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Implement fixed-point normalized atan and atan2p functions.
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Change-Id: I12463cdafb44e6bf9a66502a464187e7217e839a
Signed-off-by: Jean-Marc Valin <[email protected]>
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@jmvalin
Yunho Huh authored and jmvalin committed Dec 19, 2024
1 parent f76b610 commit 57a17aa
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Showing 3 changed files with 148 additions and 5 deletions.
66 changes: 65 additions & 1 deletion celt/mathops.h
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Original file line number Diff line number Diff line change
Expand Up @@ -128,7 +128,7 @@ static OPUS_INLINE opus_val32 celt_maxabs32(const opus_val32 *x, int len)
#endif
#endif

#if !defined(FIXED_POINT) || defined(ENABLE_QEXT)
#ifndef FIXED_POINT
/* Calculates the arctangent of x using a Remez approximation of order 15,
* incorporating only odd-powered terms. */
static OPUS_INLINE float celt_atan_norm(float x)
Expand Down Expand Up @@ -176,7 +176,9 @@ static OPUS_INLINE float celt_atan2p_norm(float y, float x)
return 1.f - celt_atan_norm(x / y);
}
}
#endif

#if !defined(FIXED_POINT) || defined(ENABLE_QEXT)
/* Computes estimated cosine values for (PI/2 * x) using only terms with even
* exponents. */
static OPUS_INLINE float celt_cos_norm2(float x)
Expand Down Expand Up @@ -521,6 +523,68 @@ opus_val32 celt_rcp(opus_val32 x);
opus_val32 frac_div32_q29(opus_val32 a, opus_val32 b);
opus_val32 frac_div32(opus_val32 a, opus_val32 b);

/* Computes atan(x) multiplied by 2/PI. The input value (x) should be within the
* range of -1 to 1 and represented in Q30 format. The function will return the
* result in Q30 format. */
static OPUS_INLINE opus_val32 celt_atan_norm(opus_val32 x)
{
/* Approximation constants. */
static const opus_int32 ATAN_2_OVER_PI = 1367130551; /* Q31 */
static const opus_int32 ATAN_COEFF_A03 = -715791936; /* Q31 */
static const opus_int32 ATAN_COEFF_A05 = 857391616; /* Q32 */
static const opus_int32 ATAN_COEFF_A07 = -1200579328; /* Q33 */
static const opus_int32 ATAN_COEFF_A09 = 1682636672; /* Q34 */
static const opus_int32 ATAN_COEFF_A11 = -1985085440; /* Q35 */
static const opus_int32 ATAN_COEFF_A13 = 1583306112; /* Q36 */
static const opus_int32 ATAN_COEFF_A15 = -598602432; /* Q37 */
opus_int32 x_sq_q30;
opus_int32 x_q31;
opus_int32 tmp;
/* The expected x is in the range of [-1.0f, 1.0f] */
celt_sig_assert((x <= 1073741824) && (x >= -1073741824));

/* If x = 1.0f, returns 0.5f */
if (x == 1073741824)
{
return 536870912; /* 0.5f (Q30) */
}
/* If x = 1.0f, returns 0.5f */
if (x == -1073741824)
{
return -536870912; /* -0.5f (Q30) */
}
x_q31 = SHL32(x, 1);
x_sq_q30 = MULT32_32_Q31(x_q31, x);
/* Split evaluation in steps to avoid exploding macro expansion. */
tmp = MULT32_32_Q31(x_sq_q30, ATAN_COEFF_A15);
tmp = MULT32_32_Q31(x_sq_q30, ADD32(ATAN_COEFF_A13, tmp));
tmp = MULT32_32_Q31(x_sq_q30, ADD32(ATAN_COEFF_A11, tmp));
tmp = MULT32_32_Q31(x_sq_q30, ADD32(ATAN_COEFF_A09, tmp));
tmp = MULT32_32_Q31(x_sq_q30, ADD32(ATAN_COEFF_A07, tmp));
tmp = MULT32_32_Q31(x_sq_q30, ADD32(ATAN_COEFF_A05, tmp));
tmp = MULT32_32_Q31(x_sq_q30, ADD32(ATAN_COEFF_A03, tmp));
tmp = ADD32(x, MULT32_32_Q31(x_q31, tmp));
return MULT32_32_Q31(ATAN_2_OVER_PI, tmp);
}

