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1 | #ifndef __INC_LIB8TION_MATH_H | ||
2 | #define __INC_LIB8TION_MATH_H | ||
3 | |||
4 | #include "scale8.h" | ||
5 | |||
6 | ///@ingroup lib8tion | ||
7 | |||
8 | ///@defgroup Math Basic math operations | ||
9 | /// Fast, efficient 8-bit math functions specifically | ||
10 | /// designed for high-performance LED programming. | ||
11 | /// | ||
12 | /// Because of the AVR(Arduino) and ARM assembly language | ||
13 | /// implementations provided, using these functions often | ||
14 | /// results in smaller and faster code than the equivalent | ||
15 | /// program using plain "C" arithmetic and logic. | ||
16 | ///@{ | ||
17 | |||
18 | |||
19 | /// add one byte to another, saturating at 0xFF | ||
20 | /// @param i - first byte to add | ||
21 | /// @param j - second byte to add | ||
22 | /// @returns the sum of i & j, capped at 0xFF | ||
23 | LIB8STATIC_ALWAYS_INLINE uint8_t qadd8( uint8_t i, uint8_t j) | ||
24 | { | ||
25 | #if QADD8_C == 1 | ||
26 | uint16_t t = i + j; | ||
27 | if (t > 255) t = 255; | ||
28 | return t; | ||
29 | #elif QADD8_AVRASM == 1 | ||
30 | asm volatile( | ||
31 | /* First, add j to i, conditioning the C flag */ | ||
32 | "add %0, %1 \n\t" | ||
33 | |||
34 | /* Now test the C flag. | ||
35 | If C is clear, we branch around a load of 0xFF into i. | ||
36 | If C is set, we go ahead and load 0xFF into i. | ||
37 | */ | ||
38 | "brcc L_%= \n\t" | ||
39 | "ldi %0, 0xFF \n\t" | ||
40 | "L_%=: " | ||
41 | : "+a" (i) | ||
42 | : "a" (j) ); | ||
43 | return i; | ||
44 | #elif QADD8_ARM_DSP_ASM == 1 | ||
45 | asm volatile( "uqadd8 %0, %0, %1" : "+r" (i) : "r" (j)); | ||
46 | return i; | ||
47 | #else | ||
48 | #error "No implementation for qadd8 available." | ||
49 | #endif | ||
50 | } | ||
51 | |||
52 | /// Add one byte to another, saturating at 0x7F | ||
53 | /// @param i - first byte to add | ||
54 | /// @param j - second byte to add | ||
55 | /// @returns the sum of i & j, capped at 0xFF | ||
56 | LIB8STATIC_ALWAYS_INLINE int8_t qadd7( int8_t i, int8_t j) | ||
57 | { | ||
58 | #if QADD7_C == 1 | ||
59 | int16_t t = i + j; | ||
60 | if (t > 127) t = 127; | ||
61 | return t; | ||
62 | #elif QADD7_AVRASM == 1 | ||
63 | asm volatile( | ||
64 | /* First, add j to i, conditioning the V flag */ | ||
65 | "add %0, %1 \n\t" | ||
66 | |||
67 | /* Now test the V flag. | ||
68 | If V is clear, we branch around a load of 0x7F into i. | ||
69 | If V is set, we go ahead and load 0x7F into i. | ||
70 | */ | ||
71 | "brvc L_%= \n\t" | ||
72 | "ldi %0, 0x7F \n\t" | ||
73 | "L_%=: " | ||
74 | : "+a" (i) | ||
75 | : "a" (j) ); | ||
76 | |||
77 | return i; | ||
78 | #elif QADD7_ARM_DSP_ASM == 1 | ||
79 | asm volatile( "qadd8 %0, %0, %1" : "+r" (i) : "r" (j)); | ||
80 | return i; | ||
81 | #else | ||
82 | #error "No implementation for qadd7 available." | ||
83 | #endif | ||
84 | } | ||
85 | |||
86 | /// subtract one byte from another, saturating at 0x00 | ||
87 | /// @returns i - j with a floor of 0 | ||
88 | LIB8STATIC_ALWAYS_INLINE uint8_t qsub8( uint8_t i, uint8_t j) | ||
89 | { | ||
