1 /*
2  * Copyright (C) 2013 The Android Open Source Project
3  *
4  * Licensed under the Apache License, Version 2.0 (the "License");
5  * you may not use this file except in compliance with the License.
6  * You may obtain a copy of the License at
7  *
8  *      http://www.apache.org/licenses/LICENSE-2.0
9  *
10  * Unless required by applicable law or agreed to in writing, software
11  * distributed under the License is distributed on an "AS IS" BASIS,
12  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13  * See the License for the specific language governing permissions and
14  * limitations under the License.
15  */
16 package android.bluetooth;
17 
18 import android.os.Parcel;
19 import android.os.Parcelable;
20 import android.os.ParcelUuid;
21 import java.util.ArrayList;
22 import java.util.List;
23 import java.util.UUID;
24 
25 /**
26  * Represents a Bluetooth GATT Characteristic
27  *
28  * <p>A GATT characteristic is a basic data element used to construct a GATT service,
29  * {@link BluetoothGattService}. The characteristic contains a value as well as
30  * additional information and optional GATT descriptors, {@link BluetoothGattDescriptor}.
31  */
32 public class BluetoothGattCharacteristic implements Parcelable {
33 
34     /**
35      * Characteristic proprty: Characteristic is broadcastable.
36      */
37     public static final int PROPERTY_BROADCAST = 0x01;
38 
39     /**
40      * Characteristic property: Characteristic is readable.
41      */
42     public static final int PROPERTY_READ = 0x02;
43 
44     /**
45      * Characteristic property: Characteristic can be written without response.
46      */
47     public static final int PROPERTY_WRITE_NO_RESPONSE = 0x04;
48 
49     /**
50      * Characteristic property: Characteristic can be written.
51      */
52     public static final int PROPERTY_WRITE = 0x08;
53 
54     /**
55      * Characteristic property: Characteristic supports notification
56      */
57     public static final int PROPERTY_NOTIFY = 0x10;
58 
59     /**
60      * Characteristic property: Characteristic supports indication
61      */
62     public static final int PROPERTY_INDICATE = 0x20;
63 
64     /**
65      * Characteristic property: Characteristic supports write with signature
66      */
67     public static final int PROPERTY_SIGNED_WRITE = 0x40;
68 
69     /**
70      * Characteristic property: Characteristic has extended properties
71      */
72     public static final int PROPERTY_EXTENDED_PROPS = 0x80;
73 
74     /**
75      * Characteristic read permission
76      */
77     public static final int PERMISSION_READ = 0x01;
78 
79     /**
80      * Characteristic permission: Allow encrypted read operations
81      */
82     public static final int PERMISSION_READ_ENCRYPTED = 0x02;
83 
84     /**
85      * Characteristic permission: Allow reading with man-in-the-middle protection
86      */
87     public static final int PERMISSION_READ_ENCRYPTED_MITM = 0x04;
88 
89     /**
90      * Characteristic write permission
91      */
92     public static final int PERMISSION_WRITE = 0x10;
93 
94     /**
95      * Characteristic permission: Allow encrypted writes
96      */
97     public static final int PERMISSION_WRITE_ENCRYPTED = 0x20;
98 
99     /**
100      * Characteristic permission: Allow encrypted writes with man-in-the-middle
101      * protection
102      */
103     public static final int PERMISSION_WRITE_ENCRYPTED_MITM = 0x40;
104 
105     /**
106      * Characteristic permission: Allow signed write operations
107      */
108     public static final int PERMISSION_WRITE_SIGNED = 0x80;
109 
110     /**
111      * Characteristic permission: Allow signed write operations with
112      * man-in-the-middle protection
113      */
114     public static final int PERMISSION_WRITE_SIGNED_MITM = 0x100;
115 
116     /**
117      * Write characteristic, requesting acknoledgement by the remote device
118      */
119     public static final int WRITE_TYPE_DEFAULT = 0x02;
120 
121     /**
122      * Wrtite characteristic without requiring a response by the remote device
123      */
124     public static final int WRITE_TYPE_NO_RESPONSE = 0x01;
125 
126     /**
127      * Write characteristic including authentication signature
128      */
129     public static final int WRITE_TYPE_SIGNED = 0x04;
130 
131     /**
132      * Characteristic value format type uint8
133      */
134     public static final int FORMAT_UINT8 = 0x11;
135 
136     /**
137      * Characteristic value format type uint16
138      */
139     public static final int FORMAT_UINT16 = 0x12;
140 
141     /**
142      * Characteristic value format type uint32
143      */
144     public static final int FORMAT_UINT32 = 0x14;
145 
146     /**
147      * Characteristic value format type sint8
148      */
149     public static final int FORMAT_SINT8 = 0x21;
150 
151     /**
152      * Characteristic value format type sint16
153      */
154     public static final int FORMAT_SINT16 = 0x22;
155 
156     /**
157      * Characteristic value format type sint32
158      */
159     public static final int FORMAT_SINT32 = 0x24;
160 
161     /**
162      * Characteristic value format type sfloat (16-bit float)
163      */
164     public static final int FORMAT_SFLOAT = 0x32;
165 
166     /**
167      * Characteristic value format type float (32-bit float)
168      */
169     public static final int FORMAT_FLOAT = 0x34;
170 
171 
172     /**
173      * The UUID of this characteristic.
