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HardenedBSD/lib/msun/ld80/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 15:13:52 +02:00
/*-
Fixes for bugs in sinpi/cospi/tanpi patch to fix half-cycle trigonometric functions Paul Zimmermann, a MPFR developer, contacted me about large errors in the half-cycle trigonometric functions. I've have investigated these issues and developed the attached patch. The float, double, and ld80 (long double) changes have been tested. Caveat emptor: The ld128 changes have not been compiled. The ld128 changes have not been tested. I do not have access to a system that uses ld128 floating point. Here is an itemized list of changes: * lib/msun/src/math_private.h: . Add fast floor macros to compute the integer part of |x| for 0 <= |x| 01xp(N-1), where N is the precision of the type of x. These macros are used in the half-cycle trigonometric functions (e.g., sinpi(x)). . The FFLOOR80 macros is used with the Intel 80-bit extended double functions. This macors corrects an off-by-one error, which led to enormous error for |x| > 0x1p32. * lib/msun/src/s_cospif.c: * lib/msun/src/s_cospi.c: * lib/msun/ld80/s_cospil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. . Correct handle the range 0x1p(N-1) <= |x| < 0x1pN. Here, one needs to determine if the integral value of |x| is even or odd to choose +1 or -1. If |x| >= 0x1pN, always return +1. * lib/msun/src/s_sinpif.c: * lib/msun/src/s_sinpi.c: * lib/msun/ld80/s_sinpil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. * lib/msun/src/s_tanpif.c: * lib/msun/src/s_tanpi.c: * lib/msun/ld80/s_tanpil.c: . Update Copyright years. . For +-0.5, return +-inf. Previously, tanpi[fl]() returned an NaN. . Use FFLOOR*() to get integer part of |x|. Need to determine if the integer part is even or odd. This is used to set +-0 for |x| integral and +-inf for (n+1/2). . For 0x1p(N-1) <= |x| < 0x1pN need to determine if x is an even or odd integer to select +0 or -0. For |x| >= 0x1pN, it is always an even integer, select 0. . Note, tanpi[fl](x) is an odd function, so one needs to consider tanpi[fl](-|x|) = - tanpi[fl](|x|). * lib/msun/ld128/s_cospil.c: * lib/msun/ld128/s_sinpil.c: * lib/msun/ld128/s_tanpil.c: . Update Copyright years. . These routines use an FFLOOR128 macros, which likely should be replaced by a bit twiddling algorithm. . The same considerations above are applied to 0x1p112 <= |x| < 0x1p113, and |x| >= 0x1p113 cases. . Note, even and odd determination used fmodl(x,2.), which is likely slow. PR: 272742 MFC after: 1 week
2023-08-01 00:34:48 +02:00
* Copyright (c) 2017, 2023 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 15:13:52 +02:00
* 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.
*/
#ifdef __i386__
#include <ieeefp.h>
#endif
#include <stdint.h>
#include "fpmath.h"
#include "math.h"
#include "math_private.h"
static const double
pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
pi_lo = -2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
static inline long double
__kernel_tanpil(long double x)
{
long double hi, lo, t;
if (x < 0.25) {
hi = (float)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 = (float)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)
{
Fixes for bugs in sinpi/cospi/tanpi patch to fix half-cycle trigonometric functions Paul Zimmermann, a MPFR developer, contacted me about large errors in the half-cycle trigonometric functions. I've have investigated these issues and developed the attached patch. The float, double, and ld80 (long double) changes have been tested. Caveat emptor: The ld128 changes have not been compiled. The ld128 changes have not been tested. I do not have access to a system that uses ld128 floating point. Here is an itemized list of changes: * lib/msun/src/math_private.h: . Add fast floor macros to compute the integer part of |x| for 0 <= |x| 01xp(N-1), where N is the precision of the type of x. These macros are used in the half-cycle trigonometric functions (e.g., sinpi(x)). . The FFLOOR80 macros is used with the Intel 80-bit extended double functions. This macors corrects an off-by-one error, which led to enormous error for |x| > 0x1p32. * lib/msun/src/s_cospif.c: * lib/msun/src/s_cospi.c: * lib/msun/ld80/s_cospil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. . Correct handle the range 0x1p(N-1) <= |x| < 0x1pN. Here, one needs to determine if the integral value of |x| is even or odd to choose +1 or -1. If |x| >= 0x1pN, always return +1. * lib/msun/src/s_sinpif.c: * lib/msun/src/s_sinpi.c: * lib/msun/ld80/s_sinpil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. * lib/msun/src/s_tanpif.c: * lib/msun/src/s_tanpi.c: * lib/msun/ld80/s_tanpil.c: . Update Copyright years. . For +-0.5, return +-inf. Previously, tanpi[fl]() returned an NaN. . Use FFLOOR*() to get integer part of |x|. Need to determine if the integer part is even or odd. This is used to set +-0 for |x| integral and +-inf for (n+1/2). . For 0x1p(N-1) <= |x| < 0x1pN need to determine if x is an even or odd integer to select +0 or -0. For |x| >= 0x1pN, it is always an even integer, select 0. . Note, tanpi[fl](x) is an odd function, so one needs to consider tanpi[fl](-|x|) = - tanpi[fl](|x|). * lib/msun/ld128/s_cospil.c: * lib/msun/ld128/s_sinpil.c: * lib/msun/ld128/s_tanpil.c: . Update Copyright years. . These routines use an FFLOOR128 macros, which likely should be replaced by a bit twiddling algorithm. . The same considerations above are applied to 0x1p112 <= |x| < 0x1p113, and |x| >= 0x1p113 cases. . Note, even and odd determination used fmodl(x,2.), which is likely slow. PR: 272742 MFC after: 1 week
2023-08-01 00:34:48 +02:00
long double ax, hi, lo, odd, 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 15:13:52 +02:00
uint64_t lx, m;
uint32_t j0;
uint16_t hx, ix;
EXTRACT_LDBL80_WORDS(hx, lx, x);
ix = hx & 0x7fff;
INSERT_LDBL80_WORDS(ax, ix, lx);
ENTERI();
if (ix < 0x3fff) { /* |x| < 1 */
if (ix < 0x3ffe) { /* |x| < 0.5 */
if (ix < 0x3fdd) { /* |x| < 0x1p-34 */
if (x == 0)
RETURNI(x);
INSERT_LDBL80_WORDS(hi, hx,
lx & 0xffffffff00000000ull);
hi *= 0x1p63L;
lo = x * 0x1p63L - hi;
t = (pi_lo + pi_hi) * lo + pi_lo * hi +
pi_hi * hi;
RETURNI(t * 0x1p-63L);
}
t = __kernel_tanpil(ax);
} else if (ax == 0.5)
Fixes for bugs in sinpi/cospi/tanpi patch to fix half-cycle trigonometric functions Paul Zimmermann, a MPFR developer, contacted me about large errors in the half-cycle trigonometric functions. I've have investigated these issues and developed the attached patch. The float, double, and ld80 (long double) changes have been tested. Caveat emptor: The ld128 changes have not been compiled. The ld128 changes have not been tested. I do not have access to a system that uses ld128 floating point. Here is an itemized list of changes: * lib/msun/src/math_private.h: . Add fast floor macros to compute the integer part of |x| for 0 <= |x| 01xp(N-1), where N is the precision of the type of x. These macros are used in the half-cycle trigonometric functions (e.g., sinpi(x)). . The FFLOOR80 macros is used with the Intel 80-bit extended double functions. This macors corrects an off-by-one error, which led to enormous error for |x| > 0x1p32. * lib/msun/src/s_cospif.c: * lib/msun/src/s_cospi.c: * lib/msun/ld80/s_cospil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. . Correct handle the range 0x1p(N-1) <= |x| < 0x1pN. Here, one needs to determine if the integral value of |x| is even or odd to choose +1 or -1. If |x| >= 0x1pN, always return +1. * lib/msun/src/s_sinpif.c: * lib/msun/src/s_sinpi.c: * lib/msun/ld80/s_sinpil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. * lib/msun/src/s_tanpif.c: * lib/msun/src/s_tanpi.c: * lib/msun/ld80/s_tanpil.c: . Update Copyright years. . For +-0.5, return +-inf. Previously, tanpi[fl]() returned an NaN. . Use FFLOOR*() to get integer part of |x|. Need to determine if the integer part is even or odd. This is used to set +-0 for |x| integral and +-inf for (n+1/2). . For 0x1p(N-1) <= |x| < 0x1pN need to determine if x is an even or odd integer to select +0 or -0. For |x| >= 0x1pN, it is always an even integer, select 0. . Note, tanpi[fl](x) is an odd function, so one needs to consider tanpi[fl](-|x|) = - tanpi[fl](|x|). * lib/msun/ld128/s_cospil.c: * lib/msun/ld128/s_sinpil.c: * lib/msun/ld128/s_tanpil.c: . Update Copyright years. . These routines use an FFLOOR128 macros, which likely should be replaced by a bit twiddling algorithm. . The same considerations above are applied to 0x1p112 <= |x| < 0x1p113, and |x| >= 0x1p113 cases. . Note, even and odd determination used fmodl(x,2.), which is likely slow. PR: 272742 MFC after: 1 week