90 | #if QSUB8_C == 1 | ||
91 | int16_t t = i - j; | ||
92 | if (t < 0) t = 0; | ||
93 | return t; | ||
94 | #elif QSUB8_AVRASM == 1 | ||
95 | |||
96 | asm volatile( | ||
97 | /* First, subtract j from i, conditioning the C flag */ | ||
98 | "sub %0, %1 \n\t" | ||
99 | |||
100 | /* Now test the C flag. | ||
101 | If C is clear, we branch around a load of 0x00 into i. | ||
102 | If C is set, we go ahead and load 0x00 into i. | ||
103 | */ | ||
104 | "brcc L_%= \n\t" | ||
105 | "ldi %0, 0x00 \n\t" | ||
106 | "L_%=: " | ||
107 | : "+a" (i) | ||
108 | : "a" (j) ); | ||
109 | |||
110 | return i; | ||
111 | #else | ||
112 | #error "No implementation for qsub8 available." | ||
113 | #endif | ||
114 | } | ||
115 | |||
116 | /// add one byte to another, with one byte result | ||
117 | LIB8STATIC_ALWAYS_INLINE uint8_t add8( uint8_t i, uint8_t j) | ||
118 | { | ||
119 | #if ADD8_C == 1 | ||
120 | uint16_t t = i + j; | ||
121 | return t; | ||
122 | #elif ADD8_AVRASM == 1 | ||
123 | // Add j to i, period. | ||
124 | asm volatile( "add %0, %1" : "+a" (i) : "a" (j)); | ||
125 | return i; | ||
126 | #else | ||
127 | #error "No implementation for add8 available." | ||
128 | #endif | ||
129 | } | ||
130 | |||
131 | /// add one byte to another, with one byte result | ||
132 | LIB8STATIC_ALWAYS_INLINE uint16_t add8to16( uint8_t i, uint16_t j) | ||
133 | { | ||
134 | #if ADD8_C == 1 | ||
135 | uint16_t t = i + j; | ||
136 | return t; | ||
137 | #elif ADD8_AVRASM == 1 | ||
138 | // Add i(one byte) to j(two bytes) | ||
139 | asm volatile( "add %A[j], %[i] \n\t" | ||
140 | "adc %B[j], __zero_reg__ \n\t" | ||
141 | : [j] "+a" (j) | ||
142 | : [i] "a" (i) | ||
143 | ); | ||
144 | return i; | ||
145 | #else | ||
146 | #error "No implementation for add8to16 available." | ||
147 | #endif | ||
148 | } | ||
149 | |||
150 | |||
151 | /// subtract one byte from another, 8-bit result | ||
152 | LIB8STATIC_ALWAYS_INLINE uint8_t sub8( uint8_t i, uint8_t j) | ||
153 | { | ||
154 | #if SUB8_C == 1 | ||
155 | int16_t t = i - j; | ||
156 | return t; | ||
157 | #elif SUB8_AVRASM == 1 | ||
158 | // Subtract j from i, period. | ||
159 | asm volatile( "sub %0, %1" : "+a" (i) : "a" (j)); | ||
160 | return i; | ||
161 | #else | ||
162 | #error "No implementation for sub8 available." | ||
163 | #endif | ||
164 | } | ||
165 | |||
166 | /// Calculate an integer average of two unsigned | ||
167 | /// 8-bit integer values (uint8_t). | ||
168 | /// Fractional results are rounded down, e.g. avg8(20,41) = 30 | ||
169 | LIB8STATIC_ALWAYS_INLINE uint8_t avg8( uint8_t i, uint8_t j) | ||
170 | { | ||
171 | #if AVG8_C == 1 | ||
172 | return (i + j) >> 1; | ||
173 | #elif AVG8_AVRASM == 1 | ||
174 | asm volatile( | ||
175 | /* First, add j to i, 9th bit overflows into C flag */ | ||
176 | "add %0, %1 \n\t" | ||
177 | /* Divide by two, moving C flag into high 8th bit */ | ||
178 | "ror %0 \n\t" | ||
179 | : "+a" (i) | ||
180 | : "a" (j) ); | ||
181 | return i; | ||
182 | #else | ||
183 | #error "No implementation for avg8 available." | ||
184 | #endif | ||
185 | } | ||
186 | |||
