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math: remove unused trig code. 

Let’s be honest, I’m never gonna use it in its current form.
legacy
Sam Hocevar 6 years ago
parent
8141a4e6f7
commit
67dd817aa2
12 changed files with 10 additions and 759 deletions
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  1. +1
    -2
      doc/samples/Makefile.am
  2. +0
    -192
      doc/samples/benchmark/trig.cpp
  3. +0
    -16
      doc/samples/benchsuite.cpp
  4. +0
    -1
      doc/samples/benchsuite.vcxproj
  5. +2
    -2
      src/Makefile.am
  6. +0
    -1
      src/lol-core.vcxproj
  7. +0
    -3
      src/lol-core.vcxproj.filter
  8. +0
    -2
      src/lol/base/features.h
  9. +0
    -11
      src/lol/math/functions.h
  10. +0
    -387
      src/math/trig.cpp
  11. +7
    -0
      src/t/math/numbers.cpp
  12. +0
    -142
      src/t/math/trig.cpp

+ 1
- 2
doc/samples/Makefile.am View File

@@ -21,8 +21,7 @@ bluenoise_CPPFLAGS = $(AM_CPPFLAGS)
bluenoise_DEPENDENCIES = @LOL_DEPS@ bluenoise_DEPENDENCIES = @LOL_DEPS@


benchsuite_SOURCES = benchsuite.cpp \ benchsuite_SOURCES = benchsuite.cpp \
benchmark/vector.cpp benchmark/half.cpp benchmark/trig.cpp \
benchmark/real.cpp
benchmark/vector.cpp benchmark/half.cpp benchmark/real.cpp
benchsuite_CPPFLAGS = $(AM_CPPFLAGS) benchsuite_CPPFLAGS = $(AM_CPPFLAGS)
benchsuite_DEPENDENCIES = @LOL_DEPS@ benchsuite_DEPENDENCIES = @LOL_DEPS@




+ 0
- 192
doc/samples/benchmark/trig.cpp View File

@@ -1,192 +0,0 @@
//
// Lol Engine — Benchmark program
//
// Copyright © 2005—2018 Sam Hocevar <sam@hocevar.net>
//
// This program is free software. It comes without any warranty, to
// the extent permitted by applicable law. You can redistribute it
// and/or modify it under the terms of the Do What the Fuck You Want
// to Public License, Version 2, as published by the WTFPL Task Force.
// See http://www.wtfpl.net/ for more details.
//

#if HAVE_CONFIG_H
# include "config.h"
#endif

#include <cstdio>

#if HAVE_FASTMATH_H
# include <fastmath.h>
#endif

#include <lol/engine.h>

using namespace lol;

static size_t const TRIG_TABLE_SIZE = 128 * 1024;
static size_t const TRIG_RUNS = 50;

void bench_trig(int mode)
{
float result[12] = { 0.0f };
lol::timer timer;

/* Set up tables */
float *pf = new float[TRIG_TABLE_SIZE];
float *pf2 = new float[TRIG_TABLE_SIZE];
float *pf3 = new float[TRIG_TABLE_SIZE];

for (size_t run = 0; run < TRIG_RUNS; run++)
{
switch (mode)
{
case 1:
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
pf[i] = rand(-1e5f, 1e5f);
break;
case 2:
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
pf[i] = rand(-F_PI, F_PI);
break;
case 3:
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
pf[i] = rand(-1e-2f, 1e-2f);
break;
}

/* Sin */
timer.get();
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
#if __GNUC__ && !__SNC__
pf2[i] = __builtin_sinf(pf[i]);
#else
pf2[i] = sinf(pf[i]);
#endif
result[0] += timer.get();

/* Fast sin */
timer.get();
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
#if HAVE_FASTMATH_H && !__native_client__ && !EMSCRIPTEN
pf2[i] = f_sinf(pf[i]);
#else
pf2[i] = sinf(pf[i]);
#endif
result[1] += timer.get();

/* Lol sin */
timer.get();
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
pf2[i] = lol_sin(pf[i]);
result[2] += timer.get();

/* Cos */
timer.get();
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
#if __GNUC__ && !__SNC__
pf2[i] = __builtin_cosf(pf[i]);
#else
pf2[i] = cosf(pf[i]);
#endif
result[3] += timer.get();

