无符号256位整数运算(转)

无符号256位整数运算

 转 https://blog.csdn.net/tigerisland45/article/details/54676554

 

源代码出处：github blue-app-eth/src_common。

这个源代码包括两个文件，分别是uint256.h和uint256.c。

有关计算是基于类型uint128_t上实现的。

uint256.h代码如下：

1.  
   /*******************************************************************************
2.  
   * Ledger Blue
3.  
   * (c) 2016 Ledger
4.  
   *
5.  
   * Licensed under the Apache License, Version 2.0 (the "License");
6.  
   * you may not use this file except in compliance with the License.
7.  
   * You may obtain a copy of the License at
8.  
   *
9.  
   * http://www.apache.org/licenses/LICENSE-2.0
10.  
    *
11.  
    * Unless required by applicable law or agreed to in writing, software
12.  
    * distributed under the License is distributed on an "AS IS" BASIS,
13.  
    * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14.  
    * See the License for the specific language governing permissions and
15.  
    * limitations under the License.
16.  
    ********************************************************************************/
17.  
     
18.  
    // Adapted from https://github.com/calccrypto/uint256_t
19.  
     
20.  
    #include <stdint.h>
21.  
    #include <stdbool.h>
22.  
     
23.  
    typedef struct uint128_t { uint64_t elements[2]; } uint128_t;
24.  
     
25.  
    typedef struct uint256_t { uint128_t elements[2]; } uint256_t;
26.  
     
27.  
    #define UPPER_P(x) x->elements[0]
28.  
    #define LOWER_P(x) x->elements[1]
29.  
    #define UPPER(x) x.elements[0]
30.  
    #define LOWER(x) x.elements[1]
31.  
     
32.  
    void readu128BE(uint8_t *buffer, uint128_t *target);
33.  
    void readu256BE(uint8_t *buffer, uint256_t *target);
34.  
    bool zero128(uint128_t *number);
35.  
    bool zero256(uint256_t *number);
36.  
    void copy128(uint128_t *target, uint128_t *number);
37.  
    void copy256(uint256_t *target, uint256_t *number);
38.  
    void clear128(uint128_t *target);
39.  
    void clear256(uint256_t *target);
40.  
    void shiftl128(uint128_t *number, uint32_t value, uint128_t *target);
41.  
    void shiftr128(uint128_t *number, uint32_t value, uint128_t *target);
42.  
    void shiftl256(uint256_t *number, uint32_t value, uint256_t *target);
43.  
    void shiftr256(uint256_t *number, uint32_t value, uint256_t *target);
44.  
    uint32_t bits128(uint128_t *number);
45.  
    uint32_t bits256(uint256_t *number);
46.  
    bool equal128(uint128_t *number1, uint128_t *number2);
47.  
    bool equal256(uint256_t *number1, uint256_t *number2);
48.  
    bool gt128(uint128_t *number1, uint128_t *number2);
49.  
    bool gt256(uint256_t *number1, uint256_t *number2);
50.  
    bool gte128(uint128_t *number1, uint128_t *number2);
51.  
    bool gte256(uint256_t *number1, uint256_t *number2);
52.  
    void add128(uint128_t *number1, uint128_t *number2, uint128_t *target);
53.  
    void add256(uint256_t *number1, uint256_t *number2, uint256_t *target);
54.  
    void minus128(uint128_t *number1, uint128_t *number2, uint128_t *target);
55.  
    void minus256(uint256_t *number1, uint256_t *number2, uint256_t *target);
56.  
    void or128(uint128_t *number1, uint128_t *number2, uint128_t *target);
57.  
    void or256(uint256_t *number1, uint256_t *number2, uint256_t *target);
58.  
    void mul128(uint128_t *number1, uint128_t *number2, uint128_t *target);
59.  
    void mul256(uint256_t *number1, uint256_t *number2, uint256_t *target);
60.  
    void divmod128(uint128_t *l, uint128_t *r, uint128_t *div, uint128_t *mod);
61.  
    void divmod256(uint256_t *l, uint256_t *r, uint256_t *div, uint256_t *mod);
62.  
    bool tostring128(uint128_t *number, uint32_t base, char *out,
63.  
    uint32_t outLength);
64.  
    bool tostring256(uint256_t *number, uint32_t base, char *out,
65.  
    uint32_t outLength);