187 | /// Calculate an integer average of two unsigned | ||
188 | /// 16-bit integer values (uint16_t). | ||
189 | /// Fractional results are rounded down, e.g. avg16(20,41) = 30 | ||
190 | LIB8STATIC_ALWAYS_INLINE uint16_t avg16( uint16_t i, uint16_t j) | ||
191 | { | ||
192 | #if AVG16_C == 1 | ||
193 | return (uint32_t)((uint32_t)(i) + (uint32_t)(j)) >> 1; | ||
194 | #elif AVG16_AVRASM == 1 | ||
195 | asm volatile( | ||
196 | /* First, add jLo (heh) to iLo, 9th bit overflows into C flag */ | ||
197 | "add %A[i], %A[j] \n\t" | ||
198 | /* Now, add C + jHi to iHi, 17th bit overflows into C flag */ | ||
199 | "adc %B[i], %B[j] \n\t" | ||
200 | /* Divide iHi by two, moving C flag into high 16th bit, old 9th bit now in C */ | ||
201 | "ror %B[i] \n\t" | ||
202 | /* Divide iLo by two, moving C flag into high 8th bit */ | ||
203 | "ror %A[i] \n\t" | ||
204 | : [i] "+a" (i) | ||
205 | : [j] "a" (j) ); | ||
206 | return i; | ||
207 | #else | ||
208 | #error "No implementation for avg16 available." | ||
209 | #endif | ||
210 | } | ||
211 | |||
212 | |||
213 | /// Calculate an integer average of two signed 7-bit | ||
214 | /// integers (int8_t) | ||
215 | /// If the first argument is even, result is rounded down. | ||
216 | /// If the first argument is odd, result is result up. | ||
217 | LIB8STATIC_ALWAYS_INLINE int8_t avg7( int8_t i, int8_t j) | ||
218 | { | ||
219 | #if AVG7_C == 1 | ||
220 | return ((i + j) >> 1) + (i & 0x1); | ||
221 | #elif AVG7_AVRASM == 1 | ||
222 | asm volatile( | ||
223 | "asr %1 \n\t" | ||
224 | "asr %0 \n\t" | ||
225 | "adc %0, %1 \n\t" | ||
226 | : "+a" (i) | ||
227 | : "a" (j) ); | ||
228 | return i; | ||
229 | #else | ||
230 | #error "No implementation for avg7 available." | ||
231 | #endif | ||
232 | } | ||
233 | |||
234 | /// Calculate an integer average of two signed 15-bit | ||
235 | /// integers (int16_t) | ||
236 | /// If the first argument is even, result is rounded down. | ||
237 | /// If the first argument is odd, result is result up. | ||
238 | LIB8STATIC_ALWAYS_INLINE int16_t avg15( int16_t i, int16_t j) | ||
239 | { | ||
240 | #if AVG15_C == 1 | ||
241 | return ((int32_t)((int32_t)(i) + (int32_t)(j)) >> 1) + (i & 0x1); | ||
242 | #elif AVG15_AVRASM == 1 | ||
243 | asm volatile( | ||
244 | /* first divide j by 2, throwing away lowest bit */ | ||
245 | "asr %B[j] \n\t" | ||
246 | "ror %A[j] \n\t" | ||
247 | /* now divide i by 2, with lowest bit going into C */ | ||
248 | "asr %B[i] \n\t" | ||
249 | "ror %A[i] \n\t" | ||
250 | /* add j + C to i */ | ||
251 | "adc %A[i], %A[j] \n\t" | ||
252 | "adc %B[i], %B[j] \n\t" | ||
253 | : [i] "+a" (i) | ||
254 | : [j] "a" (j) ); | ||
255 | return i; | ||
256 | #else | ||
257 | #error "No implementation for avg15 available." | ||
258 | #endif | ||
259 | } | ||
260 | |||
261 | |||
262 | /// Calculate the remainder of one unsigned 8-bit | ||
263 | /// value divided by anoter, aka A % M. | ||
264 | /// Implemented by repeated subtraction, which is | ||
265 | /// very compact, and very fast if A is 'probably' | ||
266 | /// less than M. If A is a large multiple of M, | ||
