This commit fixes the following libc/math issues:
1) asin[f l]() use Newton’s method to converge on a solution. But Newton’s method converges very slowly (> 500,000 iterations) for values of x close to 1.0; and, in the case of asinl(), sometimes fails to converge (loops forever). The attached patch uses an trig identity for values of x > sqrt(2). The resultant functions converge in no more than 5 iterations, 6 for asinl(). 2) The NuttX erf[f l]() functions are based on Chebyshev fitting to a good guess. The problem there’s a bug in the implementation that causes the functions to blow up with x near -3.0. This patch fixes that problem. It should be noted that this method returns the error function erf(x) with fractional error less than 1.2E-07 and that’s fine for the float version erff(), but the same method is used for double and long double version which will yield only slightly better precision. This patch doesn't address the issue of lower precision for erf() and erfl(). 3) a faster version of copysignf() for floats is included.
This commit is contained in:
David S. Alessio
Gregory Nutt
parent
d9314c1034
commit
c145159c6b
@ -35,6 +35,8 @@
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#include <math.h>
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#include <float.h>
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#ifdef CONFIG_HAVE_DOUBLE
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/****************************************************************************
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* Pre-processor Definitions
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****************************************************************************/
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@ -42,16 +44,40 @@
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#undef DBL_EPSILON
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#define DBL_EPSILON 1e-12
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/****************************************************************************
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* Private Functions
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****************************************************************************/
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/* This lib uses Newton's method to approximate asin(x). Newton's Method
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* converges very slowly for x close to 1. We can accelerate convergence
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* with the following identy: asin(x)=Sign(x)*(Pi/2-asin(sqrt(1-x^2)))
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*/
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static double asin_aux(double x)
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{
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long double y;
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double y_cos, y_sin;
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y = 0.0;
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y_sin = 0.0;
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while (fabs(y_sin - x) > DBL_EPSILON)
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{
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y_cos = cos(y);
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y -= ((long double)y_sin - (long double)x) / (long double)y_cos;
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y_sin = sin(y);
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}
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return y;
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}
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/****************************************************************************
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* Public Functions
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****************************************************************************/
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#ifdef CONFIG_HAVE_DOUBLE
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double asin(double x)
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{
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long double y;
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long double y_sin;
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long double y_cos;
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double y;
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/* Verify that the input value is in the domain of the function */
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@ -60,26 +86,19 @@ double asin(double x)
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return NAN;
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}
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y = 0;
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/* if x is > sqrt(2), use identity for faster convergence */
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while (1)
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if (fabs(x) > 0.71)
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{
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y_sin = sin(y);
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y_cos = cos(y);
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if (y > M_PI_2 || y < -M_PI_2)
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{
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y = fmod(y, M_PI);
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}
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if (y_sin + DBL_EPSILON >= x && y_sin - DBL_EPSILON <= x)
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{
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break;
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}
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y = y - (y_sin - x) / y_cos;
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y = M_PI_2 - asin_aux(sqrt(1.0 - x * x));
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y = copysign(y, x);
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}
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else
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{
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y = asin_aux(x);
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}
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return y;
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}
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#endif
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#endif /* CONFIG_HAVE_DOUBLE */
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@ -3,7 +3,7 @@
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*
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* This file is a part of NuttX:
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*
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* Copyright (C) 2012 Gregory Nutt. All rights reserved.
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* Copyright (C) 2012, 2016 Gregory Nutt. All rights reserved.
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* Ported by: Darcy Gong
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*
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* It derives from the Rhombs OS math library by Nick Johnson which has
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@ -33,33 +33,58 @@
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#include <float.h>
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/****************************************************************************
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* Public Functions
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* Private Functions
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****************************************************************************/
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float asinf(float x)
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/* This lib uses Newton's method to approximate asin(x). Newton's Method
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* converges very slowly for x close to 1. We can accelerate convergence
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* with the following identy: asin(x)=Sign(x)*(Pi/2-asin(sqrt(1-x^2)))
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*/
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static float asinf_aux(float x)
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{
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long double y, y_sin, y_cos;
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double y;
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float y_sin, y_cos;
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y = 0;
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y = 0.0;
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y_sin = 0.0F;
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while (1)
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while (fabsf(y_sin - x) > FLT_EPSILON)
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{
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y_sin = sinf(y);
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y_cos = cosf(y);
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if (y > M_PI_2_F || y < -M_PI_2_F)
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{
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y = fmodf(y, M_PI_F);
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}
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if (y_sin + FLT_EPSILON >= x && y_sin - FLT_EPSILON <= x)
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{
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break;
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}
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y = y - (y_sin - x) / y_cos;
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y -= ((double)y_sin - (double)x) / (double)y_cos;
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y_sin = sinf(y);
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}
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return y;
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}
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/****************************************************************************
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* Public Functions
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****************************************************************************/
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float asinf(float x)
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{
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float y;
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/* Verify that the input value is in the domain of the function */
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if (x < -1.0F || x > 1.0F || isnan(x))
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{
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return NAN_F;
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}
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/* if x is > sqrt(2), use identity for faster convergence */
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if (fabsf(x) > 0.71F)
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{
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y = M_PI_2_F - asinf_aux(sqrtf(1.0F - x * x));
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y = copysignf(y, x);
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}
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else
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{
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y = asinf_aux(x);
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}
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return y;
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}
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@ -3,7 +3,7 @@
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*
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* This file is a part of NuttX:
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*
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* Copyright (C) 2012 Gregory Nutt. All rights reserved.
