The branch main has been updated by kib: URL: https://cgit.FreeBSD.org/src/commit/?id=dce5f3abed7181cc533ca5ed3de44517775e78dd
commit dce5f3abed7181cc533ca5ed3de44517775e78dd Author: Steve Kargl <[email protected]> AuthorDate: 2021-10-25 13:13:52 +0000 Commit: Konstantin Belousov <[email protected]> CommitDate: 2021-10-25 23:50:20 +0000 [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 --- lib/msun/Makefile | 14 +++- lib/msun/Symbol.map | 13 ++++ lib/msun/ld128/k_cospil.h | 42 +++++++++++ lib/msun/ld128/k_sinpil.h | 42 +++++++++++ lib/msun/ld128/s_cospil.c | 109 ++++++++++++++++++++++++++++ lib/msun/ld128/s_sinpil.c | 118 +++++++++++++++++++++++++++++++ lib/msun/ld128/s_tanpil.c | 120 +++++++++++++++++++++++++++++++ lib/msun/ld80/k_cospil.h | 42 +++++++++++ lib/msun/ld80/k_sinpil.h | 42 +++++++++++ lib/msun/ld80/s_cospil.c | 129 +++++++++++++++++++++++++++++++++ lib/msun/ld80/s_sinpil.c | 140 ++++++++++++++++++++++++++++++++++++ lib/msun/ld80/s_tanpil.c | 139 ++++++++++++++++++++++++++++++++++++ lib/msun/man/cospi.3 | 111 +++++++++++++++++++++++++++++ lib/msun/man/sinpi.3 | 102 +++++++++++++++++++++++++++ lib/msun/man/tanpi.3 | 106 ++++++++++++++++++++++++++++ lib/msun/src/k_cospi.h | 44 ++++++++++++ lib/msun/src/k_sinpi.h | 43 +++++++++++ lib/msun/src/math.h | 9 +++ lib/msun/src/s_cospi.c | 151 +++++++++++++++++++++++++++++++++++++++ lib/msun/src/s_cospif.c | 109 ++++++++++++++++++++++++++++ lib/msun/src/s_sinpi.c | 168 +++++++++++++++++++++++++++++++++++++++++++ lib/msun/src/s_sinpif.c | 122 ++++++++++++++++++++++++++++++++ lib/msun/src/s_tanpi.c | 176 ++++++++++++++++++++++++++++++++++++++++++++++ lib/msun/src/s_tanpif.c | 114 ++++++++++++++++++++++++++++++ 24 files changed, 2203 insertions(+), 2 deletions(-) diff --git a/lib/msun/Makefile b/lib/msun/Makefile index 7107aad56aa7..dcee5572f949 100644 --- a/lib/msun/Makefile +++ b/lib/msun/Makefile @@ -126,6 +126,12 @@ COMMON_SRCS+= catrigl.c \ # See also: https://bugs.freebsd.org/bugzilla/show_bug.cgi?id=130067 .if ${COMPILER_TYPE} == "gcc" CFLAGS.e_powl.c+= -Wno-error=overflow + +# IEEE-754 2008 and ISO/IEC TS 18661-4 half-cycle trignometric functions +COMMON_SRCS+= s_cospi.c s_cospif.c s_cospil.c \ + s_sinpi.c s_sinpif.c s_sinpil.c \ + s_tanpi.c s_tanpif.c s_tanpil.c + .endif .endif @@ -154,7 +160,8 @@ INCS+= fenv.h math.h MAN= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 \ ceil.3 cacos.3 ccos.3 ccosh.3 cexp.3 \ - cimag.3 clog.3 copysign.3 cos.3 cosh.3 cpow.3 csqrt.3 erf.3 \ + cimag.3 clog.3 copysign.3 cos.3 cosh.3 cospi.3 \ + cpow.3 csqrt.3 erf.3 \ exp.3 fabs.3 fdim.3 \ feclearexcept.3 feenableexcept.3 fegetenv.3 \ fegetround.3 fenv.3 floor.3 \ @@ -162,7 +169,7 @@ MAN= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 \ lgamma.3 log.3 lrint.3 lround.3 math.3 nan.3 \ nextafter.3 remainder.3 rint.3 \ round.3 scalbn.3 signbit.3 sin.3 sincos.3 \ - sinh.3 sqrt.3 tan.3 tanh.3 trunc.3 \ + sinh.3 sinpi.3 sqrt.3 tan.3 tanh.3 tanpi.3 trunc.3 \ complex.3 MLINKS+=acos.3 acosf.3 acos.3 acosl.3 @@ -192,6 +199,7 @@ MLINKS+=clog.3 