Revision 0:aa2871c4c041, committed 2010-10-20

Comitter:

sravet

Date:

Wed Oct 20 02:20:46 2010 +0000

Commit message:

First checkin.

Changed in this revision

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/fixed_class.h	Wed Oct 20 02:20:46 2010 +0000
@@ -0,0 +1,189 @@
+/*
+Copyright (c) 2007, Markus Trenkwalder
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without 
+modification, are permitted provided that the following conditions are met:
+
+* Redistributions of source code must retain the above copyright notice, 
+  this list of conditions and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright notice,
+  this list of conditions and the following disclaimer in the documentation 
+  and/or other materials provided with the distribution.
+
+* Neither the name of the library's copyright owner nor the names of its 
+  contributors may be used to endorse or promote products derived from this 
+  software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
+#ifndef FIXEDP_CLASS_H_INCLUDED
+#define FIXEDP_CLASS_H_INCLUDED
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include "fixed_func.h"
+
+namespace fixedpoint {
+
+// The template argument p in all of the following functions refers to the 
+// fixed point precision (e.g. p = 8 gives 24.8 fixed point functions).
+
+template <int p>
+struct fixed_point {
+    int32_t intValue;
+    
+    fixed_point() {}
+    /*explicit*/ fixed_point(int32_t i) : intValue(i << p) {}
+    /*explicit*/ fixed_point(float f) : intValue(float2fix<p>(f)) {}
+    /*explicit*/ fixed_point(double f) : intValue(float2fix<p>((float)f)) {}
+    
+    fixed_point& operator += (fixed_point r) { intValue += r.intValue; return *this; }
+    fixed_point& operator -= (fixed_point r) { intValue -= r.intValue; return *this; }
+    fixed_point& operator *= (fixed_point r) { intValue = fixmul<p>(intValue, r.intValue); return *this; }
+    fixed_point& operator /= (fixed_point r) { intValue = fixdiv<p>(intValue, r.intValue); return *this; }
+    
+    fixed_point& operator *= (int32_t r) { intValue *= r; return *this; }
+    fixed_point& operator /= (int32_t r) { intValue /= r; return *this; }
+    
+    fixed_point operator - () const { fixed_point x; x.intValue = -intValue; return x; }
+    fixed_point operator + (fixed_point r) const { fixed_point x = *this; x += r; return x;}
+    fixed_point operator - (fixed_point r) const { fixed_point x = *this; x -= r; return x;}
+    fixed_point operator * (fixed_point r) const { fixed_point x = *this; x *= r; return x;}
+    fixed_point operator / (fixed_point r) const { fixed_point x = *this; x /= r; return x;}
+    
+    bool operator == (fixed_point r) const { return intValue == r.intValue; }
+    bool operator != (fixed_point r) const { return !(*this == r); }
+    bool operator <  (fixed_point r) const { return intValue < r.intValue; }
+    bool operator >  (fixed_point r) const { return intValue > r.intValue; }
+    bool operator <= (fixed_point r) const { return intValue <= r.intValue; }
+    bool operator >= (fixed_point r) const { return intValue >= r.intValue; }
+
+    fixed_point operator + (int32_t r) const { fixed_point x = *this; x += r; return x;}
+    fixed_point operator - (int32_t r) const { fixed_point x = *this; x -= r; return x;}
+    fixed_point operator * (int32_t r) const { fixed_point x = *this; x *= r; return x;}
+    fixed_point operator / (int32_t r) const { fixed_point x = *this; x /= r; return x;}
+    operator int()         const { return intValue>>p; }
+    operator float()       const { return fix2float<p>(intValue); }
+};
+
+// Specializations for use with plain integers
+template <int p>
+inline fixed_point<p> operator + (int32_t a, fixed_point<p> b)
+{ return b + a; }
+
+template <int p>
+inline fixed_point<p> operator - (int32_t a, fixed_point<p> b)
+{ return -b + a; }
+
+template <int p>
+inline fixed_point<p> operator * (int32_t a, fixed_point<p> b)
+{ return b * a; }
+
+template <int p>
+inline fixed_point<p> operator / (int32_t a, fixed_point<p> b)
+{ fixed_point<p> r(a); r /= b; return r; }
+
+// math functions
+// no default implementation
+
+template <int p>
+inline fixed_point<p> sin(fixed_point<p> a);
+
+template <int p>
+inline fixed_point<p> cos(fixed_point<p> a);
+
+template <int p>
+inline fixed_point<p> sqrt(fixed_point<p> a);
+
+template <int p>
+inline fixed_point<p> rsqrt(fixed_point<p> a);
+
+template <int p>
+inline fixed_point<p> inv(fixed_point<p> a);
+
+template <int p>
+inline fixed_point<p> abs(fixed_point<p> a)
+{ 
+    fixed_point<p> r; 
+    r.intValue = a.intValue > 0 ? a.intValue : -a.intValue; 
+    return r; 
+}
+
+// specializations for 16.16 format
+
+template <>
+inline fixed_point<16> sin(fixed_point<16> a)
+{
+    fixed_point<16> r;
+    r.intValue = fixsin16(a.intValue);
+    return r;
+}
+
+template <>
+inline fixed_point<16> cos(fixed_point<16> a)
+{
+    fixed_point<16> r;
+    r.intValue = fixcos16(a.intValue);
+    return r;
+}
+
+
+template <>
+inline fixed_point<16> sqrt(fixed_point<16> a)
+{
+    fixed_point<16> r;
+    r.intValue = fixsqrt16(a.intValue);
+    return r;
+}
+
+template <>
+inline fixed_point<16> rsqrt(fixed_point<16> a)
+{
+    fixed_point<16> r;
+    r.intValue = fixrsqrt16(a.intValue);
+    return r;
+}
+
+template <>
+inline fixed_point<16> inv(fixed_point<16> a)
+{
+    fixed_point<16> r;
+    r.intValue = fixinv<16>(a.intValue);
+    return r;
+}
+
+// The multiply accumulate case can be optimized.
