-sfloat number divisor)) |
|---|
| 1368 | (rational |
|---|
| 1369 | (let ((q (truncate (%numerator number) |
|---|
| 1370 | (* (%denominator number) divisor)))) |
|---|
| 1371 | Q))))))) |
|---|
| 1372 | |
|---|
| 1373 | |
|---|
| 1374 | ;;; %UNARY-ROUND -- Interface |
|---|
| 1375 | ;;; |
|---|
| 1376 | ;;; Similar to %UNARY-TRUNCATE, but rounds to the nearest integer. If we |
|---|
| 1377 | ;;; can't use the round primitive, then we do our own round-to-nearest on the |
|---|
| 1378 | ;;; result of i-d-f. [Note that this rounding will really only happen with |
|---|
| 1379 | ;;; double floats, since the whole single-float fraction will fit in a fixnum, |
|---|
| 1380 | ;;; so all single-floats larger than most-positive-fixnum can be precisely |
|---|
| 1381 | ;;; represented by an integer.] |
|---|
| 1382 | ;;; |
|---|
| 1383 | ;;; returns both values today |
|---|
| 1384 | |
|---|
| 1385 | (defun %unary-round (number) |
|---|
| 1386 | (number-case number |
|---|
| 1387 | (integer (values number 0)) |
|---|
| 1388 | (ratio (let ((q (round (%numerator number) (%denominator number)))) |
|---|
| 1389 | (values q (- number q)))) |
|---|
| 1390 | (double-float |
|---|
| 1391 | (if (and (< (the double-float number) |
|---|
| 1392 | (float (1- (ash 1 (- (1- target::nbits-in-word) target::fixnumshift))) 1.0d0)) |
|---|
| 1393 | (< (float (ash -1 (- (1- target::nbits-in-word) target::fixnumshift)) 1.0d0) |
|---|
| 1394 | (the double-float number))) |
|---|
| 1395 | (let ((round (%unary-round-to-fixnum number))) |
|---|
| 1396 | (values round (- number round))) |
|---|
| 1397 | (multiple-value-bind (trunc rem) (truncate number) |
|---|
| 1398 | (if (not (%double-float-minusp number)) |
|---|
| 1399 | (if (or (> rem 0.5d0)(and (= rem 0.5d0) (oddp trunc))) |
|---|
| 1400 | (values (+ trunc 1) (- rem 1.0d0)) |
|---|
| 1401 | (values trunc rem)) |
|---|
| 1402 | (if (or (> rem -0.5d0)(and (evenp trunc)(= rem -0.5d0))) |
|---|
| 1403 | (values trunc rem) |
|---|
| 1404 | (values (1- trunc) (+ 1.0d0 rem))))))) |
|---|
| 1405 | (short-float |
|---|
| 1406 | (if (and (< (the short-float number) |
|---|
| 1407 | (float (1- (ash 1 (- (1- target::nbits-in-word) target::fixnumshift))) 1.0s0)) |
|---|
| 1408 | (< (float (ash -1 (- (1- target::nbits-in-word) target::fixnumshift)) 1.0s0) |
|---|
| 1409 | (the double-float number))) |
|---|
| 1410 | (let ((round (%unary-round-to-fixnum number))) |
|---|
| 1411 | (values round (- number round))) |
|---|
| 1412 | (multiple-value-bind (trunc rem) (truncate number) |
|---|
| 1413 | (if (not (%short-float-minusp number)) |
|---|
| 1414 | (if (or (> rem 0.5s0)(and (= rem 0.5s0) (oddp trunc))) |
|---|
| 1415 | (values (+ trunc 1) (- rem 1.0s0)) |
|---|
| 1416 | (values trunc rem)) |
|---|
| 1417 | (if (or (> rem -0.5s0)(and (evenp trunc)(= rem -0.5s0))) |
|---|
| 1418 | (values trunc rem) |
|---|
| 1419 | (values (1- trunc) (+ 1.0s0 rem))))))))) |
|---|
| 1420 | |
|---|
| 1421 | (defun %unary-round-to-fixnum (number) |
|---|
| 1422 | (number-case number |
|---|
| 1423 | (double-float |
|---|
| 1424 | (%round-nearest-double-float->fixnum number)) |
|---|
| 1425 | (short-float |
|---|
| 1426 | (%round-nearest-short-float->fixnum number)))) |
|---|
| 1427 | |
|---|
| 1428 | |
|---|
| 1429 | |
|---|
| 1430 | |
|---|
| 1431 | ; cmucl:compiler:float-tran.lisp |
|---|
| 1432 | #| |
|---|
| 1433 | (defun xform-round (x) |
|---|
| 1434 | (let ((res (%unary-round x))) |
|---|
| 1435 | (values res (- x res)))) |
|---|
| 1436 | |# |
|---|
| 1437 | |
|---|
| 1438 | #| |
|---|
| 1439 | (defun round (number &optional divisor) |
|---|
| 1440 | "Rounds number (or number/divisor) to nearest integer. |
|---|
| 1441 | The second returned value is the remainder." |
|---|
| 1442 | (if (null divisor)(setq divisor 1)) |
|---|
| 1443 | (if (eql divisor 1) |
|---|
| 1444 | (xform-round number) |
|---|
| 1445 | (multiple-value-bind (tru rem) (truncate number divisor) |
|---|
| 1446 | (let ((thresh (if (integerp divisor) (ash (abs divisor) -1)(/ (abs divisor) 2)))) ; does this need to be a ratio? |
|---|
| 1447 | (cond ((or (> rem thresh) |
|---|
| 1448 | (and (= rem thresh) (oddp tru))) |
|---|
| 1449 | (if (minusp divisor) |
|---|
| 1450 | (values (- tru 1) (+ rem divisor)) |
|---|
| 1451 | (values (+ tru 1) (- rem divisor)))) |
|---|
| 1452 | ((let ((-thresh (- thresh))) |
|---|
| 1453 | (or (< rem -thresh) |
|---|
| 1454 | (and (= rem -thresh) (oddp tru)))) |
|---|
| 1455 | (if (minusp divisor) |
|---|