/* Fast cos */
timer.get();
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
#if HAVE_FASTMATH_H && !__native_client__ && !EMSCRIPTEN
pf2[i] = f_cosf(pf[i]);
#else
pf2[i] = cosf(pf[i]);
#endif
result[4] += timer.get();

/* Lol cos */
timer.get();
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
pf2[i] = lol_cos(pf[i]);
result[5] += timer.get();

/* Sin & cos */
timer.get();
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
{
#if __GNUC__ && !__SNC__
pf2[i] = __builtin_sinf(pf[i]);
pf3[i] = __builtin_cosf(pf[i]);
#else
pf2[i] = sinf(pf[i]);
pf3[i] = cosf(pf[i]);
#endif
}
result[6] += timer.get();

/* Fast sin & cos */
timer.get();
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
{
#if HAVE_FASTMATH_H && !__native_client__ && !EMSCRIPTEN
pf2[i] = f_sinf(pf[i]);
pf3[i] = f_cosf(pf[i]);
#else
pf2[i] = sinf(pf[i]);
pf3[i] = cosf(pf[i]);
#endif
}
result[7] += timer.get();

/* Lol sincos */
timer.get();
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
lol_sincos(pf[i], &pf2[i], &pf3[i]);
result[8] += timer.get();

/* Tan */
timer.get();
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
#if __GNUC__ && !__SNC__
pf2[i] = __builtin_tanf(pf[i]);
#else
pf2[i] = tanf(pf[i]);
#endif
result[9] += timer.get();

/* Fast tan */
timer.get();
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
#if HAVE_FASTMATH_H && !__native_client__ && !EMSCRIPTEN
pf2[i] = f_tanf(pf[i]);
#else
pf2[i] = tanf(pf[i]);
#endif
result[10] += timer.get();

/* Lol tan */
timer.get();
for (size_t i = 0; i < TRIG_TABLE_SIZE; i++)
pf2[i] = lol_tan(pf[i]);
result[11] += timer.get();
}

delete[] pf;
delete[] pf2;
delete[] pf3;

for (size_t i = 0; i < sizeof(result) / sizeof(*result); i++)
result[i] *= 1e9f / (TRIG_TABLE_SIZE * TRIG_RUNS);

msg::info(" ns/elem\n");
msg::info("float = sinf(float) %7.3f\n", result[0]);
msg::info("float = f_sinf(float) %7.3f\n", result[1]);
msg::info("float = lol_sin(float) %7.3f\n", result[2]);
msg::info("float = cosf(float) %7.3f\n", result[3]);
msg::info("float = f_cosf(float) %7.3f\n", result[4]);
msg::info("float = lol_cos(float) %7.3f\n", result[5]);
msg::info("float = sinf,cosf(float) %7.3f\n", result[6]);
msg::info("float = f_sinf,f_cosf(float) %7.3f\n", result[7]);
msg::info("float = lol_sincos(float) %7.3f\n", result[8]);
msg::info("float = tanf(float) %7.3f\n", result[9]);
msg::info("float = f_tanf(float) %7.3f\n", result[10]);
msg::info("float = lol_tanf(float) %7.3f\n", result[11]);
}


+ 0
- 16
doc/samples/benchsuite.cpp View File

@@ -21,7 +21,6 @@
using namespace lol; using namespace lol;


void bench_real(int mode); void bench_real(int mode);
void bench_trig(int mode);
void bench_matrix(int mode); void bench_matrix(int mode);
void bench_half(int mode); void bench_half(int mode);


@@ -34,21 +33,6 @@ int main(int argc, char **argv)
msg::info("-----------------------\n"); msg::info("-----------------------\n");
bench_real(1); bench_real(1);


msg::info("--------------------------\n");
msg::info(" Trigonometry [-1e5, 1e5]\n");
msg::info("--------------------------\n");
bench_trig(1);

msg::info("------------------------\n");
msg::info(" Trigonometry [-pi, pi]\n");
msg::info("------------------------\n");
bench_trig(2);

msg::info("----------------------------\n");
msg::info(" Trigonometry [-1e-2, 1e-2]\n");
msg::info("----------------------------\n");
bench_trig(3);

msg::info("----------------------------\n"); msg::info("----------------------------\n");
msg::info(" Float matrices [-2.0, 2.0]\n"); msg::info(" Float matrices [-2.0, 2.0]\n");
msg::info("----------------------------\n"); msg::info("----------------------------\n");


