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core: encode real numbers using uint32_t rather than uint16_t.

legacy
Sam Hocevar sam 13 years ago
parent
79a15eafd8
commit
9ff54f59e3
2 changed files with 80 additions and 69 deletions
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  1. +78
    -67
      src/real.cpp
  2. +2
    -2
      src/real.h

+ 78
- 67
src/real.cpp View File

@@ -22,6 +22,8 @@ using namespace std;
namespace lol
{

static int const BIGIT_BITS = 32;

real::real(float f) { *this = (double)f; }
real::real(int i) { *this = (double)i; }
real::real(unsigned int i) { *this = (double)i; }
@@ -46,11 +48,9 @@ real::real(double d)
break;
}

m_mantissa[0] = u.x >> 36;
m_mantissa[1] = u.x >> 20;
m_mantissa[2] = u.x >> 4;
m_mantissa[3] = u.x << 12;
memset(m_mantissa + 4, 0, sizeof(m_mantissa) - 4 * sizeof(m_mantissa[0]));
m_mantissa[0] = u.x >> 20;
m_mantissa[1] = u.x << 12;
memset(m_mantissa + 2, 0, (BIGITS - 2) * sizeof(m_mantissa[0]));
}

real::operator float() const { return (float)(double)(*this); }
@@ -81,16 +81,12 @@ real::operator double() const
u.x |= e;

/* Store mantissa if necessary */
u.x <<= 16;
u.x <<= 32;
u.x |= m_mantissa[0];
u.x <<= 16;
u.x |= m_mantissa[1];
u.x <<= 16;
u.x |= m_mantissa[2];
u.x <<= 4;
u.x |= m_mantissa[3] >> 12;
u.x <<= 20;
u.x |= m_mantissa[1] >> 12;
/* Rounding */
u.x += (m_mantissa[3] >> 11) & 1;
u.x += (m_mantissa[1] >> 11) & 1;
}

return u.d;
@@ -131,28 +127,28 @@ real real::operator +(real const &x) const
int e1 = m_signexp - (1 << 30) + 1;
int e2 = x.m_signexp - (1 << 30) + 1;

int bigoff = (e1 - e2) / (sizeof(uint16_t) * 8);
int off = e1 - e2 - bigoff * (sizeof(uint16_t) * 8);
int bigoff = (e1 - e2) / BIGIT_BITS;
int off = e1 - e2 - bigoff * BIGIT_BITS;

if (bigoff > BIGITS)
return *this;

ret.m_signexp = m_signexp;

uint32_t carry = 0;
uint64_t carry = 0;
for (int i = BIGITS; i--; )
{
carry += m_mantissa[i];
if (i - bigoff >= 0)
carry += x.m_mantissa[i - bigoff] >> off;

if (i - bigoff > 0)
carry += (x.m_mantissa[i - bigoff - 1] << (16 - off)) & 0xffffu;
if (off && i - bigoff > 0)
carry += (x.m_mantissa[i - bigoff - 1] << (BIGIT_BITS - off)) & 0xffffffffu;
else if (i - bigoff == 0)
carry += 0x0001u << (16 - off);
carry += (uint64_t)1 << (BIGIT_BITS - off);

ret.m_mantissa[i] = carry;
carry >>= 16;
carry >>= BIGIT_BITS;
}

/* Renormalise in case we overflowed the mantissa */
@@ -161,9 +157,9 @@ real real::operator +(real const &x) const
carry--;
for (int i = 0; i < BIGITS; i++)
{
uint16_t tmp = ret.m_mantissa[i];
ret.m_mantissa[i] = (carry << 15) | (tmp >> 1);
carry = tmp & 0x0001u;
uint32_t tmp = ret.m_mantissa[i];
ret.m_mantissa[i] = (carry << (BIGIT_BITS - 1)) | (tmp >> 1);
carry = tmp & 1u;
}
ret.m_signexp++;
}
@@ -193,22 +189,24 @@ real real::operator -(real const &x) const
int e1 = m_signexp - (1 << 30) + 1;
int e2 = x.m_signexp - (1 << 30) + 1;

int bigoff = (e1 - e2) / (sizeof(uint16_t) * 8);
int off = e1 - e2 - bigoff * (sizeof(uint16_t) * 8);
int bigoff = (e1 - e2) / BIGIT_BITS;
int off = e1 - e2 - bigoff * BIGIT_BITS;

if (bigoff > BIGITS)
return *this;

ret.m_signexp = m_signexp;