| 1456 | (values (+ tru 1) (- rem divisor)) |
|---|
| 1457 | (values (- tru 1) (+ rem divisor)))) |
|---|
| 1458 | (t (values tru rem))))))) |
|---|
| 1459 | |# |
|---|
| 1460 | |
|---|
| 1461 | |
|---|
| 1462 | (defun %fixnum-round (number divisor) |
|---|
| 1463 | (declare (fixnum number divisor)) |
|---|
| 1464 | (multiple-value-bind (quo rem)(truncate number divisor) ; should => %fixnum-truncate |
|---|
| 1465 | (if (= 0 rem) |
|---|
| 1466 | (values quo rem) |
|---|
| 1467 | (locally (declare (fixnum quo rem)) |
|---|
| 1468 | (let* ((minusp-num (minusp number)) |
|---|
| 1469 | (minusp-div (minusp divisor)) |
|---|
| 1470 | (2rem (* rem (if (neq minusp-num minusp-div) -2 2)))) |
|---|
| 1471 | ;(declare (fixnum 2rem)) ; no way jose |
|---|
| 1472 | ;(truncate (1- most-positive-fixnum) most-positive-fixnum) |
|---|
| 1473 | ; 2rem has same sign as divisor |
|---|
| 1474 | (cond (minusp-div |
|---|
| 1475 | (if (or (< 2rem divisor) |
|---|
| 1476 | (and (= 2rem divisor)(logbitp 0 quo))) |
|---|
| 1477 | (if minusp-num |
|---|
| 1478 | (values (the fixnum (+ quo 1))(the fixnum (- rem divisor))) |
|---|
| 1479 | (values (the fixnum (- quo 1))(the fixnum (+ rem divisor)))) |
|---|
| 1480 | (values quo rem))) |
|---|
| 1481 | (t (if (or (> 2rem divisor) |
|---|
| 1482 | (and (= 2rem divisor)(logbitp 0 quo))) |
|---|
| 1483 | (if minusp-num |
|---|
| 1484 | (values (the fixnum (- quo 1))(the fixnum (+ rem divisor))) |
|---|
| 1485 | (values (the fixnum (+ quo 1))(the fixnum (- rem divisor)))) |
|---|
| 1486 | (values quo rem))))))))) |
|---|
| 1487 | #| |
|---|
| 1488 | ; + + => + + |
|---|
| 1489 | ; + - => - + |
|---|
| 1490 | ; - + => - - |
|---|
| 1491 | ; - - => + - |
|---|
| 1492 | (defun %fixnum-round (number divisor) |
|---|
| 1493 | (declare (fixnum number divisor)) |
|---|
| 1494 | "Rounds number (or number/divisor) to nearest integer. |
|---|
| 1495 | The second returned value is the remainder." |
|---|
| 1496 | (if (eq divisor 1) |
|---|
| 1497 | (values number 0) |
|---|
| 1498 | (multiple-value-bind (tru rem) (truncate number divisor) |
|---|
| 1499 | (if (= 0 rem) |
|---|
| 1500 | (values tru rem) |
|---|
| 1501 | (locally (declare (fixnum tru rem)) |
|---|
| 1502 | (let* ((minusp-num (minusp number)) |
|---|
| 1503 | (minusp-div (minusp divisor)) |
|---|
| 1504 | (half-div (ash (if minusp-div (- divisor) divisor) -1)) |
|---|
| 1505 | (abs-rem (if minusp-num (- rem) rem))) |
|---|
| 1506 | (declare (fixnum half-div abs-rem)) ; true of abs-rem? |
|---|
| 1507 | (if (or (> abs-rem half-div) |
|---|
| 1508 | (and |
|---|
| 1509 | (not (logbitp 0 divisor)) |
|---|
| 1510 | (logbitp 0 tru) ; oddp |
|---|
| 1511 | (= abs-rem half-div))) |
|---|
| 1512 | (if (eq minusp-num minusp-div) |
|---|
| 1513 | (values (the fixnum (+ tru 1))(the fixnum (- rem divisor))) |
|---|
| 1514 | (values (the fixnum (- tru 1))(the fixnum (+ rem divisor)))) |
|---|
| 1515 | (values tru rem)))))))) |
|---|
| 1516 | |# |
|---|
| 1517 | |
|---|
| 1518 | |
|---|
| 1519 | |
|---|
| 1520 | ;; makes 1 piece of garbage instead of average of 2 |
|---|
| 1521 | (defun round (number &optional divisor) |
|---|
| 1522 | "Rounds number (or number/divisor) to nearest integer. |
|---|
| 1523 | The second returned value is the remainder." |
|---|
| 1524 | (if (null divisor)(setq divisor 1)) |
|---|
| 1525 | (if (eql divisor 1) |
|---|
| 1526 | (%unary-round number) |
|---|
| 1527 | (multiple-value-bind (tru rem) (truncate number divisor) |
|---|
| 1528 | (if (= 0 rem) |
|---|
| 1529 | (values tru rem) |
|---|
| 1530 | (let* ((mv-p (called-for-mv-p)) |
|---|
| 1531 | (minusp-num (minusp number)) |
|---|
| 1532 | (minusp-div (minusp divisor)) |
|---|
| 1533 | (2rem (* rem (if (neq minusp-num minusp-div) -2 2)))) |
|---|
| 1534 | ; 2rem has same sign as divisor |
|---|
| 1535 | (cond (minusp-div |
|---|
| 1536 | (if (or (< 2rem divisor) |
|---|
| 1537 | (and (= 2rem divisor)(oddp tru))) |
|---|
| 1538 | (if mv-p |
|---|
| 1539 | (if minusp-num |
|---|
| 1540 | (values (+ tru 1)(- rem divisor)) |
|---|
| 1541 | (values (- tru 1)(+ rem divisor))) |
|---|
| 1542 | (if minusp-num (+ tru 1)(- tru 1))) |
|---|
| 1543 | (values tru rem))) |
|---|
| 1544 | (t (if (or (> 2rem divisor) |
|---|
| 1545 | (and (= 2rem divisor)(oddp tru))) |
|---|
| 1546 | (if mv-p |
|---|
| 1547 | (if minusp-num |
|---|
| 1548 | (values (- tru 1)(+ rem divisor)) |
|---|
| 1549 | (values (+ tru 1)(- rem divisor))) |
|---|
| 1550 | (if minusp-num (- tru 1)(+ tru 1))) |
|---|