174      * @hide
175      */
176     protected UUID mUuid;
177 
178     /**
179      * Instance ID for this characteristic.
180      * @hide
181      */
182     protected int mInstance;
183 
184     /**
185      * Characteristic properties.
186      * @hide
187      */
188     protected int mProperties;
189 
190     /**
191      * Characteristic permissions.
192      * @hide
193      */
194     protected int mPermissions;
195 
196     /**
197      * Key size (default = 16).
198      * @hide
199      */
200     protected int mKeySize = 16;
201 
202     /**
203      * Write type for this characteristic.
204      * See WRITE_TYPE_* constants.
205      * @hide
206      */
207     protected int mWriteType;
208 
209     /**
210      * Back-reference to the service this characteristic belongs to.
211      * @hide
212      */
213     protected BluetoothGattService mService;
214 
215     /**
216      * The cached value of this characteristic.
217      * @hide
218      */
219     protected byte[] mValue;
220 
221     /**
222      * List of descriptors included in this characteristic.
223      */
224     protected List<BluetoothGattDescriptor> mDescriptors;
225 
226     /**
227      * Create a new BluetoothGattCharacteristic.
228      * <p>Requires {@link android.Manifest.permission#BLUETOOTH} permission.
229      *
230      * @param uuid The UUID for this characteristic
231      * @param properties Properties of this characteristic
232      * @param permissions Permissions for this characteristic
233      */
BluetoothGattCharacteristic(UUID uuid, int properties, int permissions)234     public BluetoothGattCharacteristic(UUID uuid, int properties, int permissions) {
235         initCharacteristic(null, uuid, 0, properties, permissions);
236     }
237 
238     /**
239      * Create a new BluetoothGattCharacteristic
240      * @hide
241      */
BluetoothGattCharacteristic(BluetoothGattService service, UUID uuid, int instanceId, int properties, int permissions)242     /*package*/ BluetoothGattCharacteristic(BluetoothGattService service,
243                                             UUID uuid, int instanceId,
244                                             int properties, int permissions) {
245         initCharacteristic(service, uuid, instanceId, properties, permissions);
246     }
247 
248     /**
249      * Create a new BluetoothGattCharacteristic
250      * @hide
251      */
BluetoothGattCharacteristic(UUID uuid, int instanceId, int properties, int permissions)252     public BluetoothGattCharacteristic(UUID uuid, int instanceId,
253                                        int properties, int permissions) {
254         initCharacteristic(null, uuid, instanceId, properties, permissions);
255     }
256 
initCharacteristic(BluetoothGattService service, UUID uuid, int instanceId, int properties, int permissions)257     private void initCharacteristic(BluetoothGattService service,
258                                     UUID uuid, int instanceId,
259                                     int properties, int permissions) {
260         mUuid = uuid;
261         mInstance = instanceId;
262         mProperties = properties;
263         mPermissions = permissions;
264         mService = service;
265         mValue = null;
266         mDescriptors = new ArrayList<BluetoothGattDescriptor>();
267 
268         if ((mProperties & PROPERTY_WRITE_NO_RESPONSE) != 0) {
269             mWriteType = WRITE_TYPE_NO_RESPONSE;
270         } else {
271             mWriteType = WRITE_TYPE_DEFAULT;
272         }
273     }
274 
275     /**
276      * @hide
277      */
describeContents()278     public int describeContents() {
279         return 0;
280     }
281 
writeToParcel(Parcel out, int flags)282     public void writeToParcel(Parcel out, int flags) {
283         out.writeParcelable(new ParcelUuid(mUuid), 0);
284         out.writeInt(mInstance);
285         out.writeInt(mProperties);
286         out.writeInt(mPermissions);
287         out.writeInt(mKeySize);
288         out.writeInt(mWriteType);
289         out.writeTypedList(mDescriptors);
290     }
291 
