michael@0: 
michael@0: /*
michael@0:  * Copyright 2008 The Android Open Source Project
michael@0:  *
michael@0:  * Use of this source code is governed by a BSD-style license that can be
michael@0:  * found in the LICENSE file.
michael@0:  */
michael@0: 
michael@0: 
michael@0: #include "SkFloat.h"
michael@0: #include "SkMathPriv.h"
michael@0: 
michael@0: #define EXP_BIAS    (127+23)
michael@0: 
michael@0: static int get_unsigned_exp(uint32_t packed)
michael@0: {
michael@0:     return (packed << 1 >> 24);
michael@0: }
michael@0: 
michael@0: static unsigned get_unsigned_value(uint32_t packed)
michael@0: {
michael@0:     return (packed << 9 >> 9) | (1 << 23);
michael@0: }
michael@0: 
michael@0: static int get_signed_value(int32_t packed)
michael@0: {
michael@0:     return SkApplySign(get_unsigned_value(packed), SkExtractSign(packed));
michael@0: }
michael@0: 
michael@0: /////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: int SkFloat::GetShift(int32_t packed, int shift)
michael@0: {
michael@0:     if (packed == 0)
michael@0:         return 0;
michael@0: 
michael@0:     int exp = get_unsigned_exp(packed) - EXP_BIAS - shift;
michael@0:     int value = get_unsigned_value(packed);
michael@0: 
michael@0:     if (exp >= 0)
michael@0:     {
michael@0:         if (exp > 8)    // overflow
michael@0:             value = SK_MaxS32;
michael@0:         else
michael@0:             value <<= exp;
michael@0:     }
michael@0:     else
michael@0:     {
michael@0:         exp = -exp;
michael@0:         if (exp > 23)   // underflow
michael@0:             value = 0;
michael@0:         else
michael@0:             value >>= exp;
michael@0:     }
michael@0:     return SkApplySign(value, SkExtractSign(packed));
michael@0: }
michael@0: 
michael@0: /////////////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: int32_t SkFloat::SetShift(int value, int shift)
michael@0: {
michael@0:     if (value == 0)
michael@0:         return 0;
michael@0: 
michael@0:     // record the sign and make value positive
michael@0:     int sign = SkExtractSign(value);
michael@0:     value = SkApplySign(value, sign);
michael@0: 
michael@0:     if (value >> 24)    // value is too big (has more than 24 bits set)
michael@0:     {
michael@0:         int bias = 8 - SkCLZ(value);
michael@0:         SkASSERT(bias > 0 && bias < 8);
michael@0:         value >>= bias;
michael@0:         shift += bias;
michael@0:     }
michael@0:     else
michael@0:     {
michael@0:         int zeros = SkCLZ(value << 8);
michael@0:         SkASSERT(zeros >= 0 && zeros <= 23);
michael@0:         value <<= zeros;
michael@0:         shift -= zeros;
michael@0:     }
michael@0:     // now value is left-aligned to 24 bits
michael@0:     SkASSERT((value >> 23) == 1);
michael@0: 
michael@0:     shift += EXP_BIAS;
michael@0:     if (shift < 0)  // underflow
michael@0:         return 0;
michael@0:     else
michael@0:     {
michael@0:         if (shift > 255)    // overflow
michael@0:         {
michael@0:             shift = 255;
michael@0:             value = 0x00FFFFFF;
michael@0:         }
michael@0:         int32_t packed = sign << 31;        // set the sign-bit
michael@0:         packed |= shift << 23;          // store the packed exponent