+ 0
- 1
doc/samples/benchsuite.vcxproj View File

@@ -33,7 +33,6 @@
<ItemGroup> <ItemGroup>
<ClCompile Include="benchmark\half.cpp" /> <ClCompile Include="benchmark\half.cpp" />
<ClCompile Include="benchmark\real.cpp" /> <ClCompile Include="benchmark\real.cpp" />
<ClCompile Include="benchmark\trig.cpp" />
<ClCompile Include="benchmark\vector.cpp" /> <ClCompile Include="benchmark\vector.cpp" />
<ClCompile Include="benchsuite.cpp" /> <ClCompile Include="benchsuite.cpp" />
</ItemGroup> </ItemGroup>


+ 2
- 2
src/Makefile.am View File

@@ -92,8 +92,8 @@ liblol_core_sources = \
\ \
base/assert.cpp base/log.cpp base/string.cpp base/enum.cpp \ base/assert.cpp base/log.cpp base/string.cpp base/enum.cpp \
\ \
math/vector.cpp math/matrix.cpp math/transform.cpp math/trig.cpp \
math/constants.cpp math/geometry.cpp math/real.cpp math/half.cpp \
math/vector.cpp math/matrix.cpp math/transform.cpp math/half.cpp \
math/constants.cpp math/geometry.cpp math/real.cpp \
\ \
gpu/shader.cpp gpu/indexbuffer.cpp gpu/vertexbuffer.cpp \ gpu/shader.cpp gpu/indexbuffer.cpp gpu/vertexbuffer.cpp \
gpu/framebuffer.cpp gpu/texture.cpp gpu/renderer.cpp \ gpu/framebuffer.cpp gpu/texture.cpp gpu/renderer.cpp \


+ 0
- 1
src/lol-core.vcxproj View File

@@ -161,7 +161,6 @@
<ClCompile Include="math\matrix.cpp" /> <ClCompile Include="math\matrix.cpp" />
<ClCompile Include="math\real.cpp" /> <ClCompile Include="math\real.cpp" />
<ClCompile Include="math\transform.cpp" /> <ClCompile Include="math\transform.cpp" />
<ClCompile Include="math\trig.cpp" />
<ClCompile Include="math\vector.cpp" /> <ClCompile Include="math\vector.cpp" />
<ClCompile Include="mesh\mesh.cpp" /> <ClCompile Include="mesh\mesh.cpp" />
<ClCompile Include="mesh\primitivemesh.cpp" /> <ClCompile Include="mesh\primitivemesh.cpp" />


+ 0
- 3
src/lol-core.vcxproj.filter View File

@@ -141,9 +141,6 @@
<ClCompile Include="math\transform.cpp"> <ClCompile Include="math\transform.cpp">
<Filter>math</Filter> <Filter>math</Filter>
</ClCompile> </ClCompile>
<ClCompile Include="math\trig.cpp">
<Filter>math</Filter>
</ClCompile>
<ClCompile Include="math\vector.cpp"> <ClCompile Include="math\vector.cpp">
<Filter>math</Filter> <Filter>math</Filter>
</ClCompile> </ClCompile>


+ 0
- 2
src/lol/base/features.h View File

@@ -22,8 +22,6 @@
*/ */


#define LOL_FEATURE_THREADS 1 #define LOL_FEATURE_THREADS 1
#define LOL_FEATURE_CHEAP_BRANCHES 1
#define LOL_FEATURE_VERY_CHEAP_BRANCHES 0
#define LOL_FEATURE_VISUAL_STUDIO_THAT_FUCKING_PIECE_OF_SHIT_COMPILER 0 #define LOL_FEATURE_VISUAL_STUDIO_THAT_FUCKING_PIECE_OF_SHIT_COMPILER 0


#if defined EMSCRIPTEN #if defined EMSCRIPTEN


+ 0
- 11
src/lol/math/functions.h View File

@@ -172,17 +172,6 @@ LOL_ATTR_NODISCARD static inline ldouble lerp(ldouble const &a, ldouble const &b
return mix(a, b, x); return mix(a, b, x);
} }


