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freebsd-dev/lib/msun/ld128/s_tanpil.c

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[LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl] Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle trignometric functions cospi, sinpi, and tanpi. The attached patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited testing on the cospi and sinpi reveal a max ULP less than 0.89; while tanpi is more problematic with a max ULP less than 2.01 in the interval [0,0.5]. The algorithms used in these functions are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c. Note. I no longer have access to a system with ld128 and adequate support to compile and test the ld128 implementations of these functions. Given the almost complete lack of input from others on improvements to libm, I doubt that anyone cares. If someone does care, the ld128 files contain a number of FIXME comments, and in particular, while the polynomial coefficients are given I did not update the polynomial algorithms to properly use the coefficients. PR: 218514 MFC after: 2 weeks
2021-10-25 13:13:52 +00:00
/*-
sinpi[fl] etc: Fix the ld128 implementations Mark Murray graciously provided access to an aarch64 system to test the ld128 implementations. This patch address * Misuses of copysignl() in sinpil() and tanpil(). * Redo the splitting of argument 'x' into an integer part and remainder. The remainder must satify 0 <= r < 1. * Update the reduction of the integer part to something that can easily be seen as even or odd, e.g., sin(pi*x) = (-1)^n*sin(pi*r) with n <= 2^112 and we an reduce n by subtracting integer powers of 2. * In s_cospil.c, fix typos where 'x' is used where 'ax', the remainder, is required. * In tanpil(), fix the use of an uninitialized variable, ax = fabsl(ax), ax should be x in fabsl(). One item of note, in the limited tested on aarch64, the max ULP for sinpil() and cospil() were less than 1.1 ULP, which is higher that the desired max ULP less than 1. This was traced to the kernel for cosl() in the fundamental interval [0,pi/4]. The coefficients in the minmax polynomial likely need refinement. PR: 218514 MFC after: 1 week
2021-10-31 22:26:20 +00:00
* Copyright (c) 2017-2021 Steven G. Kargl
[LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl] Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle trignometric functions cospi, sinpi, and tanpi. The attached patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited testing on the cospi and sinpi reveal a max ULP less than 0.89; while tanpi is more problematic with a max ULP less than 2.01 in the interval [0,0.5]. The algorithms used in these functions are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c. Note. I no longer have access to a system with ld128 and adequate support to compile and test the ld128 implementations of these functions. Given the almost complete lack of input from others on improvements to libm, I doubt that anyone cares. If someone does care, the ld128 files contain a number of FIXME comments, and in particular, while the polynomial coefficients are given I did not update the polynomial algorithms to properly use the coefficients. PR: 218514 MFC after: 2 weeks
2021-10-25 13:13:52 +00:00
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice unmodified, this list of conditions, and the following
* disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*
* See ../src/s_tanpi.c for implementation details.
*/
#include "math.h"
#include "math_private.h"
/*
* pi_hi contains the leading 56 bits of a 169 bit approximation for pi.
*/
static const long double
pi_hi = 3.14159265358979322702026593105983920e+00L,
pi_lo = 1.14423774522196636802434264184180742e-17L;
static inline long double
lib/msun/ld128/s_tanpil.c: make it compile. Declare local, add missed ';'. Name function properly. Fixes: dce5f3abed7181cc533ca5ed Reviewed by: kargl Sponsored by: The FreeBSD Foundation MFC after: 1 week
2021-10-26 21:14:35 +00:00
__kernel_tanpil(long double x)
[LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl] Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle trignometric functions cospi, sinpi, and tanpi. The attached patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited testing on the cospi and sinpi reveal a max ULP less than 0.89; while tanpi is more problematic with a max ULP less than 2.01 in the interval [0,0.5]. The algorithms used in these functions are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c. Note. I no longer have access to a system with ld128 and adequate support to compile and test the ld128 implementations of these functions. Given the almost complete lack of input from others on improvements to libm, I doubt that anyone cares. If someone does care, the ld128 files contain a number of FIXME comments, and in particular, while the polynomial coefficients are given I did not update the polynomial algorithms to properly use the coefficients. PR: 218514 MFC after: 2 weeks