+template <int p>
+inline fixed_point<p> multiply_accumulate(
+    int count, 
+    const fixed_point<p> *a,
+    const fixed_point<p> *b)
+{
+    long long result = 0;
+    for (int i = 0; i < count; ++i)
+        result += static_cast<long long>(a[i].intValue) * b[i].intValue;
+    fixed_point<p> r;
+    r.intValue = static_cast<int>(result >> p);
+    return r;
+}
+
+} // end namespace fixedpoint
+
+#endif
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/fixed_func.cpp	Wed Oct 20 02:20:46 2010 +0000
@@ -0,0 +1,133 @@
+/*
+Copyright (c) 2007, Markus Trenkwalder
+
+Portions taken from the Vicent 3D rendering library
+Copyright (c) 2004, David Blythe, Hans Martin Will
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without 
+modification, are permitted provided that the following conditions are met:
+
+* Redistributions of source code must retain the above copyright notice, 
+  this list of conditions and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright notice,
+  this list of conditions and the following disclaimer in the documentation 
+  and/or other materials provided with the distribution.
+
+* Neither the name of the library's copyright owner nor the names of its 
+  contributors may be used to endorse or promote products derived from this 
+  software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
+#include "fixed_func.h"
+
+namespace fixedpoint {
+
+static const int32_t FIX16_2PI    = float2fix<16>(6.28318530717958647692f);
+static const int32_t FIX16_R2PI = float2fix<16>(1.0f/6.28318530717958647692f);
+
+static const uint16_t sin_tab[] = {
+#include "fixsintab.h"
+};
+
+int32_t fixcos16(int32_t a) 
+{
+    int32_t v;
+    /* reduce to [0,1) */
+    while (a < 0) a += FIX16_2PI;
+    a = fixmul<16>(a, FIX16_R2PI);
+    a += 0x4000;
+
+    /* now in the range [0, 0xffff], reduce to [0, 0xfff] */
+    a >>= 4;
+
+    v = (a & 0x400) ? sin_tab[0x3ff - (a & 0x3ff)] : sin_tab[a & 0x3ff];
+    v = fixmul<16>(v, 1 << 16);
+    return (a & 0x800) ? -v : v;
+}
+
+int32_t fixsin16(int32_t a)
+{
+    int32_t v;
+
+    /* reduce to [0,1) */
+    while (a < 0) a += FIX16_2PI;
+    a = fixmul<16>(a, FIX16_R2PI);
+
+    /* now in the range [0, 0xffff], reduce to [0, 0xfff] */
+    a >>= 4;
+
+    v = (a & 0x400) ? sin_tab[0x3ff - (a & 0x3ff)] : sin_tab[a & 0x3ff];
+    v = fixmul<16>(v, 1 << 16);
+    return (a & 0x800) ? -v : v;
+}
+
+int32_t fixrsqrt16(int32_t a)
+{
+    int32_t x;
+
+    static const uint16_t rsq_tab[] = { /* domain 0.5 .. 1.0-1/16 */
+        0xb504, 0xaaaa, 0xa1e8, 0x9a5f, 0x93cd, 0x8e00, 0x88d6, 0x8432,
+    };
+
+    int32_t i, exp;
+    if (a == 0) return 0x7fffffff;
+    if (a == (1<<16)) return a;
+
+    exp = detail::CountLeadingZeros(a);
+    x = rsq_tab[(a>>(28-exp))&0x7]<<1;
+
+    exp -= 16;
+    if (exp <= 0)
+        x >>= -exp>>1;
+    else
+        x <<= (exp>>1)+(exp&1);
+    if (exp&1) x = fixmul<16>(x, rsq_tab[0]);
+
+
+    /* newton-raphson */
+    /* x = x/2*(3-(a*x)*x) */
+    i = 0;
+    do {
+
+        x = fixmul<16>((x>>1),((1<<16)*3 - fixmul<16>(fixmul<16>(a,x),x)));
+    } while(++i < 3);
+
+    return x;
+}
+