/* These accelerated functions will be merged into the above, one day */
LOL_ATTR_NODISCARD double lol_sin(double);
LOL_ATTR_NODISCARD double lol_cos(double);
LOL_ATTR_NODISCARD double lol_tan(double);
void lol_sincos(double, double*, double*);
void lol_sincos(float, float*, float*);
LOL_ATTR_NODISCARD double lol_asin(double);
LOL_ATTR_NODISCARD double lol_acos(double);
LOL_ATTR_NODISCARD double lol_atan(double);
LOL_ATTR_NODISCARD double lol_atan2(double, double);

/* C++ doesn't define abs() and fmod() for all types; we add these for /* C++ doesn't define abs() and fmod() for all types; we add these for
* convenience to avoid adding complexity to vector.h. */ * convenience to avoid adding complexity to vector.h. */
LOL_ATTR_NODISCARD static inline int8_t abs(int8_t x) { return std::abs(x); } LOL_ATTR_NODISCARD static inline int8_t abs(int8_t x) { return std::abs(x); }


+ 0
- 387
src/math/trig.cpp View File

@@ -1,387 +0,0 @@
//
// Lol Engine
//
// Copyright: (c) 2010-2011 Sam Hocevar <sam@hocevar.net>
// This program is free software; you can redistribute it and/or
// modify it under the terms of the Do What The Fuck You Want To
// Public License, Version 2, as published by Sam Hocevar. See
// http://www.wtfpl.net/ for more details.
//

#include <lol/engine-internal.h>

#if defined HAVE_FASTMATH_H
# include <fastmath.h>
#endif

// Optimisation helpers
#if defined __GNUC__
# define __likely(x) __builtin_expect(!!(x), 1)
# define __unlikely(x) __builtin_expect(!!(x), 0)
# define INLINEATTR __attribute__((always_inline))
# if defined __x86_64__
# define FP_USE(x) __asm__("" : "+x" (x))
# elif defined __i386__ /* FIXME: this isn't good */
# define FP_USE(x) __asm__("" : "+m" (x))
# else
# define FP_USE(x) (void)(x)
# endif
#else
# define __likely(x) x
# define __unlikely(x) x
# define INLINEATTR
# define FP_USE(x) (void)(x)
#endif

namespace lol
{

static const double PI_2 = 1.57079632679489661923132;
static const double PI_4 = 0.785398163397448309615661;
static const double INV_PI = 0.318309886183790671537768;
static const double ROOT3 = 1.73205080756887729352745;

static const double ZERO = 0.0;
static const double ONE = 1.0;
static const double NEG_ONE = -1.0;
static const double HALF = 0.5;
static const double QUARTER = 0.25;
static const double TWO = 2.0;
#if defined __GNUC__
static const double VERY_SMALL_NUMBER = 0x1.0p-128;
#else
static const double VERY_SMALL_NUMBER = 3e-39;
#endif
static const double TWO_EXP_52 = 4503599627370496.0;
static const double TWO_EXP_54 = 18014398509481984.0;

/** sin Taylor series coefficients. */
static const double SC[] =
{
-1.6449340668482264364724e-0, // π^2/3!
+8.1174242528335364363700e-1, // π^4/5!
-1.9075182412208421369647e-1, // π^6/7!
+2.6147847817654800504653e-2, // π^8/9!
-2.3460810354558236375089e-3, // π^10/11!
+1.4842879303107100368487e-4, // π^12/13!
-6.9758736616563804745344e-6, // π^14/15!
+2.5312174041370276513517e-7, // π^16/17!
};

/* Note: the last value should be -1.3878952462213772114468e-7 (ie.
* π^18/18!) but we tweak it in order to get the better average precision
* required for tan() computations when close to π/2+kπ values. */
static const double CC[] =
{
-4.9348022005446793094172e-0, // π^2/2!
+4.0587121264167682181850e-0, // π^4/4!
-1.3352627688545894958753e-0, // π^6/6!
+2.3533063035889320454188e-1, // π^8/8!
-2.5806891390014060012598e-2, // π^10/10!
+1.9295743094039230479033e-3, // π^12/12!
-1.0463810492484570711802e-4, // π^14/14!
+4.3030695870329470072978e-6, // π^16/16!
-1.3777e-7,
};