uint256.c代码如下：

1.  
   /*******************************************************************************
2.  
   * Ledger Blue
3.  
   * (c) 2016 Ledger
4.  
   *
5.  
   * Licensed under the Apache License, Version 2.0 (the "License");
6.  
   * you may not use this file except in compliance with the License.
7.  
   * You may obtain a copy of the License at
8.  
   *
9.  
   * http://www.apache.org/licenses/LICENSE-2.0
10.  
    *
11.  
    * Unless required by applicable law or agreed to in writing, software
12.  
    * distributed under the License is distributed on an "AS IS" BASIS,
13.  
    * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14.  
    * See the License for the specific language governing permissions and
15.  
    * limitations under the License.
16.  
    ********************************************************************************/
17.  
     
18.  
    // Adapted from https://github.com/calccrypto/uint256_t
19.  
     
20.  
    #include <stdio.h>
21.  
    #include <stdlib.h>
22.  
    #include "uint256.h"
23.  
     
24.  
    static const char HEXDIGITS[] = "0123456789abcdef";
25.  
     
26.  
    static uint64_t readUint64BE(uint8_t *buffer) {
27.  
    return (((uint64_t)buffer[0]) << 56) | (((uint64_t)buffer[1]) << 48) |
28.  
    (((uint64_t)buffer[2]) << 40) | (((uint64_t)buffer[3]) << 32) |
29.  
    (((uint64_t)buffer[4]) << 24) | (((uint64_t)buffer[5]) << 16) |
30.  
    (((uint64_t)buffer[6]) << 8) | (((uint64_t)buffer[7]));
31.  
    }
32.  
     
33.  
    void readu128BE(uint8_t *buffer, uint128_t *target) {
34.  
    UPPER_P(target) = readUint64BE(buffer);
35.  
    LOWER_P(target) = readUint64BE(buffer + 8);
36.  
    }
37.  
     
38.  
    void readu256BE(uint8_t *buffer, uint256_t *target) {
39.  
    readu128BE(buffer, &UPPER_P(target));
40.  
    readu128BE(buffer + 16, &LOWER_P(target));
41.  
    }
42.  
     
43.  
    bool zero128(uint128_t *number) {
44.  
    return ((LOWER_P(number) == 0) && (UPPER_P(number) == 0));
45.  
    }
46.  
     
47.  
    bool zero256(uint256_t *number) {
48.  
    return (zero128(&LOWER_P(number)) && zero128(&UPPER_P(number)));
49.  
    }
50.  
     
51.  
    void copy128(uint128_t *target, uint128_t *number) {
52.  
    UPPER_P(target) = UPPER_P(number);
53.  
    LOWER_P(target) = LOWER_P(number);
54.  
    }
55.  
     
56.  
    void copy256(uint256_t *target, uint256_t *number) {
57.  
    copy128(&UPPER_P(target), &UPPER_P(number));
58.  
    copy128(&LOWER_P(target), &LOWER_P(number));
59.  
    }
60.  
     
61.  
    void clear128(uint128_t *target) {
62.  
    UPPER_P(target) = 0;
63.  
    LOWER_P(target) = 0;
64.  
    }
65.  
     
66.  
    void clear256(uint256_t *target) {
67.  
    clear128(&UPPER_P(target));
68.  
    clear128(&LOWER_P(target));
69.  
    }
70.  
     
