1ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com 28a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/* 3ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * Copyright 2006 The Android Open Source Project 48a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com * 5ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * Use of this source code is governed by a BSD-style license that can be 6ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * found in the LICENSE file. 78a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com */ 88a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 9ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com 108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#ifndef SkMath_DEFINED 118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#define SkMath_DEFINED 128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#include "SkTypes.h" 148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1557212f9469c8056bab3c85243dbb904e386eab95reed@google.com// 64bit -> 32bit utilities 1657212f9469c8056bab3c85243dbb904e386eab95reed@google.com 1757212f9469c8056bab3c85243dbb904e386eab95reed@google.com/** 1857212f9469c8056bab3c85243dbb904e386eab95reed@google.com * Return true iff the 64bit value can exactly be represented in signed 32bits 1957212f9469c8056bab3c85243dbb904e386eab95reed@google.com */ 2057212f9469c8056bab3c85243dbb904e386eab95reed@google.comstatic inline bool sk_64_isS32(int64_t value) { 2157212f9469c8056bab3c85243dbb904e386eab95reed@google.com return (int32_t)value == value; 2257212f9469c8056bab3c85243dbb904e386eab95reed@google.com} 2357212f9469c8056bab3c85243dbb904e386eab95reed@google.com 2457212f9469c8056bab3c85243dbb904e386eab95reed@google.com/** 2557212f9469c8056bab3c85243dbb904e386eab95reed@google.com * Return the 64bit argument as signed 32bits, asserting in debug that the arg 2657212f9469c8056bab3c85243dbb904e386eab95reed@google.com * exactly fits in signed 32bits. In the release build, no checks are preformed 2757212f9469c8056bab3c85243dbb904e386eab95reed@google.com * and the return value if the arg does not fit is undefined. 2857212f9469c8056bab3c85243dbb904e386eab95reed@google.com */ 2957212f9469c8056bab3c85243dbb904e386eab95reed@google.comstatic inline int32_t sk_64_asS32(int64_t value) { 3057212f9469c8056bab3c85243dbb904e386eab95reed@google.com SkASSERT(sk_64_isS32(value)); 3157212f9469c8056bab3c85243dbb904e386eab95reed@google.com return (int32_t)value; 3257212f9469c8056bab3c85243dbb904e386eab95reed@google.com} 3357212f9469c8056bab3c85243dbb904e386eab95reed@google.com 3457212f9469c8056bab3c85243dbb904e386eab95reed@google.com// Handy util that can be passed two ints, and will automatically promote to 3557212f9469c8056bab3c85243dbb904e386eab95reed@google.com// 64bits before the multiply, so the caller doesn't have to remember to cast 3657212f9469c8056bab3c85243dbb904e386eab95reed@google.com// e.g. (int64_t)a * b; 3757212f9469c8056bab3c85243dbb904e386eab95reed@google.comstatic inline int64_t sk_64_mul(int64_t a, int64_t b) { 3857212f9469c8056bab3c85243dbb904e386eab95reed@google.com return a * b; 3957212f9469c8056bab3c85243dbb904e386eab95reed@google.com} 4057212f9469c8056bab3c85243dbb904e386eab95reed@google.com 414b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com/////////////////////////////////////////////////////////////////////////////// 428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 430f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org/** 440f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org * Computes numer1 * numer2 / denom in full 64 intermediate precision. 450f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org * It is an error for denom to be 0. There is no special handling if 460f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org * the result overflows 32bits. 470f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org */ 480f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.orgstatic inline int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom) { 490f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org SkASSERT(denom); 50f7927dd60761ca45f26059a8ab434018676cb2e7skia.committer@gmail.com 510f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org int64_t tmp = sk_64_mul(numer1, numer2) / denom; 520f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org return sk_64_asS32(tmp); 530f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org} 540f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org 550f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org/** 560f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org * Return the integer square root of value, with a bias of bitBias 570f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org */ 580f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.orgint32_t SkSqrtBits(int32_t value, int bitBias); 590f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org 600f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org/** Return the integer square root of n, treated as a SkFixed (16.16) 610f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org */ 620f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org#define SkSqrt32(n) SkSqrtBits(n, 15) 630f1fef834c73cb4f38023de0f98d05562d24f2bccommit-bot@chromium.org 644b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com/** 654b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com * Returns (value < 0 ? 0 : value) efficiently (i.e. no compares or branches) 664b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com */ 678a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic inline int SkClampPos(int value) { 688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return value & ~(value >> 31); 698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** Given an integer and a positive (max) integer, return the value 724b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com * pinned against 0 and max, inclusive. 