/* These coefficients use Sloane’s http://oeis.org/A002430 and
* http://oeis.org/A036279 sequences for the Taylor series of tan().
* Note: the last value should be 2.12485922978838540352881e5 (ie.
* 443861162*π^18/1856156927625), but we tweak it in order to get
* sub 1e-11 average precision in a larger range. */
static const double TC[] =
{
3.28986813369645287294483e0, // π^2/3
1.29878788045336582981920e1, // 2*π^4/15
5.18844961612069061254404e1, // 17*π^6/315
2.07509320280908496804928e2, // 62*π^8/2835
8.30024701695986756361561e2, // 1382*π^10/155925
3.32009324029001216460018e3, // 21844*π^12/6081075
1.32803704909665483598490e4, // 929569*π^14/638512875
5.31214808666037709352112e4, // 6404582*π^16/10854718875
2.373e5,
};

static inline double lol_fabs(double x) INLINEATTR;
#if defined __GNUC__
static inline double lol_round(double x) INLINEATTR;
static inline double lol_trunc(double x) INLINEATTR;
#endif

static inline double lol_fabs(double x)
{
#if defined __GNUC__
return __builtin_fabs(x);
#else
using std::fabs;
return fabs(x);
#endif
}

#if defined __GNUC__
static inline double lol_round(double x)
{
return __builtin_round(x);
}

static inline double lol_trunc(double x)
{
return __builtin_trunc(x);
}
#endif

double lol_sin(double x)
{
double absx = lol_fabs(x * INV_PI);

/* If branches are cheap, skip the cycle count when |x| < π/4,
* and only do the Taylor series up to the required precision. */
#if LOL_FEATURE_CHEAP_BRANCHES
if (absx < QUARTER)
{
/* Computing x^4 is one multiplication too many we do, but it helps
* interleave the Taylor series operations a lot better. */
double x2 = absx * absx;
double x4 = x2 * x2;
double sub1 = (SC[3] * x4 + SC[1]) * x4 + ONE;
double sub2 = (SC[4] * x4 + SC[2]) * x4 + SC[0];
double taylor = sub2 * x2 + sub1;
return x * taylor;
}
#endif

/* Wrap |x| to the range [-1, 1] and keep track of the number of
* cycles required. If odd, we'll need to change the sign of the
* result. */
double num_cycles = absx + TWO_EXP_52;
FP_USE(num_cycles); num_cycles -= TWO_EXP_52;

double is_even = TWO * num_cycles - ONE;
FP_USE(is_even); is_even += TWO_EXP_54;
FP_USE(is_even); is_even -= TWO_EXP_54;
FP_USE(is_even);
is_even -= TWO * num_cycles - ONE;
double sign = is_even;

absx -= num_cycles;

/* If branches are very cheap, we have the option to do the Taylor
* series at a much lower degree by splitting. */
#if LOL_FEATURE_VERY_CHEAP_BRANCHES
if (lol_fabs(absx) > QUARTER)
{
sign = (x * absx >= 0.0) ? sign : -sign;

double x1 = HALF - lol_fabs(absx);
double x2 = x1 * x1;
double x4 = x2 * x2;
double sub1 = ((CC[5] * x4 + CC[3]) * x4 + CC[1]) * x4 + ONE;
double sub2 = (CC[4] * x4 + CC[2]) * x4 + CC[0];
double taylor = sub2 * x2 + sub1;

return taylor * sign;
}
#endif

sign *= (x >= 0.0) ? D_PI : -D_PI;

/* Compute a Tailor series for sin() and combine sign information. */
double x2 = absx * absx;
double x4 = x2 * x2;
#if LOL_FEATURE_VERY_CHEAP_BRANCHES
double sub1 = (SC[3] * x4 + SC[1]) * x4 + ONE;
double sub2 = (SC[4] * x4 + SC[2]) * x4 + SC[0];
#else
double sub1 = (((SC[7] * x4 + SC[5]) * x4 + SC[3]) * x4 + SC[1]) * x4 + ONE;
double sub2 = ((SC[6] * x4 + SC[4]) * x4 + SC[2]) * x4 + SC[0];
#endif
double taylor = sub2 * x2 + sub1;

return absx * taylor * sign;
}

double lol_cos(double x)
{
double absx = lol_fabs(x * INV_PI);