| 1551 | (values tru rem))))))))) |
|---|
| 1552 | |
|---|
| 1553 | |
|---|
| 1554 | ;; #-PPC IN L1-NUMBERS.LISP (or implement %%numdiv) |
|---|
| 1555 | ;; Anyone caught implementing %%numdiv will be summarily executed. |
|---|
| 1556 | (defun rem (number divisor) |
|---|
| 1557 | "Returns second result of TRUNCATE." |
|---|
| 1558 | (number-case number |
|---|
| 1559 | (fixnum |
|---|
| 1560 | (number-case divisor |
|---|
| 1561 | (fixnum (nth-value 1 (%fixnum-truncate number divisor))) |
|---|
| 1562 | (bignum |
|---|
| 1563 | (if (and (eql number target::target-most-negative-fixnum) |
|---|
| 1564 | (eql divisor (- target::target-most-negative-fixnum))) |
|---|
| 1565 | 0 |
|---|
| 1566 | number)) |
|---|
| 1567 | (t (nth-value 1 (truncate number divisor))))) |
|---|
| 1568 | (bignum |
|---|
| 1569 | (number-case divisor |
|---|
| 1570 | (fixnum |
|---|
| 1571 | (if (eq divisor target::target-most-negative-fixnum) |
|---|
| 1572 | (nth-value 1 (truncate number divisor)) |
|---|
| 1573 | (bignum-truncate-by-fixnum-no-quo number divisor))) |
|---|
| 1574 | (bignum |
|---|
| 1575 | (bignum-rem number divisor)) |
|---|
| 1576 | (t (nth-value 1 (truncate number divisor))))) |
|---|
| 1577 | (t (nth-value 1 (truncate number divisor))))) |
|---|
| 1578 | |
|---|
| 1579 | ;; #-PPC IN L1-NUMBERS.LISP (or implement %%numdiv) |
|---|
| 1580 | ;; See above. |
|---|
| 1581 | (defun mod (number divisor) |
|---|
| 1582 | "Returns second result of FLOOR." |
|---|
| 1583 | (let ((rem (rem number divisor))) |
|---|
| 1584 | (if (and (not (zerop rem)) |
|---|
| 1585 | (if (minusp divisor) |
|---|
| 1586 | (plusp number) |
|---|
| 1587 | (minusp number))) |
|---|
| 1588 | (+ rem divisor) |
|---|
| 1589 | rem))) |
|---|
| 1590 | |
|---|
| 1591 | (defun cis (theta) |
|---|
| 1592 | "Return cos(Theta) + i sin(Theta), i.e. exp(i Theta)." |
|---|
| 1593 | (cond ((complexp theta) |
|---|
| 1594 | (error "Argument to CIS is complex: ~S" theta)) |
|---|
| 1595 | ((or (typep theta 'ratio) |
|---|
| 1596 | (> (abs theta) #.(ash 1 23))) |
|---|
| 1597 | (if (typep theta 'double-float) |
|---|
| 1598 | (%extended-cis theta) |
|---|
| 1599 | (coerce (%extended-cis theta) '(complex single-float)))) |
|---|
| 1600 | (t |
|---|
| 1601 | (complex (cos theta) (sin theta))))) |
|---|
| 1602 | |
|---|
| 1603 | |
|---|
| 1604 | (defun complex (realpart &optional (imagpart 0)) |
|---|
| 1605 | "Return a complex number with the specified real and imaginary components." |
|---|
| 1606 | (number-case realpart |
|---|
| 1607 | (short-float |
|---|
| 1608 | (number-case imagpart |
|---|
| 1609 | (short-float (canonical-complex realpart imagpart)) |
|---|
| 1610 | (double-float (canonical-complex (%double-float realpart) imagpart)) |
|---|
| 1611 | (rational (canonical-complex realpart (%short-float imagpart))))) |
|---|
| 1612 | (double-float |
|---|
| 1613 | (number-case imagpart |
|---|
| 1614 | (double-float (canonical-complex |
|---|
| 1615 | (the double-float realpart) |
|---|
| 1616 | (the double-float imagpart))) |
|---|
| 1617 | (short-float (canonical-complex realpart (%double-float imagpart))) |
|---|
| 1618 | (rational (canonical-complex |
|---|
| 1619 | (the double-float realpart) |
|---|
| 1620 | (the double-float (%double-float imagpart)))))) |
|---|
| 1621 | (rational (number-case imagpart |
|---|
| 1622 | (double-float (canonical-complex |
|---|
| 1623 | (the double-float (%double-float realpart)) |
|---|
| 1624 | (the double-float imagpart))) |
|---|
| 1625 | (short-float (canonical-complex (%short-float realpart) imagpart)) |
|---|
| 1626 | (rational (canonical-complex realpart imagpart)))))) |
|---|
| 1627 | |
|---|
| 1628 | ;; #-PPC IN L1-NUMBERS.LISP |
|---|
| 1629 | (defun realpart (number) |
|---|
| 1630 | "Extract the real part of a number." |
|---|
| 1631 | (number-case number |
|---|
| 1632 | (complex (%realpart number)) |
|---|
| 1633 | (number number))) |
|---|
| 1634 | |
|---|
| 1635 | ;; #-PPC IN L1-NUMBERS.LISP |
|---|
| 1636 | (defun imagpart (number) |
|---|
| 1637 | "Extract the imaginary part of a number." |
|---|
| 1638 | (number-case number |
|---|
| 1639 | (complex (%imagpart number)) |
|---|
| 1640 | (float (* 0 number)) |
|---|
| 1641 | (rational 0))) |
|---|
| 1642 | |
|---|
| 1643 | (defun logand-2 (x y) |
|---|
| 1644 | (number-case x |
|---|
| 1645 | (fixnum (number-case y |
|---|
| 1646 | (fixnum |
|---|
| 1647 | (%ilogand (the fixnum x)(the fixnum y))) |
|---|
| 1648 | (bignum (fix-big-logand x y)))) |
