src/core/SkFloat.cpp - platform/external/skia - Git at Google

 /*
  * Copyright (C) 2006-2008 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.
  */

 #include "SkFloat.h"
 #include "SkMath.h"

 #define EXP_BIAS    (127+23)

 static int get_unsigned_exp(uint32_t packed)
 {
     return (packed << 1 >> 24);
 }

 static unsigned get_unsigned_value(uint32_t packed)
 {
     return (packed << 9 >> 9) | (1 << 23);
 }

 static int get_signed_value(int32_t packed)
 {
     return SkApplySign(get_unsigned_value(packed), SkExtractSign(packed));
 }

 /////////////////////////////////////////////////////////////////////////

 int SkFloat::GetShift(int32_t packed, int shift)
 {
     if (packed == 0)
         return 0;

     int exp = get_unsigned_exp(packed) - EXP_BIAS - shift;
     int value = get_unsigned_value(packed);

     if (exp >= 0)
     {
         if (exp > 8)    // overflow
             value = SK_MaxS32;
         else
             value <<= exp;
     }
     else
     {
         exp = -exp;
         if (exp > 23)   // underflow
             value = 0;
         else
             value >>= exp;
     }
     return SkApplySign(value, SkExtractSign(packed));
 }

 /////////////////////////////////////////////////////////////////////////////////////

 int32_t SkFloat::SetShift(int value, int shift)
 {
     if (value == 0)
         return 0;

     // record the sign and make value positive
     int sign = SkExtractSign(value);
     value = SkApplySign(value, sign);

     if (value >> 24)    // value is too big (has more than 24 bits set)
     {
         int bias = 8 - SkCLZ(value);
         SkASSERT(bias > 0 && bias < 8);
         value >>= bias;
         shift += bias;
     }
     else
     {
         int zeros = SkCLZ(value << 8);
         SkASSERT(zeros >= 0 && zeros <= 23);
         value <<= zeros;
         shift -= zeros;
     }
     // now value is left-aligned to 24 bits
     SkASSERT((value >> 23) == 1);

     shift += EXP_BIAS;
     if (shift < 0)  // underflow
         return 0;
     else
     {
         if (shift > 255)    // overflow
         {
             shift = 255;
             value = 0x00FFFFFF;
         }
         int32_t packed = sign << 31;        // set the sign-bit
         packed |= shift << 23;          // store the packed exponent
         packed |= ((unsigned)(value << 9) >> 9);    // clear 24th bit of value (its implied)

 #ifdef SK_DEBUG
         {
             int n;

             n = SkExtractSign(packed);
             SkASSERT(n == sign);
             n = get_unsigned_exp(packed);
             SkASSERT(n == shift);
             n = get_unsigned_value(packed);
             SkASSERT(n == value);
         }
 #endif
         return packed;
     }
 }

 int32_t SkFloat::Neg(int32_t packed)
 {
     if (packed)
         packed = packed ^ (1 << 31);
     return packed;
 }

 int32_t SkFloat::Add(int32_t packed_a, int32_t packed_b)
 {
     if (packed_a == 0)
         return packed_b;
     if (packed_b == 0)
         return packed_a;

     int exp_a = get_unsigned_exp(packed_a);
     int exp_b = get_unsigned_exp(packed_b);
     int exp_diff = exp_a - exp_b;

     int shift_a = 0, shift_b = 0;
     int exp;

     if (exp_diff >= 0)
     {
         if (exp_diff > 24)  // B is too small to contribute
             return packed_a;
         shift_b = exp_diff;
         exp = exp_a;
     }
     else
     {
         exp_diff = -exp_diff;
         if (exp_diff > 24)  // A is too small to contribute
             return packed_b;
         shift_a = exp_diff;
         exp = exp_b;
     }

     int value_a = get_signed_value(packed_a) >> shift_a;
     int value_b = get_signed_value(packed_b) >> shift_b;

     return SkFloat::SetShift(value_a + value_b, exp - EXP_BIAS);
 }

 #include "Sk64.h"

 static inline int32_t mul24(int32_t a, int32_t b)
 {
     Sk64 tmp;

     tmp.setMul(a, b);
     tmp.roundRight(24);
     return tmp.get32();
 }

 int32_t SkFloat::Mul(int32_t packed_a, int32_t packed_b)
 {
     if (packed_a == 0 || packed_b == 0)
         return 0;