michael@0:         packed |= ((unsigned)(value << 9) >> 9);    // clear 24th bit of value (its implied)
michael@0: 
michael@0: #ifdef SK_DEBUG
michael@0:         {
michael@0:             int n;
michael@0: 
michael@0:             n = SkExtractSign(packed);
michael@0:             SkASSERT(n == sign);
michael@0:             n = get_unsigned_exp(packed);
michael@0:             SkASSERT(n == shift);
michael@0:             n = get_unsigned_value(packed);
michael@0:             SkASSERT(n == value);
michael@0:         }
michael@0: #endif
michael@0:         return packed;
michael@0:     }
michael@0: }
michael@0: 
michael@0: int32_t SkFloat::Neg(int32_t packed)
michael@0: {
michael@0:     if (packed)
michael@0:         packed = packed ^ (1 << 31);
michael@0:     return packed;
michael@0: }
michael@0: 
michael@0: int32_t SkFloat::Add(int32_t packed_a, int32_t packed_b)
michael@0: {
michael@0:     if (packed_a == 0)
michael@0:         return packed_b;
michael@0:     if (packed_b == 0)
michael@0:         return packed_a;
michael@0: 
michael@0:     int exp_a = get_unsigned_exp(packed_a);
michael@0:     int exp_b = get_unsigned_exp(packed_b);
michael@0:     int exp_diff = exp_a - exp_b;
michael@0: 
michael@0:     int shift_a = 0, shift_b = 0;
michael@0:     int exp;
michael@0: 
michael@0:     if (exp_diff >= 0)
michael@0:     {
michael@0:         if (exp_diff > 24)  // B is too small to contribute
michael@0:             return packed_a;
michael@0:         shift_b = exp_diff;
michael@0:         exp = exp_a;
michael@0:     }
michael@0:     else
michael@0:     {
michael@0:         exp_diff = -exp_diff;
michael@0:         if (exp_diff > 24)  // A is too small to contribute
michael@0:             return packed_b;
michael@0:         shift_a = exp_diff;
michael@0:         exp = exp_b;
michael@0:     }
michael@0: 
michael@0:     int value_a = get_signed_value(packed_a) >> shift_a;
michael@0:     int value_b = get_signed_value(packed_b) >> shift_b;
michael@0: 
michael@0:     return SkFloat::SetShift(value_a + value_b, exp - EXP_BIAS);
michael@0: }
michael@0: 
michael@0: static inline int32_t mul24(int32_t a, int32_t b) {
michael@0:     int64_t tmp = (sk_64_mul(a, b) + (1 << 23)) >> 24;
michael@0:     return sk_64_asS32(tmp);
michael@0: }
michael@0: 
michael@0: int32_t SkFloat::Mul(int32_t packed_a, int32_t packed_b)
michael@0: {
michael@0:     if (packed_a == 0 || packed_b == 0)
michael@0:         return 0;
michael@0: 
michael@0:     int exp_a = get_unsigned_exp(packed_a);
michael@0:     int exp_b = get_unsigned_exp(packed_b);
michael@0: 
michael@0:     int value_a = get_signed_value(packed_a);
michael@0:     int value_b = get_signed_value(packed_b);
michael@0: 
michael@0:     return SkFloat::SetShift(mul24(value_a, value_b), exp_a + exp_b - 2*EXP_BIAS + 24);
michael@0: }
michael@0: 
michael@0: int32_t SkFloat::MulInt(int32_t packed, int n)
michael@0: {
michael@0:     return Mul(packed, SetShift(n, 0));
michael@0: }
michael@0: 
michael@0: int32_t SkFloat::Div(int32_t packed_n, int32_t packed_d)
michael@0: {
michael@0:     SkASSERT(packed_d != 0);
michael@0: 
michael@0:     if (packed_n == 0)
michael@0:         return 0;
michael@0: 
michael@0:     int exp_n = get_unsigned_exp(packed_n);
michael@0:     int exp_d = get_unsigned_exp(packed_d);
