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26 #ifndef __DAL_FIXED31_32_H__
27 #define __DAL_FIXED31_32_H__
30 #define LLONG_MAX 9223372036854775807ll
33 #define LLONG_MIN (-LLONG_MAX - 1ll)
36 #define FIXED31_32_BITS_PER_FRACTIONAL_PART 32
38 #define LLONG_MIN (1LL<<63)
41 #define LLONG_MAX (-1LL>>1)
46 * Arithmetic operations on real numbers
47 * represented as fixed-point numbers.
48 * There are: 1 bit for sign,
49 * 31 bit for integer part,
50 * 32 bits for fractional part.
53 * Currently, overflows and underflows are asserted;
54 * no special result returned.
67 static const struct fixed31_32 dc_fixpt_zero = { 0 };
68 static const struct fixed31_32 dc_fixpt_epsilon = { 1LL };
69 static const struct fixed31_32 dc_fixpt_half = { 0x80000000LL };
70 static const struct fixed31_32 dc_fixpt_one = { 0x100000000LL };
72 static const struct fixed31_32 dc_fixpt_pi = { 13493037705LL };
73 static const struct fixed31_32 dc_fixpt_two_pi = { 26986075409LL };
74 static const struct fixed31_32 dc_fixpt_e = { 11674931555LL };
75 static const struct fixed31_32 dc_fixpt_ln2 = { 2977044471LL };
76 static const struct fixed31_32 dc_fixpt_ln2_div_2 = { 1488522236LL };
80 * Initialization routines
85 * result = numerator / denominator
87 struct fixed31_32 dc_fixpt_from_fraction(long long numerator, long long denominator);
93 static inline struct fixed31_32 dc_fixpt_from_int(int arg)
95 struct fixed31_32 res;
97 res.value = (long long) arg << FIXED31_32_BITS_PER_FRACTIONAL_PART;
111 static inline struct fixed31_32 dc_fixpt_neg(struct fixed31_32 arg)
113 struct fixed31_32 res;
115 res.value = -arg.value;
122 * result = abs(arg) := (arg >= 0) ? arg : -arg
124 static inline struct fixed31_32 dc_fixpt_abs(struct fixed31_32 arg)
127 return dc_fixpt_neg(arg);
134 * Binary relational operators
139 * result = arg1 < arg2
141 static inline bool dc_fixpt_lt(struct fixed31_32 arg1, struct fixed31_32 arg2)
143 return arg1.value < arg2.value;
148 * result = arg1 <= arg2
150 static inline bool dc_fixpt_le(struct fixed31_32 arg1, struct fixed31_32 arg2)
152 return arg1.value <= arg2.value;
157 * result = arg1 == arg2
159 static inline bool dc_fixpt_eq(struct fixed31_32 arg1, struct fixed31_32 arg2)
161 return arg1.value == arg2.value;
166 * result = min(arg1, arg2) := (arg1 <= arg2) ? arg1 : arg2
168 static inline struct fixed31_32 dc_fixpt_min(struct fixed31_32 arg1, struct fixed31_32 arg2)
170 if (arg1.value <= arg2.value)
178 * result = max(arg1, arg2) := (arg1 <= arg2) ? arg2 : arg1
180 static inline struct fixed31_32 dc_fixpt_max(struct fixed31_32 arg1, struct fixed31_32 arg2)
182 if (arg1.value <= arg2.value)
190 * | min_value, when arg <= min_value
191 * result = | arg, when min_value < arg < max_value
192 * | max_value, when arg >= max_value
194 static inline struct fixed31_32 dc_fixpt_clamp(
195 struct fixed31_32 arg,
196 struct fixed31_32 min_value,
197 struct fixed31_32 max_value)
199 if (dc_fixpt_le(arg, min_value))
201 else if (dc_fixpt_le(max_value, arg))
209 * Binary shift operators
214 * result = arg << shift
216 static inline struct fixed31_32 dc_fixpt_shl(struct fixed31_32 arg, unsigned char shift)
218 ASSERT(((arg.value >= 0) && (arg.value <= LLONG_MAX >> shift)) ||
219 ((arg.value < 0) && (arg.value >= ~(LLONG_MAX >> shift))));
221 arg.value = arg.value << shift;
228 * result = arg >> shift
230 static inline struct fixed31_32 dc_fixpt_shr(struct fixed31_32 arg, unsigned char shift)
232 bool negative = arg.value < 0;
235 arg.value = -arg.value;
236 arg.value = arg.value >> shift;
238 arg.value = -arg.value;
244 * Binary additive operators
249 * result = arg1 + arg2
251 static inline struct fixed31_32 dc_fixpt_add(struct fixed31_32 arg1, struct fixed31_32 arg2)
253 struct fixed31_32 res;
255 ASSERT(((arg1.value >= 0) && (LLONG_MAX - arg1.value >= arg2.value)) ||
256 ((arg1.value < 0) && (LLONG_MIN - arg1.value <= arg2.value)));
258 res.value = arg1.value + arg2.value;
265 * result = arg1 + arg2
267 static inline struct fixed31_32 dc_fixpt_add_int(struct fixed31_32 arg1, int arg2)
269 return dc_fixpt_add(arg1, dc_fixpt_from_int(arg2));
274 * result = arg1 - arg2
276 static inline struct fixed31_32 dc_fixpt_sub(struct fixed31_32 arg1, struct fixed31_32 arg2)
278 struct fixed31_32 res;
280 ASSERT(((arg2.value >= 0) && (LLONG_MIN + arg2.value <= arg1.value)) ||
281 ((arg2.value < 0) && (LLONG_MAX + arg2.value >= arg1.value)));
283 res.value = arg1.value - arg2.value;
290 * result = arg1 - arg2
292 static inline struct fixed31_32 dc_fixpt_sub_int(struct fixed31_32 arg1, int arg2)
294 return dc_fixpt_sub(arg1, dc_fixpt_from_int(arg2));
300 * Binary multiplicative operators
305 * result = arg1 * arg2
307 struct fixed31_32 dc_fixpt_mul(struct fixed31_32 arg1, struct fixed31_32 arg2);
312 * result = arg1 * arg2
314 static inline struct fixed31_32 dc_fixpt_mul_int(struct fixed31_32 arg1, int arg2)
316 return dc_fixpt_mul(arg1, dc_fixpt_from_int(arg2));
321 * result = square(arg) := arg * arg
323 struct fixed31_32 dc_fixpt_sqr(struct fixed31_32 arg);
327 * result = arg1 / arg2
329 static inline struct fixed31_32 dc_fixpt_div_int(struct fixed31_32 arg1, long long arg2)
331 return dc_fixpt_from_fraction(arg1.value, dc_fixpt_from_int(arg2).value);
336 * result = arg1 / arg2
338 static inline struct fixed31_32 dc_fixpt_div(struct fixed31_32 arg1, struct fixed31_32 arg2)
340 return dc_fixpt_from_fraction(arg1.value, arg2.value);
345 * Reciprocal function
350 * result = reciprocal(arg) := 1 / arg
353 * No special actions taken in case argument is zero.