     int exp_a = get_unsigned_exp(packed_a);
     int exp_b = get_unsigned_exp(packed_b);

     int value_a = get_signed_value(packed_a);
     int value_b = get_signed_value(packed_b);

     return SkFloat::SetShift(mul24(value_a, value_b), exp_a + exp_b - 2*EXP_BIAS + 24);
 }

 int32_t SkFloat::MulInt(int32_t packed, int n)
 {
     return Mul(packed, SetShift(n, 0));
 }

 int32_t SkFloat::Div(int32_t packed_n, int32_t packed_d)
 {
     SkASSERT(packed_d != 0);

     if (packed_n == 0)
         return 0;

     int exp_n = get_unsigned_exp(packed_n);
     int exp_d = get_unsigned_exp(packed_d);

     int value_n = get_signed_value(packed_n);
     int value_d = get_signed_value(packed_d);

     return SkFloat::SetShift(SkDivBits(value_n, value_d, 24), exp_n - exp_d - 24);
 }

 int32_t SkFloat::DivInt(int32_t packed, int n)
 {
     return Div(packed, SetShift(n, 0));
 }

 int32_t SkFloat::Invert(int32_t packed)
 {
     return Div(packed, SetShift(1, 0));
 }

 int32_t SkFloat::Sqrt(int32_t packed)
 {
     if (packed < 0)
     {
         SkASSERT(!"can't sqrt a negative number");
         return 0;
     }

     int exp = get_unsigned_exp(packed);
     int value = get_unsigned_value(packed);

     int nexp = exp - EXP_BIAS;
     int root = SkSqrtBits(value << (nexp & 1), 26);
     nexp >>= 1;
     return SkFloat::SetShift(root, nexp - 11);
 }

 #if defined _WIN32 && _MSC_VER >= 1300  // disable warning : unreachable code
 #pragma warning ( push )
 #pragma warning ( disable : 4702 )
 #endif

 int32_t SkFloat::CubeRoot(int32_t packed)
 {
     sk_throw();
     return 0;
 }

 #if defined _WIN32 && _MSC_VER >= 1300
 #pragma warning ( pop )
 #endif

 static inline int32_t clear_high_bit(int32_t n)
 {
     return ((uint32_t)(n << 1)) >> 1;
 }

 static inline int int_sign(int32_t a, int32_t b)
 {
     return a > b ? 1 : (a < b ? -1 : 0);
 }

 int SkFloat::Cmp(int32_t packed_a, int32_t packed_b)
 {
     packed_a = SkApplySign(clear_high_bit(packed_a), SkExtractSign(packed_a));
     packed_b = SkApplySign(clear_high_bit(packed_b), SkExtractSign(packed_b));

     return int_sign(packed_a, packed_b);
 }

 /////////////////////////////////////////////////////////////////////////////////////
 /////////////////////////////////////////////////////////////////////////////////////

 #ifdef SK_DEBUG

 #include "SkRandom.h"
 #ifdef SK_CAN_USE_FLOAT
     #include "SkFloatingPoint.h"
 #endif

 void SkFloat::UnitTest()
 {
 #ifdef SK_SUPPORT_UNITTEST
     SkFloat a, b, c, d;
     int     n;

     a.setZero();
     n = a.getInt();
     SkASSERT(n == 0);

     b.setInt(5);
     n = b.getInt();
     SkASSERT(n == 5);

     c.setInt(-3);
     n = c.getInt();
     SkASSERT(n == -3);

     d.setAdd(c, b);
     SkDebugf("SkFloat: %d + %d = %d\n", c.getInt(), b.getInt(), d.getInt());

     SkRandom    rand;

 #ifdef SK_CAN_USE_FLOAT
     int i;
     for (i = 0; i < 1000; i++)
     {
         float fa, fb;
         int aa = rand.nextS() >> 14;
         int bb = rand.nextS() >> 14;
         a.setInt(aa);
         b.setInt(bb);
         SkASSERT(a.getInt() == aa);
         SkASSERT(b.getInt() == bb);

         c.setAdd(a, b);
         int cc = c.getInt();
         SkASSERT(cc == aa + bb);

         c.setSub(a, b);
         cc = c.getInt();
         SkASSERT(cc == aa - bb);

