2 * Copyright 2012-15 Advanced Micro Devices, Inc.
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26 #include "dm_services.h"
27 #include "include/fixed31_32.h"
29 static inline unsigned long long abs_i64(
33 return (unsigned long long)arg;
35 return (unsigned long long)(-arg);
40 * result = dividend / divisor
41 * *remainder = dividend % divisor
43 static inline unsigned long long complete_integer_division_u64(
44 unsigned long long dividend,
45 unsigned long long divisor,
46 unsigned long long *remainder)
48 unsigned long long result;
52 result = div64_u64_rem(dividend, divisor, remainder);
58 #define FRACTIONAL_PART_MASK \
59 ((1ULL << FIXED31_32_BITS_PER_FRACTIONAL_PART) - 1)
61 #define GET_INTEGER_PART(x) \
62 ((x) >> FIXED31_32_BITS_PER_FRACTIONAL_PART)
64 #define GET_FRACTIONAL_PART(x) \
65 (FRACTIONAL_PART_MASK & (x))
67 struct fixed31_32 dc_fixpt_from_fraction(long long numerator, long long denominator)
69 struct fixed31_32 res;
71 bool arg1_negative = numerator < 0;
72 bool arg2_negative = denominator < 0;
74 unsigned long long arg1_value = arg1_negative ? -numerator : numerator;
75 unsigned long long arg2_value = arg2_negative ? -denominator : denominator;
77 unsigned long long remainder;
79 /* determine integer part */
81 unsigned long long res_value = complete_integer_division_u64(
82 arg1_value, arg2_value, &remainder);
84 ASSERT(res_value <= LONG_MAX);
86 /* determine fractional part */
88 unsigned int i = FIXED31_32_BITS_PER_FRACTIONAL_PART;
95 if (remainder >= arg2_value) {
97 remainder -= arg2_value;
104 unsigned long long summand = (remainder << 1) >= arg2_value;
106 ASSERT(res_value <= LLONG_MAX - summand);
108 res_value += summand;
111 res.value = (long long)res_value;
113 if (arg1_negative ^ arg2_negative)
114 res.value = -res.value;
119 struct fixed31_32 dc_fixpt_mul(struct fixed31_32 arg1, struct fixed31_32 arg2)
121 struct fixed31_32 res;
123 bool arg1_negative = arg1.value < 0;
124 bool arg2_negative = arg2.value < 0;
126 unsigned long long arg1_value = arg1_negative ? -arg1.value : arg1.value;
127 unsigned long long arg2_value = arg2_negative ? -arg2.value : arg2.value;
129 unsigned long long arg1_int = GET_INTEGER_PART(arg1_value);
130 unsigned long long arg2_int = GET_INTEGER_PART(arg2_value);
132 unsigned long long arg1_fra = GET_FRACTIONAL_PART(arg1_value);
133 unsigned long long arg2_fra = GET_FRACTIONAL_PART(arg2_value);
135 unsigned long long tmp;
137 res.value = arg1_int * arg2_int;
139 ASSERT(res.value <= LONG_MAX);
141 res.value <<= FIXED31_32_BITS_PER_FRACTIONAL_PART;
143 tmp = arg1_int * arg2_fra;
145 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
149 tmp = arg2_int * arg1_fra;
151 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
155 tmp = arg1_fra * arg2_fra;
157 tmp = (tmp >> FIXED31_32_BITS_PER_FRACTIONAL_PART) +
158 (tmp >= (unsigned long long)dc_fixpt_half.value);
160 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
164 if (arg1_negative ^ arg2_negative)
165 res.value = -res.value;
170 struct fixed31_32 dc_fixpt_sqr(struct fixed31_32 arg)
172 struct fixed31_32 res;
174 unsigned long long arg_value = abs_i64(arg.value);
176 unsigned long long arg_int = GET_INTEGER_PART(arg_value);
178 unsigned long long arg_fra = GET_FRACTIONAL_PART(arg_value);
180 unsigned long long tmp;
182 res.value = arg_int * arg_int;
184 ASSERT(res.value <= LONG_MAX);
186 res.value <<= FIXED31_32_BITS_PER_FRACTIONAL_PART;
188 tmp = arg_int * arg_fra;
190 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
194 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
198 tmp = arg_fra * arg_fra;
200 tmp = (tmp >> FIXED31_32_BITS_PER_FRACTIONAL_PART) +
201 (tmp >= (unsigned long long)dc_fixpt_half.value);
203 ASSERT(tmp <= (unsigned long long)(LLONG_MAX - res.value));
210 struct fixed31_32 dc_fixpt_recip(struct fixed31_32 arg)
214 * Good idea to use Newton's method
219 return dc_fixpt_from_fraction(
224 struct fixed31_32 dc_fixpt_sinc(struct fixed31_32 arg)
226 struct fixed31_32 square;
228 struct fixed31_32 res = dc_fixpt_one;
232 struct fixed31_32 arg_norm = arg;
236 dc_fixpt_abs(arg))) {
237 arg_norm = dc_fixpt_sub(
243 dc_fixpt_two_pi.value)));
246 square = dc_fixpt_sqr(arg_norm);
260 if (arg.value != arg_norm.value)
262 dc_fixpt_mul(res, arg_norm),
268 struct fixed31_32 dc_fixpt_sin(struct fixed31_32 arg)
275 struct fixed31_32 dc_fixpt_cos(struct fixed31_32 arg)
277 /* TODO implement argument normalization */
279 const struct fixed31_32 square = dc_fixpt_sqr(arg);
281 struct fixed31_32 res = dc_fixpt_one;
305 * Calculated as Taylor series.