292     public static final Parcelable.Creator<BluetoothGattCharacteristic> CREATOR
293             = new Parcelable.Creator<BluetoothGattCharacteristic>() {
294         public BluetoothGattCharacteristic createFromParcel(Parcel in) {
295             return new BluetoothGattCharacteristic(in);
296         }
297 
298         public BluetoothGattCharacteristic[] newArray(int size) {
299             return new BluetoothGattCharacteristic[size];
300         }
301     };
302 
BluetoothGattCharacteristic(Parcel in)303     private BluetoothGattCharacteristic(Parcel in) {
304         mUuid = ((ParcelUuid)in.readParcelable(null)).getUuid();
305         mInstance = in.readInt();
306         mProperties = in.readInt();
307         mPermissions = in.readInt();
308         mKeySize = in.readInt();
309         mWriteType = in.readInt();
310 
311         mDescriptors = new ArrayList<BluetoothGattDescriptor>();
312 
313         ArrayList<BluetoothGattDescriptor> descs =
314                 in.createTypedArrayList(BluetoothGattDescriptor.CREATOR);
315         if (descs != null) {
316             for (BluetoothGattDescriptor desc: descs) {
317                 desc.setCharacteristic(this);
318                 mDescriptors.add(desc);
319             }
320         }
321     }
322 
323     /**
324      * Returns the deisred key size.
325      * @hide
326      */
getKeySize()327     /*package*/ int getKeySize() {
328         return mKeySize;
329     }
330 
331     /**
332      * Adds a descriptor to this characteristic.
333      * <p>Requires {@link android.Manifest.permission#BLUETOOTH} permission.
334      *
335      * @param descriptor Descriptor to be added to this characteristic.
336      * @return true, if the descriptor was added to the characteristic
337      */
addDescriptor(BluetoothGattDescriptor descriptor)338     public boolean addDescriptor(BluetoothGattDescriptor descriptor) {
339         mDescriptors.add(descriptor);
340         descriptor.setCharacteristic(this);
341         return true;
342     }
343 
344     /**
345      * Get a descriptor by UUID and isntance id.
346      * @hide
347      */
getDescriptor(UUID uuid, int instanceId)348     /*package*/  BluetoothGattDescriptor getDescriptor(UUID uuid, int instanceId) {
349         for(BluetoothGattDescriptor descriptor : mDescriptors) {
350             if (descriptor.getUuid().equals(uuid)
351              && descriptor.getInstanceId() == instanceId) {
352                 return descriptor;
353             }
354         }
355         return null;
356     }
357 
358     /**
359      * Returns the service this characteristic belongs to.
360      * @return The asscociated service
361      */
getService()362     public BluetoothGattService getService() {
363         return mService;
364     }
365 
366     /**
367      * Sets the service associated with this device.
368      * @hide
369      */
setService(BluetoothGattService service)370     /*package*/ void setService(BluetoothGattService service) {
371         mService = service;
372     }
373 
374     /**
375      * Returns the UUID of this characteristic
376      *
377      * @return UUID of this characteristic
378      */
getUuid()379     public UUID getUuid() {
380         return mUuid;
381     }
382 
383     /**
384      * Returns the instance ID for this characteristic.
385      *
386      * <p>If a remote device offers multiple characteristics with the same UUID,
387      * the instance ID is used to distuinguish between characteristics.
388      *
389      * @return Instance ID of this characteristic
390      */
getInstanceId()391     public int getInstanceId() {
392         return mInstance;
393     }
394 
395     /**
396      * Returns the properties of this characteristic.
397      *
398      * <p>The properties contain a bit mask of property flags indicating
399      * the features of this characteristic.
400      *
401      * @return Properties of this characteristic
402      */
getProperties()403     public int getProperties() {
404         return mProperties;
405     }
406 
407     /**
408      * Returns the permissions for this characteristic.