71.  
    void shiftl128(uint128_t *number, uint32_t value, uint128_t *target) {
72.  
    if (value >= 128) {
73.  
    clear128(target);
74.  
    } else if (value == 64) {
75.  
    UPPER_P(target) = LOWER_P(number);
76.  
    LOWER_P(target) = 0;
77.  
    } else if (value == 0) {
78.  
    copy128(target, number);
79.  
    } else if (value < 64) {
80.  
    UPPER_P(target) =
81.  
    (UPPER_P(number) << value) + (LOWER_P(number) >> (64 - value));
82.  
    LOWER_P(target) = (LOWER_P(number) << value);
83.  
    } else if ((128 > value) && (value > 64)) {
84.  
    UPPER_P(target) = LOWER_P(number) << (value - 64);
85.  
    LOWER_P(target) = 0;
86.  
    } else {
87.  
    clear128(target);
88.  
    }
89.  
    }
90.  
     
91.  
    void shiftl256(uint256_t *number, uint32_t value, uint256_t *target) {
92.  
    if (value >= 256) {
93.  
    clear256(target);
94.  
    } else if (value == 128) {
95.  
    copy128(&UPPER_P(target), &LOWER_P(number));
96.  
    clear128(&LOWER_P(target));
97.  
    } else if (value == 0) {
98.  
    copy256(target, number);
99.  
    } else if (value < 128) {
100.  
     uint128_t tmp1;
101.  
     uint128_t tmp2;
102.  
     uint256_t result;
103.  
     shiftl128(&UPPER_P(number), value, &tmp1);
104.  
     shiftr128(&LOWER_P(number), (128 - value), &tmp2);
105.  
     add128(&tmp1, &tmp2, &UPPER(result));
106.  
     shiftl128(&LOWER_P(number), value, &LOWER(result));
107.  
     copy256(target, &result);
108.  
     } else if ((256 > value) && (value > 128)) {
109.  
     shiftl128(&LOWER_P(number), (value - 128), &UPPER_P(target));
110.  
     clear128(&LOWER_P(target));
111.  
     } else {
112.  
     clear256(target);
113.  
     }
114.  
     }
115.  
      
116.  
     void shiftr128(uint128_t *number, uint32_t value, uint128_t *target) {
117.  
     if (value >= 128) {
118.  
     clear128(target);
119.  
     } else if (value == 64) {
120.  
     UPPER_P(target) = 0;
121.  
     LOWER_P(target) = UPPER_P(number);
122.  
     } else if (value == 0) {
123.  
     copy128(target, number);
124.  
     } else if (value < 64) {
125.  
     uint128_t result;
126.  
     UPPER(result) = UPPER_P(number) >> value;
127.  
     LOWER(result) =
128.  
     (UPPER_P(number) << (64 - value)) + (LOWER_P(number) >> value);
129.  
     copy128(target, &result);
130.  
     } else if ((128 > value) && (value > 64)) {
131.  
     LOWER_P(target) = UPPER_P(number) >> (value - 64);
132.  
     UPPER_P(target) = 0;
133.  
     } else {
134.  
     clear128(target);
135.  
     }
136.  
     }
137.  
      
138.  
     void shiftr256(uint256_t *number, uint32_t value, uint256_t *target) {
139.  
     if (value >= 256) {
140.  
     clear256(target);
141.  
     } else if (value == 128) {
142.  
     copy128(&LOWER_P(target), &UPPER_P(number));
143.  
     clear128(&UPPER_P(target));
144.  
     } else if (value == 0) {
145.  
     copy256(target, number);
146.  
     } else if (value < 128) {
147.  
     uint128_t tmp1;
148.  
     uint128_t tmp2;
149.  
     uint256_t result;
150.  
     shiftr128(&UPPER_P(number), value, &UPPER(result));
151.  
     shiftr128(&LOWER_P(number), value, &tmp1);
152.  
     shiftl128(&UPPER_P(number), (128 - value), &tmp2);
153.  
     add128(&tmp1, &tmp2, &LOWER(result));
154.  
     copy256(target, &result);
155.  
     } else if ((256 > value) && (value > 128)) {
156.  
     shiftr128(&UPPER_P(number), (value - 128), &LOWER_P(target));
157.  
     clear128(&UPPER_P(target));
158.  
     } else {
159.  
     clear256(target);
160.  
     }
161.  
     }
162.  
      
