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linux/arch/sh/kernel/cpu/sh4/softfloat.c

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/*
* Floating point emulation support for subnormalised numbers on SH4
* architecture This file is derived from the SoftFloat IEC/IEEE
* Floating-point Arithmetic Package, Release 2 the original license of
* which is reproduced below.
*
* ========================================================================
*
* This C source file is part of the SoftFloat IEC/IEEE Floating-point
* Arithmetic Package, Release 2.
*
* Written by John R. Hauser. This work was made possible in part by the
* International Computer Science Institute, located at Suite 600, 1947 Center
* Street, Berkeley, California 94704. Funding was partially provided by the
* National Science Foundation under grant MIP-9311980. The original version
* of this code was written as part of a project to build a fixed-point vector
* processor in collaboration with the University of California at Berkeley,
* overseen by Profs. Nelson Morgan and John Wawrzynek. More information
* is available through the web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
* arithmetic/softfloat.html'.
*
* THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
* has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
* TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
* PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
* AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
*
* Derivative works are acceptable, even for commercial purposes, so long as
* (1) they include prominent notice that the work is derivative, and (2) they
* include prominent notice akin to these three paragraphs for those parts of
* this code that are retained.
*
* ========================================================================
*
* SH4 modifications by Ismail Dhaoui <ismail.dhaoui@st.com>
* and Kamel Khelifi <kamel.khelifi@st.com>
*/
#include <linux/kernel.h>
#include <cpu/fpu.h>
#include <asm/div64.h>
#define LIT64( a ) a##LL
typedef char flag;
typedef unsigned char uint8;
typedef signed char int8;
typedef int uint16;
typedef int int16;
typedef unsigned int uint32;
typedef signed int int32;
typedef unsigned long long int bits64;
typedef signed long long int sbits64;
typedef unsigned char bits8;
typedef signed char sbits8;
typedef unsigned short int bits16;
typedef signed short int sbits16;
typedef unsigned int bits32;
typedef signed int sbits32;
typedef unsigned long long int uint64;
typedef signed long long int int64;
typedef unsigned long int float32;
typedef unsigned long long float64;
extern void float_raise(unsigned int flags); /* in fpu.c */
extern int float_rounding_mode(void); /* in fpu.c */
bits64 extractFloat64Frac(float64 a);
flag extractFloat64Sign(float64 a);
int16 extractFloat64Exp(float64 a);
int16 extractFloat32Exp(float32 a);
flag extractFloat32Sign(float32 a);
bits32 extractFloat32Frac(float32 a);
float64 packFloat64(flag zSign, int16 zExp, bits64 zSig);