2023-08-01 00:34:48 +02:00
t = 1 / vzero;
[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 15:13:52 +02:00
else
t = -__kernel_tanpil(1 - ax);
RETURNI((hx & 0x8000) ? -t : t);
}
Fixes for bugs in sinpi/cospi/tanpi patch to fix half-cycle trigonometric functions Paul Zimmermann, a MPFR developer, contacted me about large errors in the half-cycle trigonometric functions. I've have investigated these issues and developed the attached patch. The float, double, and ld80 (long double) changes have been tested. Caveat emptor: The ld128 changes have not been compiled. The ld128 changes have not been tested. I do not have access to a system that uses ld128 floating point. Here is an itemized list of changes: * lib/msun/src/math_private.h: . Add fast floor macros to compute the integer part of |x| for 0 <= |x| 01xp(N-1), where N is the precision of the type of x. These macros are used in the half-cycle trigonometric functions (e.g., sinpi(x)). . The FFLOOR80 macros is used with the Intel 80-bit extended double functions. This macors corrects an off-by-one error, which led to enormous error for |x| > 0x1p32. * lib/msun/src/s_cospif.c: * lib/msun/src/s_cospi.c: * lib/msun/ld80/s_cospil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. . Correct handle the range 0x1p(N-1) <= |x| < 0x1pN. Here, one needs to determine if the integral value of |x| is even or odd to choose +1 or -1. If |x| >= 0x1pN, always return +1. * lib/msun/src/s_sinpif.c: * lib/msun/src/s_sinpi.c: * lib/msun/ld80/s_sinpil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. * lib/msun/src/s_tanpif.c: * lib/msun/src/s_tanpi.c: * lib/msun/ld80/s_tanpil.c: . Update Copyright years. . For +-0.5, return +-inf. Previously, tanpi[fl]() returned an NaN. . Use FFLOOR*() to get integer part of |x|. Need to determine if the integer part is even or odd. This is used to set +-0 for |x| integral and +-inf for (n+1/2). . For 0x1p(N-1) <= |x| < 0x1pN need to determine if x is an even or odd integer to select +0 or -0. For |x| >= 0x1pN, it is always an even integer, select 0. . Note, tanpi[fl](x) is an odd function, so one needs to consider tanpi[fl](-|x|) = - tanpi[fl](|x|). * lib/msun/ld128/s_cospil.c: * lib/msun/ld128/s_sinpil.c: * lib/msun/ld128/s_tanpil.c: . Update Copyright years. . These routines use an FFLOOR128 macros, which likely should be replaced by a bit twiddling algorithm. . The same considerations above are applied to 0x1p112 <= |x| < 0x1p113, and |x| >= 0x1p113 cases. . Note, even and odd determination used fmodl(x,2.), which is likely slow. PR: 272742 MFC after: 1 week
2023-08-01 00:34:48 +02:00
if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */
FFLOORL80(x, j0, ix, lx); /* Integer part of ax. */
odd = (uint64_t)x & 1 ? -1 : 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 15:13:52 +02:00
ax -= x;
EXTRACT_LDBL80_WORDS(ix, lx, ax);
if (ix < 0x3ffe) /* |x| < 0.5 */
Fixes for bugs in sinpi/cospi/tanpi patch to fix half-cycle trigonometric functions Paul Zimmermann, a MPFR developer, contacted me about large errors in the half-cycle trigonometric functions. I've have investigated these issues and developed the attached patch. The float, double, and ld80 (long double) changes have been tested. Caveat emptor: The ld128 changes have not been compiled. The ld128 changes have not been tested. I do not have access to a system that uses ld128 floating point. Here is an itemized list of changes: * lib/msun/src/math_private.h: . Add fast floor macros to compute the integer part of |x| for 0 <= |x| 01xp(N-1), where N is the precision of the type of x. These macros are used in the half-cycle trigonometric functions (e.g., sinpi(x)). . The FFLOOR80 macros is used with the Intel 80-bit extended double functions. This macors corrects an off-by-one error, which led to enormous error for |x| > 0x1p32. * lib/msun/src/s_cospif.c: * lib/msun/src/s_cospi.c: * lib/msun/ld80/s_cospil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. . Correct