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UnitTest: Remove the old asin and sin/cos approximation experiments
They only printed comparisons against libm and checked nothing. The VFPU functions are exact now and have their own tests. Co-Authored-By: Claude Opus 5.5 (1M context) <[email protected]>
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Henrik RydgårdandClaude Opus 5.5 committed
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@@ -181,196 +181,6 @@ bool System_AudioRecordingState() { return false; }
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#define M_PI_2 1.57079632679489661923
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#endif
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// asin acos atan: https://github.com/michaldrobot/ShaderFastLibs/blob/master/ShaderFastMathLib.h
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// TODO:
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// Fast approximate sincos for NEON
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// http://blog.julien.cayzac.name/2009/12/fast-sinecosine-for-armv7neon.html
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// Fast sincos
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// http://www.dspguru.com/dsp/tricks/parabolic-approximation-of-sin-and-cos
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// minimax (surprisingly terrible! something must be wrong)
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// double asin_plus_sqrtthing = .9998421793 + (1.012386649 + (-.6575341673 + .8999841642 + (-1.669668977 + (1.571945105 - .5860008052 * x) * x) * x) * x) * x;
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// VERY good. 6 MAD, one division.
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// double asin_plus_sqrtthing = (1.807607311 + (.191900116 + (-2.511278506 + (1.062519236 + (-.3572142480 + .1087063463 * x) * x) * x) * x) * x) / (1.807601897 - 1.615203794 * x);
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// float asin_plus_sqrtthing_correct_ends =
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// (1.807607311f + (.191900116f + (-2.511278506f + (1.062519236f + (-.3572142480f + .1087063463f * x) * x) * x) * x) * x) / (1.807607311f - 1.615195094 * x);
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// Unfortunately this is very serial.
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// At least there are only 8 constants needed - load them into two low quads and go to town.
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// For every step, VDUP the constant into a new register (out of two alternating), then VMLA or VFMA into it.
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// http://www.ecse.rpi.edu/~wrf/Research/Short_Notes/arcsin/
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// minimax polynomial rational approx, pretty good, get four digits consistently.
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// unfortunately fastasin(1.0) / M_PI_2 != 1.0f, but it's pretty close.
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float fastasin(double x) {
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float sign = x >= 0.0f ? 1.0f : -1.0f;
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x = fabs(x);
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float sqrtthing = sqrt(1.0f - x * x);
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// note that the sqrt can run parallel while we do the rest
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// if the hardware supports it
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float y = -.3572142480f + .1087063463f * x;
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y = y * x + 1.062519236f;
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y = y * x + -2.511278506f;
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y = y * x + .191900116f;
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y = y * x + 1.807607311f;
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y /= (1.807607311f - 1.615195094 * x);
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return sign * (y - sqrtthing);
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}
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double atan_66s(double x) {
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const double c1=1.6867629106;
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const double c2=0.4378497304;
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const double c3=1.6867633134;
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double x2; // The input argument squared
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x2 = x * x;
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return (x*(c1 + x2*c2)/(c3 + x2));
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}
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// Terrible.
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double fastasin2(double x) {
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return atan_66s(x / sqrt(1 - x * x));
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}
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// Also terrible.
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float fastasin3(float x) {
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return x + x * x * x * x * x * 0.4971;
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}
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// Great! This is the one we'll use. Can be easily rescaled to get the right range for free.
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// http://mathforum.org/library/drmath/view/54137.html
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// http://www.musicdsp.org/showone.php?id=115
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float fastasin4(float x) {
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float sign = x >= 0.0f ? 1.0f : -1.0f;
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x = fabs(x);
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x = M_PI/2 - sqrtf(1.0f - x) * (1.5707288 + -0.2121144*x + 0.0742610*x*x + -0.0187293*x*x*x);
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return sign * x;
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}
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// Or this:
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float fastasin5(float x)
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{
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float sign = x >= 0.0f ? 1.0f : -1.0f;
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x = fabs(x);
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float fRoot = sqrtf(1.0f - x);
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float fResult = 0.0742610f + -0.0187293f * x;
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fResult = -0.2121144f + fResult * x;
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fResult = 1.5707288f + fResult * x;
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fResult = M_PI/2 - fRoot*fResult;
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return sign * fResult;
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}
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// This one is unfortunately not very good. But lets us avoid PI entirely
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// thanks to the special arguments of the PSP functions.
