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authorJames Cook <james@lindenlab.com>2007-01-02 08:33:20 +0000
committerJames Cook <james@lindenlab.com>2007-01-02 08:33:20 +0000
commit420b91db29485df39fd6e724e782c449158811cb (patch)
treeb471a94563af914d3ed3edd3e856d21cb1b69945 /indra/llmath/llmath.h
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+/**
+ * @file llmath.h
+ * @brief Useful math constants and macros.
+ *
+ * Copyright (c) 2000-$CurrentYear$, Linden Research, Inc.
+ * $License$
+ */
+
+#ifndef LLMATH_H
+#define LLMATH_H
+
+#include <cmath>
+#include <math.h>
+#include <stdlib.h>
+
+#include "lldefs.h"
+
+// work around for Windows & older gcc non-standard function names.
+#if LL_WINDOWS
+#define llisnan(val) _isnan(val)
+#define llfinite(val) _finite(val)
+#elif (LL_LINUX && __GNUC__ <= 2)
+#define llisnan(val) isnan(val)
+#define llfinite(val) isfinite(val)
+#else
+#define llisnan(val) std::isnan(val)
+#define llfinite(val) std::isfinite(val)
+#endif
+
+// Single Precision Floating Point Routines
+#ifndef fsqrtf
+#define fsqrtf(x) ((F32)sqrt((F64)(x)))
+#endif
+#ifndef sqrtf
+#define sqrtf(x) ((F32)sqrt((F64)(x)))
+#endif
+
+#ifndef cosf
+#define cosf(x) ((F32)cos((F64)(x)))
+#endif
+#ifndef sinf
+#define sinf(x) ((F32)sin((F64)(x)))
+#endif
+#ifndef tanf
+#define tanf(x) ((F32)tan((F64)(x)))
+#endif
+#ifndef acosf
+#define acosf(x) ((F32)acos((F64)(x)))
+#endif
+
+#ifndef powf
+#define powf(x,y) ((F32)pow((F64)(x),(F64)(y)))
+#endif
+
+const F32 GRAVITY = -9.8f;
+
+// mathematical constants
+const F32 F_PI = 3.1415926535897932384626433832795f;
+const F32 F_TWO_PI = 6.283185307179586476925286766559f;
+const F32 F_PI_BY_TWO = 1.5707963267948966192313216916398f;
+const F32 F_SQRT2 = 1.4142135623730950488016887242097f;
+const F32 F_SQRT3 = 1.73205080756888288657986402541f;
+const F32 OO_SQRT2 = 0.7071067811865475244008443621049f;
+const F32 DEG_TO_RAD = 0.017453292519943295769236907684886f;
+const F32 RAD_TO_DEG = 57.295779513082320876798154814105f;
+const F32 F_APPROXIMATELY_ZERO = 0.00001f;
+const F32 F_LN2 = 0.69314718056f;
+const F32 OO_LN2 = 1.4426950408889634073599246810019f;
+
+// BUG: Eliminate in favor of F_APPROXIMATELY_ZERO above?
+const F32 FP_MAG_THRESHOLD = 0.0000001f;
+
+// TODO: Replace with logic like is_approx_equal
+inline BOOL is_approx_zero( F32 f ) { return (-F_APPROXIMATELY_ZERO < f) && (f < F_APPROXIMATELY_ZERO); }
+
+inline BOOL is_approx_equal(F32 x, F32 y)
+{
+ const S32 COMPARE_MANTISSA_UP_TO_BIT = 0x02;
+ return (abs((S32) ((U32&)x - (U32&)y) ) < COMPARE_MANTISSA_UP_TO_BIT);
+}
+
+inline S32 llabs(const S32 a)
+{
+ return S32(labs(a));
+}
+
+inline F32 llabs(const F32 a)
+{
+ return F32(fabs(a));
+}
+
+inline F64 llabs(const F64 a)
+{
+ return F64(fabs(a));
+}
+
+inline S32 lltrunc( F32 f )
+{
+#if LL_WINDOWS && !defined( __INTEL_COMPILER )
+ // Avoids changing the floating point control word.