+static inline int32_t fast_div16(int32_t a, int32_t b)
+{
+    if ((b >> 24) && (b >> 24) + 1) {
+        return fixmul<16>(a >> 8, fixinv<16>(b >> 8));
+    } else {
+        return fixmul<16>(a, fixinv<16>(b));
+    }
+}
+
+int32_t fixsqrt16(int32_t a) 
+{
+    int32_t s;
+    int32_t i;
+    s = (a + (1<<16)) >> 1;
+    /* 6 iterations to converge */
+    for (i = 0; i < 6; i++)
+        s = (s + fast_div16(a, s)) >> 1;
+    return s;
+}
+
+} // end namespace fixedpoint

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/fixed_func.h	Wed Oct 20 02:20:46 2010 +0000
@@ -0,0 +1,184 @@
+/*
+Copyright (c) 2007, Markus Trenkwalder
+
+Portions taken from the Vicent 3D rendering library
+Copyright (c) 2004, David Blythe, Hans Martin Will
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without 
+modification, are permitted provided that the following conditions are met:
+
+* Redistributions of source code must retain the above copyright notice, 
+  this list of conditions and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright notice,
+  this list of conditions and the following disclaimer in the documentation 
+  and/or other materials provided with the distribution.
+
+* Neither the name of the library's copyright owner nor the names of its 
+  contributors may be used to endorse or promote products derived from this 
+  software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
+#ifndef FIXEDP_FUNC_H_INCLUDED
+#define FIXEDP_FUNC_H_INCLUDED
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#ifndef _MSC_VER
+#include <stdint.h>
+#else
+#include "stdint.h"
+#endif
+
+namespace fixedpoint {
+
+// The template argument p in all of the following functions refers to the 
+// fixed point precision (e.g. p = 8 gives 24.8 fixed point functions).
+
+// Perform a fixed point multiplication without a 64-bit intermediate result.
+// This is fast but beware of overflow!
+template <int p> 
+inline int32_t fixmulf(int32_t a, int32_t b)
+{
+    return (a * b) >> p;
+}
+
+// Perform a fixed point multiplication using a 64-bit intermediate result to
+// prevent overflow problems.
+template <int p>
+inline int32_t fixmul(int32_t a, int32_t b)
+{
+    return (int32_t)(((int64_t)a * b) >> p);
+}
+
+// Fixed point division
+template <int p>
+inline int fixdiv(int32_t a, int32_t b)
+{
+#if 0
+    return (int32_t)((((int64_t)a) << p) / b);
+#else    
+    // The following produces the same results as the above but gcc 4.0.3 
+    // generates fewer instructions (at least on the ARM processor).
+    union {
+        int64_t a;
+        struct {
+            int32_t l;
+            int32_t h;
+        };
+    } x;
+
+    x.l = a << p;
+    x.h = a >> (sizeof(int32_t) * 8 - p);
+    return (int32_t)(x.a / b);
+#endif
+}
+
+namespace detail {
+    inline uint32_t CountLeadingZeros(uint32_t x)
+    {
+        uint32_t exp = 31;
+    
+        if (x & 0xffff0000) { 
+            exp -= 16; 
+            x >>= 16; 
+        }
+    
+        if (x & 0xff00) { 
+            exp -= 8; 
+            x >>= 8; 
+        }
+        
+        if (x & 0xf0) { 
+            exp -= 4; 
+            x >>= 4; 