void shift64RightJamming(bits64 a, int16 count, bits64 * zPtr);
float32 packFloat32(flag zSign, int16 zExp, bits32 zSig);
void shift32RightJamming(bits32 a, int16 count, bits32 * zPtr);
float64 float64_sub(float64 a, float64 b);
float32 float32_sub(float32 a, float32 b);
float32 float32_add(float32 a, float32 b);
float64 float64_add(float64 a, float64 b);
float64 float64_div(float64 a, float64 b);
float32 float32_div(float32 a, float32 b);
float32 float32_mul(float32 a, float32 b);
float64 float64_mul(float64 a, float64 b);
float32 float64_to_float32(float64 a);
void add128(bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 * z0Ptr,
bits64 * z1Ptr);
void sub128(bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 * z0Ptr,
bits64 * z1Ptr);
void mul64To128(bits64 a, bits64 b, bits64 * z0Ptr, bits64 * z1Ptr);
static int8 countLeadingZeros32(bits32 a);
static int8 countLeadingZeros64(bits64 a);
static float64 normalizeRoundAndPackFloat64(flag zSign, int16 zExp,
bits64 zSig);
static float64 subFloat64Sigs(float64 a, float64 b, flag zSign);
static float64 addFloat64Sigs(float64 a, float64 b, flag zSign);
static float32 roundAndPackFloat32(flag zSign, int16 zExp, bits32 zSig);
static float32 normalizeRoundAndPackFloat32(flag zSign, int16 zExp,
bits32 zSig);
static float64 roundAndPackFloat64(flag zSign, int16 zExp, bits64 zSig);
static float32 subFloat32Sigs(float32 a, float32 b, flag zSign);
static float32 addFloat32Sigs(float32 a, float32 b, flag zSign);
static void normalizeFloat64Subnormal(bits64 aSig, int16 * zExpPtr,
bits64 * zSigPtr);
static bits64 estimateDiv128To64(bits64 a0, bits64 a1, bits64 b);
static void normalizeFloat32Subnormal(bits32 aSig, int16 * zExpPtr,
bits32 * zSigPtr);
bits64 extractFloat64Frac(float64 a)
{
return a & LIT64(0x000FFFFFFFFFFFFF);
}
flag extractFloat64Sign(float64 a)
{
return a >> 63;
}
int16 extractFloat64Exp(float64 a)
{
return (a >> 52) & 0x7FF;
}
int16 extractFloat32Exp(float32 a)
{
return (a >> 23) & 0xFF;
}
flag extractFloat32Sign(float32 a)
{
return a >> 31;
}
bits32 extractFloat32Frac(float32 a)
{
return a & 0x007FFFFF;
}
float64 packFloat64(flag zSign, int16 zExp, bits64 zSig)
{
return (((bits64) zSign) << 63) + (((bits64) zExp) << 52) + zSig;
}
void shift64RightJamming(bits64 a, int16 count, bits64 * zPtr)
{
bits64 z;
if (count == 0) {
z = a;
} else if (count < 64) {
z = (a >> count) | ((a << ((-count) & 63)) != 0);
} else {
z = (a != 0);
}
*zPtr = z;
}
static int8 countLeadingZeros32(bits32 a)
{
static const int8 countLeadingZerosHigh[] = {
8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
};
int8 shiftCount;
shiftCount = 0;
if (a < 0x10000) {
shiftCount += 16;
a <<= 16;
}
if (a < 0x1000000) {
shiftCount += 8;
a <<= 8;
}
shiftCount += countLeadingZerosHigh[a >> 24];
return shiftCount;
}
static int8 countLeadingZeros64(bits64 a)
{
int8 shiftCount;
shiftCount = 0;
if (a < ((bits64) 1) << 32) {
shiftCount += 32;
} else {
a >>= 32;
}
shiftCount += countLeadingZeros32(a);
return shiftCount;
}