163.  
     uint32_t bits128(uint128_t *number) {
164.  
     uint32_t result = 0;
165.  
     if (UPPER_P(number)) {
166.  
     result = 64;
167.  
     uint64_t up = UPPER_P(number);
168.  
     while (up) {
169.  
     up >>= 1;
170.  
     result++;
171.  
     }
172.  
     } else {
173.  
     uint64_t low = LOWER_P(number);
174.  
     while (low) {
175.  
     low >>= 1;
176.  
     result++;
177.  
     }
178.  
     }
179.  
     return result;
180.  
     }
181.  
      
182.  
     uint32_t bits256(uint256_t *number) {
183.  
     uint32_t result = 0;
184.  
     if (!zero128(&UPPER_P(number))) {
185.  
     result = 128;
186.  
     uint128_t up;
187.  
     copy128(&up, &UPPER_P(number));
188.  
     while (!zero128(&up)) {
189.  
     shiftr128(&up, 1, &up);
190.  
     result++;
191.  
     }
192.  
     } else {
193.  
     uint128_t low;
194.  
     copy128(&low, &LOWER_P(number));
195.  
     while (!zero128(&low)) {
196.  
     shiftr128(&low, 1, &low);
197.  
     result++;
198.  
     }
199.  
     }
200.  
     return result;
201.  
     }
202.  
      
203.  
     bool equal128(uint128_t *number1, uint128_t *number2) {
204.  
     return (UPPER_P(number1) == UPPER_P(number2)) &&
205.  
     (LOWER_P(number1) == LOWER_P(number2));
206.  
     }
207.  
      
208.  
     bool equal256(uint256_t *number1, uint256_t *number2) {
209.  
     return (equal128(&UPPER_P(number1), &UPPER_P(number2)) &&
210.  
     equal128(&LOWER_P(number1), &LOWER_P(number2)));
211.  
     }
212.  
      
213.  
     bool gt128(uint128_t *number1, uint128_t *number2) {
214.  
     if (UPPER_P(number1) == UPPER_P(number2)) {
215.  
     return (LOWER_P(number1) > LOWER_P(number2));
216.  
     }
217.  
     return (UPPER_P(number1) > UPPER_P(number2));
218.  
     }
219.  
      
220.  
     bool gt256(uint256_t *number1, uint256_t *number2) {
221.  
     if (equal128(&UPPER_P(number1), &UPPER_P(number2))) {
222.  
     return gt128(&LOWER_P(number1), &LOWER_P(number2));
223.  
     }
224.  
     return gt128(&UPPER_P(number1), &UPPER_P(number2));
225.  
     }
226.  
      
227.  
     bool gte128(uint128_t *number1, uint128_t *number2) {
228.  
     return gt128(number1, number2) || equal128(number1, number2);
229.  
     }
230.  
      
231.  
     bool gte256(uint256_t *number1, uint256_t *number2) {
232.  
     return gt256(number1, number2) || equal256(number1, number2);
233.  
     }
234.  
      
235.  
     void add128(uint128_t *number1, uint128_t *number2, uint128_t *target) {
236.  
     UPPER_P(target) =
237.  
     UPPER_P(number1) + UPPER_P(number2) +
238.  
     ((LOWER_P(number1) + LOWER_P(number2)) < LOWER_P(number1));
239.  
     LOWER_P(target) = LOWER_P(number1) + LOWER_P(number2);
240.  
     }
241.  
      