#if LOL_FEATURE_CHEAP_BRANCHES
if (absx < QUARTER)
{
double x2 = absx * absx;
double x4 = x2 * x2;
double sub1 = (CC[5] * x4 + CC[3]) * x4 + CC[1];
double sub2 = (CC[4] * x4 + CC[2]) * x4 + CC[0];
double taylor = (sub1 * x2 + sub2) * x2 + ONE;
return taylor;
}
#endif

double num_cycles = absx + TWO_EXP_52;
FP_USE(num_cycles); num_cycles -= TWO_EXP_52;

double is_even = TWO * num_cycles - ONE;
FP_USE(is_even); is_even += TWO_EXP_54;
FP_USE(is_even); is_even -= TWO_EXP_54;
FP_USE(is_even);
is_even -= TWO * num_cycles - ONE;
double sign = is_even;

absx -= num_cycles;

#if LOL_FEATURE_VERY_CHEAP_BRANCHES
if (lol_fabs(absx) > QUARTER)
{
double x1 = HALF - lol_fabs(absx);
double x2 = x1 * x1;
double x4 = x2 * x2;
double sub1 = (SC[3] * x4 + SC[1]) * x4 + ONE;
double sub2 = (SC[4] * x4 + SC[2]) * x4 + SC[0];
double taylor = sub2 * x2 + sub1;

return x1 * taylor * sign * D_PI;
}
#endif

double x2 = absx * absx;
double x4 = x2 * x2;
#if LOL_FEATURE_VERY_CHEAP_BRANCHES
double sub1 = ((CC[5] * x4 + CC[3]) * x4 + CC[1]) * x4 + ONE;
double sub2 = (CC[4] * x4 + CC[2]) * x4 + CC[0];
#else
double sub1 = (((CC[7] * x4 + CC[5]) * x4 + CC[3]) * x4 + CC[1]) * x4 + ONE;
double sub2 = ((CC[6] * x4 + CC[4]) * x4 + CC[2]) * x4 + CC[0];
#endif
double taylor = sub2 * x2 + sub1;

return taylor * sign;
}

void lol_sincos(double x, double *sinx, double *cosx)
{
double absx = lol_fabs(x * INV_PI);

#if LOL_FEATURE_CHEAP_BRANCHES
if (absx < QUARTER)
{
double x2 = absx * absx;
double x4 = x2 * x2;

/* Computing the Taylor series to the 11th order is enough to get
* x * 1e-11 precision, but we push it to the 13th order so that
* tan() has a better precision. */
double subs1 = ((SC[5] * x4 + SC[3]) * x4 + SC[1]) * x4 + ONE;
double subs2 = (SC[4] * x4 + SC[2]) * x4 + SC[0];
double taylors = subs2 * x2 + subs1;
*sinx = x * taylors;

double subc1 = (CC[5] * x4 + CC[3]) * x4 + CC[1];
double subc2 = (CC[4] * x4 + CC[2]) * x4 + CC[0];
double taylorc = (subc1 * x2 + subc2) * x2 + ONE;
*cosx = taylorc;

return;
}
#endif

double num_cycles = absx + TWO_EXP_52;
FP_USE(num_cycles); num_cycles -= TWO_EXP_52;

double is_even = TWO * num_cycles - ONE;
FP_USE(is_even); is_even += TWO_EXP_54;
FP_USE(is_even); is_even -= TWO_EXP_54;
FP_USE(is_even);
is_even -= TWO * num_cycles - ONE;
double sin_sign = is_even;
double cos_sign = is_even;

absx -= num_cycles;

#if LOL_FEATURE_VERY_CHEAP_BRANCHES
if (lol_fabs(absx) > QUARTER)
{
cos_sign = sin_sign;
sin_sign = (x * absx >= 0.0) ? sin_sign : -sin_sign;

double x1 = HALF - lol_fabs(absx);
double x2 = x1 * x1;
double x4 = x2 * x2;

double subs1 = ((CC[5] * x4 + CC[3]) * x4 + CC[1]) * x4 + ONE;
double subs2 = (CC[4] * x4 + CC[2]) * x4 + CC[0];
double taylors = subs2 * x2 + subs1;
*sinx = taylors * sin_sign;

double subc1 = ((SC[5] * x4 + SC[3]) * x4 + SC[1]) * x4 + ONE;
double subc2 = (SC[4] * x4 + SC[2]) * x4 + SC[0];
double taylorc = subc2 * x2 + subc1;
*cosx = x1 * taylorc * cos_sign * D_PI;

