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// Copyright 2019 The libgav1 Authors
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// Constants and utility functions used for inverse transform implementations.
// This will be included inside an anonymous namespace on files where these are
// necessary.
// The value at index i is derived as: round(cos(pi * i / 128) * (1 << 12)).
constexpr int16_t kCos128[65] = {
4096, 4095, 4091, 4085, 4076, 4065, 4052, 4036, 4017, 3996, 3973,
3948, 3920, 3889, 3857, 3822, 3784, 3745, 3703, 3659, 3612, 3564,
3513, 3461, 3406, 3349, 3290, 3229, 3166, 3102, 3035, 2967, 2896,
2824, 2751, 2675, 2598, 2520, 2440, 2359, 2276, 2191, 2106, 2019,
1931, 1842, 1751, 1660, 1567, 1474, 1380, 1285, 1189, 1092, 995,
897, 799, 700, 601, 501, 401, 301, 201, 101, 0};
inline int16_t Cos128(int angle) {
angle &= 0xff;
// If |angle| is 128, this function returns -4096 (= -2^12), which will
// cause the 32-bit multiplications in ButterflyRotation() to overflow if
// dst[a] or dst[b] is -2^19 (a possible corner case when |range| is 20):
//
// (-2^12) * (-2^19) = 2^31, which cannot be represented as an int32_t.
//
// Note: |range| is 20 when bitdepth is 12 and a row transform is performed.
//
// Assert that this angle is never used by DCT or ADST.
assert(angle != 128);
if (angle <= 64) return kCos128[angle];
if (angle <= 128) return -kCos128[128 - angle];
if (angle <= 192) return -kCos128[angle - 128];
return kCos128[256 - angle];
}
inline int16_t Sin128(int angle) { return Cos128(angle - 64); }
// The value for index i is derived as:
// round(sqrt(2) * sin(i * pi / 9) * 2 / 3 * (1 << 12)).
constexpr int16_t kAdst4Multiplier[4] = {1321, 2482, 3344, 3803};
constexpr uint8_t kTransformRowShift[kNumTransformSizes] = {
0, 0, 1, 0, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2};
constexpr bool kShouldRound[kNumTransformSizes] = {
false, true, false, true, false, true, false, false, true, false,
true, false, false, true, false, true, false, true, false};
constexpr int16_t kIdentity4Multiplier /* round(2^12 * sqrt(2)) */ = 0x16A1;
constexpr int16_t kIdentity4MultiplierFraction /* round(2^12 * (sqrt(2) - 1))*/
= 0x6A1;
constexpr int16_t kIdentity16Multiplier /* 2 * round(2^12 * sqrt(2)) */ = 11586;
constexpr int16_t kTransformRowMultiplier /* round(2^12 / sqrt(2)) */ = 2896;
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