clogf.3 clog.3 clogl.3 MLINKS+=copysign.3 copysignf.3 copysign.3 copysignl.3 MLINKS+=cos.3 cosf.3 cos.3 cosl.3 MLINKS+=cosh.3 coshf.3 cosh.3 coshl.3 +MLINKS+=cospi.3 cospif.3 cospi.3 cospil.3 MLINKS+=cpow.3 cpowf.3 cpow.3 cpowl.3 MLINKS+=csqrt.3 csqrtf.3 csqrt.3 csqrtl.3 MLINKS+=erf.3 erfc.3 erf.3 erff.3 erf.3 erfcf.3 erf.3 erfl.3 erf.3 erfcl.3 @@ -244,10 +252,12 @@ MLINKS+=scalbn.3 scalbnf.3 scalbn.3 scalbnl.3 MLINKS+=sin.3 sinf.3 sin.3 sinl.3 MLINKS+=sincos.3 sincosf.3 sin.3 sincosl.3 MLINKS+=sinh.3 sinhf.3 sinh.3 sinhl.3 +MLINKS+=sinpi.3 sinpif.3 sinpi.3 sinpil.3 MLINKS+=sqrt.3 cbrt.3 sqrt.3 cbrtf.3 sqrt.3 cbrtl.3 sqrt.3 sqrtf.3 \ sqrt.3 sqrtl.3 MLINKS+=tan.3 tanf.3 tan.3 tanl.3 MLINKS+=tanh.3 tanhf.3 tanh.3 tanhl.3 +MLINKS+=tanpi.3 tanpif.3 tanpi.3 tanpil.3 MLINKS+=trunc.3 truncf.3 trunc.3 truncl.3 .include <src.opts.mk> diff --git a/lib/msun/Symbol.map b/lib/msun/Symbol.map index 51deded732f0..7229e7ef31fd 100644 --- a/lib/msun/Symbol.map +++ b/lib/msun/Symbol.map @@ -304,3 +304,16 @@ FBSD_1.5 { sincosf; sincosl; }; + +/* First added in 14.0-CURRENT */ +FBSD_1.7 { + cospi; + cospif; + cospil; + sinpi; + sinpif; + sinpil; + tanpi; + tanpif; + tanpil; +}; diff --git a/lib/msun/ld128/k_cospil.h b/lib/msun/ld128/k_cospil.h new file mode 100644 index 000000000000..592f19229532 --- /dev/null +++ b/lib/msun/ld128/k_cospil.h @@ -0,0 +1,42 @@ +/*- + * Copyright (c) 2017 Steven G. Kargl + * 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/k_cospi.c for implementation details. + */ + +static inline long double +__kernel_cospil(long double x) +{ + long double hi, lo; + + hi = (double)x; + lo = x - hi; + lo = lo * (pi_lo + pi_hi) + hi * pi_lo; + hi *= pi_hi; + _2sumF(hi, lo); + return (__kernel_cosl(hi, lo)); +} diff --git a/lib/msun/ld128/k_sinpil.h b/lib/msun/ld128/k_sinpil.h new file mode 100644 index 000000000000..fa4e7d6336d7 --- /dev/null +++ b/lib/msun/ld128/k_sinpil.h @@ -0,0 +1,42 @@ +/*- + * Copyright (c) 2017 Steven G. Kargl + * 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/k_sinpi.c for implementation details. + */ + +static inline long double +__kernel_sinpil(long double x) +{ + long double hi, lo; + + hi = (double)x; + lo = x - hi; + lo = lo * (pi_lo + pi_hi) + hi * pi_lo; + hi *= pi_hi; + _2sumF(hi, lo); + return (__kernel_sinl(hi, lo, 1)); +} diff --git a/lib/msun/ld128/s_cospil.c b/lib/msun/ld128/s_cospil.c new file mode 100644 index 000000000000..b4bc50bb4d89 --- /dev/null +++ b/lib/msun/ld128/s_cospil.c @@ -0,0 +1,109 @@ +/*- + * Copyright (c) 2017 Steven G. Kargl + * 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_cospi.c for implementation details. + * + * FIXME: This has not been compiled nor has it been tested for accuracy. + * FIXME: This should use bit twiddling. + */ + +#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; + +#include "k_cospil.h" +#include "k_sinpil.h" + +volatile static const double vzero = 0; + +long double +cospil(long double x) +{ + long double ax, c, xf; + uint32_t ix; + + ax = fabsl(x); + + if (ax < 1) { + if (ax < 0.25) { + if (ax < 0x1p-60) { + if ((int)x == 0) + return (1); + } + return (__kernel_cospil(ax)); + } + + if (ax < 0.5) + c = __kernel_sinpil(0.5 - ax); + else if (ax < 0.75) { + if (ax == 0.5) + return (0); + c = -__kernel_sinpil(ax - 0.5); + } else + c = -__kernel_cospil(1 - ax); + return (c); + } + + if (ax < 0x1p112) { + xf = floorl(ax); + ax -= xf; + if (x < 0.5) { + if (x < 0.25) + c = ax == 0 ? 