         aa >>= 5;
         bb >>= 5;
         a.setInt(aa);
         b.setInt(bb);
         c.setMul(a, b);
         cc = c.getInt();
         SkASSERT(cc == aa * bb);
         /////////////////////////////////////

         aa = rand.nextS() >> 11;
         a.setFixed(aa);
         cc = a.getFixed();
         SkASSERT(aa == cc);

         bb = rand.nextS() >> 11;
         b.setFixed(bb);
         cc = b.getFixed();
         SkASSERT(bb == cc);

         cc = SkFixedMul(aa, bb);
         c.setMul(a, b);
         SkFixed dd = c.getFixed();
         int diff = cc - dd;
         SkASSERT(SkAbs32(diff) <= 1);

         fa = (float)aa / 65536.0f;
         fb = (float)bb / 65536.0f;
         a.assertEquals(fa);
         b.assertEquals(fb);
         fa = a.getFloat();
         fb = b.getFloat();

         c.assertEquals(fa * fb, 1);

         c.setDiv(a, b);
         cc = SkFixedDiv(aa, bb);
         dd = c.getFixed();
         diff = cc - dd;
         SkASSERT(SkAbs32(diff) <= 3);

         c.assertEquals(fa / fb, 1);

         SkASSERT((aa == bb) == (a == b));
         SkASSERT((aa != bb) == (a != b));
         SkASSERT((aa < bb) == (a < b));
         SkASSERT((aa <= bb) == (a <= b));
         SkASSERT((aa > bb) == (a > b));
         SkASSERT((aa >= bb) == (a >= b));

         if (aa < 0)
         {
             aa = -aa;
             fa = -fa;
         }
         a.setFixed(aa);
         c.setSqrt(a);
         cc = SkFixedSqrt(aa);
         dd = c.getFixed();
         SkASSERT(dd == cc);

         c.assertEquals(sk_float_sqrt(fa), 2);

         // cuberoot
 #if 0
         a.setInt(1);
         a.cubeRoot();
         a.assertEquals(1.0f, 0);
         a.setInt(8);
         a.cubeRoot();
         a.assertEquals(2.0f, 0);
         a.setInt(27);
         a.cubeRoot();
         a.assertEquals(3.0f, 0);
 #endif
     }
 #endif
 #endif
 }

 #endif
	/*
	* Copyright (C) 2006-2008 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.
	*/

	#include "SkFloat.h"
	#include "SkMath.h"

	#define EXP_BIAS (127+23)

	static int get_unsigned_exp(uint32_t packed)
	{
	return (packed << 1 >> 24);
	}

	static unsigned get_unsigned_value(uint32_t packed)
	{
	return (packed << 9 >> 9) \| (1 << 23);
	}

	static int get_signed_value(int32_t packed)
	{
	return SkApplySign(get_unsigned_value(packed), SkExtractSign(packed));
	}

	/////////////////////////////////////////////////////////////////////////

	int SkFloat::GetShift(int32_t packed, int shift)
	{
	if (packed == 0)
	return 0;

	int exp = get_unsigned_exp(packed) - EXP_BIAS - shift;
	int value = get_unsigned_value(packed);

	if (exp >= 0)
	{
	if (exp > 8) // overflow
	value = SK_MaxS32;
	else
	value <<= exp;
	}
	else
	{
	exp = -exp;
	if (exp > 23) // underflow
	value = 0;
	else
	value >>= exp;
	}
	return SkApplySign(value, SkExtractSign(packed));
	}

	/////////////////////////////////////////////////////////////////////////////////////

	int32_t SkFloat::SetShift(int value, int shift)
	{
	if (value == 0)
	return 0;

	// record the sign and make value positive
	int sign = SkExtractSign(value);
	value = SkApplySign(value, sign);

	if (value >> 24) // value is too big (has more than 24 bits set)
	{
	int bias = 8 - SkCLZ(value);
	SkASSERT(bias > 0 && bias < 8);
	value >>= bias;
	shift += bias;
	}
	else
	{
	int zeros = SkCLZ(value << 8);
	SkASSERT(zeros >= 0 && zeros <= 23);
	value <<= zeros;
	shift -= zeros;
	}
	// now value is left-aligned to 24 bits
	SkASSERT((value >> 23) == 1);

	shift += EXP_BIAS;
	if (shift < 0) // underflow
	return 0;
	else
	{
	if (shift > 255) // overflow
	{
	shift = 255;
	value = 0x00FFFFFF;
	}
	int32_t packed = sign << 31; // set the sign-bit
	packed \|= shift << 23; // store the packed exponent
	packed \|= ((unsigned)(value << 9) >> 9); // clear 24th bit of value (its implied)