return;
}
#endif

sin_sign *= (x >= 0.0) ? D_PI : -D_PI;

double x2 = absx * absx;
double x4 = x2 * x2;
#if LOL_FEATURE_VERY_CHEAP_BRANCHES
double subs1 = ((SC[5] * x4 + SC[3]) * x4 + SC[1]) * x4 + ONE;
double subs2 = (SC[4] * x4 + SC[2]) * x4 + SC[0];
double subc1 = ((CC[5] * x4 + CC[3]) * x4 + CC[1]) * x4 + ONE;
double subc2 = (CC[4] * x4 + CC[2]) * x4 + CC[0];
#else
double subs1 = (((SC[7] * x4 + SC[5]) * x4 + SC[3]) * x4 + SC[1]) * x4 + ONE;
double subs2 = ((SC[6] * x4 + SC[4]) * x4 + SC[2]) * x4 + SC[0];
/* Push Taylor series to the 19th order to enhance tan() accuracy. */
double subc1 = (((CC[7] * x4 + CC[5]) * x4 + CC[3]) * x4 + CC[1]) * x4 + ONE;
double subc2 = (((CC[8] * x4 + CC[6]) * x4 + CC[4]) * x4 + CC[2]) * x4 + CC[0];
#endif
double taylors = subs2 * x2 + subs1;
*sinx = absx * taylors * sin_sign;

double taylorc = subc2 * x2 + subc1;
*cosx = taylorc * cos_sign;
}

void lol_sincos(float x, float *sinx, float *cosx)
{
double x2 = static_cast<double>(x);
double s2, c2;
lol_sincos(x2, &s2, &c2);
*sinx = static_cast<float>(s2);
*cosx = static_cast<float>(c2);
}

double lol_tan(double x)
{
#if LOL_FEATURE_CHEAP_BRANCHES
double absx = lol_fabs(x * INV_PI);

/* This value was determined empirically to ensure an error of no
* more than x * 1e-11 in this range. */
if (absx < 0.163)
{
double x2 = absx * absx;
double x4 = x2 * x2;
double sub1 = (((TC[7] * x4 + TC[5]) * x4
+ TC[3]) * x4 + TC[1]) * x4 + ONE;
double sub2 = (((TC[8] * x4 + TC[6]) * x4
+ TC[4]) * x4 + TC[2]) * x4 + TC[0];
double taylor = sub2 * x2 + sub1;
return x * taylor;
}
#endif

double sinx, cosx;
lol_sincos(x, &sinx, &cosx);

/* Ensure cosx isn't zero. FIXME: we lose the cosx sign here. */
double absc = lol_fabs(cosx);

if (__unlikely(absc < VERY_SMALL_NUMBER))
cosx = VERY_SMALL_NUMBER;
return sinx / cosx;
}

} /* namespace lol */


+ 7
- 0
src/t/math/numbers.cpp View File

@@ -29,6 +29,13 @@ lolunit_declare_fixture(gcd_test)
lolunit_assert_equal(18913, lol::gcd(624129, 2061517)); lolunit_assert_equal(18913, lol::gcd(624129, 2061517));
} }


lolunit_declare_test(gcd_double)
{
lolunit_assert_equal(2.0, lol::gcd(4.0, 6.0));
lolunit_assert_equal(2.5, lol::gcd(5.0, 7.5));
lolunit_assert_equal(0.125, lol::gcd(4.625, 75.0));
}

lolunit_declare_test(gcd_negative) lolunit_declare_test(gcd_negative)
{ {
lolunit_assert_equal(2, lol::gcd(4, -6)); lolunit_assert_equal(2, lol::gcd(4, -6));


+ 0
- 142
src/t/math/trig.cpp View File

@@ -60,148 +60,6 @@ lolunit_declare_fixture(trig_test)
lolunit_assert_doubles_equal(degrees((uint64_t)1), degrees(1.0), 1e-5); lolunit_assert_doubles_equal(degrees((uint64_t)1), degrees(1.0), 1e-5);
lolunit_assert_doubles_equal(degrees((int64_t)1), degrees(1.0), 1e-5); lolunit_assert_doubles_equal(degrees((int64_t)1), degrees(1.0), 1e-5);
} }

lolunit_declare_test(sin)
{
using std::fabs;