1 : __kernel_cospil(ax); + else + c = __kernel_sinpil(0.5 - ax); + } else { + if (x < 0.75) { + if (ax == 0.5) + return (0); + c = -__kernel_sinpil(ax - 0.5); + } else + c = -__kernel_cospil(1 - ax); + } + + if (xf > 0x1p50) + xf -= 0x1p50; + if (xf > 0x1p30) + xf -= 0x1p30; + ix = (uint32_t)xf; + return (ix & 1 ? -c : c); + } + + if (isinf(x) || isnan(x)) + return (vzero / vzero); + + /* + * |x| >= 0x1p112 is always an even integer, so return 1. + */ + return (1); +} diff --git a/lib/msun/ld128/s_sinpil.c b/lib/msun/ld128/s_sinpil.c new file mode 100644 index 000000000000..39eed9b007bc --- /dev/null +++ b/lib/msun/ld128/s_sinpil.c @@ -0,0 +1,118 @@ +/*- + * Copyright (c) 2017 Steven G. Kargl + * 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_sinpi.c for implementation details. + * + * FIXME: This has not been compiled nor has it been tested for accuracy. + * FIXME: This should use bit twiddling. + */ + +#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; + +#include "k_cospil.h" +#include "k_sinpil.h" + +volatile static const double vzero = 0; + +long double +sinpil(long double x) +{ + long double ax, hi, lo, s, xf, xhi, xlo; + uint32_t ix; + + ax = fabsl(x); + + if (ax < 1) { + if (ax < 0.25) { + if (ax < 0x1p-60) { + if (x == 0) + return (x); + hi = (double)x; + hi *= 0x1p113L; + lo = x * 0x1p113L - hi; + s = (pi_lo + pi_hi) * lo + pi_lo * lo + + pi_hi * hi; + return (s * 0x1p-113L); + } + + s = __kernel_sinpil(ax); + return (copysignl(s, x)); + } + + if (ax < 0.5) + s = __kernel_cospil(0.5 - ax); + else if (ax < 0.75) + s = __kernel_cospil(ax - 0.5); + else + s = __kernel_sinpil(1 - ax); + return (copysignl(s, x)); + } + + if (ax < 0x1p112) { + xf = floorl(ax); + ax -= xf; + if (ax == 0) { + s = 0; + } else { + if (ax < 0.5) { + if (ax <= 0.25) + s = __kernel_sinpil(ax); + else + s = __kernel_cospil(0.5 - ax); + } else { + if (ax < 0.75) + s = __kernel_cospil(ax - 0.5); + else + s = __kernel_sinpil(1 - ax); + } + + if (xf > 0x1p50) + xf -= 0x1p50; + if (xf > 0x1p30) + xf -= 0x1p30; + ix = (uint32_t)xf; + if (ix & 1) s = -s; + } + return (copysignl(s, x)); + } + + if (isinf(x) || isnan(x)) + return (vzero / vzero); + + /* + * |x| >= 0x1p112 is always an integer, so return +-0. + */ + return (copysignl(0, x)); +} diff --git a/lib/msun/ld128/s_tanpil.c b/lib/msun/ld128/s_tanpil.c new file mode 100644 index 000000000000..33a61cf3115d --- /dev/null +++ b/lib/msun/ld128/s_tanpil.c @@ -0,0 +1,120 @@ +/*- + * Copyright (c) 2017 Steven G. Kargl + * 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. + * + * FIXME: This has not been compiled nor has it been tested for