|---|
| 1649 | (bignum (number-case y |
|---|
| 1650 | (fixnum (fix-big-logand y x)) |
|---|
| 1651 | (bignum (bignum-logical-and x y)))))) |
|---|
| 1652 | |
|---|
| 1653 | (defun logior-2 (x y) |
|---|
| 1654 | (number-case x |
|---|
| 1655 | (fixnum (number-case y |
|---|
| 1656 | (fixnum (%ilogior2 x y)) |
|---|
| 1657 | (bignum |
|---|
| 1658 | (if (zerop x) |
|---|
| 1659 | y |
|---|
| 1660 | (with-small-bignum-buffers ((bx x)) |
|---|
| 1661 | (bignum-logical-ior bx y)))))) |
|---|
| 1662 | (bignum (number-case y |
|---|
| 1663 | (fixnum (if (zerop y) |
|---|
| 1664 | x |
|---|
| 1665 | (with-small-bignum-buffers ((by y)) |
|---|
| 1666 | (bignum-logical-ior x by)))) |
|---|
| 1667 | (bignum (bignum-logical-ior x y)))))) |
|---|
| 1668 | |
|---|
| 1669 | (defun logxor-2 (x y) |
|---|
| 1670 | (number-case x |
|---|
| 1671 | (fixnum (number-case y |
|---|
| 1672 | (fixnum (%ilogxor2 x y)) |
|---|
| 1673 | (bignum |
|---|
| 1674 | (with-small-bignum-buffers ((bx x)) |
|---|
| 1675 | (bignum-logical-xor bx y))))) |
|---|
| 1676 | (bignum (number-case y |
|---|
| 1677 | (fixnum (with-small-bignum-buffers ((by y)) |
|---|
| 1678 | (bignum-logical-xor x by))) |
|---|
| 1679 | (bignum (bignum-logical-xor x y)))))) |
|---|
| 1680 | |
|---|
| 1681 | |
|---|
| 1682 | |
|---|
| 1683 | ; see cmucl:compiler:srctran.lisp for transforms |
|---|
| 1684 | |
|---|
| 1685 | (defun lognand (integer1 integer2) |
|---|
| 1686 | "Complement the logical AND of INTEGER1 and INTEGER2." |
|---|
| 1687 | (lognot (logand integer1 integer2))) |
|---|
| 1688 | |
|---|
| 1689 | (defun lognor (integer1 integer2) |
|---|
| 1690 | "Complement the logical AND of INTEGER1 and INTEGER2." |
|---|
| 1691 | (lognot (logior integer1 integer2))) |
|---|
| 1692 | |
|---|
| 1693 | (defun logandc1 (x y) |
|---|
| 1694 | "Return the logical AND of (LOGNOT integer1) and integer2." |
|---|
| 1695 | (number-case x |
|---|
| 1696 | (fixnum (number-case y |
|---|
| 1697 | (fixnum (%ilogand (%ilognot x) y)) |
|---|
| 1698 | (bignum (fix-big-logandc1 x y)))) ; (%ilogand-fix-big (%ilognot x) y)))) |
|---|
| 1699 | (bignum (number-case y |
|---|
| 1700 | (fixnum (fix-big-logandc2 y x)) ; (%ilogandc2-fix-big y x)) |
|---|
| 1701 | (bignum (bignum-logandc2 y x)))))) ;(bignum-logical-and (bignum-logical-not x) y)))))) |
|---|
| 1702 | |
|---|
| 1703 | |
|---|
| 1704 | #| ; its in numbers |
|---|
| 1705 | (defun logandc2 (integer1 integer2) |
|---|
| 1706 | "Returns the logical AND of integer1 and (LOGNOT integer2)." |
|---|
| 1707 | (logand integer1 (lognot integer2))) |
|---|
| 1708 | |# |
|---|
| 1709 | |
|---|
| 1710 | (defun logorc1 (integer1 integer2) |
|---|
| 1711 | "Return the logical OR of (LOGNOT integer1) and integer2." |
|---|
| 1712 | (logior (lognot integer1) integer2)) |
|---|
| 1713 | |
|---|
| 1714 | #| |
|---|
| 1715 | (defun logorc2 (integer1 integer2) |
|---|
| 1716 | "Returns the logical OR of integer1 and (LOGNOT integer2)." |
|---|
| 1717 | (logior integer1 (lognot integer2))) |
|---|
| 1718 | |# |
|---|
| 1719 | |
|---|
| 1720 | (defun logtest (integer1 integer2) |
|---|
| 1721 | "Predicate which returns T if logand of integer1 and integer2 is not zero." |
|---|
| 1722 | ; (not (zerop (logand integer1 integer2))) |
|---|
| 1723 | (number-case integer1 |
|---|
| 1724 | (fixnum (number-case integer2 |
|---|
| 1725 | (fixnum (not (= 0 (%ilogand integer1 integer2)))) |
|---|
| 1726 | (bignum (logtest-fix-big integer1 integer2)))) |
|---|
| 1727 | (bignum (number-case integer2 |
|---|
| 1728 | (fixnum (logtest-fix-big integer2 integer1)) |
|---|
| 1729 | (bignum (bignum-logtest integer1 integer2)))))) |
|---|
| 1730 | |
|---|
| 1731 | |
|---|
| 1732 | |
|---|
| 1733 | (defun lognot (number) |
|---|
| 1734 | "Return the bit-wise logical not of integer." |
|---|
| 1735 | (number-case number |
|---|
| 1736 | (fixnum (%ilognot number)) |
|---|
| 1737 | (bignum (bignum-logical-not number)))) |
|---|
| 1738 | |
|---|
| 1739 | (defun logcount (integer) |
|---|
| 1740 | "Count the number of 1 bits if INTEGER is positive, and the number of 0 bits |
|---|
| 1741 | if INTEGER is negative." |
|---|
| 1742 | (number-case integer |
|---|
| 1743 | (fixnum |
|---|
| 1744 | (%ilogcount (if (minusp (the fixnum integer)) |
|---|
| 1745 | (%ilognot integer) |
|---|
| 1746 | integer))) |
|---|
| 1747 | (bignum |
|---|
| 1748 | (bignum-logcount integer)))) |
|---|
| 1749 | |
|---|
| 1750 | |
|---|
| 1751 | |
|---|
| 1752 | (defun ash (integer count) |