2021-10-25 13:13:52 +00:00
{
long double hi, lo, t;
if (x < 0.25) {
hi = (double)x;
lo = x - hi;
lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
hi *= pi_hi;
_2sumF(hi, lo);
t = __kernel_tanl(hi, lo, -1);
} else if (x > 0.25) {
x = 0.5 - x;
hi = (double)x;
lo = x - hi;
lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
hi *= pi_hi;
_2sumF(hi, lo);
t = - __kernel_tanl(hi, lo, 1);
} else
t = 1;
return (t);
}
volatile static const double vzero = 0;
long double
tanpil(long double x)
{
lib/msun/ld128/s_tanpil.c: make it compile. Declare local, add missed ';'. Name function properly. Fixes: dce5f3abed7181cc533ca5ed Reviewed by: kargl Sponsored by: The FreeBSD Foundation MFC after: 1 week
2021-10-26 21:14:35 +00:00
long double ax, hi, lo, xf, t;
[LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl] Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle trignometric functions cospi, sinpi, and tanpi. The attached patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited testing on the cospi and sinpi reveal a max ULP less than 0.89; while tanpi is more problematic with a max ULP less than 2.01 in the interval [0,0.5]. The algorithms used in these functions are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c. Note. I no longer have access to a system with ld128 and adequate support to compile and test the ld128 implementations of these functions. Given the almost complete lack of input from others on improvements to libm, I doubt that anyone cares. If someone does care, the ld128 files contain a number of FIXME comments, and in particular, while the polynomial coefficients are given I did not update the polynomial algorithms to properly use the coefficients. PR: 218514 MFC after: 2 weeks
2021-10-25 13:13:52 +00:00
uint32_t ix;
sinpi[fl] etc: Fix the ld128 implementations Mark Murray graciously provided access to an aarch64 system to test the ld128 implementations. This patch address * Misuses of copysignl() in sinpil() and tanpil(). * Redo the splitting of argument 'x' into an integer part and remainder. The remainder must satify 0 <= r < 1. * Update the reduction of the integer part to something that can easily be seen as even or odd, e.g., sin(pi*x) = (-1)^n*sin(pi*r) with n <= 2^112 and we an reduce n by subtracting integer powers of 2. * In s_cospil.c, fix typos where 'x' is used where 'ax', the remainder, is required. * In tanpil(), fix the use of an uninitialized variable, ax = fabsl(ax), ax should be x in fabsl(). One item of note, in the limited tested on aarch64, the max ULP for sinpil() and cospil() were less than 1.1 ULP, which is higher that the desired max ULP less than 1. This was traced to the kernel for cosl() in the fundamental interval [0,pi/4]. The coefficients in the minmax polynomial likely need refinement. PR: 218514 MFC after: 1 week
2021-10-31 22:26:20 +00:00
ax = fabsl(x);
[LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl] Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle trignometric functions cospi, sinpi, and tanpi. The attached patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited testing on the cospi and sinpi reveal a max ULP less than 0.89; while tanpi is more problematic with a max ULP less than 2.01 in the interval [0,0.5]. The algorithms used in these functions are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c. Note. I no longer have access to a system with ld128 and adequate support to compile and test the ld128 implementations of these functions. Given the almost complete lack of input from others on improvements to libm, I doubt that anyone cares. If someone does care, the ld128 files contain a number of FIXME comments, and in particular, while the polynomial coefficients are given I did not update the polynomial algorithms to properly use the coefficients. PR: 218514 MFC after: 2 weeks
2021-10-25 13:13:52 +00:00
if (ax < 1) {
if (ax < 0.5) {
if (ax < 0x1p-60) {
if (x == 0)
return (x);
hi = (double)x;
lib/msun/ld128/s_tanpil.c: make it compile. Declare local, add missed ';'. Name function properly. Fixes: dce5f3abed7181cc533ca5ed Reviewed by: kargl Sponsored by: The FreeBSD Foundation MFC after: 1 week
2021-10-26 21:14:35 +00:00
hi *= 0x1p113L;
[LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl] Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle trignometric functions cospi, sinpi, and tanpi. The attached patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited testing on the cospi and sinpi reveal a max ULP less than 0.89; while tanpi is more problematic with a max ULP less than 2.01 in the interval [0,0.5]. The algorithms used in these functions are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c. Note. I no longer have access to a system with ld128 and adequate support to compile and test the ld128 implementations of these functions. Given the almost complete lack of input from others on improvements to libm, I doubt that anyone cares. If someone does care, the ld128 files contain a number of FIXME comments, and in particular, while the polynomial coefficients are given I did not update the polynomial algorithms to properly use the coefficients. PR: 218514 MFC after: 2 weeks
2021-10-25 13:13:52 +00:00
lo = x * 0x1p113L - hi;
t = (pi_lo + pi_hi) * lo + pi_lo * lo +
pi_hi * hi;
return (t * 0x1p-113L);
}
t = __kernel_tanpil(ax);
} else if (ax == 0.5)
return ((ax - ax) / (ax - ax));
else
t = -__kernel_tanpil(1 - ax);
sinpi[fl] etc: Fix the ld128 implementations Mark Murray graciously provided access to an aarch64 system to test the ld128 implementations. This patch address * Misuses of copysignl() in sinpil() and tanpil(). * Redo the splitting of argument 'x' into an integer part and remainder. The remainder must satify 0 <= r < 1. * Update the reduction of the integer part to something that can easily be seen as even or odd, e.g., sin(pi*x) = (-1)^n*sin(pi*r) with n <= 2^112 and we an reduce n by subtracting integer powers of 2. * In s_cospil.c, fix typos where 'x' is used where 'ax', the remainder, is required. * In tanpil(), fix the use of an uninitialized variable, ax = fabsl(ax), ax should be x in fabsl(). One item of note, in the limited tested on aarch64, the max ULP for sinpil() and cospil() were less than 1.1 ULP, which is higher that the desired max ULP less than 1. This was traced to the kernel for cosl() in the fundamental interval [0,pi/4]. The coefficients in the minmax polynomial likely need refinement. PR: 218514 MFC after: 1 week
2021-10-31 22:26:20 +00:00
return (x < 0 ? -t : t);
[LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl] Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle trignometric functions cospi, sinpi, and tanpi. The attached patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited testing on the cospi and sinpi reveal a max ULP less than 0.89; while tanpi is more problematic with a max ULP less than 2.01 in the interval [0,0.5]. The algorithms used in these functions are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c. Note. I no longer have access to a system with ld128 and adequate support to compile and test the ld128 implementations of these functions. Given the almost complete lack of input from others on improvements to libm, I doubt that anyone cares. If someone does care, the ld128 files contain a number of FIXME comments, and in particular, while the polynomial coefficients are given I did not update the polynomial algorithms to properly use the coefficients. PR: 218514 MFC after: 2 weeks
2021-10-25 13:13:52 +00:00
}
if (ix < 0x1p112) {
sinpi[fl] etc: Fix the ld128 implementations Mark Murray graciously provided access to an aarch64 system to test the ld128 implementations. This patch address * Misuses of copysignl() in sinpil() and tanpil(). * Redo the splitting of argument 'x' into an integer part and remainder. The remainder must satify 0 <= r < 1. * Update the reduction of the integer part to something that can easily be seen as even or odd, e.g., sin(pi*x) = (-1)^n*sin(pi*r) with n <= 2^112 and we an reduce n by subtracting integer powers of 2. * In s_cospil.c, fix typos where 'x' is used where 'ax', the remainder, is required. * In tanpil(), fix the use of an uninitialized variable, ax = fabsl(ax), ax should be x in fabsl(). One item of note, in the limited tested on aarch64, the max ULP for sinpil() and cospil() were less than 1.1 ULP, which is higher that the desired max ULP less than 1. This was traced to the kernel for cosl() in the fundamental interval [0,pi/4]. The coefficients in the minmax polynomial likely need refinement. PR: 218514 MFC after: 1 week
2021-10-31 22:26:20 +00:00
/* Split x = n + r with 0 <= r < 1. */
xf = (ax + 0x1p112L) - 0x1p112L; /* Integer part */
ax -= xf; /* Remainder */
if (ax < 0) {
ax += 1;
xf -= 1;
}
[LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl] Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle trignometric functions cospi, sinpi, and tanpi. The attached patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited testing on the cospi and sinpi reveal a max ULP less than 0.89; while tanpi is more problematic with a max ULP less than 2.01 in the interval [0,0.5]. The algorithms used in these functions are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c. Note. I no longer have access to a system with ld128 and adequate support to compile and test the ld128 implementations of these functions. Given the almost complete lack of input from others on improvements to libm, I doubt that anyone cares. If someone does care, the ld128 files contain a number of FIXME comments, and in particular, while the polynomial coefficients are given I did not update the polynomial algorithms to properly use the coefficients. PR: 218514 MFC after: 2 weeks