accuracy. + * FIXME: This should use bit twiddling. + */ + +#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 +__kernel_tanpi(long double x) +{ + 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) +{ + long double ax, hi, lo, xf; + uint32_t ix; + + ax = fabsl(ax); + + if (ax < 1) { + if (ax < 0.5) { + if (ax < 0x1p-60) { + if (x == 0) + return (x); + hi = (double)x; + hi *= 0x1p113L + 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); + return (copysignl(t, x)); + } + + if (ix < 0x1p112) { + xf = floorl(ax); + ax -= xf; + 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); + return (copysignl(t, x)); + } + + /* x = +-inf or nan. */ + if (isinf(x) || isnan(x)) + return (vzero / vzero); + + /* + * |x| >= 0x1p53 is always an integer, so return +-0. + */ + return (copysignl(0, x)); +} diff --git a/lib/msun/ld80/k_cospil.h b/lib/msun/ld80/k_cospil.h new file mode 100644 index 000000000000..6e13ef02aea2 --- /dev/null +++ b/lib/msun/ld80/k_cospil.h @@ -0,0 +1,42 @@ +/*- + * Copyright (c) 2017 Steven G. Kargl + * 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/k_cospi.c for implementation details. + */ + +static inline long double +__kernel_cospil(long double x) +{ + long double hi, lo; + + hi = (float)x; + lo = x - hi; + lo = lo * (pi_lo + pi_hi) + hi * pi_lo; + hi *= pi_hi; + _2sumF(hi, lo); + return (__kernel_cosl(hi, lo)); +} diff --git a/lib/msun/ld80/k_sinpil.h b/lib/msun/ld80/k_sinpil.h new file mode 100644 index 000000000000..00241b932e9e --- /dev/null +++ b/lib/msun/ld80/k_sinpil.h @@ -0,0 +1,42 @@ +/*- + * Copyright (c) 2017 Steven G. Kargl + * 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/k_sinpi.c for implementation details. + */ + +static inline long double +__kernel_sinpil(long double x) +{ + long double hi, lo; + + hi = (float)x; + lo = x - hi; + lo = lo * (pi_lo + pi_hi) + hi * pi_lo; + hi *= pi_hi; + _2sumF(hi, lo); + return (__kernel_sinl(hi, lo, 1)); +} diff --git a/lib/msun/ld80/s_cospil.c b/lib/msun/ld80/s_cospil.c new file mode 100644 index 000000000000..199479e9eaf9 --- /dev/null +++ b/lib/msun/ld80/s_cospil.c @@ -0,0 +1,129 @@ +/*- + * Copyright (c) 2017 Steven G. Kargl + * 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_cospi.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 */ + +#include "k_cospil.h" +#include "k_sinpil.h" + +volatile static const double vzero = 0; + +long double +cospil(long double x) +{ + long double ax, c; + 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 < 0x3ffd) { /* |x| < 0.25 */ + if (ix < 0x3fdd) { /* |x| < 0x1p-34 */ + if ((int)x == 0) + RETURNI(1); + } + RETURNI(__kernel_cospil(ax)); + } + + if (ix < 0x3ffe) /* |x| < 0.5 */ + c = __kernel_sinpil(0.5 - ax); + else if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */ + if (ax == 0.5) + RETURNI(0); + c = -__kernel_sinpil(ax - 0.5); + } else + c = -__kernel_cospil(1 - ax); + RETURNI(c); + } + + if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */ + /* Determine integer part of ax. */ + j0 = ix - 0x3fff + 1; + if (j0 < 32) { + lx = (lx >> 32) << 32; + lx &= ~(((lx << 32)-1) >> j0); + } else { + m = (uint64_t)-1 >> (j0 + 1); + if (lx & m) lx &= ~m; + } + INSERT_LDBL80_WORDS(x, ix, lx); + + ax -= x; + EXTRACT_LDBL80_WORDS(ix, lx, ax); + + if (ix < 0x3ffe) { /* |x| < 0.5 */ + if (ix < 0x3ffd) /* |x| < 0.25 */ + c = ix == 0 ? 