static float64 normalizeRoundAndPackFloat64(flag zSign, int16 zExp, bits64 zSig)
{
int8 shiftCount;
shiftCount = countLeadingZeros64(zSig) - 1;
return roundAndPackFloat64(zSign, zExp - shiftCount,
zSig << shiftCount);
}
static float64 subFloat64Sigs(float64 a, float64 b, flag zSign)
{
int16 aExp, bExp, zExp;
bits64 aSig, bSig, zSig;
int16 expDiff;
aSig = extractFloat64Frac(a);
aExp = extractFloat64Exp(a);
bSig = extractFloat64Frac(b);
bExp = extractFloat64Exp(b);
expDiff = aExp - bExp;
aSig <<= 10;
bSig <<= 10;
if (0 < expDiff)
goto aExpBigger;
if (expDiff < 0)
goto bExpBigger;
if (aExp == 0) {
aExp = 1;
bExp = 1;
}
if (bSig < aSig)
goto aBigger;
if (aSig < bSig)
goto bBigger;
return packFloat64(float_rounding_mode() == FPSCR_RM_ZERO, 0, 0);
bExpBigger:
if (bExp == 0x7FF) {
return packFloat64(zSign ^ 1, 0x7FF, 0);
}
if (aExp == 0) {
++expDiff;
} else {
aSig |= LIT64(0x4000000000000000);
}
shift64RightJamming(aSig, -expDiff, &aSig);
bSig |= LIT64(0x4000000000000000);
bBigger:
zSig = bSig - aSig;
zExp = bExp;
zSign ^= 1;
goto normalizeRoundAndPack;
aExpBigger:
if (aExp == 0x7FF) {
return a;
}
if (bExp == 0) {
--expDiff;
} else {
bSig |= LIT64(0x4000000000000000);
}
shift64RightJamming(bSig, expDiff, &bSig);
aSig |= LIT64(0x4000000000000000);
aBigger:
zSig = aSig - bSig;
zExp = aExp;
normalizeRoundAndPack:
--zExp;
return normalizeRoundAndPackFloat64(zSign, zExp, zSig);
}
static float64 addFloat64Sigs(float64 a, float64 b, flag zSign)
{
int16 aExp, bExp, zExp;
bits64 aSig, bSig, zSig;
int16 expDiff;
aSig = extractFloat64Frac(a);
aExp = extractFloat64Exp(a);
bSig = extractFloat64Frac(b);
bExp = extractFloat64Exp(b);
expDiff = aExp - bExp;
aSig <<= 9;
bSig <<= 9;
if (0 < expDiff) {
if (aExp == 0x7FF) {
return a;
}
if (bExp == 0) {
--expDiff;
} else {
bSig |= LIT64(0x2000000000000000);
}
shift64RightJamming(bSig, expDiff, &bSig);
zExp = aExp;
} else if (expDiff < 0) {
if (bExp == 0x7FF) {
return packFloat64(zSign, 0x7FF, 0);
}
if (aExp == 0) {
++expDiff;
} else {
aSig |= LIT64(0x2000000000000000);
}
shift64RightJamming(aSig, -expDiff, &aSig);
zExp = bExp;
} else {
if (aExp == 0x7FF) {
return a;
}
if (aExp == 0)
return packFloat64(zSign, 0, (aSig + bSig) >> 9);
zSig = LIT64(0x4000000000000000) + aSig + bSig;
zExp = aExp;
goto roundAndPack;
}
aSig |= LIT64(0x2000000000000000);
zSig = (aSig + bSig) << 1;
--zExp;
if ((sbits64) zSig < 0) {
zSig = aSig + bSig;
++zExp;
}
roundAndPack:
return roundAndPackFloat64(zSign, zExp, zSig);
}
float32 packFloat32(flag zSign, int16 zExp, bits32 zSig)
{
return (((bits32) zSign) << 31) + (((bits32) zExp) << 23) + zSig;
}
void shift32RightJamming(bits32 a, int16 count, bits32 * zPtr)
{
bits32 z;
if (count == 0) {
z = a;
} else if (count < 32) {
z = (a >> count) | ((a << ((-count) & 31)) != 0);
} else {
z = (a != 0);
}
*zPtr = z;
}
static float32 roundAndPackFloat32(flag zSign, int16 zExp, bits32 zSig)
{
flag roundNearestEven;
int8 roundIncrement, roundBits;
flag isTiny;
/* SH4 has only 2 rounding modes - round to nearest and round to zero */