2021-10-25 13:13:52 +00:00
if (ax < 0.5)
t = ax == 0 ? 0 : __kernel_tanpil(ax);
else if (ax == 0.5)
return ((ax - ax) / (ax - ax));
else
t = -__kernel_tanpil(1 - ax);
sinpi[fl] etc: Fix the ld128 implementations Mark Murray graciously provided access to an aarch64 system to test the ld128 implementations. This patch address * Misuses of copysignl() in sinpil() and tanpil(). * Redo the splitting of argument 'x' into an integer part and remainder. The remainder must satify 0 <= r < 1. * Update the reduction of the integer part to something that can easily be seen as even or odd, e.g., sin(pi*x) = (-1)^n*sin(pi*r) with n <= 2^112 and we an reduce n by subtracting integer powers of 2. * In s_cospil.c, fix typos where 'x' is used where 'ax', the remainder, is required. * In tanpil(), fix the use of an uninitialized variable, ax = fabsl(ax), ax should be x in fabsl(). One item of note, in the limited tested on aarch64, the max ULP for sinpil() and cospil() were less than 1.1 ULP, which is higher that the desired max ULP less than 1. This was traced to the kernel for cosl() in the fundamental interval [0,pi/4]. The coefficients in the minmax polynomial likely need refinement. PR: 218514 MFC after: 1 week
2021-10-31 22:26:20 +00:00
return (x < 0 ? -t : t);
[LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl] Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle trignometric functions cospi, sinpi, and tanpi. The attached patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited testing on the cospi and sinpi reveal a max ULP less than 0.89; while tanpi is more problematic with a max ULP less than 2.01 in the interval [0,0.5]. The algorithms used in these functions are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c. Note. I no longer have access to a system with ld128 and adequate support to compile and test the ld128 implementations of these functions. Given the almost complete lack of input from others on improvements to libm, I doubt that anyone cares. If someone does care, the ld128 files contain a number of FIXME comments, and in particular, while the polynomial coefficients are given I did not update the polynomial algorithms to properly use the coefficients. PR: 218514 MFC after: 2 weeks
2021-10-25 13:13:52 +00:00
}
/* x = +-inf or nan. */
if (isinf(x) || isnan(x))
return (vzero / vzero);
/*
sinpi[fl] etc: Fix the ld128 implementations Mark Murray graciously provided access to an aarch64 system to test the ld128 implementations. This patch address * Misuses of copysignl() in sinpil() and tanpil(). * Redo the splitting of argument 'x' into an integer part and remainder. The remainder must satify 0 <= r < 1. * Update the reduction of the integer part to something that can easily be seen as even or odd, e.g., sin(pi*x) = (-1)^n*sin(pi*r) with n <= 2^112 and we an reduce n by subtracting integer powers of 2. * In s_cospil.c, fix typos where 'x' is used where 'ax', the remainder, is required. * In tanpil(), fix the use of an uninitialized variable, ax = fabsl(ax), ax should be x in fabsl(). One item of note, in the limited tested on aarch64, the max ULP for sinpil() and cospil() were less than 1.1 ULP, which is higher that the desired max ULP less than 1. This was traced to the kernel for cosl() in the fundamental interval [0,pi/4]. The coefficients in the minmax polynomial likely need refinement. PR: 218514 MFC after: 1 week
2021-10-31 22:26:20 +00:00
* |x| >= 0x1p112 is always an integer, so return +-0.
[LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl] Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle trignometric functions cospi, sinpi, and tanpi. The attached patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited testing on the cospi and sinpi reveal a max ULP less than 0.89; while tanpi is more problematic with a max ULP less than 2.01 in the interval [0,0.5]. The algorithms used in these functions are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c. Note. I no longer have access to a system with ld128 and adequate support to compile and test the ld128 implementations of these functions. Given the almost complete lack of input from others on improvements to libm, I doubt that anyone cares. If someone does care, the ld128 files contain a number of FIXME comments, and in particular, while the polynomial coefficients are given I did not update the polynomial algorithms to properly use the coefficients. PR: 218514 MFC after: 2 weeks
2021-10-25 13:13:52 +00:00
*/
return (copysignl(0, x));
}
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