|---|
| 1753 | "Shifts integer left by count places preserving sign. - count shifts right." |
|---|
| 1754 | (etypecase integer |
|---|
| 1755 | (fixnum |
|---|
| 1756 | (etypecase count |
|---|
| 1757 | (fixnum |
|---|
| 1758 | (if (eql integer 0) |
|---|
| 1759 | 0 |
|---|
| 1760 | (if (eql count 0) |
|---|
| 1761 | integer |
|---|
| 1762 | (let ((length (integer-length (the fixnum integer)))) |
|---|
| 1763 | (declare (fixnum length count)) |
|---|
| 1764 | (cond ((and (plusp count) |
|---|
| 1765 | (> (+ length count) |
|---|
| 1766 | (- (1- target::nbits-in-word) target::fixnumshift))) |
|---|
| 1767 | (with-small-bignum-buffers ((bi integer)) |
|---|
| 1768 | (bignum-ashift-left bi count))) |
|---|
| 1769 | ((and (minusp count) (< count (- (1- target::nbits-in-word)))) |
|---|
| 1770 | (if (minusp integer) -1 0)) |
|---|
| 1771 | (t (%iash (the fixnum integer) count))))))) |
|---|
| 1772 | (bignum |
|---|
| 1773 | (if (minusp count) |
|---|
| 1774 | (if (minusp integer) -1 0) |
|---|
| 1775 | (error "Count ~s too large for ASH" count))))) |
|---|
| 1776 | (bignum |
|---|
| 1777 | (etypecase count |
|---|
| 1778 | (fixnum |
|---|
| 1779 | (if (eql count 0) |
|---|
| 1780 | integer |
|---|
| 1781 | (if (plusp count) |
|---|
| 1782 | (bignum-ashift-left integer count) |
|---|
| 1783 | (bignum-ashift-right integer (- count))))) |
|---|
| 1784 | (bignum |
|---|
| 1785 | (if (minusp count) |
|---|
| 1786 | (if (minusp integer) -1 0) |
|---|
| 1787 | (error "Count ~s too large for ASH" count))))))) |
|---|
| 1788 | |
|---|
| 1789 | (defun integer-length (integer) |
|---|
| 1790 | "Return the number of significant bits in the absolute value of integer." |
|---|
| 1791 | (number-case integer |
|---|
| 1792 | (fixnum |
|---|
| 1793 | (%fixnum-intlen (the fixnum integer))) |
|---|
| 1794 | (bignum |
|---|
| 1795 | (bignum-integer-length integer)))) |
|---|
| 1796 | |
|---|
| 1797 | |
|---|
| 1798 | ; not CL, used below |
|---|
| 1799 | (defun byte-mask (size) |
|---|
| 1800 | (1- (ash 1 (the fixnum size)))) |
|---|
| 1801 | |
|---|
| 1802 | (defun byte-position (bytespec) |
|---|
| 1803 | "Return the position part of the byte specifier bytespec." |
|---|
| 1804 | (if (> bytespec 0) |
|---|
| 1805 | (- (integer-length bytespec) (logcount bytespec)) |
|---|
| 1806 | (- bytespec))) |
|---|
| 1807 | |
|---|
| 1808 | |
|---|
| 1809 | ; CMU CL returns T. |
|---|
| 1810 | (defun upgraded-complex-part-type (type) |
|---|
| 1811 | "Return the element type of the most specialized COMPLEX number type that |
|---|
| 1812 | can hold parts of type SPEC." |
|---|
| 1813 | (declare (ignore type)) |
|---|
| 1814 | 'real) |
|---|
| 1815 | |
|---|
| 1816 | ;;; This is the MRG31k3p random number generator described in |
|---|
| 1817 | ;;; P. L'Ecuyer and R. Touzin, "Fast Combined Multiple Recursive |
|---|
| 1818 | ;;; Generators with Multipliers of the form a = +/- 2^d +/- 2^e", |
|---|
| 1819 | ;;; Proceedings of the 2000 Winter Simulation Conference, Dec. 2000, |
|---|
| 1820 | ;;; 683--689. |
|---|
| 1821 | ;;; |
|---|
| 1822 | ;;; A link to the paper is available on L'Ecuyer's web site: |
|---|
| 1823 | ;;; http://www.iro.umontreal.ca/~lecuyer/papers.html. |
|---|
| 1824 | ;;; |
|---|
| 1825 | ;;; This generator has a period of about 2^185. It produces values in |
|---|
| 1826 | ;;; in the half-open interval [0, 2^31 - 1). |
|---|
| 1827 | ;;; |
|---|
| 1828 | ;;; It uses 6 words of state. |
|---|
| 1829 | |
|---|
| 1830 | (defconstant mrg31k3p-m1 #.(- (expt 2 31) 1)) |
|---|
| 1831 | (defconstant mrg31k3p-m2 #.(- (expt 2 31) 21069)) |
|---|
| 1832 | (defconstant mrg31k3p-limit #.(1- (expt 2 31)) |
|---|
| 1833 | "Exclusive upper bound on values returned by %mrg31k3p.") |
|---|
| 1834 | |
|---|
| 1835 | |
|---|
| 1836 | ;;; This is a portable version of the MRG31k3p generator. It's not |
|---|
| 1837 | ;;; too bad in a 64-bit CCL, but the generator pretty much has to be |
|---|
| 1838 | ;;; in LAP for 32-bit ports. |
|---|
| 1839 | #-(or x8632-target ppc32-target x8664-target ppc64-target arm-target) |
|---|
| 1840 | (defun %mrg31k3p (state) |
|---|
| 1841 | (let* ((v (random.mrg31k3p-state state))) |
|---|
| 1842 | (declare (type (simple-array (unsigned-byte 32) (*)) v) |
|---|
| 1843 | (optimize speed)) |
|---|
| 1844 | (let ((y1 (+ (+ (ash (logand (aref v 1) #x1ff) 22) |
|---|
| 1845 | (ash (aref v 1) -9)) |
|---|
| 1846 | (+ (ash (logand (aref v 2) #xffffff) 7) |
|---|
| 1847 | (ash (aref v 2) -24))))) |
|---|