355 struct fixed31_32 dc_fixpt_recip(struct fixed31_32 arg);
359 * Trigonometric functions
364 * result = sinc(arg) := sin(arg) / arg
367 * Argument specified in radians,
368 * internally it's normalized to [-2pi...2pi] range.
370 struct fixed31_32 dc_fixpt_sinc(struct fixed31_32 arg);
377 * Argument specified in radians,
378 * internally it's normalized to [-2pi...2pi] range.
380 struct fixed31_32 dc_fixpt_sin(struct fixed31_32 arg);
387 * Argument specified in radians
388 * and should be in [-2pi...2pi] range -
389 * passing arguments outside that range
390 * will cause incorrect result!
392 struct fixed31_32 dc_fixpt_cos(struct fixed31_32 arg);
396 * Transcendent functions
404 * Currently, function is verified for abs(arg) <= 1.
406 struct fixed31_32 dc_fixpt_exp(struct fixed31_32 arg);
413 * Currently, abs(arg) should be less than 1.
414 * No normalization is done.
415 * Currently, no special actions taken
416 * in case of invalid argument(s). Take care!
418 struct fixed31_32 dc_fixpt_log(struct fixed31_32 arg);
427 * result = pow(arg1, arg2)
430 * Currently, abs(arg1) should be less than 1. Take care!
432 static inline struct fixed31_32 dc_fixpt_pow(struct fixed31_32 arg1, struct fixed31_32 arg2)
435 return arg2.value == 0 ? dc_fixpt_one : dc_fixpt_zero;
450 * result = floor(arg) := greatest integer lower than or equal to arg
452 static inline int dc_fixpt_floor(struct fixed31_32 arg)
454 unsigned long long arg_value = arg.value > 0 ? arg.value : -arg.value;
457 return (int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
459 return -(int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
464 * result = round(arg) := integer nearest to arg
466 static inline int dc_fixpt_round(struct fixed31_32 arg)
468 unsigned long long arg_value = arg.value > 0 ? arg.value : -arg.value;
470 const long long summand = dc_fixpt_half.value;
472 ASSERT(LLONG_MAX - (long long)arg_value >= summand);
474 arg_value += summand;
477 return (int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
479 return -(int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
484 * result = ceil(arg) := lowest integer greater than or equal to arg
486 static inline int dc_fixpt_ceil(struct fixed31_32 arg)
488 unsigned long long arg_value = arg.value > 0 ? arg.value : -arg.value;
490 const long long summand = dc_fixpt_one.value -
491 dc_fixpt_epsilon.value;
493 ASSERT(LLONG_MAX - (long long)arg_value >= summand);
495 arg_value += summand;
498 return (int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
500 return -(int)(arg_value >> FIXED31_32_BITS_PER_FRACTIONAL_PART);
503 /* the following two function are used in scaler hw programming to convert fixed
504 * point value to format 2 bits from integer part and 19 bits from fractional
505 * part. The same applies for u0d19, 0 bits from integer part and 19 bits from
509 unsigned int dc_fixpt_u3d19(struct fixed31_32 arg);
511 unsigned int dc_fixpt_u2d19(struct fixed31_32 arg);
513 unsigned int dc_fixpt_u0d19(struct fixed31_32 arg);
515 unsigned int dc_fixpt_clamp_u0d14(struct fixed31_32 arg);
517 unsigned int dc_fixpt_clamp_u0d10(struct fixed31_32 arg);
519 int dc_fixpt_s4d19(struct fixed31_32 arg);
521 static inline struct fixed31_32 dc_fixpt_truncate(struct fixed31_32 arg, unsigned int frac_bits)
523 bool negative = arg.value < 0;
525 if (frac_bits >= FIXED31_32_BITS_PER_FRACTIONAL_PART) {
526 ASSERT(frac_bits == FIXED31_32_BITS_PER_FRACTIONAL_PART);
531 arg.value = -arg.value;
532 arg.value &= (~0LL) << (FIXED31_32_BITS_PER_FRACTIONAL_PART - frac_bits);
534 arg.value = -arg.value;