+        }
+    
+        if (x & 0xc) { 
+            exp -= 2; 
+            x >>= 2; 
+        }
+        
+        if (x & 0x2) { 
+            exp -= 1; 
+        }
+    
+        return exp;
+    }
+}
+
+// q is the precision of the input
+// output has 32-q bits of fraction
+template <int q>
+inline int fixinv(int32_t a)
+{
+    int32_t x;
+
+    bool sign = false;
+
+    if (a < 0) {
+        sign = true;
+        a = -a;
+    }
+
+    static const uint16_t rcp_tab[] = { 
+        0x8000, 0x71c7, 0x6666, 0x5d17, 0x5555, 0x4ec4, 0x4924, 0x4444
+    };
+        
+    int32_t exp = detail::CountLeadingZeros(a);
+    x = ((int32_t)rcp_tab[(a>>(28-exp))&0x7]) << 2;
+    exp -= 16;
+
+    if (exp <= 0)
+        x >>= -exp;
+    else
+        x <<= exp;
+
+    /* two iterations of newton-raphson  x = x(2-ax) */
+    x = fixmul<(32-q)>(x,((2<<(32-q)) - fixmul<q>(a,x)));
+    x = fixmul<(32-q)>(x,((2<<(32-q)) - fixmul<q>(a,x)));
+
+    if (sign)
+        return -x;
+    else
+        return x;
+}
+
+// Conversion from and to float
+
+template <int p>
+float fix2float(int32_t f)
+{
+    return (float)f / (1 << p);
+}
+
+template <int p>
+int32_t float2fix(float f)
+{
+    return (int32_t)(f * (1 << p));
+}
+
+int32_t fixcos16(int32_t a);
+int32_t fixsin16(int32_t a);
+int32_t fixrsqrt16(int32_t a);
+int32_t fixsqrt16(int32_t a);
+
+} // end namespace fixedpoint
+
+#endif

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/fixsintab.h	Wed Oct 20 02:20:46 2010 +0000
@@ -0,0 +1,1024 @@
+0x0000, /* 0.000000	 0.000000 */
+0x0064, /* 0.001535	 0.001535 */
+0x00c9, /* 0.003071	 0.003071 */
+0x012d, /* 0.004606	 0.004606 */
+0x0192, /* 0.006142	 0.006142 */
+0x01f7, /* 0.007677	 0.007677 */
+0x025b, /* 0.009213	 0.009213 */
+0x02c0, /* 0.010748	 0.010748 */
+0x0325, /* 0.012284	 0.012284 */
+0x0389, /* 0.013819	 0.013819 */
+0x03ee, /* 0.015355	 0.015354 */
+0x0452, /* 0.016890	 0.016889 */
+0x04b7, /* 0.018426	 0.018425 */
+0x051c, /* 0.019961	 0.019960 */
+0x0580, /* 0.021497	 0.021495 */
+0x05e5, /* 0.023032	 0.023030 */
+0x0649, /* 0.024568	 0.024565 */
+0x06ae, /* 0.026103	 0.026100 */
+0x0713, /* 0.027639	 0.027635 */
+0x0777, /* 0.029174	 0.029170 */
+0x07dc, /* 0.030710	 0.030705 */
+0x0840, /* 0.032245	 0.032239 */
+0x08a5, /* 0.033781	 0.033774 */
+0x0909, /* 0.035316	 0.035309 */
+0x096e, /* 0.036852	 0.036843 */
+0x09d3, /* 0.038387	 0.038378 */
+0x0a37, /* 0.039922	 0.039912 */
+0x0a9c, /* 0.041458	 0.041446 */
+0x0b00, /* 0.042993	 0.042980 */
+0x0b65, /* 0.044529	 0.044514 */
+0x0bc9, /* 0.046064	 0.046048 */
+0x0c2e, /* 0.047600	 0.047582 */
+0x0c92, /* 0.049135	 0.049116 */
+0x0cf7, /* 0.050671	 0.050649 */
+0x0d5b, /* 0.052206	 0.052183 */
+0x0dc0, /* 0.053742	 0.053716 */
+0x0e24, /* 0.055277	 0.055249 */
+0x0e89, /* 0.056813	 0.056782 */
+0x0eed, /* 0.058348	 0.058315 */
+0x0f52, /* 0.059884	 0.059848 */
+0x0fb6, /* 0.061419	 0.061381 */
+0x101b, /* 0.062955	 0.062913 */
+0x107f, /* 0.064490	 0.064445 */
+0x10e3, /* 0.066026	 0.065978 */
+0x1148, /* 0.067561	 0.067510 */
+0x11ac, /* 0.069097	 0.069042 */
+0x1211, /* 0.070632	 0.070573 */
+0x1275, /* 0.072168	 0.072105 */
