| /* |
| * 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 |