409      *
410      * @return Permissions of this characteristic
411      */
getPermissions()412     public int getPermissions() {
413         return mPermissions;
414     }
415 
416     /**
417      * Gets the write type for this characteristic.
418      *
419      * @return Write type for this characteristic
420      */
getWriteType()421     public int getWriteType() {
422         return mWriteType;
423     }
424 
425     /**
426      * Set the write type for this characteristic
427      *
428      * <p>Setting the write type of a characteristic determines how the
429      * {@link BluetoothGatt#writeCharacteristic} function write this
430      * characteristic.
431      *
432      * @param writeType The write type to for this characteristic. Can be one
433      *                  of:
434      *                  {@link #WRITE_TYPE_DEFAULT},
435      *                  {@link #WRITE_TYPE_NO_RESPONSE} or
436      *                  {@link #WRITE_TYPE_SIGNED}.
437      */
setWriteType(int writeType)438     public void setWriteType(int writeType) {
439         mWriteType = writeType;
440     }
441 
442     /**
443      * Set the desired key size.
444      * @hide
445      */
setKeySize(int keySize)446     public void setKeySize(int keySize) {
447         mKeySize = keySize;
448     }
449 
450     /**
451      * Returns a list of descriptors for this characteristic.
452      *
453      * @return Descriptors for this characteristic
454      */
getDescriptors()455     public List<BluetoothGattDescriptor> getDescriptors() {
456         return mDescriptors;
457     }
458 
459     /**
460      * Returns a descriptor with a given UUID out of the list of
461      * descriptors for this characteristic.
462      *
463      * @return GATT descriptor object or null if no descriptor with the
464      *         given UUID was found.
465      */
getDescriptor(UUID uuid)466     public BluetoothGattDescriptor getDescriptor(UUID uuid) {
467         for(BluetoothGattDescriptor descriptor : mDescriptors) {
468             if (descriptor.getUuid().equals(uuid)) {
469                 return descriptor;
470             }
471         }
472         return null;
473     }
474 
475     /**
476      * Get the stored value for this characteristic.
477      *
478      * <p>This function returns the stored value for this characteristic as
479      * retrieved by calling {@link BluetoothGatt#readCharacteristic}. The cached
480      * value of the characteristic is updated as a result of a read characteristic
481      * operation or if a characteristic update notification has been received.
482      *
483      * @return Cached value of the characteristic
484      */
getValue()485     public byte[] getValue() {
486         return mValue;
487     }
488 
489     /**
490      * Return the stored value of this characteristic.
491      *
492      * <p>The formatType parameter determines how the characteristic value
493      * is to be interpreted. For example, settting formatType to
494      * {@link #FORMAT_UINT16} specifies that the first two bytes of the
495      * characteristic value at the given offset are interpreted to generate the
496      * return value.
497      *
498      * @param formatType The format type used to interpret the characteristic
499      *                   value.
500      * @param offset Offset at which the integer value can be found.
501      * @return Cached value of the characteristic or null of offset exceeds
502      *         value size.
503      */
getIntValue(int formatType, int offset)504     public Integer getIntValue(int formatType, int offset) {
505         if ((offset + getTypeLen(formatType)) > mValue.length) return null;
506 
507         switch (formatType) {
508             case FORMAT_UINT8:
509                 return unsignedByteToInt(mValue[offset]);
510 
511             case FORMAT_UINT16:
512                 return unsignedBytesToInt(mValue[offset], mValue[offset+1]);
513 
514             case FORMAT_UINT32:
515                 return unsignedBytesToInt(mValue[offset],   mValue[offset+1],
516                                           mValue[offset+2], mValue[offset+3]);
517             case FORMAT_SINT8:
518                 return unsignedToSigned(unsignedByteToInt(mValue[offset]), 8);
519 
520             case FORMAT_SINT16:
521                 return unsignedToSigned(unsignedBytesToInt(mValue[offset],
522                                                            mValue[offset+1]), 16);
523 
524             case FORMAT_SINT32:
525                 return unsignedToSigned(unsignedBytesToInt(mValue[offset],
526                         mValue[offset+1], mValue[offset+2], mValue[offset+3]), 32);
527         }
528 
529         return null;
530     }
531 
532     /**
533      * Return the stored value of this characteristic.
534      * <p>See {@link #getValue} for details.