267 | /// the loop has to execute multiple times. However, | ||
268 | /// even in that case, the loop is only two | ||
269 | /// instructions long on AVR, i.e., quick. | ||
270 | LIB8STATIC_ALWAYS_INLINE uint8_t mod8( uint8_t a, uint8_t m) | ||
271 | { | ||
272 | #if defined(__AVR__) | ||
273 | asm volatile ( | ||
274 | "L_%=: sub %[a],%[m] \n\t" | ||
275 | " brcc L_%= \n\t" | ||
276 | " add %[a],%[m] \n\t" | ||
277 | : [a] "+r" (a) | ||
278 | : [m] "r" (m) | ||
279 | ); | ||
280 | #else | ||
281 | while( a >= m) a -= m; | ||
282 | #endif | ||
283 | return a; | ||
284 | } | ||
285 | |||
286 | /// Add two numbers, and calculate the modulo | ||
287 | /// of the sum and a third number, M. | ||
288 | /// In other words, it returns (A+B) % M. | ||
289 | /// It is designed as a compact mechanism for | ||
290 | /// incrementing a 'mode' switch and wrapping | ||
291 | /// around back to 'mode 0' when the switch | ||
292 | /// goes past the end of the available range. | ||
293 | /// e.g. if you have seven modes, this switches | ||
294 | /// to the next one and wraps around if needed: | ||
295 | /// mode = addmod8( mode, 1, 7); | ||
296 | ///LIB8STATIC_ALWAYS_INLINESee 'mod8' for notes on performance. | ||
297 | LIB8STATIC uint8_t addmod8( uint8_t a, uint8_t b, uint8_t m) | ||
298 | { | ||
299 | #if defined(__AVR__) | ||
300 | asm volatile ( | ||
301 | " add %[a],%[b] \n\t" | ||
302 | "L_%=: sub %[a],%[m] \n\t" | ||
303 | " brcc L_%= \n\t" | ||
304 | " add %[a],%[m] \n\t" | ||
305 | : [a] "+r" (a) | ||
306 | : [b] "r" (b), [m] "r" (m) | ||
307 | ); | ||
308 | #else | ||
309 | a += b; | ||
310 | while( a >= m) a -= m; | ||
311 | #endif | ||
312 | return a; | ||
313 | } | ||
314 | |||
315 | /// Subtract two numbers, and calculate the modulo | ||
316 | /// of the difference and a third number, M. | ||
317 | /// In other words, it returns (A-B) % M. | ||
318 | /// It is designed as a compact mechanism for | ||
319 | /// incrementing a 'mode' switch and wrapping | ||
320 | /// around back to 'mode 0' when the switch | ||
321 | /// goes past the end of the available range. | ||
322 | /// e.g. if you have seven modes, this switches | ||
323 | /// to the next one and wraps around if needed: | ||
324 | /// mode = addmod8( mode, 1, 7); | ||
325 | ///LIB8STATIC_ALWAYS_INLINESee 'mod8' for notes on performance. | ||
326 | LIB8STATIC uint8_t submod8( uint8_t a, uint8_t b, uint8_t m) | ||
327 | { | ||
328 | #if defined(__AVR__) | ||
329 | asm volatile ( | ||
330 | " sub %[a],%[b] \n\t" | ||
331 | "L_%=: sub %[a],%[m] \n\t" | ||
332 | " brcc L_%= \n\t" | ||
333 | " add %[a],%[m] \n\t" | ||
334 | : [a] "+r" (a) | ||
335 | : [b] "r" (b), [m] "r" (m) | ||
336 | ); | ||
337 | #else | ||
338 | a -= b; | ||
339 | while( a >= m) a -= m; | ||
340 | #endif | ||
341 | return a; | ||
342 | } | ||
343 | |||
344 | /// 8x8 bit multiplication, with 8 bit result | ||
345 | LIB8STATIC_ALWAYS_INLINE uint8_t mul8( uint8_t i, uint8_t j) | ||
346 | { | ||
347 | #if MUL8_C == 1 | ||
348 | return ((uint16_t)i * (uint16_t)(j) ) & 0xFF; | ||
349 | #elif MUL8_AVRASM == 1 | ||
350 | asm volatile( | ||