roundNearestEven = (float_rounding_mode() == FPSCR_RM_NEAREST);
roundIncrement = 0x40;
if (!roundNearestEven) {
roundIncrement = 0;
}
roundBits = zSig & 0x7F;
if (0xFD <= (bits16) zExp) {
if ((0xFD < zExp)
|| ((zExp == 0xFD)
&& ((sbits32) (zSig + roundIncrement) < 0))
) {
float_raise(FPSCR_CAUSE_OVERFLOW | FPSCR_CAUSE_INEXACT);
return packFloat32(zSign, 0xFF,
0) - (roundIncrement == 0);
}
if (zExp < 0) {
isTiny = (zExp < -1)
|| (zSig + roundIncrement < 0x80000000);
shift32RightJamming(zSig, -zExp, &zSig);
zExp = 0;
roundBits = zSig & 0x7F;
if (isTiny && roundBits)
float_raise(FPSCR_CAUSE_UNDERFLOW);
}
}
if (roundBits)
float_raise(FPSCR_CAUSE_INEXACT);
zSig = (zSig + roundIncrement) >> 7;
zSig &= ~(((roundBits ^ 0x40) == 0) & roundNearestEven);
if (zSig == 0)
zExp = 0;
return packFloat32(zSign, zExp, zSig);
}
static float32 normalizeRoundAndPackFloat32(flag zSign, int16 zExp, bits32 zSig)
{
int8 shiftCount;
shiftCount = countLeadingZeros32(zSig) - 1;
return roundAndPackFloat32(zSign, zExp - shiftCount,
zSig << shiftCount);
}
static float64 roundAndPackFloat64(flag zSign, int16 zExp, bits64 zSig)
{
flag roundNearestEven;
int16 roundIncrement, roundBits;
flag isTiny;
/* SH4 has only 2 rounding modes - round to nearest and round to zero */
roundNearestEven = (float_rounding_mode() == FPSCR_RM_NEAREST);
roundIncrement = 0x200;
if (!roundNearestEven) {
roundIncrement = 0;
}
roundBits = zSig & 0x3FF;
if (0x7FD <= (bits16) zExp) {
if ((0x7FD < zExp)
|| ((zExp == 0x7FD)
&& ((sbits64) (zSig + roundIncrement) < 0))
) {
float_raise(FPSCR_CAUSE_OVERFLOW | FPSCR_CAUSE_INEXACT);
return packFloat64(zSign, 0x7FF,
0) - (roundIncrement == 0);
}
if (zExp < 0) {
isTiny = (zExp < -1)
|| (zSig + roundIncrement <
LIT64(0x8000000000000000));
shift64RightJamming(zSig, -zExp, &zSig);
zExp = 0;
roundBits = zSig & 0x3FF;
if (isTiny && roundBits)
float_raise(FPSCR_CAUSE_UNDERFLOW);
}
}
if (roundBits)
float_raise(FPSCR_CAUSE_INEXACT);
zSig = (zSig + roundIncrement) >> 10;
zSig &= ~(((roundBits ^ 0x200) == 0) & roundNearestEven);
if (zSig == 0)
zExp = 0;
return packFloat64(zSign, zExp, zSig);
}
static float32 subFloat32Sigs(float32 a, float32 b, flag zSign)
{
int16 aExp, bExp, zExp;
bits32 aSig, bSig, zSig;
int16 expDiff;
aSig = extractFloat32Frac(a);
aExp = extractFloat32Exp(a);
bSig = extractFloat32Frac(b);
bExp = extractFloat32Exp(b);
expDiff = aExp - bExp;
aSig <<= 7;
bSig <<= 7;
if (0 < expDiff)
goto aExpBigger;
if (expDiff < 0)
goto bExpBigger;
if (aExp == 0) {
aExp = 1;
bExp = 1;
}
if (bSig < aSig)
goto aBigger;
if (aSig < bSig)
goto bBigger;
return packFloat32(float_rounding_mode() == FPSCR_RM_ZERO, 0, 0);
bExpBigger:
if (bExp == 0xFF) {
return packFloat32(zSign ^ 1, 0xFF, 0);
}
if (aExp == 0) {
++expDiff;
} else {
aSig |= 0x40000000;
}
shift32RightJamming(aSig, -expDiff, &aSig);
bSig |= 0x40000000;
bBigger:
zSig = bSig - aSig;
zExp = bExp;
zSign ^= 1;
goto normalizeRoundAndPack;
aExpBigger:
if (aExp == 0xFF) {
return a;
}
if (bExp == 0) {
--expDiff;
} else {
bSig |= 0x40000000;