242.  
     void add256(uint256_t *number1, uint256_t *number2, uint256_t *target) {
243.  
     uint128_t tmp;
244.  
     add128(&UPPER_P(number1), &UPPER_P(number2), &UPPER_P(target));
245.  
     add128(&LOWER_P(number1), &LOWER_P(number2), &tmp);
246.  
     if (gt128(&LOWER_P(number1), &tmp)) {
247.  
     uint128_t one;
248.  
     UPPER(one) = 0;
249.  
     LOWER(one) = 1;
250.  
     add128(&UPPER_P(target), &one, &UPPER_P(target));
251.  
     }
252.  
     add128(&LOWER_P(number1), &LOWER_P(number2), &LOWER_P(target));
253.  
     }
254.  
      
255.  
     void minus128(uint128_t *number1, uint128_t *number2, uint128_t *target) {
256.  
     UPPER_P(target) =
257.  
     UPPER_P(number1) - UPPER_P(number2) -
258.  
     ((LOWER_P(number1) - LOWER_P(number2)) > LOWER_P(number1));
259.  
     LOWER_P(target) = LOWER_P(number1) - LOWER_P(number2);
260.  
     }
261.  
      
262.  
     void minus256(uint256_t *number1, uint256_t *number2, uint256_t *target) {
263.  
     uint128_t tmp;
264.  
     minus128(&UPPER_P(number1), &UPPER_P(number2), &UPPER_P(target));
265.  
     minus128(&LOWER_P(number1), &LOWER_P(number2), &tmp);
266.  
     if (gt128(&tmp, &LOWER_P(number1))) {
267.  
     uint128_t one;
268.  
     UPPER(one) = 0;
269.  
     LOWER(one) = 1;
270.  
     minus128(&UPPER_P(target), &one, &UPPER_P(target));
271.  
     }
272.  
     minus128(&LOWER_P(number1), &LOWER_P(number2), &LOWER_P(target));
273.  
     }
274.  
      
275.  
     void or128(uint128_t *number1, uint128_t *number2, uint128_t *target) {
276.  
     UPPER_P(target) = UPPER_P(number1) | UPPER_P(number2);
277.  
     LOWER_P(target) = LOWER_P(number1) | LOWER_P(number2);
278.  
     }
279.  
      
280.  
     void or256(uint256_t *number1, uint256_t *number2, uint256_t *target) {
281.  
     or128(&UPPER_P(number1), &UPPER_P(number2), &UPPER_P(target));
282.  
     or128(&LOWER_P(number1), &LOWER_P(number2), &LOWER_P(target));
283.  
     }
284.  
      
285.  
     void mul128(uint128_t *number1, uint128_t *number2, uint128_t *target) {
286.  
     uint64_t top[4] = {UPPER_P(number1) >> 32, UPPER_P(number1) & 0xffffffff,
287.  
     LOWER_P(number1) >> 32, LOWER_P(number1) & 0xffffffff};
288.  
     uint64_t bottom[4] = {UPPER_P(number2) >> 32, UPPER_P(number2) & 0xffffffff,
289.  
     LOWER_P(number2) >> 32,
290.  
     LOWER_P(number2) & 0xffffffff};
291.  
     uint64_t products[4][4];
292.  
     uint128_t tmp, tmp2;
293.  
      
294.  
     for (int y = 3; y > -1; y--) {
295.  
     for (int x = 3; x > -1; x--) {
296.  
     products[3 - x][y] = top[x] * bottom[y];
297.  
     }
298.  
     }
299.  
      
300.  
     uint64_t fourth32 = products[0][3] & 0xffffffff;
301.  
     uint64_t third32 = (products[0][2] & 0xffffffff) + (products[0][3] >> 32);
302.  
     uint64_t second32 = (products[0][1] & 0xffffffff) + (products[0][2] >> 32);
303.  
     uint64_t first32 = (products[0][0] & 0xffffffff) + (products[0][1] >> 32);
304.  
      
305.  
     third32 += products[1][3] & 0xffffffff;
306.  
     second32 += (products[1][2] & 0xffffffff) + (products[1][3] >> 32);
307.  
     first32 += (products[1][1] & 0xffffffff) + (products[1][2] >> 32);
308.  
      