734b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com * @param value The value we want returned pinned between [0...max] 744b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com * @param max The positive max value 754b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com * @return 0 if value < 0, max if value > max, else value 764b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com */ 778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.comstatic inline int SkClampMax(int value, int max) { 788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com // ensure that max is positive 798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(max >= 0); 808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (value < 0) { 818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com value = 0; 828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com if (value > max) { 848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com value = max; 858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com } 868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return value; 878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 894b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com/** 904b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com * Returns true if value is a power of 2. Does not explicitly check for 914b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com * value <= 0. 92f2b98d67dcb6fcb3120feede9c72016fc7b3ead8reed@android.com */ 93883c8efae702462fa28e7ce4f17199bbfa1ce360mtkleintemplate <typename T> constexpr inline bool SkIsPow2(T value) { 94f2b98d67dcb6fcb3120feede9c72016fc7b3ead8reed@android.com return (value & (value - 1)) == 0; 95f2b98d67dcb6fcb3120feede9c72016fc7b3ead8reed@android.com} 96f2b98d67dcb6fcb3120feede9c72016fc7b3ead8reed@android.com 978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/////////////////////////////////////////////////////////////////////////////// 988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 994b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com/** 1004b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com * Return a*b/((1 << shift) - 1), rounding any fractional bits. 1014b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com * Only valid if a and b are unsigned and <= 32767 and shift is > 0 and <= 8 1028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com */ 103ea774d2a5a049bf89474c0f047ed6a4e521de126reed@google.comstatic inline unsigned SkMul16ShiftRound(U16CPU a, U16CPU b, int shift) { 1048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(a <= 32767); 1058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(b <= 32767); 1068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com SkASSERT(shift > 0 && shift <= 8); 1073848427d884b72114854c8eef9662691f23fae7bmtklein unsigned prod = a*b + (1 << (shift - 1)); 1088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com return (prod + (prod >> shift)) >> shift; 1098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com} 1108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com 1114b163ed2c22facbe8891616874ae07ba7827d9c9reed@google.com/** 112ea774d2a5a049bf89474c0f047ed6a4e521de126reed@google.com * Return a*b/255, rounding any fractional bits. 113ea774d2a5a049bf89474c0f047ed6a4e521de126reed@google.com * Only valid if a and b are unsigned and <= 32767. 114a0f5d1546d499ef0cd7dbfba9a866ae5a27e1541reed@android.com */ 115ea774d2a5a049bf89474c0f047ed6a4e521de126reed@google.comstatic inline U8CPU SkMulDiv255Round(U16CPU a, U16CPU b) { 116ea774d2a5a049bf89474c0f047ed6a4e521de126reed@google.com SkASSERT(a <= 32767); 117ea774d2a5a049bf89474c0f047ed6a4e521de126reed@google.com SkASSERT(b <= 32767); 1183848427d884b72114854c8eef9662691f23fae7bmtklein unsigned prod = a*b + 128; 119a0f5d1546d499ef0cd7dbfba9a866ae5a27e1541reed@android.com return (prod + (prod >> 8)) >> 8; 120a0f5d1546d499ef0cd7dbfba9a866ae5a27e1541reed@android.com} 121a0f5d1546d499ef0cd7dbfba9a866ae5a27e1541reed@android.com 1222c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org/** 1232c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org * Stores numer/denom and numer%denom into div and mod respectively. 1242c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org */ 1252c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.orgtemplate <typename In, typename Out> 1262c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.orginline void SkTDivMod(In numer, In denom, Out* div, Out* mod) { 1273a2682a77f996f649de7699c9f7bee046c6d4f17mtklein#ifdef SK_CPU_ARM32 1282c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org // If we wrote this as in the else branch, GCC won't fuse the two into one 1292c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org // divmod call, but rather a div call followed by a divmod. Silly! This 1302c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org // version is just as fast as calling __aeabi_[u]idivmod manually, but with 1312c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org // prettier code. 1322c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org // 1332c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org // This benches as around 2x faster than the code in the else branch. 1342c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org const In d = numer/denom; 1352c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org *div = static_cast<Out>(d); 1362c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org *mod = static_cast<Out>(numer-d*denom); 1372c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org#else 1382c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org // On x86 this will just be a single idiv. 1392c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org *div = static_cast<Out>(numer/denom); 1402c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org *mod = static_cast<Out>(numer%denom); 1413a2682a77f996f649de7699c9f7bee046c6d4f17mtklein#endif 1422c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org} 1432c86fbb0b14a1f674bf56ea5ad6a086cc004a76ecommit-bot@chromium.org 1448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#endif 145