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// http://www.dspguru.com/dsp/tricks/parabolic-approximation-of-sin-and-cos
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#define C 0.70710678118654752440f // 1.0f / sqrt(2.0f)
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// Some useful constants (PI and <math.h> are not part of algo)
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#define BITSPERQUARTER (20)
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void fcs(float angle, float &sinout, float &cosout) {
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int phasein = angle * (1 << BITSPERQUARTER);
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// Modulo phase into quarter, convert to float 0..1
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float modphase = (phasein & ((1<<BITSPERQUARTER)-1)) * (1.0f / (1<<BITSPERQUARTER));
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// Extract quarter bits
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int quarter = phasein >> BITSPERQUARTER;
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// Recognize quarter
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if (!quarter) {
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// First quarter, angle = 0 .. pi/2
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float x = modphase - 0.5f; // 1 sub
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float temp = (2 - 4*C)*x*x + C; // 2 mul, 1 add
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sinout = temp + x; // 1 add
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cosout = temp - x; // 1 sub
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} else if (quarter == 1) {
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// Second quarter, angle = pi/2 .. pi
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float x = 0.5f - modphase; // 1 sub
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float temp = (2 - 4*C)*x*x + C; // 2 mul, 1 add
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sinout = x + temp; // 1 add
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cosout = x - temp; // 1 sub
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} else if (quarter == 2) {
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// Third quarter, angle = pi .. 1.5pi
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float x = modphase - 0.5f; // 1 sub
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float temp = (4*C - 2)*x*x - C; // 2 mul, 1 sub
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sinout = temp - x; // 1 sub
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cosout = temp + x; // 1 add
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} else if (quarter == 3) {
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// Fourth quarter, angle = 1.5pi..2pi
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float x = modphase - 0.5f; // 1 sub
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float temp = (2 - 4*C)*x*x + C; // 2 mul, 1 add
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sinout = x - temp; // 1 sub
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cosout = x + temp; // 1 add
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}
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}
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#undef C
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const float PI_SQR = 9.86960440108935861883449099987615114f;
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//https://code.google.com/p/math-neon/source/browse/trunk/math_floorf.c?r=18
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// About 2 correct decimals. Not great.
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void fcs2(float theta, float &outsine, float &outcosine) {
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float gamma = theta + 1;
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gamma += 2;
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gamma /= 4;
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theta += 2;
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theta /= 4;
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//theta -= (float)(int)theta;
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//gamma -= (float)(int)gamma;
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theta -= floorf(theta);
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gamma -= floorf(gamma);
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theta *= 4;
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theta -= 2;
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gamma *= 4;
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gamma -= 2;
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float x = 2 * gamma - gamma * fabs(gamma);
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float y = 2 * theta - theta * fabs(theta);
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const float P = 0.225f;
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outsine = P * (y * fabsf(y) - y) + y; // Q * y + P * y * abs(y)
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outcosine = P * (x * fabsf(x) - x) + x; // Q * y + P * y * abs(y)
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}
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void fastsincos(float x, float &sine, float &cosine) {
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fcs2(x, sine, cosine);
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}
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bool TestSinCos() {
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for (int i = -100; i <= 100; i++) {
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float f = i / 30.0f;
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// The PSP sin/cos take as argument angle * M_PI_2.
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// We need to match that.
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float slowsin = sinf(f * M_PI_2), slowcos = cosf(f * M_PI_2);
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float fastsin, fastcos;
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fastsincos(f, fastsin, fastcos);
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if (g_testLog) {
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printf("%f: slow: %0.8f, %0.8f fast: %0.8f, %0.8f\n", f, slowsin, slowcos, fastsin, fastcos);
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}
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}
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return true;
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}
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bool TestAsin() {
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for (int i = -100; i <= 100; i++) {
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float f = i / 100.0f;
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float slowval = asinf(f) / M_PI_2;
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float fastval = fastasin5(f) / M_PI_2;
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if (g_testLog) {
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printf("slow: %0.16f fast: %0.16f\n", slowval, fastval);
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}
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float diff = fabsf(slowval - fastval);
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// EXPECT_TRUE(diff < 0.0001f);
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}
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// EXPECT_TRUE(fastasin(1.0) / M_PI_2 <= 1.0f);
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return true;
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}
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bool TestMathUtil() {
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EXPECT_FALSE(my_isinf(1.0));
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volatile float zero = 0.0f;
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@@ -3233,8 +3043,6 @@ TestItem availableTests[] = {
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TEST_ITEM(LoongArch64Emitter),
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#endif
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TEST_ITEM(VertexJit),
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TEST_ITEM(Asin),
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TEST_ITEM(SinCos),
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TEST_ITEM(VFPUSinCos),
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TEST_ITEM(VFPUDot),
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TEST_ITEM(MathUtil),
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