309.  
     second32 += products[2][3] & 0xffffffff;
310.  
     first32 += (products[2][2] & 0xffffffff) + (products[2][3] >> 32);
311.  
      
312.  
     first32 += products[3][3] & 0xffffffff;
313.  
      
314.  
     UPPER(tmp) = first32 << 32;
315.  
     LOWER(tmp) = 0;
316.  
     UPPER(tmp2) = third32 >> 32;
317.  
     LOWER(tmp2) = third32 << 32;
318.  
     add128(&tmp, &tmp2, target);
319.  
     UPPER(tmp) = second32;
320.  
     LOWER(tmp) = 0;
321.  
     add128(&tmp, target, &tmp2);
322.  
     UPPER(tmp) = 0;
323.  
     LOWER(tmp) = fourth32;
324.  
     add128(&tmp, &tmp2, target);
325.  
     }
326.  
      
327.  
     void mul256(uint256_t *number1, uint256_t *number2, uint256_t *target) {
328.  
     uint128_t top[4];
329.  
     uint128_t bottom[4];
330.  
     uint128_t products[4][4];
331.  
     uint128_t tmp, tmp2, fourth64, third64, second64, first64;
332.  
     uint256_t target1, target2;
333.  
     UPPER(top[0]) = 0;
334.  
     LOWER(top[0]) = UPPER(UPPER_P(number1));
335.  
     UPPER(top[1]) = 0;
336.  
     LOWER(top[1]) = LOWER(UPPER_P(number1));
337.  
     UPPER(top[2]) = 0;
338.  
     LOWER(top[2]) = UPPER(LOWER_P(number1));
339.  
     UPPER(top[3]) = 0;
340.  
     LOWER(top[3]) = LOWER(LOWER_P(number1));
341.  
     UPPER(bottom[0]) = 0;
342.  
     LOWER(bottom[0]) = UPPER(UPPER_P(number2));
343.  
     UPPER(bottom[1]) = 0;
344.  
     LOWER(bottom[1]) = LOWER(UPPER_P(number2));
345.  
     UPPER(bottom[2]) = 0;
346.  
     LOWER(bottom[2]) = UPPER(LOWER_P(number2));
347.  
     UPPER(bottom[3]) = 0;
348.  
     LOWER(bottom[3]) = LOWER(LOWER_P(number2));
349.  
      
350.  
     for (int y = 3; y > -1; y--) {
351.  
     for (int x = 3; x > -1; x--) {
352.  
     mul128(&top[x], &bottom[y], &products[3 - x][y]);
353.  
     }
354.  
     }
355.  
      
356.  
     UPPER(fourth64) = 0;
357.  
     LOWER(fourth64) = LOWER(products[0][3]);
358.  
     UPPER(tmp) = 0;
359.  
     LOWER(tmp) = LOWER(products[0][2]);
360.  
     UPPER(tmp2) = 0;
361.  
     LOWER(tmp2) = UPPER(products[0][3]);
362.  
     add128(&tmp, &tmp2, &third64);
363.  
     UPPER(tmp) = 0;
364.  
     LOWER(tmp) = LOWER(products[0][1]);
365.  
     UPPER(tmp2) = 0;
366.  
     LOWER(tmp2) = UPPER(products[0][2]);
367.  
     add128(&tmp, &tmp2, &second64);
368.  
     UPPER(tmp) = 0;
369.  
     LOWER(tmp) = LOWER(products[0][0]);
370.  
     UPPER(tmp2) = 0;
371.  
     LOWER(tmp2) = UPPER(products[0][1]);
372.  
     add128(&tmp, &tmp2, &first64);
373.  
      