307 static struct fixed31_32 fixed31_32_exp_from_taylor_series(struct fixed31_32 arg)
311 struct fixed31_32 res = dc_fixpt_from_fraction(
314 /* TODO find correct res */
316 ASSERT(dc_fixpt_lt(arg, dc_fixpt_one));
335 struct fixed31_32 dc_fixpt_exp(struct fixed31_32 arg)
340 * exp(x) = exp(r + m * ln(2)) = (1 << m) * exp(r),
341 * where m = round(x / ln(2)), r = x - m * ln(2)
346 dc_fixpt_abs(arg))) {
347 int m = dc_fixpt_round(
352 struct fixed31_32 r = dc_fixpt_sub(
366 fixed31_32_exp_from_taylor_series(r),
369 return dc_fixpt_div_int(
370 fixed31_32_exp_from_taylor_series(r),
372 } else if (arg.value != 0)
373 return fixed31_32_exp_from_taylor_series(arg);
378 struct fixed31_32 dc_fixpt_log(struct fixed31_32 arg)
380 struct fixed31_32 res = dc_fixpt_neg(dc_fixpt_one);
381 /* TODO improve 1st estimation */
383 struct fixed31_32 error;
385 ASSERT(arg.value > 0);
386 /* TODO if arg is negative, return NaN */
387 /* TODO if arg is zero, return -INF */
390 struct fixed31_32 res1 = dc_fixpt_add(
398 error = dc_fixpt_sub(
403 /* TODO determine max_allowed_error based on quality of exp() */
404 } while (abs_i64(error.value) > 100ULL);
410 /* this function is a generic helper to translate fixed point value to
411 * specified integer format that will consist of integer_bits integer part and
412 * fractional_bits fractional part. For example it is used in
413 * dc_fixpt_u2d19 to receive 2 bits integer part and 19 bits fractional
414 * part in 32 bits. It is used in hw programming (scaler)
417 static inline unsigned int ux_dy(
419 unsigned int integer_bits,
420 unsigned int fractional_bits)
422 /* 1. create mask of integer part */
423 unsigned int result = (1 << integer_bits) - 1;
424 /* 2. mask out fractional part */
425 unsigned int fractional_part = FRACTIONAL_PART_MASK & value;
426 /* 3. shrink fixed point integer part to be of integer_bits width*/
427 result &= GET_INTEGER_PART(value);
428 /* 4. make space for fractional part to be filled in after integer */
429 result <<= fractional_bits;
430 /* 5. shrink fixed point fractional part to of fractional_bits width*/
431 fractional_part >>= FIXED31_32_BITS_PER_FRACTIONAL_PART - fractional_bits;
432 /* 6. merge the result */
433 return result | fractional_part;
436 static inline unsigned int clamp_ux_dy(
438 unsigned int integer_bits,
439 unsigned int fractional_bits,
440 unsigned int min_clamp)
442 unsigned int truncated_val = ux_dy(value, integer_bits, fractional_bits);
444 if (value >= (1LL << (integer_bits + FIXED31_32_BITS_PER_FRACTIONAL_PART)))
445 return (1 << (integer_bits + fractional_bits)) - 1;
446 else if (truncated_val > min_clamp)
447 return truncated_val;
452 unsigned int dc_fixpt_u4d19(struct fixed31_32 arg)
454 return ux_dy(arg.value, 4, 19);
457 unsigned int dc_fixpt_u3d19(struct fixed31_32 arg)
459 return ux_dy(arg.value, 3, 19);
462 unsigned int dc_fixpt_u2d19(struct fixed31_32 arg)
464 return ux_dy(arg.value, 2, 19);
467 unsigned int dc_fixpt_u0d19(struct fixed31_32 arg)
469 return ux_dy(arg.value, 0, 19);
472 unsigned int dc_fixpt_clamp_u0d14(struct fixed31_32 arg)
474 return clamp_ux_dy(arg.value, 0, 14, 1);
477 unsigned int dc_fixpt_clamp_u0d10(struct fixed31_32 arg)
479 return clamp_ux_dy(arg.value, 0, 10, 1);
482 int dc_fixpt_s4d19(struct fixed31_32 arg)
485 return -(int)ux_dy(dc_fixpt_abs(arg).value, 4, 19);
487 return ux_dy(arg.value, 4, 19);