| /* | |
| * Copyright (C) 2011 The Android Open Source Project | |
| * | |
| * 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. | |
| */ | |
| #define __STDC_LIMIT_MACROS | |
| #include <assert.h> | |
| #include <stdint.h> | |
| #include <utils/LinearTransform.h> | |
| namespace android { | |
| template<class T> static inline T ABS(T x) { return (x < 0) ? -x : x; } | |
| // Static math methods involving linear transformations | |
| static bool scale_u64_to_u64( | |
| uint64_t val, | |
| uint32_t N, | |
| uint32_t D, | |
| uint64_t* res, | |
| bool round_up_not_down) { | |
| uint64_t tmp1, tmp2; | |
| uint32_t r; | |
| assert(res); | |
| assert(D); | |
| // Let U32(X) denote a uint32_t containing the upper 32 bits of a 64 bit | |
| // integer X. | |
| // Let L32(X) denote a uint32_t containing the lower 32 bits of a 64 bit | |
| // integer X. | |
| // Let X[A, B] with A <= B denote bits A through B of the integer X. | |
| // Let (A | B) denote the concatination of two 32 bit ints, A and B. | |
| // IOW X = (A | B) => U32(X) == A && L32(X) == B | |
| // | |
| // compute M = val * N (a 96 bit int) | |
| // --------------------------------- | |
| // tmp2 = U32(val) * N (a 64 bit int) | |
| // tmp1 = L32(val) * N (a 64 bit int) | |
| // which means | |
| // M = val * N = (tmp2 << 32) + tmp1 | |
| tmp2 = (val >> 32) * N; | |
| tmp1 = (val & UINT32_MAX) * N; | |
| // compute M[32, 95] | |
| // tmp2 = tmp2 + U32(tmp1) | |
| // = (U32(val) * N) + U32(L32(val) * N) | |
| // = M[32, 95] | |
| tmp2 += tmp1 >> 32; | |
| // if M[64, 95] >= D, then M/D has bits > 63 set and we have | |
| // an overflow. | |
| if ((tmp2 >> 32) >= D) { | |
| *res = UINT64_MAX; | |
| return false; | |
| } | |
| // Divide. Going in we know | |
| // tmp2 = M[32, 95] | |
| // U32(tmp2) < D | |
| r = tmp2 % D; | |
| tmp2 /= D; | |
| // At this point | |
| // tmp1 = L32(val) * N | |
| // tmp2 = M[32, 95] / D | |
| // = (M / D)[32, 95] | |
| // r = M[32, 95] % D | |
| // U32(tmp2) = 0 | |
| // | |
| // compute tmp1 = (r | M[0, 31]) | |
| tmp1 = (tmp1 & UINT32_MAX) | ((uint64_t)r << 32); | |
| // Divide again. Keep the remainder around in order to round properly. | |
| r = tmp1 % D; | |
| tmp1 /= D; | |
| // At this point | |
| // tmp2 = (M / D)[32, 95] | |
| // tmp1 = (M / D)[ 0, 31] | |
| // r = M % D | |
| // U32(tmp1) = 0 | |
| // U32(tmp2) = 0 | |
| // Pack the result and deal with the round-up case (As well as the | |
| // remote possiblility over overflow in such a case). | |
| *res = (tmp2 << 32) | tmp1; | |
| if (r && round_up_not_down) { | |
| ++(*res); | |
| if (!(*res)) { | |
| *res = UINT64_MAX; | |
| return false; | |
| } | |
| } | |
| return true; | |
| } | |
| static bool linear_transform_s64_to_s64( | |
| int64_t val, | |
| int64_t basis1, | |
| int32_t N, | |
| uint32_t D, | |
| bool invert_frac, | |
| int64_t basis2, | |
| int64_t* out) { | |
| uint64_t scaled, res; | |
| uint64_t abs_val; | |
| bool is_neg; | |
| if (!out) | |
| return false; | |
| // Compute abs(val - basis_64). Keep track of whether or not this delta | |
| // will be negative after the scale opertaion. | |
| if (val < basis1) { | |
| is_neg = true; | |
| abs_val = basis1 - val; | |
| } else { | |
| is_neg = false; | |
| abs_val = val - basis1; | |
| } | |