}
shift32RightJamming(bSig, expDiff, &bSig);
aSig |= 0x40000000;
aBigger:
zSig = aSig - bSig;
zExp = aExp;
normalizeRoundAndPack:
--zExp;
return normalizeRoundAndPackFloat32(zSign, zExp, zSig);
}
static float32 addFloat32Sigs(float32 a, float32 b, flag zSign)
{
int16 aExp, bExp, zExp;
bits32 aSig, bSig, zSig;
int16 expDiff;
aSig = extractFloat32Frac(a);
aExp = extractFloat32Exp(a);
bSig = extractFloat32Frac(b);
bExp = extractFloat32Exp(b);
expDiff = aExp - bExp;
aSig <<= 6;
bSig <<= 6;
if (0 < expDiff) {
if (aExp == 0xFF) {
return a;
}
if (bExp == 0) {
--expDiff;
} else {
bSig |= 0x20000000;
}
shift32RightJamming(bSig, expDiff, &bSig);
zExp = aExp;
} else if (expDiff < 0) {
if (bExp == 0xFF) {
return packFloat32(zSign, 0xFF, 0);
}
if (aExp == 0) {
++expDiff;
} else {
aSig |= 0x20000000;
}
shift32RightJamming(aSig, -expDiff, &aSig);
zExp = bExp;
} else {
if (aExp == 0xFF) {
return a;
}
if (aExp == 0)
return packFloat32(zSign, 0, (aSig + bSig) >> 6);
zSig = 0x40000000 + aSig + bSig;
zExp = aExp;
goto roundAndPack;
}
aSig |= 0x20000000;
zSig = (aSig + bSig) << 1;
--zExp;
if ((sbits32) zSig < 0) {
zSig = aSig + bSig;
++zExp;
}
roundAndPack:
return roundAndPackFloat32(zSign, zExp, zSig);
}
float64 float64_sub(float64 a, float64 b)
{
flag aSign, bSign;
aSign = extractFloat64Sign(a);
bSign = extractFloat64Sign(b);
if (aSign == bSign) {
return subFloat64Sigs(a, b, aSign);
} else {
return addFloat64Sigs(a, b, aSign);
}
}
float32 float32_sub(float32 a, float32 b)
{
flag aSign, bSign;
aSign = extractFloat32Sign(a);
bSign = extractFloat32Sign(b);
if (aSign == bSign) {
return subFloat32Sigs(a, b, aSign);
} else {
return addFloat32Sigs(a, b, aSign);
}
}
float32 float32_add(float32 a, float32 b)
{
flag aSign, bSign;
aSign = extractFloat32Sign(a);
bSign = extractFloat32Sign(b);
if (aSign == bSign) {
return addFloat32Sigs(a, b, aSign);
} else {
return subFloat32Sigs(a, b, aSign);
}
}
float64 float64_add(float64 a, float64 b)
{
flag aSign, bSign;
aSign = extractFloat64Sign(a);
bSign = extractFloat64Sign(b);
if (aSign == bSign) {
return addFloat64Sigs(a, b, aSign);
} else {
return subFloat64Sigs(a, b, aSign);
}
}
static void
normalizeFloat64Subnormal(bits64 aSig, int16 * zExpPtr, bits64 * zSigPtr)
{
int8 shiftCount;
shiftCount = countLeadingZeros64(aSig) - 11;
*zSigPtr = aSig << shiftCount;
*zExpPtr = 1 - shiftCount;
}
void add128(bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 * z0Ptr,
bits64 * z1Ptr)
{
bits64 z1;
z1 = a1 + b1;
*z1Ptr = z1;
*z0Ptr = a0 + b0 + (z1 < a1);
}
void
sub128(bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 * z0Ptr,
bits64 * z1Ptr)
{
*z1Ptr = a1 - b1;
*z0Ptr = a0 - b0 - (a1 < b1);
}
static bits64 estimateDiv128To64(bits64 a0, bits64 a1, bits64 b)
{
bits64 b0, b1;
bits64 rem0, rem1, term0, term1;
bits64 z, tmp;
if (b <= a0)
return LIT64(0xFFFFFFFFFFFFFFFF);
b0 = b >> 32;
tmp = a0;
do_div(tmp, b0);
z = (b0 << 32 <= a0) ? LIT64(0xFFFFFFFF00000000) : tmp << 32;
mul64To128(b, z, &term0, &term1);
sub128(a0, a1, term0, term1, &rem0, &rem1);