374.  
     UPPER(tmp) = 0;
375.  
     LOWER(tmp) = LOWER(products[1][3]);
376.  
     add128(&tmp, &third64, &tmp2);
377.  
     copy128(&third64, &tmp2);
378.  
     UPPER(tmp) = 0;
379.  
     LOWER(tmp) = LOWER(products[1][2]);
380.  
     add128(&tmp, &second64, &tmp2);
381.  
     UPPER(tmp) = 0;
382.  
     LOWER(tmp) = UPPER(products[1][3]);
383.  
     add128(&tmp, &tmp2, &second64);
384.  
     UPPER(tmp) = 0;
385.  
     LOWER(tmp) = LOWER(products[1][1]);
386.  
     add128(&tmp, &first64, &tmp2);
387.  
     UPPER(tmp) = 0;
388.  
     LOWER(tmp) = UPPER(products[1][2]);
389.  
     add128(&tmp, &tmp2, &first64);
390.  
      
391.  
     UPPER(tmp) = 0;
392.  
     LOWER(tmp) = LOWER(products[2][3]);
393.  
     add128(&tmp, &second64, &tmp2);
394.  
     copy128(&second64, &tmp2);
395.  
     UPPER(tmp) = 0;
396.  
     LOWER(tmp) = LOWER(products[2][2]);
397.  
     add128(&tmp, &first64, &tmp2);
398.  
     UPPER(tmp) = 0;
399.  
     LOWER(tmp) = UPPER(products[2][3]);
400.  
     add128(&tmp, &tmp2, &first64);
401.  
      
402.  
     UPPER(tmp) = 0;
403.  
     LOWER(tmp) = LOWER(products[3][3]);
404.  
     add128(&tmp, &first64, &tmp2);
405.  
     copy128(&first64, &tmp2);
406.  
      
407.  
     clear256(&target1);
408.  
     shiftl128(&first64, 64, &UPPER(target1));
409.  
     clear256(&target2);
410.  
     UPPER(UPPER(target2)) = UPPER(third64);
411.  
     shiftl128(&third64, 64, &LOWER(target2));
412.  
     add256(&target1, &target2, target);
413.  
     clear256(&target1);
414.  
     copy128(&UPPER(target1), &second64);
415.  
     add256(&target1, target, &target2);
416.  
     clear256(&target1);
417.  
     copy128(&LOWER(target1), &fourth64);
418.  
     add256(&target1, &target2, target);
419.  
     }
420.  
      
421.  
     void divmod128(uint128_t *l, uint128_t *r, uint128_t *retDiv,
422.  
     uint128_t *retMod) {
423.  
     uint128_t copyd, adder, resDiv, resMod;
424.  
     uint128_t one;
425.  
     UPPER(one) = 0;
426.  
     LOWER(one) = 1;
427.  
     uint32_t diffBits = bits128(l) - bits128(r);
428.  
     clear128(&resDiv);
429.  
     copy128(&resMod, l);
430.  
     if (gt128(r, l)) {
431.  
     copy128(retMod, l);
432.  
     clear128(retDiv);
433.  
     } else {
434.  
     shiftl128(r, diffBits, &copyd);
435.  
     shiftl128(&one, diffBits, &adder);
436.  
     if (gt128(&copyd, &resMod)) {
437.  
     shiftr128(&copyd, 1, &copyd);
438.  
     shiftr128(&adder, 1, &adder);
439.  
     }
440.  
     while (gte128(&resMod, r)) {
441.  
     if (gte128(&resMod, &copyd)) {
442.  
     minus128(&resMod, &copyd, &resMod);
443.  
     or128(&resDiv, &adder, &resDiv);
444.  
     }
445.  
     shiftr128(&copyd, 1, &copyd);
446.  
     shiftr128(&adder, 1, &adder);
447.  
     }
448.  
     copy128(retDiv, &resDiv);
449.  
     copy128(retMod, &resMod);
450.  
     }
451.  
     }
452.  
      