+0x12d9, /* 0.073703	 0.073636 */
+0x133e, /* 0.075239	 0.075168 */
+0x13a2, /* 0.076774	 0.076699 */
+0x1406, /* 0.078309	 0.078229 */
+0x146b, /* 0.079845	 0.079760 */
+0x14cf, /* 0.081380	 0.081291 */
+0x1533, /* 0.082916	 0.082821 */
+0x1597, /* 0.084451	 0.084351 */
+0x15fc, /* 0.085987	 0.085881 */
+0x1660, /* 0.087522	 0.087411 */
+0x16c4, /* 0.089058	 0.088940 */
+0x1728, /* 0.090593	 0.090469 */
+0x178d, /* 0.092129	 0.091999 */
+0x17f1, /* 0.093664	 0.093527 */
+0x1855, /* 0.095200	 0.095056 */
+0x18b9, /* 0.096735	 0.096584 */
+0x191d, /* 0.098271	 0.098113 */
+0x1981, /* 0.099806	 0.099641 */
+0x19e6, /* 0.101342	 0.101168 */
+0x1a4a, /* 0.102877	 0.102696 */
+0x1aae, /* 0.104413	 0.104223 */
+0x1b12, /* 0.105948	 0.105750 */
+0x1b76, /* 0.107484	 0.107277 */
+0x1bda, /* 0.109019	 0.108803 */
+0x1c3e, /* 0.110555	 0.110330 */
+0x1ca2, /* 0.112090	 0.111855 */
+0x1d06, /* 0.113626	 0.113381 */
+0x1d6a, /* 0.115161	 0.114907 */
+0x1dce, /* 0.116697	 0.116432 */
+0x1e32, /* 0.118232	 0.117957 */
+0x1e96, /* 0.119767	 0.119481 */
+0x1efa, /* 0.121303	 0.121006 */
+0x1f5d, /* 0.122838	 0.122530 */
+0x1fc1, /* 0.124374	 0.124054 */
+0x2025, /* 0.125909	 0.125577 */
+0x2089, /* 0.127445	 0.127100 */
+0x20ed, /* 0.128980	 0.128623 */
+0x2151, /* 0.130516	 0.130146 */
+0x21b4, /* 0.132051	 0.131668 */
+0x2218, /* 0.133587	 0.133190 */
+0x227c, /* 0.135122	 0.134711 */
+0x22e0, /* 0.136658	 0.136233 */
+0x2343, /* 0.138193	 0.137754 */
+0x23a7, /* 0.139729	 0.139274 */
+0x240a, /* 0.141264	 0.140795 */
+0x246e, /* 0.142800	 0.142315 */
+0x24d2, /* 0.144335	 0.143835 */
+0x2535, /* 0.145871	 0.145354 */
+0x2599, /* 0.147406	 0.146873 */
+0x25fc, /* 0.148942	 0.148392 */
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+0xaf3a, /* 0.753921	 0.684502 */
+0xaf84, /* 0.755456	 0.685621 */
+0xafcd, /* 0.756992	 0.686738 */
+0xb016, /* 0.758527	 0.687853 */
+0xb05f, /* 0.760063	 0.688967 */
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+0xb333, /* 0.775418	 0.700014 */
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+0xba5a, /* 0.815340	 0.727959 */
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+0xc02d, /* 0.849121	 0.750700 */
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+0xc136, /* 0.855263	 0.754743 */
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+0xd012, /* 0.948927	 0.812791 */
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+0xd135, /* 0.956604	 0.817239 */
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+0xd21c, /* 0.962746	 0.820763 */
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+0xf30c, /* 1.251416	 0.949430 */
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+0xf34b, /* 1.254487	 0.950390 */
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+0xf49b, /* 1.271378	 0.955508 */
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+0xf54a, /* 1.280591	 0.958185 */
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+0xf704, /* 1.305158	 0.964925 */
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+0xf8df, /* 1.334332	 0.972172 */
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+0xfa84, /* 1.363507	 0.978592 */