351 | /* Multiply 8-bit i * 8-bit j, giving 16-bit r1,r0 */ | ||
352 | "mul %0, %1 \n\t" | ||
353 | /* Extract the LOW 8-bits (r0) */ | ||
354 | "mov %0, r0 \n\t" | ||
355 | /* Restore r1 to "0"; it's expected to always be that */ | ||
356 | "clr __zero_reg__ \n\t" | ||
357 | : "+a" (i) | ||
358 | : "a" (j) | ||
359 | : "r0", "r1"); | ||
360 | |||
361 | return i; | ||
362 | #else | ||
363 | #error "No implementation for mul8 available." | ||
364 | #endif | ||
365 | } | ||
366 | |||
367 | |||
368 | /// saturating 8x8 bit multiplication, with 8 bit result | ||
369 | /// @returns the product of i * j, capping at 0xFF | ||
370 | LIB8STATIC_ALWAYS_INLINE uint8_t qmul8( uint8_t i, uint8_t j) | ||
371 | { | ||
372 | #if QMUL8_C == 1 | ||
373 | int p = ((uint16_t)i * (uint16_t)(j) ); | ||
374 | if( p > 255) p = 255; | ||
375 | return p; | ||
376 | #elif QMUL8_AVRASM == 1 | ||
377 | asm volatile( | ||
378 | /* Multiply 8-bit i * 8-bit j, giving 16-bit r1,r0 */ | ||
379 | " mul %0, %1 \n\t" | ||
380 | /* If high byte of result is zero, all is well. */ | ||
381 | " tst r1 \n\t" | ||
382 | " breq Lnospill_%= \n\t" | ||
383 | /* If high byte of result > 0, saturate low byte to 0xFF */ | ||
384 | " ldi %0,0xFF \n\t" | ||
385 | " rjmp Ldone_%= \n\t" | ||
386 | "Lnospill_%=: \n\t" | ||
387 | /* Extract the LOW 8-bits (r0) */ | ||
388 | " mov %0, r0 \n\t" | ||
389 | "Ldone_%=: \n\t" | ||
390 | /* Restore r1 to "0"; it's expected to always be that */ | ||
391 | " clr __zero_reg__ \n\t" | ||
392 | : "+a" (i) | ||
393 | : "a" (j) | ||
394 | : "r0", "r1"); | ||
395 | |||
396 | return i; | ||
397 | #else | ||
398 | #error "No implementation for qmul8 available." | ||
399 | #endif | ||
400 | } | ||
401 | |||
402 | |||
403 | /// take abs() of a signed 8-bit uint8_t | ||
404 | LIB8STATIC_ALWAYS_INLINE int8_t abs8( int8_t i) | ||
405 | { | ||
406 | #if ABS8_C == 1 | ||
407 | if( i < 0) i = -i; | ||
408 | return i; | ||
409 | #elif ABS8_AVRASM == 1 | ||
410 | |||
411 | |||
412 | asm volatile( | ||
413 | /* First, check the high bit, and prepare to skip if it's clear */ | ||
414 | "sbrc %0, 7 \n" | ||
415 | |||
416 | /* Negate the value */ | ||
417 | "neg %0 \n" | ||
418 | |||
419 | : "+r" (i) : "r" (i) ); | ||
420 | return i; | ||
421 | #else | ||
422 | #error "No implementation for abs8 available." | ||
423 | #endif | ||
424 | } | ||
425 | |||
426 | /// square root for 16-bit integers | ||
427 | /// About three times faster and five times smaller | ||
428 | /// than Arduino's general sqrt on AVR. | ||
429 | LIB8STATIC uint8_t sqrt16(uint16_t x) | ||
430 | { | ||
431 | if( x <= 1) { | ||
432 | return x; | ||
433 | } | ||
434 | |||
435 | uint8_t low = 1; // lower bound | ||
436 | uint8_t hi, mid; | ||
437 | |||
438 | if( x > 7904) { | ||
439 | hi = 255; | ||
440 | } else { | ||
441 | hi = (x >> 5) + 8; // initial estimate for upper bound | ||
442 | } | ||
443 | |||
444 | do { | ||
445 | mid = (low + hi) >> 1; | ||
446 | if ((uint16_t)(mid * mid) > x) { | ||
447 | hi = mid - 1; | ||
448 | } else { | ||
449 | if( mid == 255) { | ||
450 | return 255; | ||
451 | } | ||