| 1848 | (declare (type (unsigned-byte 32) y1)) |
|---|
| 1849 | (if (>= y1 mrg31k3p-m1) (decf y1 mrg31k3p-m1)) |
|---|
| 1850 | (incf y1 (aref v 2)) |
|---|
| 1851 | (if (>= y1 mrg31k3p-m1) (decf y1 mrg31k3p-m1)) |
|---|
| 1852 | (setf (aref v 2) (aref v 1) |
|---|
| 1853 | (aref v 1) (aref v 0) |
|---|
| 1854 | (aref v 0) y1)) |
|---|
| 1855 | (let ((y1 (+ (ash (logand (aref v 3) #xffff) 15) |
|---|
| 1856 | (* 21069 (ash (aref v 3) -16)))) |
|---|
| 1857 | (y2 (+ (ash (logand (aref v 5) #xffff) 15) |
|---|
| 1858 | (* 21069 (ash (aref v 5) -16))))) |
|---|
| 1859 | (declare (type (unsigned-byte 32) y1 y2)) |
|---|
| 1860 | (if (>= y1 mrg31k3p-m2) (decf y1 mrg31k3p-m2)) |
|---|
| 1861 | (if (>= y2 mrg31k3p-m2) (decf y2 mrg31k3p-m2)) |
|---|
| 1862 | (incf y2 (aref v 5)) |
|---|
| 1863 | (if (>= y2 mrg31k3p-m2) (decf y2 mrg31k3p-m2)) |
|---|
| 1864 | (incf y2 y1) |
|---|
| 1865 | (if (>= y2 mrg31k3p-m2) (decf y2 mrg31k3p-m2)) |
|---|
| 1866 | (setf (aref v 5) (aref v 4) |
|---|
| 1867 | (aref v 4) (aref v 3) |
|---|
| 1868 | (aref v 3) y2)) |
|---|
| 1869 | (let* ((x10 (aref v 0)) |
|---|
| 1870 | (x20 (aref v 3))) |
|---|
| 1871 | (if (<= x10 x20) |
|---|
| 1872 | (+ (- x10 x20) mrg31k3p-m1) |
|---|
| 1873 | (- x10 x20))))) |
|---|
| 1874 | |
|---|
| 1875 | (eval-when (:compile-toplevel :execute) |
|---|
| 1876 | (declaim (inline %16-random-bits))) |
|---|
| 1877 | |
|---|
| 1878 | (defun %16-random-bits (state) |
|---|
| 1879 | (logand #xffff (the fixnum (%mrg31k3p state)))) |
|---|
| 1880 | |
|---|
| 1881 | #+64-bit-target |
|---|
| 1882 | (defun %big-fixnum-random (number state) |
|---|
| 1883 | (declare (fixnum number) |
|---|
| 1884 | (ftype (function (random-state) fixnum) %mrg31k3p)) |
|---|
| 1885 | (let ((low (ldb (byte 30 0) (%mrg31k3p state))) |
|---|
| 1886 | (high (ldb (byte 30 0) (%mrg31k3p state)))) |
|---|
| 1887 | (declare (fixnum low high)) |
|---|
| 1888 | (fast-mod (logior low (the fixnum (ash high 30))) |
|---|
| 1889 | number))) |
|---|
| 1890 | |
|---|
| 1891 | ;;; When using a dead simple random number generator, it's reasonable |
|---|
| 1892 | ;;; to take 16 bits of the output and discard the rest. With a more |
|---|
| 1893 | ;;; expensive generator, however, it may be worthwhile to do more bit |
|---|
| 1894 | ;;; fiddling here here so that we can use all of the random bits |
|---|
| 1895 | ;;; produced by %mrg31k2p. |
|---|
| 1896 | #+32-bit-target |
|---|
| 1897 | (defun %bignum-random (number state) |
|---|
| 1898 | (let* ((bits (+ (integer-length number) 8)) |
|---|
| 1899 | (half-words (ash (the fixnum (+ bits 15)) -4)) |
|---|
| 1900 | (long-words (ash (+ half-words 1) -1)) |
|---|
| 1901 | (dividend (%alloc-misc long-words target::subtag-bignum)) |
|---|
| 1902 | (16-bit-dividend dividend) |
|---|
| 1903 | (index 1)) |
|---|
| 1904 | (declare (fixnum long-words index bits) |
|---|
| 1905 | (dynamic-extent dividend) |
|---|
| 1906 | (type (simple-array (unsigned-byte 16) (*)) 16-bit-dividend) ;lie |
|---|
| 1907 | (optimize (speed 3) (safety 0))) |
|---|
| 1908 | (loop |
|---|
| 1909 | ;; This had better inline due to the lie above, or it will error |
|---|
| 1910 | #+big-endian-target |
|---|
| 1911 | (setf (aref 16-bit-dividend index) (%16-random-bits state)) |
|---|
| 1912 | #+little-endian-target |
|---|
| 1913 | (setf (aref 16-bit-dividend (the fixnum (1- index))) |
|---|
| 1914 | (%16-random-bits state)) |
|---|
| 1915 | (decf half-words) |
|---|
| 1916 | (when (<= half-words 0) (return)) |
|---|
| 1917 | #+big-endian-target |
|---|
| 1918 | (setf (aref 16-bit-dividend (the fixnum (1- index))) |
|---|
| 1919 | (%16-random-bits state)) |
|---|
| 1920 | #+little-endian-target |
|---|
| 1921 | (setf (aref 16-bit-dividend index) (%16-random-bits state)) |
|---|
| 1922 | (decf half-words) |
|---|
| 1923 | (when (<= half-words 0) (return)) |
|---|
| 1924 | (incf index 2)) |
|---|
| 1925 | ;; The bignum code expects normalized bignums |
|---|
| 1926 | (let* ((result (mod dividend number))) |
|---|
| 1927 | (if (eq dividend result) |
|---|
| 1928 | (copy-uvector result) |
|---|
| 1929 | result)))) |
|---|
| 1930 | |
|---|
| 1931 | (defun %float-random (number state) |
|---|
| 1932 | (let ((ratio (gvector :ratio (random target::target-most-positive-fixnum state) target::target-most-positive-fixnum))) |
|---|
| 1933 | (declare (dynamic-extent ratio)) |
|---|
| 1934 | (* number ratio))) |
|---|
| 1935 | |
|---|
| 1936 | (defun random (number &optional (state *random-state*)) |
|---|