+0xfa98, /* 1.365042	 0.978907 */
+0xfaad, /* 1.366577	 0.979220 */
+0xfac1, /* 1.368113	 0.979530 */
+0xfad5, /* 1.369648	 0.979838 */
+0xfae9, /* 1.371184	 0.980144 */
+0xfafd, /* 1.372719	 0.980447 */
+0xfb11, /* 1.374255	 0.980748 */
+0xfb24, /* 1.375790	 0.981047 */
+0xfb38, /* 1.377326	 0.981343 */
+0xfb4b, /* 1.378861	 0.981637 */
+0xfb5e, /* 1.380397	 0.981929 */
+0xfb71, /* 1.381932	 0.982218 */
+0xfb84, /* 1.383468	 0.982505 */
+0xfb97, /* 1.385003	 0.982790 */
+0xfba9, /* 1.386539	 0.983073 */
+0xfbbc, /* 1.388074	 0.983353 */
+0xfbce, /* 1.389610	 0.983631 */
+0xfbe0, /* 1.391145	 0.983906 */
+0xfbf2, /* 1.392681	 0.984179 */
+0xfc03, /* 1.394216	 0.984450 */
+0xfc15, /* 1.395752	 0.984719 */
+0xfc26, /* 1.397287	 0.984985 */
+0xfc38, /* 1.398823	 0.985249 */
+0xfc49, /* 1.400358	 0.985511 */
+0xfc5a, /* 1.401894	 0.985770 */
+0xfc6b, /* 1.403429	 0.986027 */
+0xfc7b, /* 1.404964	 0.986281 */
+0xfc8c, /* 1.406500	 0.986534 */
+0xfc9c, /* 1.408035	 0.986784 */
+0xfcad, /* 1.409571	 0.987031 */
+0xfcbd, /* 1.411106	 0.987277 */
+0xfccd, /* 1.412642	 0.987520 */
+0xfcdc, /* 1.414177	 0.987760 */
+0xfcec, /* 1.415713	 0.987999 */
+0xfcfb, /* 1.417248	 0.988235 */
+0xfd0b, /* 1.418784	 0.988468 */
+0xfd1a, /* 1.420319	 0.988700 */
+0xfd29, /* 1.421855	 0.988929 */
+0xfd38, /* 1.423390	 0.989155 */
+0xfd47, /* 1.424926	 0.989380 */
+0xfd55, /* 1.426461	 0.989602 */
+0xfd63, /* 1.427997	 0.989821 */
+0xfd72, /* 1.429532	 0.990039 */
+0xfd80, /* 1.431068	 0.990254 */
+0xfd8e, /* 1.432603	 0.990467 */
+0xfd9c, /* 1.434139	 0.990677 */
+0xfda9, /* 1.435674	 0.990885 */
+0xfdb7, /* 1.437210	 0.991091 */
+0xfdc4, /* 1.438745	 0.991294 */
+0xfdd1, /* 1.440281	 0.991495 */
+0xfdde, /* 1.441816	 0.991694 */
+0xfdeb, /* 1.443352	 0.991890 */
+0xfdf8, /* 1.444887	 0.992084 */
+0xfe04, /* 1.446422	 0.992276 */
+0xfe11, /* 1.447958	 0.992465 */
+0xfe1d, /* 1.449493	 0.992652 */
+0xfe29, /* 1.451029	 0.992836 */
+0xfe35, /* 1.452564	 0.993019 */
+0xfe41, /* 1.454100	 0.993199 */
+0xfe4c, /* 1.455635	 0.993376 */
+0xfe58, /* 1.457171	 0.993552 */
+0xfe63, /* 1.458706	 0.993724 */
+0xfe6e, /* 1.460242	 0.993895 */
+0xfe79, /* 1.461777	 0.994063 */
+0xfe84, /* 1.463313	 0.994229 */
+0xfe8f, /* 1.464848	 0.994393 */
+0xfe9a, /* 1.466384	 0.994554 */
+0xfea4, /* 1.467919	 0.994713 */
+0xfeae, /* 1.469455	 0.994869 */
+0xfeb8, /* 1.470990	 0.995023 */
+0xfec2, /* 1.472526	 0.995175 */
+0xfecc, /* 1.474061	 0.995325 */
+0xfed6, /* 1.475597	 0.995472 */
+0xfedf, /* 1.477132	 0.995617 */
+0xfee9, /* 1.478668	 0.995759 */
+0xfef2, /* 1.480203	 0.995899 */
+0xfefb, /* 1.481739	 0.996037 */
+0xff04, /* 1.483274	 0.996172 */
+0xff0c, /* 1.484809	 0.996305 */
+0xff15, /* 1.486345	 0.996436 */
+0xff1d, /* 1.487880	 0.996564 */
+0xff26, /* 1.489416	 0.996690 */
+0xff2e, /* 1.490951	 0.996814 */
+0xff36, /* 1.492487	 0.996935 */
+0xff3d, /* 1.494022	 0.997054 */
+0xff45, /* 1.495558	 0.997171 */
+0xff4d, /* 1.497093	 0.997285 */
+0xff54, /* 1.498629	 0.997397 */
+0xff5b, /* 1.500164	 0.997507 */
+0xff62, /* 1.501700	 0.997614 */
+0xff69, /* 1.503235	 0.997719 */
+0xff70, /* 1.504771	 0.997821 */