int32_t carry = 0;
int64_t carry = 0;
for (int i = 0; i < bigoff; i++)
{
carry -= x.m_mantissa[BIGITS - i];
carry = (carry & 0xffff0000u) | (carry >> 16);
/* Emulates a signed shift */
carry >>= BIGIT_BITS;
carry |= carry << BIGIT_BITS;
}
carry -= x.m_mantissa[BIGITS - 1 - bigoff] & ((1 << off) - 1);
carry /= (1 << off);
carry -= x.m_mantissa[BIGITS - 1 - bigoff] & (((int64_t)1 << off) - 1);
carry /= (int64_t)1 << off;

for (int i = BIGITS; i--; )
{
@@ -216,13 +214,14 @@ real real::operator -(real const &x) const
if (i - bigoff >= 0)
carry -= x.m_mantissa[i - bigoff] >> off;

if (i - bigoff > 0)
carry -= (x.m_mantissa[i - bigoff - 1] << (16 - off)) & 0xffffu;
if (off && i - bigoff > 0)
carry -= (x.m_mantissa[i - bigoff - 1] << (BIGIT_BITS - off)) & 0xffffffffu;
else if (i - bigoff == 0)
carry -= 0x0001u << (16 - off);
carry -= (uint64_t)1 << (BIGIT_BITS - off);

ret.m_mantissa[i] = carry;
carry = (carry & 0xffff0000u) | (carry >> 16);
carry >>= BIGIT_BITS;
carry |= carry << BIGIT_BITS;
}

carry += 1;
@@ -237,31 +236,31 @@ real real::operator -(real const &x) const
{
if (!ret.m_mantissa[i])
{
off += sizeof(uint16_t) * 8;
off += BIGIT_BITS;
continue;
}

for (uint16_t tmp = ret.m_mantissa[i]; tmp < 0x8000u; tmp <<= 1)
for (uint32_t tmp = ret.m_mantissa[i]; tmp < 0x80000000u; tmp <<= 1)
off++;
break;
}
if (off == BIGITS * sizeof(uint16_t) * 8)
if (off == BIGITS * BIGIT_BITS)
ret.m_signexp &= 0x80000000u;
else
{
off++; /* Shift one more to get rid of the leading one */
ret.m_signexp -= off;

bigoff = off / (sizeof(uint16_t) * 8);
off -= bigoff * sizeof(uint16_t) * 8;
bigoff = off / BIGIT_BITS;
off -= bigoff * BIGIT_BITS;

for (int i = 0; i < BIGITS; i++)
{
uint16_t tmp = 0;
uint32_t tmp = 0;
if (i + bigoff < BIGITS)
tmp |= ret.m_mantissa[i + bigoff] << off;
if (i + bigoff + 1 < BIGITS)
tmp |= ret.m_mantissa[i + bigoff + 1] >> (16 - off);
if (off && i + bigoff + 1 < BIGITS)
tmp |= ret.m_mantissa[i + bigoff + 1] >> (BIGIT_BITS - off);
ret.m_mantissa[i] = tmp;
}
}
@@ -287,25 +286,41 @@ real real::operator *(real const &x) const

/* Accumulate low order product; no need to store it, we just
* want the carry value */
uint64_t carry = 0;
uint64_t carry = 0, hicarry = 0, prev;
for (int i = 0; i < BIGITS; i++)
{
for (int j = 0; j < i + 1; j++)
carry += (uint32_t)m_mantissa[BIGITS - 1 - j]
* (uint32_t)x.m_mantissa[BIGITS - 1 + j - i];
carry >>= 16;
{
prev = carry;
carry += (uint64_t)m_mantissa[BIGITS - 1 - j]
* (uint64_t)x.m_mantissa[BIGITS - 1 + j - i];
if (carry < prev)
hicarry++;
}
carry >>= BIGIT_BITS;
carry |= hicarry << BIGIT_BITS;
hicarry >>= BIGIT_BITS;
}

for (int i = 0; i < BIGITS; i++)
{
for (int j = i + 1; j < BIGITS; j++)
carry += (uint32_t)m_mantissa[BIGITS - 1 - j]
* (uint32_t)x.m_mantissa[j - 1 - i];

{
prev = carry;
carry += (uint64_t)m_mantissa[BIGITS - 1 - j]
* (uint64_t)x.m_mantissa[j - 1 - i];
if (carry < prev)
hicarry++;
}
prev = carry;
carry += m_mantissa[BIGITS - 1 - i];
carry += x.m_mantissa[BIGITS - 1 - i];
ret.m_mantissa[BIGITS - 1 - i] = carry & 0xffffu;
carry >>= 16;
if (carry < prev)
hicarry++;
ret.m_mantissa[BIGITS - 1 - i] = carry & 0xffffffffu;
carry >>= BIGIT_BITS;
carry |= hicarry << BIGIT_BITS;
hicarry >>= BIGIT_BITS;
}