michael@0: 
michael@0:     int value_n = get_signed_value(packed_n);
michael@0:     int value_d = get_signed_value(packed_d);
michael@0: 
michael@0:     return SkFloat::SetShift(SkDivBits(value_n, value_d, 24), exp_n - exp_d - 24);
michael@0: }
michael@0: 
michael@0: int32_t SkFloat::DivInt(int32_t packed, int n)
michael@0: {
michael@0:     return Div(packed, SetShift(n, 0));
michael@0: }
michael@0: 
michael@0: int32_t SkFloat::Invert(int32_t packed)
michael@0: {
michael@0:     return Div(packed, SetShift(1, 0));
michael@0: }
michael@0: 
michael@0: int32_t SkFloat::Sqrt(int32_t packed)
michael@0: {
michael@0:     if (packed < 0)
michael@0:     {
michael@0:         SkDEBUGFAIL("can't sqrt a negative number");
michael@0:         return 0;
michael@0:     }
michael@0: 
michael@0:     int exp = get_unsigned_exp(packed);
michael@0:     int value = get_unsigned_value(packed);
michael@0: 
michael@0:     int nexp = exp - EXP_BIAS;
michael@0:     int root = SkSqrtBits(value << (nexp & 1), 26);
michael@0:     nexp >>= 1;
michael@0:     return SkFloat::SetShift(root, nexp - 11);
michael@0: }
michael@0: 
michael@0: #if defined _WIN32 && _MSC_VER >= 1300  // disable warning : unreachable code
michael@0: #pragma warning ( push )
michael@0: #pragma warning ( disable : 4702 )
michael@0: #endif
michael@0: 
michael@0: int32_t SkFloat::CubeRoot(int32_t packed)
michael@0: {
michael@0:     sk_throw();
michael@0:     return 0;
michael@0: }
michael@0: 
michael@0: #if defined _WIN32 && _MSC_VER >= 1300
michael@0: #pragma warning ( pop )
michael@0: #endif
michael@0: 
michael@0: static inline int32_t clear_high_bit(int32_t n)
michael@0: {
michael@0:     return ((uint32_t)(n << 1)) >> 1;
michael@0: }
michael@0: 
michael@0: static inline int int_sign(int32_t a, int32_t b)
michael@0: {
michael@0:     return a > b ? 1 : (a < b ? -1 : 0);
michael@0: }
michael@0: 
michael@0: int SkFloat::Cmp(int32_t packed_a, int32_t packed_b)
michael@0: {
michael@0:     packed_a = SkApplySign(clear_high_bit(packed_a), SkExtractSign(packed_a));
michael@0:     packed_b = SkApplySign(clear_high_bit(packed_b), SkExtractSign(packed_b));
michael@0: 
michael@0:     return int_sign(packed_a, packed_b);
michael@0: }
michael@0: 
michael@0: /////////////////////////////////////////////////////////////////////////////////////
michael@0: /////////////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: #ifdef SK_DEBUG
michael@0: 
michael@0: #include "SkRandom.h"
michael@0: #include "SkFloatingPoint.h"
michael@0: 
michael@0: void SkFloat::UnitTest()
michael@0: {
michael@0: #if 0 // def SK_SUPPORT_UNITTEST
michael@0:     SkFloat a, b, c, d;
michael@0:     int     n;
michael@0: 
michael@0:     a.setZero();
michael@0:     n = a.getInt();
michael@0:     SkASSERT(n == 0);
michael@0: 
michael@0:     b.setInt(5);
michael@0:     n = b.getInt();
michael@0:     SkASSERT(n == 5);
michael@0: 
michael@0:     c.setInt(-3);
michael@0:     n = c.getInt();
michael@0:     SkASSERT(n == -3);
michael@0: 
michael@0:     d.setAdd(c, b);
michael@0:     SkDebugf("SkFloat: %d + %d = %d\n", c.getInt(), b.getInt(), d.getInt());
michael@0: 
michael@0:     SkRandom    rand;
michael@0: 
michael@0:     int i;
michael@0:     for (i = 0; i < 1000; i++)