452 | low = mid + 1; | ||
453 | } | ||
454 | } while (hi >= low); | ||
455 | |||
456 | return low - 1; | ||
457 | } | ||
458 | |||
459 | /// blend a variable proproportion(0-255) of one byte to another | ||
460 | /// @param a - the starting byte value | ||
461 | /// @param b - the byte value to blend toward | ||
462 | /// @param amountOfB - the proportion (0-255) of b to blend | ||
463 | /// @returns a byte value between a and b, inclusive | ||
464 | #if (FASTLED_BLEND_FIXED == 1) | ||
465 | LIB8STATIC uint8_t blend8( uint8_t a, uint8_t b, uint8_t amountOfB) | ||
466 | { | ||
467 | #if BLEND8_C == 1 | ||
468 | uint16_t partial; | ||
469 | uint8_t result; | ||
470 | |||
471 | uint8_t amountOfA = 255 - amountOfB; | ||
472 | |||
473 | partial = (a * amountOfA); | ||
474 | #if (FASTLED_SCALE8_FIXED == 1) | ||
475 | partial += a; | ||
476 | //partial = add8to16( a, partial); | ||
477 | #endif | ||
478 | |||
479 | partial += (b * amountOfB); | ||
480 | #if (FASTLED_SCALE8_FIXED == 1) | ||
481 | partial += b; | ||
482 | //partial = add8to16( b, partial); | ||
483 | #endif | ||
484 | |||
485 | result = partial >> 8; | ||
486 | |||
487 | return result; | ||
488 | |||
489 | #elif BLEND8_AVRASM == 1 | ||
490 | uint16_t partial; | ||
491 | uint8_t result; | ||
492 | |||
493 | asm volatile ( | ||
494 | /* partial = b * amountOfB */ | ||
495 | " mul %[b], %[amountOfB] \n\t" | ||
496 | " movw %A[partial], r0 \n\t" | ||
497 | |||
498 | /* amountOfB (aka amountOfA) = 255 - amountOfB */ | ||
499 | " com %[amountOfB] \n\t" | ||
500 | |||
501 | /* partial += a * amountOfB (aka amountOfA) */ | ||
502 | " mul %[a], %[amountOfB] \n\t" | ||
503 | |||
504 | " add %A[partial], r0 \n\t" | ||
505 | " adc %B[partial], r1 \n\t" | ||
506 | |||
507 | " clr __zero_reg__ \n\t" | ||
508 | |||
509 | #if (FASTLED_SCALE8_FIXED == 1) | ||
510 | /* partial += a */ | ||
511 | " add %A[partial], %[a] \n\t" | ||
512 | " adc %B[partial], __zero_reg__ \n\t" | ||
513 | |||
514 | // partial += b | ||
515 | " add %A[partial], %[b] \n\t" | ||
516 | " adc %B[partial], __zero_reg__ \n\t" | ||
517 | #endif | ||
518 | |||
519 | : [partial] "=r" (partial), | ||
520 | [amountOfB] "+a" (amountOfB) | ||
521 | : [a] "a" (a), | ||
522 | [b] "a" (b) | ||
523 | : "r0", "r1" | ||
524 | ); | ||
525 | |||
526 | result = partial >> 8; | ||
527 | |||
528 | return result; | ||
529 | |||
530 | #else | ||
531 | #error "No implementation for blend8 available." | ||
532 | #endif | ||
533 | } | ||
534 | |||
535 | #else | ||
536 | LIB8STATIC uint8_t blend8( uint8_t a, uint8_t b, uint8_t amountOfB) | ||
537 | { | ||
538 | // This version loses precision in the integer math | ||
539 | // and can actually return results outside of the range | ||
540 | // from a to b. Its use is not recommended. | ||
541 | uint8_t result; | ||
542 | uint8_t amountOfA = 255 - amountOfB; | ||
543 | result = scale8_LEAVING_R1_DIRTY( a, amountOfA) | ||
544 | + scale8_LEAVING_R1_DIRTY( b, amountOfB); | ||
545 | cleanup_R1(); | ||
546 | return result; | ||
547 | } | ||
548 | #endif | ||
549 | |||
550 | |||
551 | ///@} | ||
552 | #endif | ||