for (int i = -10000; i < 10000; i++)
{
double f = (double)i * (1.0 / 1000.0);
#if defined __GNUC__ && !defined __SNC__
double a = __builtin_sin(f);
#else
double a = std::sin(f);
#endif
double b = lol_sin(f);
lolunit_set_context(f);
lolunit_assert_doubles_equal(a, b, fabs(f) * 1e-11);
}

for (int i = -10000; i < 10000; i++)
{
double f = (double)i * (1.0 / 100000.0);
#if defined __GNUC__ && !defined __SNC__
double a = __builtin_sin(f);
#else
double a = std::sin(f);
#endif
double b = lol_sin(f);
lolunit_set_context(f);
lolunit_assert_doubles_equal(a, b, fabs(f) * 1e-11);
}
}

lolunit_declare_test(cos)
{
using std::fabs;

for (int i = -10000; i < 10000; i++)
{
double f = (double)i * (1.0 / 1000.0);
#if defined __GNUC__ && !defined __SNC__
double a = __builtin_cos(f);
#else
double a = std::cos(f);
#endif
double b = lol_cos(f);
lolunit_set_context(f);
lolunit_assert_doubles_equal(a, b, fabs(f) * 1e-11);
}

for (int i = -10000; i < 10000; i++)
{
double f = (double)i * (1.0 / 100000.0);
#if defined __GNUC__ && !defined __SNC__
double a = __builtin_cos(f);
#else
double a = std::cos(f);
#endif
double b = lol_cos(f);
lolunit_set_context(f);
lolunit_assert_doubles_equal(a, b, fabs(f) * 1e-11);
}
}

lolunit_declare_test(sin_cos)
{
using std::fabs;

for (int i = -10000; i < 10000; i++)
{
double f = (double)i * (1.0 / 1000.0);
#if defined __GNUC__ && !defined __SNC__
double a1 = __builtin_sin(f);
double a2 = __builtin_cos(f);
#else
double a1 = std::sin(f);
double a2 = std::cos(f);
#endif
double b1, b2;
lol_sincos(f, &b1, &b2);
lolunit_set_context(f);
lolunit_assert_doubles_equal(a1, b1, fabs(f) * 1e-11);
lolunit_assert_doubles_equal(a2, b2, fabs(f) * 1e-11);
}

for (int i = -10000; i < 10000; i++)
{
double f = (double)i * (1.0 / 100000.0);
#if defined __GNUC__ && !defined __SNC__
double a1 = __builtin_sin(f);
double a2 = __builtin_cos(f);
#else
double a1 = std::sin(f);
double a2 = std::cos(f);
#endif
double b1, b2;
lol_sincos(f, &b1, &b2);
lolunit_set_context(f);
lolunit_assert_doubles_equal(a1, b1, fabs(f) * 1e-11);
lolunit_assert_doubles_equal(a2, b2, fabs(f) * 1e-11);
}
}

lolunit_declare_test(tan)
{
using std::fabs;

for (int i = -100000; i < 100000; i++)
{
double f = (double)i * (1.0 / 10000.0);
#if defined __GNUC__ && !defined __SNC__
double a = __builtin_tan(f);
#else
double a = std::tan(f);
#endif
double b = lol_tan(f);
lolunit_set_context(f);
if (fabs(a) > 1e4)
lolunit_assert_doubles_equal(a, b, fabs(a) * fabs(a) * 1e-11);
else if (fabs(a) > 1.0)
lolunit_assert_doubles_equal(a, b, fabs(a) * 1e-11);
else
lolunit_assert_doubles_equal(a, b, fabs(f) * 1e-11);
}

for (int i = -10000; i < 10000; i++)
{
double f = (double)i * (1.0 / 100000.0);
#if defined __GNUC__ && !defined __SNC__
double a = __builtin_tan(f);
#else
double a = std::tan(f);
#endif
double b = lol_tan(f);
lolunit_set_context(f);
if (fabs(a) > 1e4)
lolunit_assert_doubles_equal(a, b, fabs(a) * fabs(a) * 1e-11);
else if (fabs(a) > 1.0)
lolunit_assert_doubles_equal(a, b, fabs(a) * 1e-11);
else
lolunit_assert_doubles_equal(a, b, fabs(f) * 1e-11);
}
}
}; };


} /* namespace lol */ } /* namespace lol */


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