453.  
     void divmod256(uint256_t *l, uint256_t *r, uint256_t *retDiv,
454.  
     uint256_t *retMod) {
455.  
     uint256_t copyd, adder, resDiv, resMod;
456.  
     uint256_t one;
457.  
     clear256(&one);
458.  
     UPPER(LOWER(one)) = 0;
459.  
     LOWER(LOWER(one)) = 1;
460.  
     uint32_t diffBits = bits256(l) - bits256(r);
461.  
     clear256(&resDiv);
462.  
     copy256(&resMod, l);
463.  
     if (gt256(r, l)) {
464.  
     copy256(retMod, l);
465.  
     clear256(retDiv);
466.  
     } else {
467.  
     shiftl256(r, diffBits, &copyd);
468.  
     shiftl256(&one, diffBits, &adder);
469.  
     if (gt256(&copyd, &resMod)) {
470.  
     shiftr256(&copyd, 1, &copyd);
471.  
     shiftr256(&adder, 1, &adder);
472.  
     }
473.  
     while (gte256(&resMod, r)) {
474.  
     if (gte256(&resMod, &copyd)) {
475.  
     minus256(&resMod, &copyd, &resMod);
476.  
     or256(&resDiv, &adder, &resDiv);
477.  
     }
478.  
     shiftr256(&copyd, 1, &copyd);
479.  
     shiftr256(&adder, 1, &adder);
480.  
     }
481.  
     copy256(retDiv, &resDiv);
482.  
     copy256(retMod, &resMod);
483.  
     }
484.  
     }
485.  
      
486.  
     static void reverseString(char *str, uint32_t length) {
487.  
     uint32_t i, j;
488.  
     for (i = 0, j = length - 1; i < j; i++, j--) {
489.  
     uint8_t c;
490.  
     c = str[i];
491.  
     str[i] = str[j];
492.  
     str[j] = c;
493.  
     }
494.  
     }
495.  
      
496.  
     bool tostring128(uint128_t *number, uint32_t baseParam, char *out,
497.  
     uint32_t outLength) {
498.  
     uint128_t rDiv;
499.  
     uint128_t rMod;
500.  
     uint128_t base;
501.  
     copy128(&rDiv, number);
502.  
     clear128(&rMod);
503.  
     clear128(&base);
504.  
     LOWER(base) = baseParam;
505.  
     uint32_t offset = 0;
506.  
     if ((baseParam < 2) || (baseParam > 16)) {
507.  
     return false;
508.  
     }
509.  
     do {
510.  
     if (offset > (outLength - 1)) {
511.  
     return false;
512.  
     }
513.  
     divmod128(&rDiv, &base, &rDiv, &rMod);
514.  
     out[offset++] = HEXDIGITS[(uint8_t)LOWER(rMod)];
515.  
     } while (!zero128(&rDiv));
516.  
     out[offset] = '';
517.  
     reverseString(out, offset);
518.  
     return true;
519.  
     }
520.  
      
521.  
     bool tostring256(uint256_t *number, uint32_t baseParam, char *out,
522.  
     uint32_t outLength) {
523.  
     uint256_t rDiv;
524.  
     uint256_t rMod;
525.  
     uint256_t base;
526.  
     copy256(&rDiv, number);
527.  
     clear256(&rMod);
528.  
     clear256(&base);
529.  
     UPPER(LOWER(base)) = 0;
530.  
     LOWER(LOWER(base)) = baseParam;
531.  
     uint32_t offset = 0;
532.  
     if ((baseParam < 2) || (baseParam > 16)) {
533.  
     return false;
534.  
     }
535.  
     do {
536.  
     if (offset > (outLength - 1)) {
537.  
     return false;
538.  
     }
539.  
     divmod256(&rDiv, &base, &rDiv, &rMod);
540.  
     out[offset++] = HEXDIGITS[(uint8_t)LOWER(LOWER(rMod))];
541.  
     } while (!zero256(&rDiv));
542.  
     out[offset] = '';
543.  
     reverseString(out, offset);
544.  
     return true;
545.  
     }