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* Copyright (C) 2012, 2016 Gregory Nutt. All rights reserved.
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* Ported by: Darcy Gong
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*
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* It derives from the Rhombs OS math library by Nick Johnson which has
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@ -35,35 +35,57 @@
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#include <math.h>
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#include <float.h>
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#ifdef CONFIG_HAVE_LONG_DOUBLE
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/****************************************************************************
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* Public Functions
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****************************************************************************/
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#ifdef CONFIG_HAVE_LONG_DOUBLE
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long double asinl(long double x)
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static long double asinl_aux(long double x)
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{
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long double y, y_sin, y_cos;
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long double y, y_cos, y_sin;
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y = 0;
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y = 0.0;
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y_sin = 0.0;
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while (1)
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while (fabsl(y_sin - x) > DBL_EPSILON)
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{
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y_sin = sinl(y);
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y_cos = cosl(y);
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if (y > M_PI_2 || y < -M_PI_2)
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{
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y = fmodl(y, M_PI);
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}
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if (y_sin + LDBL_EPSILON >= x && y_sin - LDBL_EPSILON <= x)
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{
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break;
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}
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y = y - (y_sin - x) / y_cos;
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y -= (y_sin - x) / y_cos;
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y_sin = sinl(y);
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}
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return y;
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}
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#endif
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/****************************************************************************
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* Public Functions
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****************************************************************************/
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long double asinl(long double x)
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{
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long double y;
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/* Verify that the input value is in the domain of the function */
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if (x < -1.0 || x > 1.0 || isnan(x))
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{
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return NAN;
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}
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/* if x is > sqrt(2), use identity for faster convergence */
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if (fabsl(x) > 0.71)
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{
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y = M_PI_2 - asinl_aux(sqrtl(1.0 - x * x));
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y = copysignl(y, x);
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}
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else
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{
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y = asinl_aux(x);
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}
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return y;
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}
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endif /* CONFIG_HAVE_LONG_DOUBLE */
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@ -1,10 +1,20 @@
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/****************************************************************************
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* libc/math/lib_copysignf.c
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*
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* Copyright (C) 2015 Gregory Nutt. All rights reserved.
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* Copyright (C) 2015, 2016 Gregory Nutt. All rights reserved.
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* Authors: Gregory Nutt <gnutt@nuttx.org>
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* Dave Marples <dave@marples.net>
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*
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* Replaced on 2016-07-30 by David Alession with a faster version of
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* copysignf() from NetBSD with the following Copyright:
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*
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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@ -42,6 +52,44 @@
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#include <nuttx/compiler.h>
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#include <math.h>
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#include <stdint.h>
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/****************************************************************************
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* Pre-processor Definitions
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****************************************************************************/
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/* Get a 32 bit int from a float. */
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#define GET_FLOAT_WORD(i,d) \
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do \
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{ \
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ieee_float_shape_type gf_u; \
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gf_u.value = (d); \
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(i) = gf_u.word; \
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} while (0)
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/* Set a float from a 32 bit int. */
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#define SET_FLOAT_WORD(d,i) \
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do \
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{ \
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ieee_float_shape_type sf_u; \
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sf_u.word = (i); \
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(d) = sf_u.value; \
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} while (0)
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/****************************************************************************
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* Private Types
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****************************************************************************/
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/* union which permits us to convert between a float and a 32 bit int. */
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typedef union
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{
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float value;
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uint32_t word;
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}
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ieee_float_shape_type;
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/****************************************************************************
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* Public Functions
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@ -49,10 +97,12 @@
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float copysignf(float x, float y)
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{
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if (y < 0)
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{
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return -fabsf(x);
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}
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uint32_t ix;
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uint32_t iy;
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return fabsf(x);
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GET_FLOAT_WORD(ix, x);
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GET_FLOAT_WORD(iy, y);
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SET_FLOAT_WORD(x, (ix & 0x7fffffff) | (iy & 0x80000000));
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return x;
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}
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@ -1,6 +1,7 @@
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/****************************************************************************
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* libc/math/lib_erf.c
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*
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* Copyright (C) 2016 Gregory Nutt. All rights reserved.
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* Copyright (C) 2015 Brennan Ashton. All rights reserved.
