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 /* * 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 #include #include namespace android { template 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, 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(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 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* N, uint64_t* D); template void LinearTransform::reduce(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(N), D); *N = -(*N); } else { reduce(reinterpret_cast(N), D); } } } } // namespace android