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Improve exp2's precision to 20-24 bits.

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The exp2 function was approximated using lolremez, achieving an
accuracy of less than 2*10^-7 within the range of 0 to 1.

Signed-off-by: Jean-Marc Valin <jeanmarcv@google.com>
This commit is contained in:
Yunho Huh 2024-11-02 13:02:16 -04:00 • committed by Jean-Marc Valin
parent 7fa23b4ed0
commit 255f013035
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GPG key ID: 8D2952BBB52C646D
2 changed files with 38 additions and 9 deletions
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27
celt/mathops.h
View file

@ -1,7 +1,7 @@
/* Copyright (c) 2002-2008 Jean-Marc Valin
Copyright (c) 2007-2008 CSIRO
Copyright (c) 2007-2009 Xiph.Org Foundation
Written by Jean-Marc Valin */
Written by Jean-Marc Valin, and Yunho Huh */
/**
@file mathops.h
@brief Various math functions
@ -214,7 +214,11 @@ static OPUS_INLINE float celt_log2(float x)
return integer + in.f + log2_y_norm_coeff[range_idx];
}
/** Base-2 exponential approximation (2^x). */
/* Calculates an approximation of 2^x. The approximation was achieved by
* employing a base-2 exponential function and utilizing a Remez approximation
* of order 5, ensuring a controlled relative error.
* exp2(x) = exp2(integer + fraction)
* ~ exp2(integer) + exp2(fraction) */
static OPUS_INLINE float celt_exp2(float x)
{
int integer;
@ -227,9 +231,22 @@ static OPUS_INLINE float celt_exp2(float x)
if (integer < -50)
return 0;
frac = x-integer;
/* K0 = 1, K1 = log(2), K2 = 3-4*log(2), K3 = 3*log(2) - 2 */
res.f = 0.99992522f + frac * (0.69583354f
+ frac * (0.22606716f + 0.078024523f*frac));
/* Polynomial coefficients approximated in the [0, 1] range.
* Lolremez command: lolremez --degree 5 --range 0:1
* "exp(x*0.693147180559945)" "exp(x*0.693147180559945)"
* NOTE: log(2) ~ 0.693147180559945 */
#define EXP2_COEFF_A0 9.999999403953552246093750000000e-01f
#define EXP2_COEFF_A1 6.931530833244323730468750000000e-01f
#define EXP2_COEFF_A2 2.401536107063293457031250000000e-01f
#define EXP2_COEFF_A3 5.582631751894950866699218750000e-02f
#define EXP2_COEFF_A4 8.989339694380760192871093750000e-03f
#define EXP2_COEFF_A5 1.877576694823801517486572265625e-03f
res.f = EXP2_COEFF_A0 + frac * (EXP2_COEFF_A1
+ frac * (EXP2_COEFF_A2
+ frac * (EXP2_COEFF_A3
+ frac * (EXP2_COEFF_A4
+ frac * (EXP2_COEFF_A5)))));
res.i = (res.i + ((opus_uint32)integer<<23)) & 0x7fffffff;
return res.f;
}

20
celt/tests/test_unit_mathops.c
View file

@ -1,6 +1,7 @@
/* Copyright (c) 2008-2011 Xiph.Org Foundation, Mozilla Corporation,
Gregory Maxwell
Written by Jean-Marc Valin, Gregory Maxwell, and Timothy B. Terriberry */
Written by Jean-Marc Valin, Gregory Maxwell, Timothy B. Terriberry,
and Yunho Huh */
/*
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
@ -170,21 +171,32 @@ void testlog2(void)
void testexp2(void)
{
float x;
float error_threshold = 2.3e-07;
float max_error = 0;
for (x=-11.0;x<24.0;x+=0.0007f)
{
float error = fabs(x-(1.442695040888963387*log(celt_exp2(x))));
if (error>0.0002)
if (max_error < error)
{
fprintf (stderr, "celt_exp2 failed: fabs(x-(1.442695040888963387*log(celt_exp2(x))))>0.0005 (x = %f, error = %f)\n", x,error);
max_error = error;
}
if (error > error_threshold)
{
fprintf (stderr,
"celt_exp2 failed: "
"fabs(x-(1.442695040888963387*log(celt_exp2(x))))>%15.25e "
"(x = %f, error = %15.25e)\n", error_threshold, x, error);
ret = 1;
}
}
fprintf (stdout, "celt_exp2 max_error: %15.25e\n", max_error);
}
void testexp2log2(void)
{
float x;
float error_threshold = 5.0e-04;
float error_threshold = 2.0e-06;
float max_error = 0;
for (x=-11.0;x<24.0;x+=0.0007f)
{