| if (N < 0) | |
| is_neg = !is_neg; | |
| if (!scale_u64_to_u64(abs_val, | |
| invert_frac ? D : ABS(N), | |
| invert_frac ? ABS(N) : D, | |
| &scaled, | |
| is_neg)) | |
| return false; // overflow/undeflow | |
| // if scaled is >= 0x8000<etc>, then we are going to overflow or | |
| // underflow unless ABS(basis2) is large enough to pull us back into the | |
| // non-overflow/underflow region. | |
| if (scaled & INT64_MIN) { | |
| if (is_neg && (basis2 < 0)) | |
| return false; // certain underflow | |
| if (!is_neg && (basis2 >= 0)) | |
| return false; // certain overflow | |
| if (ABS(basis2) <= static_cast<int64_t>(scaled & INT64_MAX)) | |
| return false; // not enough | |
| // Looks like we are OK | |
| *out = (is_neg ? (-scaled) : scaled) + basis2; | |
| } else { | |
| // Scaled fits within signed bounds, so we just need to check for | |
| // over/underflow for two signed integers. Basically, if both scaled | |
| // and basis2 have the same sign bit, and the result has a different | |
| // sign bit, then we have under/overflow. An easy way to compute this | |
| // is | |
| // (scaled_signbit XNOR basis_signbit) && | |
| // (scaled_signbit XOR res_signbit) | |
| // == | |
| // (scaled_signbit XOR basis_signbit XOR 1) && | |
| // (scaled_signbit XOR res_signbit) | |
| if (is_neg) | |
| scaled = -scaled; | |
| res = scaled + basis2; | |
| if ((scaled ^ basis2 ^ INT64_MIN) & (scaled ^ res) & INT64_MIN) | |
| return false; | |
| *out = res; | |
| } | |
| return true; | |
| } | |
| bool LinearTransform::doForwardTransform(int64_t a_in, int64_t* b_out) const { | |
| if (0 == a_to_b_denom) | |
| return false; | |
| return linear_transform_s64_to_s64(a_in, | |
| a_zero, | |
| a_to_b_numer, | |
| a_to_b_denom, | |
| false, | |
| b_zero, | |
| b_out); | |
| } | |
| bool LinearTransform::doReverseTransform(int64_t b_in, int64_t* a_out) const { | |
| if (0 == a_to_b_numer) | |
| return false; | |
| return linear_transform_s64_to_s64(b_in, | |
| b_zero, | |
| a_to_b_numer, | |
| a_to_b_denom, | |
| true, | |
| a_zero, | |
| a_out); | |
| } | |
| template <class T> void LinearTransform::reduce(T* N, T* D) { | |
| T a, b; | |
| if (!N || !D || !(*D)) { | |
| assert(false); | |
| return; | |
| } | |
| a = *N; | |
| b = *D; | |
| if (a == 0) { | |
| *D = 1; | |
| return; | |
| } | |
| // This implements Euclid's method to find GCD. | |
| if (a < b) { | |
| T tmp = a; | |
| a = b; | |
| b = tmp; | |
| } | |
| while (1) { | |
| // a is now the greater of the two. | |
| const T remainder = a % b; | |
| if (remainder == 0) { | |
| *N /= b; | |
| *D /= b; | |
| return; | |
| } | |
| // by swapping remainder and b, we are guaranteeing that a is | |
| // still the greater of the two upon entrance to the loop. | |
| a = b; | |
| b = remainder; | |
| } | |
| }; | |
| template void LinearTransform::reduce<uint64_t>(uint64_t* N, uint64_t* D); | |
| template void LinearTransform::reduce<uint32_t>(uint32_t* N, uint32_t* D); | |
| void LinearTransform::reduce(int32_t* N, uint32_t* D) { | |
| if (N && D && *D) { | |
| if (*N < 0) { | |
| *N = -(*N); | |
| reduce(reinterpret_cast<uint32_t*>(N), D); | |
| *N = -(*N); | |
| } else { | |
| reduce(reinterpret_cast<uint32_t*>(N), D); | |
| } | |
| } | |
| } | |
| } // namespace android |