| 1937 | (if (not (typep state 'random-state)) (report-bad-arg state 'random-state)) |
|---|
| 1938 | (cond |
|---|
| 1939 | ((and (fixnump number) (> (the fixnum number) 0)) |
|---|
| 1940 | #+32-bit-target |
|---|
| 1941 | (fast-mod (%mrg31k3p state) number) |
|---|
| 1942 | #+64-bit-target |
|---|
| 1943 | (if (< number mrg31k3p-limit) |
|---|
| 1944 | (fast-mod (%mrg31k3p state) number) |
|---|
| 1945 | (%big-fixnum-random number state))) |
|---|
| 1946 | ((and (typep number 'double-float) (> (the double-float number) 0.0)) |
|---|
| 1947 | (%float-random number state)) |
|---|
| 1948 | ((and (typep number 'short-float) (> (the short-float number) 0.0s0)) |
|---|
| 1949 | (%float-random number state)) |
|---|
| 1950 | ((and (bignump number) (> number 0)) |
|---|
| 1951 | (%bignum-random number state)) |
|---|
| 1952 | (t (report-bad-arg number '(or (integer (0)) (float (0.0))))))) |
|---|
| 1953 | |
|---|
| 1954 | (eval-when (:compile-toplevel :execute) |
|---|
| 1955 | (defmacro bignum-abs (nexp) |
|---|
| 1956 | (let ((n (gensym))) |
|---|
| 1957 | `(let ((,n ,nexp)) |
|---|
| 1958 | (if (bignum-minusp ,n) (negate-bignum ,n) ,n)))) |
|---|
| 1959 | |
|---|
| 1960 | (defmacro fixnum-abs (nexp) |
|---|
| 1961 | (let ((n (gensym))) |
|---|
| 1962 | `(let ((,n ,nexp)) |
|---|
| 1963 | (if (minusp (the fixnum ,n)) |
|---|
| 1964 | (if (eq ,n target::target-most-negative-fixnum) |
|---|
| 1965 | (- ,n) |
|---|
| 1966 | (the fixnum (- (the fixnum ,n)))) |
|---|
| 1967 | ,n)))) |
|---|
| 1968 | ) |
|---|
| 1969 | |
|---|
| 1970 | |
|---|
| 1971 | ;;; TWO-ARG-GCD -- Internal |
|---|
| 1972 | ;;; |
|---|
| 1973 | ;;; Do the GCD of two integer arguments. With fixnum arguments, we use the |
|---|
| 1974 | ;;; binary GCD algorithm from Knuth's seminumerical algorithms (slightly |
|---|
| 1975 | ;;; structurified), otherwise we call BIGNUM-GCD. We pick off the special case |
|---|
| 1976 | ;;; of 0 before the dispatch so that the bignum code doesn't have to worry |
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| 1977 | ;;; about "small bignum" zeros. |
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| 1978 | ;;; |
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| 1979 | (defun gcd-2 (n1 n2) |
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| 1980 | ;(declare (optimize (speed 3)(safety 0))) |
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| 1981 | (cond |
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| 1982 | ((eql n1 0) (%integer-abs n2)) |
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| 1983 | ((eql n2 0) (%integer-abs n1)) |
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| 1984 | (t (number-case n1 |
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| 1985 | (fixnum |
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| 1986 | (number-case n2 |
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| 1987 | (fixnum |
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| 1988 | (if (eql n1 target::target-most-negative-fixnum) |
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| 1989 | (if (eql n2 target::target-most-negative-fixnum) |
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| 1990 | (- target::target-most-negative-fixnum) |
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| 1991 | (bignum-fixnum-gcd (- target::target-most-negative-fixnum) (abs n2))) |
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| 1992 | (if (eql n2 target::target-most-negative-fixnum) |
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| 1993 | (bignum-fixnum-gcd (- target::target-most-negative-fixnum) (abs n1)) |
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| 1994 | (locally |
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| 1995 | (declare (optimize (speed 3) (safety 0)) |
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| 1996 | (fixnum n1 n2)) |
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| 1997 | (if (minusp n1)(setq n1 (the fixnum (- n1)))) |
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| 1998 | (if (minusp n2)(setq n2 (the fixnum (- n2)))) |
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| 1999 | (%fixnum-gcd n1 n2))))) |
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| 2000 | (bignum (if (eql n1 target::target-most-negative-fixnum) |
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| 2001 | (%bignum-bignum-gcd n2 (- target::target-most-negative-fixnum)) |