while (((sbits64) rem0) < 0) {
z -= LIT64(0x100000000);
b1 = b << 32;
add128(rem0, rem1, b0, b1, &rem0, &rem1);
}
rem0 = (rem0 << 32) | (rem1 >> 32);
tmp = rem0;
do_div(tmp, b0);
z |= (b0 << 32 <= rem0) ? 0xFFFFFFFF : tmp;
return z;
}
void mul64To128(bits64 a, bits64 b, bits64 * z0Ptr, bits64 * z1Ptr)
{
bits32 aHigh, aLow, bHigh, bLow;
bits64 z0, zMiddleA, zMiddleB, z1;
aLow = a;
aHigh = a >> 32;
bLow = b;
bHigh = b >> 32;
z1 = ((bits64) aLow) * bLow;
zMiddleA = ((bits64) aLow) * bHigh;
zMiddleB = ((bits64) aHigh) * bLow;
z0 = ((bits64) aHigh) * bHigh;
zMiddleA += zMiddleB;
z0 += (((bits64) (zMiddleA < zMiddleB)) << 32) + (zMiddleA >> 32);
zMiddleA <<= 32;
z1 += zMiddleA;
z0 += (z1 < zMiddleA);
*z1Ptr = z1;
*z0Ptr = z0;
}
static void normalizeFloat32Subnormal(bits32 aSig, int16 * zExpPtr,
bits32 * zSigPtr)
{
int8 shiftCount;
shiftCount = countLeadingZeros32(aSig) - 8;
*zSigPtr = aSig << shiftCount;
*zExpPtr = 1 - shiftCount;
}
float64 float64_div(float64 a, float64 b)
{
flag aSign, bSign, zSign;
int16 aExp, bExp, zExp;
bits64 aSig, bSig, zSig;
bits64 rem0, rem1;
bits64 term0, term1;
aSig = extractFloat64Frac(a);
aExp = extractFloat64Exp(a);
aSign = extractFloat64Sign(a);
bSig = extractFloat64Frac(b);
bExp = extractFloat64Exp(b);
bSign = extractFloat64Sign(b);
zSign = aSign ^ bSign;
if (aExp == 0x7FF) {
if (bExp == 0x7FF) {
}
return packFloat64(zSign, 0x7FF, 0);
}
if (bExp == 0x7FF) {
return packFloat64(zSign, 0, 0);
}
if (bExp == 0) {
if (bSig == 0) {
if ((aExp | aSig) == 0) {
float_raise(FPSCR_CAUSE_INVALID);
}
return packFloat64(zSign, 0x7FF, 0);
}
normalizeFloat64Subnormal(bSig, &bExp, &bSig);
}
if (aExp == 0) {
if (aSig == 0)
return packFloat64(zSign, 0, 0);
normalizeFloat64Subnormal(aSig, &aExp, &aSig);
}
zExp = aExp - bExp + 0x3FD;
aSig = (aSig | LIT64(0x0010000000000000)) << 10;
bSig = (bSig | LIT64(0x0010000000000000)) << 11;
if (bSig <= (aSig + aSig)) {
aSig >>= 1;
++zExp;
}
zSig = estimateDiv128To64(aSig, 0, bSig);
if ((zSig & 0x1FF) <= 2) {
mul64To128(bSig, zSig, &term0, &term1);
sub128(aSig, 0, term0, term1, &rem0, &rem1);
while ((sbits64) rem0 < 0) {
--zSig;
add128(rem0, rem1, 0, bSig, &rem0, &rem1);
}
zSig |= (rem1 != 0);
}
return roundAndPackFloat64(zSign, zExp, zSig);
}
float32 float32_div(float32 a, float32 b)
{
flag aSign, bSign, zSign;
int16 aExp, bExp, zExp;
bits32 aSig, bSig;
uint64_t zSig;
aSig = extractFloat32Frac(a);
aExp = extractFloat32Exp(a);
aSign = extractFloat32Sign(a);
bSig = extractFloat32Frac(b);
bExp = extractFloat32Exp(b);
bSign = extractFloat32Sign(b);
zSign = aSign ^ bSign;
if (aExp == 0xFF) {
if (bExp == 0xFF) {
}
return packFloat32(zSign, 0xFF, 0);
}
if (bExp == 0xFF) {
return packFloat32(zSign, 0, 0);
}
if (bExp == 0) {
if (bSig == 0) {
return packFloat32(zSign, 0xFF, 0);
}
normalizeFloat32Subnormal(bSig, &bExp, &bSig);
}
if (aExp == 0) {
if (aSig == 0)
return packFloat32(zSign, 0, 0);
normalizeFloat32Subnormal(aSig, &aExp, &aSig);
}
zExp = aExp - bExp + 0x7D;
aSig = (aSig | 0x00800000) << 7;