+0xff76, /* 1.506306	 0.997921 */
+0xff7d, /* 1.507842	 0.998019 */
+0xff83, /* 1.509377	 0.998114 */
+0xff89, /* 1.510913	 0.998208 */
+0xff8f, /* 1.512448	 0.998298 */
+0xff95, /* 1.513984	 0.998387 */
+0xff9a, /* 1.515519	 0.998473 */
+0xffa0, /* 1.517055	 0.998556 */
+0xffa5, /* 1.518590	 0.998638 */
+0xffaa, /* 1.520126	 0.998717 */
+0xffaf, /* 1.521661	 0.998793 */
+0xffb4, /* 1.523196	 0.998867 */
+0xffb9, /* 1.524732	 0.998939 */
+0xffbe, /* 1.526267	 0.999009 */
+0xffc2, /* 1.527803	 0.999076 */
+0xffc6, /* 1.529338	 0.999141 */
+0xffca, /* 1.530874	 0.999203 */
+0xffce, /* 1.532409	 0.999263 */
+0xffd2, /* 1.533945	 0.999321 */
+0xffd6, /* 1.535480	 0.999376 */
+0xffd9, /* 1.537016	 0.999429 */
+0xffdc, /* 1.538551	 0.999480 */
+0xffe0, /* 1.540087	 0.999528 */
+0xffe3, /* 1.541622	 0.999574 */
+0xffe5, /* 1.543158	 0.999618 */
+0xffe8, /* 1.544693	 0.999659 */
+0xffeb, /* 1.546229	 0.999698 */
+0xffed, /* 1.547764	 0.999735 */
+0xffef, /* 1.549300	 0.999769 */
+0xfff1, /* 1.550835	 0.999801 */
+0xfff3, /* 1.552371	 0.999830 */
+0xfff5, /* 1.553906	 0.999857 */
+0xfff7, /* 1.555442	 0.999882 */
+0xfff8, /* 1.556977	 0.999905 */
+0xfffa, /* 1.558513	 0.999925 */
+0xfffb, /* 1.560048	 0.999942 */
+0xfffc, /* 1.561583	 0.999958 */
+0xfffd, /* 1.563119	 0.999971 */
+0xfffd, /* 1.564654	 0.999981 */
+0xfffe, /* 1.566190	 0.999989 */
+0xfffe, /* 1.567725	 0.999995 */
+0xfffe, /* 1.569261	 0.999999 */
+0xfffe, /* 1.570796	 1.000000 */

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/stdint.h	Wed Oct 20 02:20:46 2010 +0000
@@ -0,0 +1,184 @@
+/* ISO C9x  7.18  Integer types <stdint.h>
+ * Based on ISO/IEC SC22/WG14 9899 Committee draft (SC22 N2794)
+ *
+ *  THIS SOFTWARE IS NOT COPYRIGHTED
+ *
+ *  Contributor: Danny Smith <danny_r_smith_2001@yahoo.co.nz>
+ *
+ *  This source code is offered for use in the public domain. You may
+ *  use, modify or distribute it freely.
+ *
+ *  This code is distributed in the hope that it will be useful but
+ *  WITHOUT ANY WARRANTY. ALL WARRANTIES, EXPRESS OR IMPLIED ARE HEREBY
+ *  DISCLAIMED. This includes but is not limited to warranties of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+ *
+ *  Date: 2000-12-02
+ */
+
+
+#ifndef _STDINT_H
+#define _STDINT_H
+#define __need_wint_t
+#define __need_wchar_t
+#include <stddef.h>
+
+/* 7.18.1.1  Exact-width integer types */
+typedef signed char int8_t;
+typedef unsigned char   uint8_t;
+typedef short  int16_t;
+typedef unsigned short  uint16_t;
+typedef int  int32_t;
+typedef unsigned   uint32_t;
+typedef long long  int64_t;
+typedef unsigned long long   uint64_t;
+
+/* 7.18.1.2  Minimum-width integer types */
+typedef signed char int_least8_t;
+typedef unsigned char   uint_least8_t;
+typedef short  int_least16_t;
+typedef unsigned short  uint_least16_t;
+typedef int  int_least32_t;
+typedef unsigned   uint_least32_t;
+typedef long long  int_least64_t;
+typedef unsigned long long   uint_least64_t;
+
+/*  7.18.1.3  Fastest minimum-width integer types 
+ *  Not actually guaranteed to be fastest for all purposes
+ *  Here we use the exact-width types for 8 and 16-bit ints. 