+ // Add or subtract 0.5 - epsilon and then round
+ const static U32 zpfp[] = { 0xBEFFFFFF, 0x3EFFFFFF };
+ S32 result;
+ __asm {
+ fld f
+ mov eax, f
+ shr eax, 29
+ and eax, 4
+ fadd dword ptr [zpfp + eax]
+ fistp result
+ }
+ return result;
+#else
+ return (S32)f;
+#endif
+}
+
+inline S32 lltrunc( F64 f )
+{
+ return (S32)f;
+}
+
+inline S32 llfloor( F32 f )
+{
+#if LL_WINDOWS && !defined( __INTEL_COMPILER )
+ // Avoids changing the floating point control word.
+ // Accurate (unlike Stereopsis version) for all values between S32_MIN and S32_MAX and slightly faster than Stereopsis version.
+ // Add -(0.5 - epsilon) and then round
+ const U32 zpfp = 0xBEFFFFFF;
+ S32 result;
+ __asm {
+ fld f
+ fadd dword ptr [zpfp]
+ fistp result
+ }
+ return result;
+#else
+ return (S32)floor(f);
+#endif
+}
+
+
+inline S32 llceil( F32 f )
+{
+ // This could probably be optimized, but this works.
+ return (S32)ceil(f);
+}
+
+
+#ifndef BOGUS_ROUND
+// Use this round. Does an arithmetic round (0.5 always rounds up)
+inline S32 llround(const F32 val)
+{
+ return llfloor(val + 0.5f);
+}
+
+#else // BOGUS_ROUND
+// Old llround implementation - does banker's round (toward nearest even in the case of a 0.5.
+// Not using this because we don't have a consistent implementation on both platforms, use
+// llfloor(val + 0.5f), which is consistent on all platforms.
+inline S32 llround(const F32 val)
+{
+ #if LL_WINDOWS
+ // Note: assumes that the floating point control word is set to rounding mode (the default)
+ S32 ret_val;
+ _asm fld val
+ _asm fistp ret_val;
+ return ret_val;
+ #elif LL_LINUX
+ // Note: assumes that the floating point control word is set
+ // to rounding mode (the default)
+ S32 ret_val;
+ __asm__ __volatile__( "flds %1 \n\t"
+ "fistpl %0 \n\t"
+ : "=m" (ret_val)
+ : "m" (val) );
+ return ret_val;
+ #else
+ return llfloor(val + 0.5f);
+ #endif
+}
+
+// A fast arithmentic round on intel, from Laurent de Soras http://ldesoras.free.fr
+inline int round_int(double x)
+{
+ const float round_to_nearest = 0.5f;
+ int i;
+ __asm
+ {
+ fld x
+ fadd st, st (0)
+ fadd round_to_nearest
+ fistp i
+ sar i, 1
+ }
+ return (i);
+}
+#endif // BOGUS_ROUND
+
+inline F32 llround( F32 val, F32 nearest )
+{
+ return F32(floor(val * (1.0f / nearest) + 0.5f)) * nearest;
+}
+
+inline F64 llround( F64 val, F64 nearest )
+{
+ return F64(floor(val * (1.0 / nearest) + 0.5)) * nearest;
+}
+
+// these provide minimum peak error
+//
+// avg error = -0.013049
+// peak error = -31.4 dB
+// RMS error = -28.1 dB
+
+const F32 FAST_MAG_ALPHA = 0.960433870103f;
+const F32 FAST_MAG_BETA = 0.397824734759f;
+
+// these provide minimum RMS error
+//
+// avg error = 0.000003
+// peak error = -32.6 dB
+// RMS error = -25.7 dB
+//
+//const F32 FAST_MAG_ALPHA = 0.948059448969f;
+//const F32 FAST_MAG_BETA = 0.392699081699f;
+
+inline F32 fastMagnitude(F32 a, F32 b)
+{
+ a = (a > 0) ? a : -a;
+ b = (b > 0) ? b : -b;
+ return(FAST_MAG_ALPHA * llmax(a,b) + FAST_MAG_BETA * llmin(a,b));
+}
+
+
+
+////////////////////
+//
+// Fast F32/S32 conversions
+//
+// Culled from www.stereopsis.com/FPU.html
+
+const F64 LL_DOUBLE_TO_FIX_MAGIC = 68719476736.0*1.5; //2^36 * 1.5, (52-_shiftamt=36) uses limited precisicion to floor