	#ifdef SK_DEBUG
	{
	int n;

	n = SkExtractSign(packed);
	SkASSERT(n == sign);
	n = get_unsigned_exp(packed);
	SkASSERT(n == shift);
	n = get_unsigned_value(packed);
	SkASSERT(n == value);
	}
	#endif
	return packed;
	}
	}

	int32_t SkFloat::Neg(int32_t packed)
	{
	if (packed)
	packed = packed ^ (1 << 31);
	return packed;
	}

	int32_t SkFloat::Add(int32_t packed_a, int32_t packed_b)
	{
	if (packed_a == 0)
	return packed_b;
	if (packed_b == 0)
	return packed_a;

	int exp_a = get_unsigned_exp(packed_a);
	int exp_b = get_unsigned_exp(packed_b);
	int exp_diff = exp_a - exp_b;

	int shift_a = 0, shift_b = 0;
	int exp;

	if (exp_diff >= 0)
	{
	if (exp_diff > 24) // B is too small to contribute
	return packed_a;
	shift_b = exp_diff;
	exp = exp_a;
	}
	else
	{
	exp_diff = -exp_diff;
	if (exp_diff > 24) // A is too small to contribute
	return packed_b;
	shift_a = exp_diff;
	exp = exp_b;
	}

	int value_a = get_signed_value(packed_a) >> shift_a;
	int value_b = get_signed_value(packed_b) >> shift_b;

	return SkFloat::SetShift(value_a + value_b, exp - EXP_BIAS);
	}

	#include "Sk64.h"

	static inline int32_t mul24(int32_t a, int32_t b)
	{
	Sk64 tmp;

	tmp.setMul(a, b);
	tmp.roundRight(24);
	return tmp.get32();
	}

	int32_t SkFloat::Mul(int32_t packed_a, int32_t packed_b)
	{
	if (packed_a == 0 \|\| packed_b == 0)
	return 0;

	int exp_a = get_unsigned_exp(packed_a);
	int exp_b = get_unsigned_exp(packed_b);

	int value_a = get_signed_value(packed_a);
	int value_b = get_signed_value(packed_b);

	return SkFloat::SetShift(mul24(value_a, value_b), exp_a + exp_b - 2*EXP_BIAS + 24);
	}

	int32_t SkFloat::MulInt(int32_t packed, int n)
	{
	return Mul(packed, SetShift(n, 0));
	}

	int32_t SkFloat::Div(int32_t packed_n, int32_t packed_d)
	{
	SkASSERT(packed_d != 0);

	if (packed_n == 0)
	return 0;

	int exp_n = get_unsigned_exp(packed_n);
	int exp_d = get_unsigned_exp(packed_d);

	int value_n = get_signed_value(packed_n);
	int value_d = get_signed_value(packed_d);

	return SkFloat::SetShift(SkDivBits(value_n, value_d, 24), exp_n - exp_d - 24);
	}

	int32_t SkFloat::DivInt(int32_t packed, int n)
	{
	return Div(packed, SetShift(n, 0));
	}

	int32_t SkFloat::Invert(int32_t packed)
	{
	return Div(packed, SetShift(1, 0));
	}

	int32_t SkFloat::Sqrt(int32_t packed)
	{
	if (packed < 0)
	{
	SkASSERT(!"can't sqrt a negative number");
	return 0;
	}

	int exp = get_unsigned_exp(packed);
	int value = get_unsigned_value(packed);

	int nexp = exp - EXP_BIAS;
	int root = SkSqrtBits(value << (nexp & 1), 26);
	nexp >>= 1;
	return SkFloat::SetShift(root, nexp - 11);
	}