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* Author: Brennan Ashton <bashton@brennanashton.com>
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*
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@ -42,32 +43,42 @@
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#include <math.h>
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#ifdef CONFIG_HAVE_DOUBLE
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/****************************************************************************
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* Pre-processor Definitions
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****************************************************************************/
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#define A1 0.254829592
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#define A2 (-0.284496736)
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#define A3 1.421413741
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#define A4 (-1.453152027)
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#define A5 1.061405429
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#define P 0.3275911
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/****************************************************************************
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* Public Functions
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****************************************************************************/
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#ifdef CONFIG_HAVE_DOUBLE
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/****************************************************************************
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* Name: erf
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*
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* Description:
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* This implementation comes from the Handbook of Mathmatical Functions
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* The implementations in this book are not protected by copyright.
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* erf comes from formula 7.1.26
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*
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****************************************************************************/
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double erf(double x)
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{
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/* This implementation comes from the Handbook of Mathmatical Functions
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* The implementations in this book are not protected by copyright.
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* erf comes from formula 7.1.26
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*/
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char sign;
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double t;
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double a1, a2, a3, a4, a5, p;
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double z;
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a1 = 0.254829592;
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a2 = -0.284496736;
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a3 = 1.421413741;
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a4 = -1.453152027;
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a5 = 1.061405429;
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p = 0.3275911;
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sign = (x >= 0 ? 1 : -1);
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t = 1.0/(1.0 + p*x);
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return sign * (1.0 - (((((a5 * t + a4) * t) + a3) * t + a2) * t + a1) * t *
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(double)expf(-x * x));
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z = fabs(x);
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t = 1.0 / (1.0 + P * z);
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t = 1.0 - (((((A5 * t + A4) * t) + A3) * t + A2) * t + A1) * t * exp(-z * z);
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return copysign(t, x);
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}
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#endif
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#endif /* CONFIG_HAVE_DOUBLE */
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@ -1,6 +1,7 @@
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/****************************************************************************
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* libc/math/lib_erff.c
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*
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* Copyright (C) 2016 Gregory Nutt. All rights reserved.
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* Copyright (C) 2015 Brennan Ashton. All rights reserved.
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* Author: Brennan Ashton <bashton@brennanashton.com>
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*
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@ -42,29 +43,38 @@
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#include <math.h>
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/****************************************************************************
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* Pre-processor Definitions
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****************************************************************************/
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#define A1 0.254829592F
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#define A2 (-0.284496736F)
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#define A3 1.421413741F
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#define A4 (-1.453152027F)
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#define A5 1.061405429F
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#define P 0.3275911F
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/****************************************************************************
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* Public Functions
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****************************************************************************/
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/****************************************************************************
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* Name: erff
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*
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* Description:
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* This implementation comes from the Handbook of Mathmatical Functions
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* The implementations in this book are not protected by copyright.
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* erf comes from formula 7.1.26
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*
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****************************************************************************/
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float erff(float x)
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{
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/* This implementation comes from the Handbook of Mathmatical Functions
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* The implementations in this book are not protected by copyright.
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* erf comes from formula 7.1.26
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*/
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char sign;
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float t;
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float a1, a2, a3, a4, a5, p;
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float z;
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a1 = 0.254829592F;
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a2 = -0.284496736F;
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a3 = 1.421413741F;
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a4 = -1.453152027F;
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a5 = 1.061405429F;
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p = 0.3275911F;
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sign = (x >= 0 ? 1 : -1);
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t = 1.0F/(1.0F + p*x);
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return sign * (1.0F - (((((a5 * t + a4) * t) + a3) * t + a2) * t + a1) * t * expf(-x * x));
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z = fabsf(x);
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t = 1.0F / (1.0F + P * z);
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t = 1.0F - (((((A5 * t + A4) * t) + A3) * t + A2) * t + A1) * t * expf(-z * z);
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return copysignf(t, x);
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}
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@ -46,6 +46,13 @@
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* Public Functions
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****************************************************************************/
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#define A1 0.254829592
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#define A2 (-0.284496736)
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#define A3 1.421413741
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#define A4 (-1.453152027)
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#define A5 1.061405429
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#define P 0.3275911
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#ifdef CONFIG_HAVE_LONG_DOUBLE
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long double erfl(long double x)
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{
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@ -54,19 +61,11 @@ long double erfl(long double x)
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* erf comes from formula 7.1.26
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*/
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char sign;
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long double t;
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long double a1, a2, a3, a4, a5, p;
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long double t, z;
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a1 = 0.254829592;
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a2 = -0.284496736;
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a3 = 1.421413741;
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a4 = -1.453152027;
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a5 = 1.061405429;
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p = 0.3275911;
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||||
sign = (x >= 0 ? 1 : -1);
|
||||
t = 1.0/(1.0 + p*x);
|
||||
return sign * (1.0 - (((((a5 * t + a4) * t) + a3) * t + a2) * t + a1) * t * expf(-x * x));
|
||||
z = fabsl(x);
|
||||
t = 1.0 / (1.0 + P * z);
|
||||
t = 1.0 - (((((A5 * t + A4) * t) + A3) * t + A2) * t + A1) * t * expl(-z * z);
|
||||
return copysignl(t, x);
|
||||
}
|
||||
#endif
|
||||
|
||||
Loading…
Reference in New Issue
Block a user