+const S32 LL_SHIFT_AMOUNT = 16; //16.16 fixed point representation,
+
+// Endian dependent code
+#ifdef LL_LITTLE_ENDIAN
+ #define LL_EXP_INDEX 1
+ #define LL_MAN_INDEX 0
+#else
+ #define LL_EXP_INDEX 0
+ #define LL_MAN_INDEX 1
+#endif
+
+/* Deprecated: use llround(), lltrunc(), or llfloor() instead
+// ================================================================================================
+// Real2Int
+// ================================================================================================
+inline S32 F64toS32(F64 val)
+{
+ val = val + LL_DOUBLE_TO_FIX_MAGIC;
+ return ((S32*)&val)[LL_MAN_INDEX] >> LL_SHIFT_AMOUNT;
+}
+
+// ================================================================================================
+// Real2Int
+// ================================================================================================
+inline S32 F32toS32(F32 val)
+{
+ return F64toS32 ((F64)val);
+}
+*/
+
+////////////////////////////////////////////////
+//
+// Fast exp and log
+//
+
+// Implementation of fast exp() approximation (from a paper by Nicol N. Schraudolph
+// http://www.inf.ethz.ch/~schraudo/pubs/exp.pdf
+static union
+{
+ double d;
+ struct
+ {
+#ifdef LL_LITTLE_ENDIAN
+ S32 j, i;
+#else
+ S32 i, j;
+#endif
+ } n;
+} LLECO; // not sure what the name means
+
+#define LL_EXP_A (1048576 * OO_LN2) // use 1512775 for integer
+#define LL_EXP_C (60801) // this value of C good for -4 < y < 4
+
+#define LL_FAST_EXP(y) (LLECO.n.i = llround(F32(LL_EXP_A*(y))) + (1072693248 - LL_EXP_C), LLECO.d)
+
+
+
+inline F32 llfastpow(const F32 x, const F32 y)
+{
+ return (F32)(LL_FAST_EXP(y * log(x)));
+}
+
+
+inline F32 snap_to_sig_figs(F32 foo, S32 sig_figs)
+{
+ // compute the power of ten
+ F32 bar = 1.f;
+ for (S32 i = 0; i < sig_figs; i++)
+ {
+ bar *= 10.f;
+ }
+
+ foo = (F32)llround(foo * bar);
+
+ // shift back
+ foo /= bar;
+ return foo;
+}
+
+inline F32 lerp(F32 a, F32 b, F32 u)
+{
+ return a + ((b - a) * u);
+}
+
+inline F32 lerp2d(F32 x00, F32 x01, F32 x10, F32 x11, F32 u, F32 v)
+{
+ F32 a = x00 + (x01-x00)*u;
+ F32 b = x10 + (x11-x10)*u;
+ F32 r = a + (b-a)*v;
+ return r;
+}
+
+inline F32 ramp(F32 x, F32 a, F32 b)
+{
+ return (a == b) ? 0.0f : ((a - x) / (a - b));
+}
+
+inline F32 rescale(F32 x, F32 x1, F32 x2, F32 y1, F32 y2)
+{
+ return lerp(y1, y2, ramp(x, x1, x2));
+}
+
+inline F32 clamp_rescale(F32 x, F32 x1, F32 x2, F32 y1, F32 y2)
+{
+ if (y1 < y2)
+ {
+ return llclamp(rescale(x,x1,x2,y1,y2),y1,y2);
+ }
+ else
+ {
+ return llclamp(rescale(x,x1,x2,y1,y2),y2,y1);
+ }
+}
+
+
+inline F32 cubic_step( F32 x, F32 x0, F32 x1, F32 s0, F32 s1 )
+{
+ if (x <= x0)
+ return s0;
+
+ if (x >= x1)
+ return s1;
+
+ F32 f = (x - x0) / (x1 - x0);
+
+ return s0 + (s1 - s0) * (f * f) * (3.0f - 2.0f * f);
+}
+
+inline F32 cubic_step( F32 x )
+{
+ x = llclampf(x);
+
+ return (x * x) * (3.0f - 2.0f * x);
+}
+
+inline F32 quadratic_step( F32 x, F32 x0, F32 x1, F32 s0, F32 s1 )
+{
+ if (x <= x0)
+ return s0;
+
+ if (x >= x1)
+ return s1;
+
+ F32 f = (x - x0) / (x1 - x0);
+ F32 f_squared = f * f;
+
+ return (s0 * (1.f - f_squared)) + ((s1 - s0) * f_squared);
+}
+
+inline F32 llsimple_angle(F32 angle)
+{
+ while(angle <= -F_PI)
+ angle += F_TWO_PI;
+ while(angle > F_PI)
+ angle -= F_TWO_PI;
+ return angle;
+}
+
+#endif