535      *
536      * @param formatType The format type used to interpret the characteristic
537      *                   value.
538      * @param offset Offset at which the float value can be found.
539      * @return Cached value of the characteristic at a given offset or null
540      *         if the requested offset exceeds the value size.
541      */
getFloatValue(int formatType, int offset)542     public Float getFloatValue(int formatType, int offset) {
543         if ((offset + getTypeLen(formatType)) > mValue.length) return null;
544 
545         switch (formatType) {
546             case FORMAT_SFLOAT:
547                 return bytesToFloat(mValue[offset], mValue[offset+1]);
548 
549             case FORMAT_FLOAT:
550                 return bytesToFloat(mValue[offset],   mValue[offset+1],
551                                     mValue[offset+2], mValue[offset+3]);
552         }
553 
554         return null;
555     }
556 
557     /**
558      * Return the stored value of this characteristic.
559      * <p>See {@link #getValue} for details.
560      *
561      * @param offset Offset at which the string value can be found.
562      * @return Cached value of the characteristic
563      */
getStringValue(int offset)564     public String getStringValue(int offset) {
565         if (mValue == null || offset > mValue.length) return null;
566         byte[] strBytes = new byte[mValue.length - offset];
567         for (int i=0; i != (mValue.length-offset); ++i) strBytes[i] = mValue[offset+i];
568         return new String(strBytes);
569     }
570 
571     /**
572      * Updates the locally stored value of this characteristic.
573      *
574      * <p>This function modifies the locally stored cached value of this
575      * characteristic. To send the value to the remote device, call
576      * {@link BluetoothGatt#writeCharacteristic} to send the value to the
577      * remote device.
578      *
579      * @param value New value for this characteristic
580      * @return true if the locally stored value has been set, false if the
581      *              requested value could not be stored locally.
582      */
setValue(byte[] value)583     public boolean setValue(byte[] value) {
584         mValue = value;
585         return true;
586     }
587 
588     /**
589      * Set the locally stored value of this characteristic.
590      * <p>See {@link #setValue(byte[])} for details.
591      *
592      * @param value New value for this characteristic
593      * @param formatType Integer format type used to transform the value parameter
594      * @param offset Offset at which the value should be placed
595      * @return true if the locally stored value has been set
596      */
setValue(int value, int formatType, int offset)597     public boolean setValue(int value, int formatType, int offset) {
598         int len = offset + getTypeLen(formatType);
599         if (mValue == null) mValue = new byte[len];
600         if (len > mValue.length) return false;
601 
602         switch (formatType) {
603             case FORMAT_SINT8:
604                 value = intToSignedBits(value, 8);
605                 // Fall-through intended
606             case FORMAT_UINT8:
607                 mValue[offset] = (byte)(value & 0xFF);
608                 break;
609 
610             case FORMAT_SINT16:
611                 value = intToSignedBits(value, 16);
612                 // Fall-through intended
613             case FORMAT_UINT16:
614                 mValue[offset++] = (byte)(value & 0xFF);
615                 mValue[offset] = (byte)((value >> 8) & 0xFF);
616                 break;
617 
618             case FORMAT_SINT32:
619                 value = intToSignedBits(value, 32);
620                 // Fall-through intended
621             case FORMAT_UINT32:
622                 mValue[offset++] = (byte)(value & 0xFF);
623                 mValue[offset++] = (byte)((value >> 8) & 0xFF);
624                 mValue[offset++] = (byte)((value >> 16) & 0xFF);
625                 mValue[offset] = (byte)((value >> 24) & 0xFF);
626                 break;
627 
628             default:
629                 return false;
630         }
631         return true;
632     }
633 
634     /**
635      * Set the locally stored value of this characteristic.
636      * <p>See {@link #setValue(byte[])} for details.