michael@0:     {
michael@0:         float fa, fb;
michael@0:         int aa = rand.nextS() >> 14;
michael@0:         int bb = rand.nextS() >> 14;
michael@0:         a.setInt(aa);
michael@0:         b.setInt(bb);
michael@0:         SkASSERT(a.getInt() == aa);
michael@0:         SkASSERT(b.getInt() == bb);
michael@0: 
michael@0:         c.setAdd(a, b);
michael@0:         int cc = c.getInt();
michael@0:         SkASSERT(cc == aa + bb);
michael@0: 
michael@0:         c.setSub(a, b);
michael@0:         cc = c.getInt();
michael@0:         SkASSERT(cc == aa - bb);
michael@0: 
michael@0:         aa >>= 5;
michael@0:         bb >>= 5;
michael@0:         a.setInt(aa);
michael@0:         b.setInt(bb);
michael@0:         c.setMul(a, b);
michael@0:         cc = c.getInt();
michael@0:         SkASSERT(cc == aa * bb);
michael@0:         /////////////////////////////////////
michael@0: 
michael@0:         aa = rand.nextS() >> 11;
michael@0:         a.setFixed(aa);
michael@0:         cc = a.getFixed();
michael@0:         SkASSERT(aa == cc);
michael@0: 
michael@0:         bb = rand.nextS() >> 11;
michael@0:         b.setFixed(bb);
michael@0:         cc = b.getFixed();
michael@0:         SkASSERT(bb == cc);
michael@0: 
michael@0:         cc = SkFixedMul(aa, bb);
michael@0:         c.setMul(a, b);
michael@0:         SkFixed dd = c.getFixed();
michael@0:         int diff = cc - dd;
michael@0:         SkASSERT(SkAbs32(diff) <= 1);
michael@0: 
michael@0:         fa = (float)aa / 65536.0f;
michael@0:         fb = (float)bb / 65536.0f;
michael@0:         a.assertEquals(fa);
michael@0:         b.assertEquals(fb);
michael@0:         fa = a.getFloat();
michael@0:         fb = b.getFloat();
michael@0: 
michael@0:         c.assertEquals(fa * fb, 1);
michael@0: 
michael@0:         c.setDiv(a, b);
michael@0:         cc = SkFixedDiv(aa, bb);
michael@0:         dd = c.getFixed();
michael@0:         diff = cc - dd;
michael@0:         SkASSERT(SkAbs32(diff) <= 3);
michael@0: 
michael@0:         c.assertEquals(fa / fb, 1);
michael@0: 
michael@0:         SkASSERT((aa == bb) == (a == b));
michael@0:         SkASSERT((aa != bb) == (a != b));
michael@0:         SkASSERT((aa < bb) == (a < b));
michael@0:         SkASSERT((aa <= bb) == (a <= b));
michael@0:         SkASSERT((aa > bb) == (a > b));
michael@0:         SkASSERT((aa >= bb) == (a >= b));
michael@0: 
michael@0:         if (aa < 0)
michael@0:         {
michael@0:             aa = -aa;
michael@0:             fa = -fa;
michael@0:         }
michael@0:         a.setFixed(aa);
michael@0:         c.setSqrt(a);
michael@0:         cc = SkFixedSqrt(aa);
michael@0:         dd = c.getFixed();
michael@0:         SkASSERT(dd == cc);
michael@0: 
michael@0:         c.assertEquals(sk_float_sqrt(fa), 2);
michael@0: 
michael@0:         // cuberoot
michael@0: #if 0
michael@0:         a.setInt(1);
michael@0:         a.cubeRoot();
michael@0:         a.assertEquals(1.0f, 0);
michael@0:         a.setInt(8);
michael@0:         a.cubeRoot();
michael@0:         a.assertEquals(2.0f, 0);
michael@0:         a.setInt(27);
michael@0:         a.cubeRoot();
michael@0:         a.assertEquals(3.0f, 0);
michael@0: #endif
michael@0:     }
michael@0: #endif
michael@0: }
michael@0: 
michael@0: #endif