handle the range 0x1p(N-1) <= |x| < 0x1pN. Here, one needs to determine if the integral value of |x| is even or odd to choose +1 or -1. If |x| >= 0x1pN, always return +1. * lib/msun/src/s_sinpif.c: * lib/msun/src/s_sinpi.c: * lib/msun/ld80/s_sinpil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. * lib/msun/src/s_tanpif.c: * lib/msun/src/s_tanpi.c: * lib/msun/ld80/s_tanpil.c: . Update Copyright years. . For +-0.5, return +-inf. Previously, tanpi[fl]() returned an NaN. . Use FFLOOR*() to get integer part of |x|. Need to determine if the integer part is even or odd. This is used to set +-0 for |x| integral and +-inf for (n+1/2). . For 0x1p(N-1) <= |x| < 0x1pN need to determine if x is an even or odd integer to select +0 or -0. For |x| >= 0x1pN, it is always an even integer, select 0. . Note, tanpi[fl](x) is an odd function, so one needs to consider tanpi[fl](-|x|) = - tanpi[fl](|x|). * lib/msun/ld128/s_cospil.c: * lib/msun/ld128/s_sinpil.c: * lib/msun/ld128/s_tanpil.c: . Update Copyright years. . These routines use an FFLOOR128 macros, which likely should be replaced by a bit twiddling algorithm. . The same considerations above are applied to 0x1p112 <= |x| < 0x1p113, and |x| >= 0x1p113 cases. . Note, even and odd determination used fmodl(x,2.), which is likely slow. PR: 272742 MFC after: 1 week
2023-08-01 00:34:48 +02:00
t = ix == 0 ? copysignl(0, odd) : __kernel_tanpil(ax);
else if (ax == 0.5L)
t = odd / vzero;
[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 15:13:52 +02:00
else
t = -__kernel_tanpil(1 - ax);
RETURNI((hx & 0x8000) ? -t : t);
}
/* x = +-inf or nan. */
if (ix >= 0x7fff)
RETURNI(vzero / vzero);
/*
Fixes for bugs in sinpi/cospi/tanpi patch to fix half-cycle trigonometric functions Paul Zimmermann, a MPFR developer, contacted me about large errors in the half-cycle trigonometric functions. I've have investigated these issues and developed the attached patch. The float, double, and ld80 (long double) changes have been tested. Caveat emptor: The ld128 changes have not been compiled. The ld128 changes have not been tested. I do not have access to a system that uses ld128 floating point. Here is an itemized list of changes: * lib/msun/src/math_private.h: . Add fast floor macros to compute the integer part of |x| for 0 <= |x| 01xp(N-1), where N is the precision of the type of x. These macros are used in the half-cycle trigonometric functions (e.g., sinpi(x)). . The FFLOOR80 macros is used with the Intel 80-bit extended double functions. This macors corrects an off-by-one error, which led to enormous error for |x| > 0x1p32. * lib/msun/src/s_cospif.c: * lib/msun/src/s_cospi.c: * lib/msun/ld80/s_cospil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. . Correct handle the range 0x1p(N-1) <= |x| < 0x1pN. Here, one needs to determine if the integral value of |x| is even or odd to choose +1 or -1. If |x| >= 0x1pN, always return +1. * lib/msun/src/s_sinpif.c: * lib/msun/src/s_sinpi.c: * lib/msun/ld80/s_sinpil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. * lib/msun/src/s_tanpif.c: * lib/msun/src/s_tanpi.c: * lib/msun/ld80/s_tanpil.c: . Update Copyright years. . For +-0.5, return +-inf. Previously, tanpi[fl]() returned an NaN. . Use FFLOOR*() to get integer part of |x|. Need to determine if the integer part is even or odd. This is used to set +-0 for |x| integral and +-inf for (n+1/2). . For 0x1p(N-1) <= |x| < 0x1pN need to determine if x is an even or odd integer to select +0 or -0. For |x| >= 0x1pN, it is always an even integer, select 0. . Note, tanpi[fl](x) is an odd function, so one needs to consider tanpi[fl](-|x|) = - tanpi[fl](|x|). * lib/msun/ld128/s_cospil.c: * lib/msun/ld128/s_sinpil.c: * lib/msun/ld128/s_tanpil.c: . Update Copyright years. . These routines use an FFLOOR128 macros, which likely should be replaced by a bit twiddling algorithm. . The same considerations above are applied to 0x1p112 <= |x| < 0x1p113, and |x| >= 0x1p113 cases. . Note, even and odd determination used fmodl(x,2.), which is likely slow. PR: 272742 MFC after: 1 week
2023-08-01 00:34:48 +02:00
* For 0x1p63 <= |x| < 0x1p64 need to determine if x is an even
* or odd integer to set t = +0 or -0.