	#if defined _WIN32 && _MSC_VER >= 1300 // disable warning : unreachable code
	#pragma warning ( push )
	#pragma warning ( disable : 4702 )
	#endif

	int32_t SkFloat::CubeRoot(int32_t packed)
	{
	sk_throw();
	return 0;
	}

	#if defined _WIN32 && _MSC_VER >= 1300
	#pragma warning ( pop )
	#endif

	static inline int32_t clear_high_bit(int32_t n)
	{
	return ((uint32_t)(n << 1)) >> 1;
	}

	static inline int int_sign(int32_t a, int32_t b)
	{
	return a > b ? 1 : (a < b ? -1 : 0);
	}

	int SkFloat::Cmp(int32_t packed_a, int32_t packed_b)
	{
	packed_a = SkApplySign(clear_high_bit(packed_a), SkExtractSign(packed_a));
	packed_b = SkApplySign(clear_high_bit(packed_b), SkExtractSign(packed_b));

	return int_sign(packed_a, packed_b);
	}

	/////////////////////////////////////////////////////////////////////////////////////
	/////////////////////////////////////////////////////////////////////////////////////

	#ifdef SK_DEBUG

	#include "SkRandom.h"
	#ifdef SK_CAN_USE_FLOAT
	#include "SkFloatingPoint.h"
	#endif

	void SkFloat::UnitTest()
	{
	#ifdef SK_SUPPORT_UNITTEST
	SkFloat a, b, c, d;
	int n;

	a.setZero();
	n = a.getInt();
	SkASSERT(n == 0);

	b.setInt(5);
	n = b.getInt();
	SkASSERT(n == 5);

	c.setInt(-3);
	n = c.getInt();
	SkASSERT(n == -3);

	d.setAdd(c, b);
	SkDebugf("SkFloat: %d + %d = %d\n", c.getInt(), b.getInt(), d.getInt());

	SkRandom rand;

	#ifdef SK_CAN_USE_FLOAT
	int i;
	for (i = 0; i < 1000; i++)
	{
	float fa, fb;
	int aa = rand.nextS() >> 14;
	int bb = rand.nextS() >> 14;
	a.setInt(aa);
	b.setInt(bb);
	SkASSERT(a.getInt() == aa);
	SkASSERT(b.getInt() == bb);

	c.setAdd(a, b);
	int cc = c.getInt();
	SkASSERT(cc == aa + bb);

	c.setSub(a, b);
	cc = c.getInt();
	SkASSERT(cc == aa - bb);

	aa >>= 5;
	bb >>= 5;
	a.setInt(aa);
	b.setInt(bb);
	c.setMul(a, b);
	cc = c.getInt();
	SkASSERT(cc == aa * bb);
	/////////////////////////////////////

	aa = rand.nextS() >> 11;
	a.setFixed(aa);
	cc = a.getFixed();
	SkASSERT(aa == cc);

	bb = rand.nextS() >> 11;
	b.setFixed(bb);
	cc = b.getFixed();
	SkASSERT(bb == cc);

	cc = SkFixedMul(aa, bb);
	c.setMul(a, b);
	SkFixed dd = c.getFixed();
	int diff = cc - dd;
	SkASSERT(SkAbs32(diff) <= 1);

	fa = (float)aa / 65536.0f;
	fb = (float)bb / 65536.0f;
	a.assertEquals(fa);
	b.assertEquals(fb);
	fa = a.getFloat();
	fb = b.getFloat();

	c.assertEquals(fa * fb, 1);

	c.setDiv(a, b);
	cc = SkFixedDiv(aa, bb);
	dd = c.getFixed();
	diff = cc - dd;
	SkASSERT(SkAbs32(diff) <= 3);

	c.assertEquals(fa / fb, 1);

	SkASSERT((aa == bb) == (a == b));
	SkASSERT((aa != bb) == (a != b));
	SkASSERT((aa < bb) == (a < b));
	SkASSERT((aa <= bb) == (a <= b));
	SkASSERT((aa > bb) == (a > b));
	SkASSERT((aa >= bb) == (a >= b));

	if (aa < 0)
	{
	aa = -aa;
	fa = -fa;
	}
	a.setFixed(aa);
	c.setSqrt(a);
	cc = SkFixedSqrt(aa);
	dd = c.getFixed();
	SkASSERT(dd == cc);

	c.assertEquals(sk_float_sqrt(fa), 2);

	// cuberoot
	#if 0
	a.setInt(1);
	a.cubeRoot();
	a.assertEquals(1.0f, 0);
	a.setInt(8);
	a.cubeRoot();
	a.assertEquals(2.0f, 0);
	a.setInt(27);
	a.cubeRoot();
	a.assertEquals(3.0f, 0);
	#endif
	}
	#endif
	#endif
	}

	#endif