/* Renormalise in case we overflowed the mantissa */
@@ -314,9 +329,9 @@ real real::operator *(real const &x) const
carry--;
for (int i = 0; i < BIGITS; i++)
{
uint16_t tmp = ret.m_mantissa[i];
ret.m_mantissa[i] = (carry << 15) | (tmp >> 1);
carry = tmp & 0x0001u;
uint32_t tmp = ret.m_mantissa[i];
ret.m_mantissa[i] = (carry << (BIGIT_BITS - 1)) | (tmp >> 1);
carry = tmp & 1u;
}
e++;
}
@@ -472,13 +487,11 @@ real re(real const &x)

/* Use the system's float inversion to approximate 1/x */
union { float f; uint32_t x; } u = { 1.0f }, v = { 1.0f };
v.x |= (uint32_t)x.m_mantissa[0] << 7;
v.x |= (uint32_t)x.m_mantissa[1] >> 9;
v.x |= x.m_mantissa[0] >> 9;
v.f = 1.0 / v.f;

real ret;
ret.m_mantissa[0] = (v.x >> 7) & 0xffffu;
ret.m_mantissa[1] = (v.x << 9) & 0xffffu;
ret.m_mantissa[0] = v.x << 9;

uint32_t sign = x.m_signexp & 0x80000000u;
ret.m_signexp = sign;
@@ -489,7 +502,7 @@ real re(real const &x)

/* FIXME: log2(BIGITS) steps of Newton-Raphson seems to be enough for
* convergence, but this hasn't been checked seriously. */
for (int i = 1; i < real::BIGITS; i *= 2)
for (int i = 2; i < real::BIGITS; i *= 2)
ret = ret * (real::R_2 - ret * x);

return ret;
@@ -517,13 +530,11 @@ real sqrt(real const &x)
* exponent and final mantissa to pre-fill the result. */
union { float f; uint32_t x; } u = { 1.0f }, v = { 2.0f };
v.x -= ((x.m_signexp & 1) << 23);
v.x |= (uint32_t)x.m_mantissa[0] << 7;
v.x |= (uint32_t)x.m_mantissa[1] >> 9;
v.x |= x.m_mantissa[0] >> 9;
v.f = 1.0 / sqrtf(v.f);

real ret;
ret.m_mantissa[0] = (v.x >> 7) & 0xffffu;
ret.m_mantissa[1] = (v.x << 9) & 0xffffu;
ret.m_mantissa[0] = v.x << 9;

uint32_t sign = x.m_signexp & 0x80000000u;
ret.m_signexp = sign;
@@ -535,7 +546,7 @@ real sqrt(real const &x)

/* FIXME: log2(BIGITS) steps of Newton-Raphson seems to be enough for
* convergence, but this hasn't been checked seriously. */
for (int i = 1; i < real::BIGITS; i *= 2)
for (int i = 2; i < real::BIGITS; i *= 2)
{
ret = ret * (real::R_3 - ret * ret * x);
ret.m_signexp--;
@@ -592,7 +603,7 @@ real log(real const &x)
if (x.m_signexp >> 31 || x.m_signexp == 0)
{
tmp.m_signexp = 0xffffffffu;
tmp.m_mantissa[0] = 0xffffu;
tmp.m_mantissa[0] = 0xffffffffu;
return tmp;
}
tmp.m_signexp = (1 << 30) - 1;
@@ -657,10 +668,10 @@ real floor(real const &x)
{
if (exponent <= 0)
ret.m_mantissa[i] = 0;
else if (exponent < 8 * (int)sizeof(uint16_t))
ret.m_mantissa[i] &= ~((1 << (16 - exponent)) - 1);
else if (exponent < BIGIT_BITS)
ret.m_mantissa[i] &= ~((1 << (BIGIT_BITS - exponent)) - 1);

exponent -= 8 * sizeof(uint16_t);
exponent -= BIGIT_BITS;
}

return ret;


+ 2
- 2
src/real.h View File

@@ -108,11 +108,11 @@ private:
/* XXX: changing this requires tuning real::fres (the number of
* Newton-Raphson iterations) and real::print (the number of printed
* digits) */
static int const BIGITS = 32;
static int const BIGITS = 16;

uint32_t m_size;
uint32_t m_signexp;
uint16_t m_mantissa[BIGITS];
uint32_t m_mantissa[BIGITS];
};

} /* namespace lol */


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