bSig = (bSig | 0x00800000) << 8;
if (bSig <= (aSig + aSig)) {
aSig >>= 1;
++zExp;
}
zSig = (((bits64) aSig) << 32);
do_div(zSig, bSig);
if ((zSig & 0x3F) == 0) {
zSig |= (((bits64) bSig) * zSig != ((bits64) aSig) << 32);
}
return roundAndPackFloat32(zSign, zExp, (bits32)zSig);
}
float32 float32_mul(float32 a, float32 b)
{
char aSign, bSign, zSign;
int aExp, bExp, zExp;
unsigned int aSig, bSig;
unsigned long long zSig64;
unsigned int zSig;
aSig = extractFloat32Frac(a);
aExp = extractFloat32Exp(a);
aSign = extractFloat32Sign(a);
bSig = extractFloat32Frac(b);
bExp = extractFloat32Exp(b);
bSign = extractFloat32Sign(b);
zSign = aSign ^ bSign;
if (aExp == 0) {
if (aSig == 0)
return packFloat32(zSign, 0, 0);
normalizeFloat32Subnormal(aSig, &aExp, &aSig);
}
if (bExp == 0) {
if (bSig == 0)
return packFloat32(zSign, 0, 0);
normalizeFloat32Subnormal(bSig, &bExp, &bSig);
}
if ((bExp == 0xff && bSig == 0) || (aExp == 0xff && aSig == 0))
return roundAndPackFloat32(zSign, 0xff, 0);
zExp = aExp + bExp - 0x7F;
aSig = (aSig | 0x00800000) << 7;
bSig = (bSig | 0x00800000) << 8;
shift64RightJamming(((unsigned long long)aSig) * bSig, 32, &zSig64);
zSig = zSig64;
if (0 <= (signed int)(zSig << 1)) {
zSig <<= 1;
--zExp;
}
return roundAndPackFloat32(zSign, zExp, zSig);
}
float64 float64_mul(float64 a, float64 b)
{
char aSign, bSign, zSign;
int aExp, bExp, zExp;
unsigned long long int aSig, bSig, zSig0, zSig1;
aSig = extractFloat64Frac(a);
aExp = extractFloat64Exp(a);
aSign = extractFloat64Sign(a);
bSig = extractFloat64Frac(b);
bExp = extractFloat64Exp(b);
bSign = extractFloat64Sign(b);
zSign = aSign ^ bSign;
if (aExp == 0) {
if (aSig == 0)
return packFloat64(zSign, 0, 0);
normalizeFloat64Subnormal(aSig, &aExp, &aSig);
}
if (bExp == 0) {
if (bSig == 0)
return packFloat64(zSign, 0, 0);
normalizeFloat64Subnormal(bSig, &bExp, &bSig);
}
if ((aExp == 0x7ff && aSig == 0) || (bExp == 0x7ff && bSig == 0))
return roundAndPackFloat64(zSign, 0x7ff, 0);
zExp = aExp + bExp - 0x3FF;
aSig = (aSig | 0x0010000000000000LL) << 10;
bSig = (bSig | 0x0010000000000000LL) << 11;
mul64To128(aSig, bSig, &zSig0, &zSig1);
zSig0 |= (zSig1 != 0);
if (0 <= (signed long long int)(zSig0 << 1)) {
zSig0 <<= 1;
--zExp;
}
return roundAndPackFloat64(zSign, zExp, zSig0);
}
/*
* -------------------------------------------------------------------------------
* Returns the result of converting the double-precision floating-point value
* `a' to the single-precision floating-point format. The conversion is
* performed according to the IEC/IEEE Standard for Binary Floating-point
* Arithmetic.
* -------------------------------------------------------------------------------
* */
float32 float64_to_float32(float64 a)
{
flag aSign;
int16 aExp;
bits64 aSig;
bits32 zSig;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
shift64RightJamming( aSig, 22, &aSig );
zSig = aSig;
if ( aExp || zSig ) {
zSig |= 0x40000000;
aExp -= 0x381;
}
return roundAndPackFloat32(aSign, aExp, zSig);
}
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