/* Calculates the arctangent of y/x, multiplies the result by 2/pi, and returns
* the value in Q30 format. Both input values (x and y) must be within the range
* of 0 to 1 and represented in Q30 format. Inputs must be zero or greater, and
* at least one input must be non-zero. */
static OPUS_INLINE opus_val32 celt_atan2p_norm(opus_val32 y, opus_val32 x)
{
celt_sig_assert(x>=0 && y>=0);
if (y==0 && x==0) {
return 0;
} else if (y < x) {
return celt_atan_norm(SHR32(frac_div32(y, x), 1));
} else {
celt_sig_assert(y > 0);
return 1073741824 /* 1.0f Q30 */ -
celt_atan_norm(SHR32(frac_div32(x, y), 1));
}
}

#define M1 32767
#define M2 -21
#define M3 -11943
Expand Down
81 changes: 81 additions & 0 deletions celt/tests/test_unit_mathops.c
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Original file line number Diff line number Diff line change
Expand Up @@ -439,6 +439,86 @@ void testrsqrt(void)
}
fprintf (stdout, "celt_rsqrt_norm32 max_error: %.7e\n", max_error);
}

void testatan_norm(void)
{
#if defined(ENABLE_QEXT)
float error = -1;
float max_error = -2;
float error_threshold = 5.97e-08;
float fx = 0;
opus_int32 x = 0;
int q_input = 30;
int q_output = 30;
#define ATAN2_2_OVER_PI 0.636619772367581f
for (fx = -1.0f; fx <= 1.0f; fx += 0.007f)
{
x = DOUBLE_TO_FIX_INT(fx, q_input);
error = fabs(atan(FIX_INT_TO_DOUBLE(x, q_input)) * ATAN2_2_OVER_PI -
FIX_INT_TO_DOUBLE(celt_atan_norm(x), q_output));
if (error > max_error)
{
max_error = error;
}
if (error > error_threshold)
{
fprintf(stderr,
"celt_atan_norm failed: error: [%.5e > %.5e] (x = %f)\n",
error, error_threshold, FIX_INT_TO_DOUBLE(x, DB_SHIFT));
ret = 1;
}
}
fprintf(stdout, "celt_atan_norm max_error: %.7e\n", max_error);
#endif /* defined(ENABLE_QEXT) */
}

void testatan2p_norm(void)
{
#if defined(ENABLE_QEXT)
float error = -1;
float max_error = -2;
float error_threshold = 1.2e-07;
float fx = 0;
float fy = 0;
opus_int32 x = 0;
opus_int32 y = 0;
int q_input = 30;
int q_output = 30;
#define ATAN2_2_OVER_PI 0.636619772367581f
for (fx = 0.0f; fx <= 1.0f; fx += 0.007f)
{
x = DOUBLE_TO_FIX_INT(fx, q_input);
for (fy = 0.0f; fy <= 1.0f; fy += 0.007f)
{
y = DOUBLE_TO_FIX_INT(fy, q_input);
if (x == 0 && x == 0)
continue;

error = fabs(atan2(FIX_INT_TO_DOUBLE(y, q_input),
FIX_INT_TO_DOUBLE(x, q_input)) * ATAN2_2_OVER_PI -
FIX_INT_TO_DOUBLE(celt_atan2p_norm(y, x), q_output));
if (error > max_error)
{
max_error = error;
}
if (error > error_threshold)
{
fprintf(stderr,
"celt_atan2p_norm failed: error: [%.5e > %.5e] (x = %f)\n",
error, error_threshold, FIX_INT_TO_DOUBLE(x, DB_SHIFT));
ret = 1;
}
}
}
fprintf(stdout, "celt_atan2p_norm max_error: %.7e\n", max_error);
#endif /* defined(ENABLE_QEXT) */
}

void testatan(void)
{
testatan_norm();
testatan2p_norm();
}
#endif

int main(void)
Expand All @@ -455,6 +535,7 @@ int main(void)
testlog2_db();
testexp2_db();
testrsqrt();
testatan();
#else
test_cos();
test_atan2();
Expand Down
6 changes: 2 additions & 4 deletions celt/vq.c
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Original file line number Diff line number Diff line change
Expand Up @@ -693,10 +693,8 @@ opus_int32 stereo_itheta(const celt_norm *X, const celt_norm *Y, int stereo, int
}
mid = celt_sqrt(Emid);
side = celt_sqrt(Eside);
/* FIXME: Add a fixed-point version for ENABLE_QEXT*/
#if defined(FIXED_POINT) && !defined(ENABLE_QEXT)
/* 0.63662 = 2/pi */
itheta = MULT16_16(QCONST16(0.63662f,15),celt_atan2p(side, mid))<<1;
#if defined(FIXED_POINT)
itheta = celt_atan2p_norm(side, mid);
#else
itheta = (int)floor(.5f+65536.f*16384*celt_atan2p_norm(side,mid));
#endif
Expand Down

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