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| 2002 | (bignum-fixnum-gcd (bignum-abs n2)(fixnum-abs n1)))))) |
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| 2003 | (bignum |
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| 2004 | (number-case n2 |
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| 2005 | (fixnum |
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| 2006 | (if (eql n2 target::target-most-negative-fixnum) |
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| 2007 | (%bignum-bignum-gcd (bignum-abs n1)(fixnum-abs n2)) |
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| 2008 | (bignum-fixnum-gcd (bignum-abs n1)(fixnum-abs n2)))) |
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| 2009 | (bignum (%bignum-bignum-gcd n1 n2)))))))) |
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| 2010 | |
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| 2011 | #| |
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| 2012 | (defun fixnum-gcd (n1 n2) |
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| 2013 | (declare (optimize (speed 3) (safety 0)) |
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| 2014 | (fixnum n1 n2)) |
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| 2015 | (do* ((k 0 (%i+ 1 k)) |
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| 2016 | (n1 n1 (%iasr 1 n1)) |
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| 2017 | (n2 n2 (%iasr 1 n2))) |
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| 2018 | ((oddp (logior n1 n2)) |
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| 2019 | (do ((temp (if (oddp n1) (the fixnum (- n2)) (%iasr 1 n1)) |
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| 2020 | (%iasr 1 temp))) |
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| 2021 | (nil) |
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| 2022 | (declare (fixnum temp)) |
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| 2023 | (when (oddp temp) |
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| 2024 | (if (plusp temp) |
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| 2025 | (setq n1 temp) |
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| 2026 | (setq n2 (- temp))) |
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| 2027 | (setq temp (the fixnum (- n1 n2))) |
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| 2028 | (when (zerop temp) |
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| 2029 | (let ((res (%ilsl k n1))) |
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| 2030 | (return res)))))) |
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| 2031 | (declare (fixnum n1 n2 k)))) |
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| 2032 | |# |
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| 2033 | |
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| 2034 | |
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| 2035 | |
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| 2036 | (defun %quo-1 (n) |
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| 2037 | (/ 1 n)) |
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| 2038 | |
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| 2039 | ;; Compute (sqrt (+ (* x x) (* y y))), but |
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| 2040 | ;; try to be a little more careful about it. |
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| 2041 | ;; Both x and y must be double-floats. |
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| 2042 | (defun %double-float-hypot (x y) |
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| 2043 | (with-stack-double-floats ((a) (b) (c)) |
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| 2044 | (%%double-float-abs! x a) |
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| 2045 | (%%double-float-abs! y b) |
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| 2046 | (when (> a b) |
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| 2047 | (psetq a b b a)) |
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| 2048 | (if (= b 0d0) |
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| 2049 | 0d0 |
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| 2050 | (progn |
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| 2051 | (%double-float/-2! a b c) |
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| 2052 | (* b (fsqrt (+ 1d0 (* c c)))))))) |
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| 2053 | |
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