637      *
638      * @param mantissa Mantissa for this characteristic
639      * @param exponent  exponent value for this characteristic
640      * @param formatType Float format type used to transform the value parameter
641      * @param offset Offset at which the value should be placed
642      * @return true if the locally stored value has been set
643      */
setValue(int mantissa, int exponent, int formatType, int offset)644     public boolean setValue(int mantissa, int exponent, int formatType, int offset) {
645         int len = offset + getTypeLen(formatType);
646         if (mValue == null) mValue = new byte[len];
647         if (len > mValue.length) return false;
648 
649         switch (formatType) {
650             case FORMAT_SFLOAT:
651                 mantissa = intToSignedBits(mantissa, 12);
652                 exponent = intToSignedBits(exponent, 4);
653                 mValue[offset++] = (byte)(mantissa & 0xFF);
654                 mValue[offset] = (byte)((mantissa >> 8) & 0x0F);
655                 mValue[offset] += (byte)((exponent & 0x0F) << 4);
656                 break;
657 
658             case FORMAT_FLOAT:
659                 mantissa = intToSignedBits(mantissa, 24);
660                 exponent = intToSignedBits(exponent, 8);
661                 mValue[offset++] = (byte)(mantissa & 0xFF);
662                 mValue[offset++] = (byte)((mantissa >> 8) & 0xFF);
663                 mValue[offset++] = (byte)((mantissa >> 16) & 0xFF);
664                 mValue[offset] += (byte)(exponent & 0xFF);
665                 break;
666 
667             default:
668                 return false;
669         }
670 
671         return true;
672     }
673 
674     /**
675      * Set the locally stored value of this characteristic.
676      * <p>See {@link #setValue(byte[])} for details.
677      *
678      * @param value New value for this characteristic
679      * @return true if the locally stored value has been set
680      */
setValue(String value)681     public boolean setValue(String value) {
682         mValue = value.getBytes();
683         return true;
684     }
685 
686     /**
687      * Returns the size of a give value type.
688      */
getTypeLen(int formatType)689     private int getTypeLen(int formatType) {
690         return formatType & 0xF;
691     }
692 
693     /**
694      * Convert a signed byte to an unsigned int.
695      */
unsignedByteToInt(byte b)696     private int unsignedByteToInt(byte b) {
697         return b & 0xFF;
698     }
699 
700     /**
701      * Convert signed bytes to a 16-bit unsigned int.
702      */
unsignedBytesToInt(byte b0, byte b1)703     private int unsignedBytesToInt(byte b0, byte b1) {
704         return (unsignedByteToInt(b0) + (unsignedByteToInt(b1) << 8));
705     }
706 
707     /**
708      * Convert signed bytes to a 32-bit unsigned int.
709      */
unsignedBytesToInt(byte b0, byte b1, byte b2, byte b3)710     private int unsignedBytesToInt(byte b0, byte b1, byte b2, byte b3) {
711         return (unsignedByteToInt(b0) + (unsignedByteToInt(b1) << 8))
712              + (unsignedByteToInt(b2) << 16) + (unsignedByteToInt(b3) << 24);
713     }
714 
715     /**
716      * Convert signed bytes to a 16-bit short float value.
717      */
bytesToFloat(byte b0, byte b1)718     private float bytesToFloat(byte b0, byte b1) {
719         int mantissa = unsignedToSigned(unsignedByteToInt(b0)
720                         + ((unsignedByteToInt(b1) & 0x0F) << 8), 12);
721         int exponent = unsignedToSigned(unsignedByteToInt(b1) >> 4, 4);
722         return (float)(mantissa * Math.pow(10, exponent));
723     }
724 
725     /**
726      * Convert signed bytes to a 32-bit short float value.
727      */
bytesToFloat(byte b0, byte b1, byte b2, byte b3)728     private float bytesToFloat(byte b0, byte b1, byte b2, byte b3) {
729         int mantissa = unsignedToSigned(unsignedByteToInt(b0)
730                         + (unsignedByteToInt(b1) << 8)
731                         + (unsignedByteToInt(b2) << 16), 24);
732         return (float)(mantissa * Math.pow(10, b3));
733     }
734 
735     /**
736      * Convert an unsigned integer value to a two's-complement encoded
737      * signed value.
738      */
unsignedToSigned(int unsigned, int size)739     private int unsignedToSigned(int unsigned, int size) {
740         if ((unsigned & (1 << size-1)) != 0) {
741             unsigned = -1 * ((1 << size-1) - (unsigned & ((1 << size-1) - 1)));
742         }
743         return unsigned;
744     }
745 
746     /**
747      * Convert an integer into the signed bits of a given length.
748      */
intToSignedBits(int i, int size)749     private int intToSignedBits(int i, int size) {
750         if (i < 0) {
751             i = (1 << size-1) + (i & ((1 << size-1) - 1));
752         }
753         return i;
754     }
755 }
756