+ */
+typedef char int_fast8_t;
+typedef unsigned char uint_fast8_t;
+typedef short  int_fast16_t;
+typedef unsigned short  uint_fast16_t;
+typedef int  int_fast32_t;
+typedef unsigned  int  uint_fast32_t;
+typedef long long  int_fast64_t;
+typedef unsigned long long   uint_fast64_t;
+
+/* 7.18.1.4  Integer types capable of holding object pointers */
+typedef int intptr_t;
+typedef unsigned uintptr_t;
+
+/* 7.18.1.5  Greatest-width integer types */
+typedef long long  intmax_t;
+typedef unsigned long long   uintmax_t;
+
+/* 7.18.2  Limits of specified-width integer types */
+#if !defined ( __cplusplus) || defined (__STDC_LIMIT_MACROS)
+
+/* 7.18.2.1  Limits of exact-width integer types */
+#define INT8_MIN (-128) 
+#define INT16_MIN (-32768)
+#define INT32_MIN (-2147483647 - 1)
+#define INT64_MIN  (-9223372036854775807LL - 1)
+
+#define INT8_MAX 127
+#define INT16_MAX 32767
+#define INT32_MAX 2147483647
+#define INT64_MAX 9223372036854775807LL
+
+#define UINT8_MAX 0xff /* 255U */
+#define UINT16_MAX 0xffff /* 65535U */
+#define UINT32_MAX 0xffffffff  /* 4294967295U */
+#define UINT64_MAX 0xffffffffffffffffULL /* 18446744073709551615ULL */
+
+/* 7.18.2.2  Limits of minimum-width integer types */
+#define INT_LEAST8_MIN INT8_MIN
+#define INT_LEAST16_MIN INT16_MIN
+#define INT_LEAST32_MIN INT32_MIN
+#define INT_LEAST64_MIN INT64_MIN
+
+#define INT_LEAST8_MAX INT8_MAX
+#define INT_LEAST16_MAX INT16_MAX
+#define INT_LEAST32_MAX INT32_MAX
+#define INT_LEAST64_MAX INT64_MAX
+
+#define UINT_LEAST8_MAX UINT8_MAX
+#define UINT_LEAST16_MAX UINT16_MAX
+#define UINT_LEAST32_MAX UINT32_MAX
+#define UINT_LEAST64_MAX UINT64_MAX
+
+/* 7.18.2.3  Limits of fastest minimum-width integer types */
+#define INT_FAST8_MIN INT8_MIN
+#define INT_FAST16_MIN INT16_MIN
+#define INT_FAST32_MIN INT32_MIN
+#define INT_FAST64_MIN INT64_MIN
+
+#define INT_FAST8_MAX INT8_MAX
+#define INT_FAST16_MAX INT16_MAX
+#define INT_FAST32_MAX INT32_MAX
+#define INT_FAST64_MAX INT64_MAX
+
+#define UINT_FAST8_MAX UINT8_MAX
+#define UINT_FAST16_MAX UINT16_MAX
+#define UINT_FAST32_MAX UINT32_MAX
+#define UINT_FAST64_MAX UINT64_MAX
+
+/* 7.18.2.4  Limits of integer types capable of holding
+    object pointers */ 
+#define INTPTR_MIN INT32_MIN
+#define INTPTR_MAX INT32_MAX
+#define UINTPTR_MAX UINT32_MAX
+
+/* 7.18.2.5  Limits of greatest-width integer types */
+#define INTMAX_MIN INT64_MIN
+#define INTMAX_MAX INT64_MAX
+#define UINTMAX_MAX UINT64_MAX
+
+/* 7.18.3  Limits of other integer types */
+#define PTRDIFF_MIN INT32_MIN
+#define PTRDIFF_MAX INT32_MAX
+
+#define SIG_ATOMIC_MIN INT32_MIN
+#define SIG_ATOMIC_MAX INT32_MAX
+
+#define SIZE_MAX UINT32_MAX
+
+#ifndef WCHAR_MIN  /* also in wchar.h */ 
+#define WCHAR_MIN 0
+#define WCHAR_MAX 0xffff /* UINT16_MAX */
+#endif
+
+/*
+ * wint_t is unsigned short for compatibility with MS runtime
+ */
+#define WINT_MIN 0
+#define WINT_MAX 0xffff /* UINT16_MAX */
+
+#endif /* !defined ( __cplusplus) || defined __STDC_LIMIT_MACROS */
+
+
+/* 7.18.4  Macros for integer constants */
+#if !defined ( __cplusplus) || defined (__STDC_CONSTANT_MACROS)
+
+/* 7.18.4.1  Macros for minimum-width integer constants
+
+    Accoding to Douglas Gwyn <gwyn@arl.mil>:
+	"This spec was changed in ISO/IEC 9899:1999 TC1; in ISO/IEC
+	9899:1999 as initially published, the expansion was required
+	to be an integer constant of precisely matching type, which
+	is impossible to accomplish for the shorter types on most
+	platforms, because C99 provides no standard way to designate
+	an integer constant with width less than that of type int.
+	TC1 changed this to require just an integer constant
+	*expression* with *promoted* type."
+*/
+
+#define INT8_C(val) ((int8_t) + (val))
+#define UINT8_C(val) ((uint8_t) + (val##U))
+#define INT16_C(val) ((int16_t) + (val))
+#define UINT16_C(val) ((uint16_t) + (val##U))
+
+#define INT32_C(val) val##L
+#define UINT32_C(val) val##UL
+#define INT64_C(val) val##LL
+#define UINT64_C(val) val##ULL
+
+/* 7.18.4.2  Macros for greatest-width integer constants */
+#define INTMAX_C(val)  INT64_C(val)
+#define UINTMAX_C(val) UINT64_C(val)
+
+#endif  /* !defined ( __cplusplus) || defined __STDC_CONSTANT_MACROS */
+
+#endif