* For |x| >= 0x1p64, it is always an even integer, so t = 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 15:13:52 +02:00
*/
Fixes for bugs in sinpi/cospi/tanpi patch to fix half-cycle trigonometric functions Paul Zimmermann, a MPFR developer, contacted me about large errors in the half-cycle trigonometric functions. I've have investigated these issues and developed the attached patch. The float, double, and ld80 (long double) changes have been tested. Caveat emptor: The ld128 changes have not been compiled. The ld128 changes have not been tested. I do not have access to a system that uses ld128 floating point. Here is an itemized list of changes: * lib/msun/src/math_private.h: . Add fast floor macros to compute the integer part of |x| for 0 <= |x| 01xp(N-1), where N is the precision of the type of x. These macros are used in the half-cycle trigonometric functions (e.g., sinpi(x)). . The FFLOOR80 macros is used with the Intel 80-bit extended double functions. This macors corrects an off-by-one error, which led to enormous error for |x| > 0x1p32. * lib/msun/src/s_cospif.c: * lib/msun/src/s_cospi.c: * lib/msun/ld80/s_cospil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. . Correct handle the range 0x1p(N-1) <= |x| < 0x1pN. Here, one needs to determine if the integral value of |x| is even or odd to choose +1 or -1. If |x| >= 0x1pN, always return +1. * lib/msun/src/s_sinpif.c: * lib/msun/src/s_sinpi.c: * lib/msun/ld80/s_sinpil.c: . Update Copyright years. . Use FFLOOR*() macro to get integer part of |x|. * lib/msun/src/s_tanpif.c: * lib/msun/src/s_tanpi.c: * lib/msun/ld80/s_tanpil.c: . Update Copyright years. . For +-0.5, return +-inf. Previously, tanpi[fl]() returned an NaN. . Use FFLOOR*() to get integer part of |x|. Need to determine if the integer part is even or odd. This is used to set +-0 for |x| integral and +-inf for (n+1/2). . For 0x1p(N-1) <= |x| < 0x1pN need to determine if x is an even or odd integer to select +0 or -0. For |x| >= 0x1pN, it is always an even integer, select 0. . Note, tanpi[fl](x) is an odd function, so one needs to consider tanpi[fl](-|x|) = - tanpi[fl](|x|). * lib/msun/ld128/s_cospil.c: * lib/msun/ld128/s_sinpil.c: * lib/msun/ld128/s_tanpil.c: . Update Copyright years. . These routines use an FFLOOR128 macros, which likely should be replaced by a bit twiddling algorithm. . The same considerations above are applied to 0x1p112 <= |x| < 0x1p113, and |x| >= 0x1p113 cases. . Note, even and odd determination used fmodl(x,2.), which is likely slow. PR: 272742 MFC after: 1 week
2023-08-01 00:34:48 +02:00
t = ix >= 0x403f ? 0 : (copysignl(0, (lx & 1) ? -1 : 1));
RETURNI((hx & 0x8000) ? -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 15:13:52 +02:00
}
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