1 : __kernel_cospil(ax); + else + c = __kernel_sinpil(0.5 - ax); + + } else { + if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */ + if (ax == 0.5) + RETURNI(0); + c = -__kernel_sinpil(ax - 0.5); + } else + c = -__kernel_cospil(1 - ax); + } + + if (j0 > 40) + x -= 0x1p40; + if (j0 > 30) + x -= 0x1p30; + j0 = (uint32_t)x; + + RETURNI(j0 & 1 ? -c : c); + } + + if (ix >= 0x7fff) + RETURNI(vzero / vzero); + + /* + * |x| >= 0x1p63 is always an even integer, so return 1. + */ + RETURNI(1); +} diff --git a/lib/msun/ld80/s_sinpil.c b/lib/msun/ld80/s_sinpil.c new file mode 100644 index 000000000000..4cefa92352e1 --- /dev/null +++ b/lib/msun/ld80/s_sinpil.c @@ -0,0 +1,140 @@ +/*- + * Copyright (c) 2017 Steven G. Kargl + * 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_sinpi.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 union IEEEl2bits +pi_hi_u = LD80C(0xc90fdaa200000000, 1, 3.14159265346825122833e+00L), +pi_lo_u = LD80C(0x85a308d313198a2e, -33, 1.21542010130123852029e-10L); +#define pi_hi (pi_hi_u.e) +#define pi_lo (pi_lo_u.e) + +#include "k_cospil.h" +#include "k_sinpil.h" + +volatile static const double vzero = 0; + +long double +sinpil(long double x) +{ + long double ax, hi, lo, s; + 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 < 0x3ffd) { /* |x| < 0.25 */ + if (ix < 0x3fdd) { /* |x| < 0x1p-34 */ + if (x == 0) + RETURNI(x); + INSERT_LDBL80_WORDS(hi, hx, + lx & 0xffffffff00000000ull); + hi *= 0x1p63L; + lo = x * 0x1p63L - hi; + s = (pi_lo + pi_hi) * lo + pi_lo * hi + + pi_hi * hi; + RETURNI(s * 0x1p-63L); + } + s = __kernel_sinpil(ax); + RETURNI((hx & 0x8000) ? -s : s); + } + + if (ix < 0x3ffe) /* |x| < 0.5 */ + s = __kernel_cospil(0.5 - ax); + else if (lx < 0xc000000000000000ull) /* |x| < 0.75 */ + s = __kernel_cospil(ax - 0.5); + else + s = __kernel_sinpil(1 - ax); + RETURNI((hx & 0x8000) ? -s : s); + } + + if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */ + /* Determine integer part of ax. */ + j0 = ix - 0x3fff + 1; + if (j0 < 32) { + lx = (lx >> 32) << 32; + lx &= ~(((lx << 32)-1) >> j0); + } else { + m = (uint64_t)-1 >> (j0 + 1); + if (lx & m) lx &= ~m; + } + INSERT_LDBL80_WORDS(x, ix, lx); + + ax -= x; + EXTRACT_LDBL80_WORDS(ix, lx, ax); + + if (ix == 0) { + s = 0; + } else { + if (ix < 0x3ffe) { /* |x| < 0.5 */ + if (ix < 0x3ffd) /* |x| < 0.25 */ + s = __kernel_sinpil(ax); + else + s = __kernel_cospil(0.5 - ax); + } else { + /* |x| < 0.75 */ + if (lx < 0xc000000000000000ull) + s = __kernel_cospil(ax - 0.5); + else + s = __kernel_sinpil(1 - ax); + } + + if (j0 > 40) + x -= 0x1p40; + if (j0 > 30) + x -= 0x1p30; + j0 = (uint32_t)x; + if (j0 & 1) s = -s; + } + RETURNI((hx & 0x8000) ? -s : s); + } + + /* x = +-inf or nan. */ + if (ix >= 0x7fff) + RETURNI(vzero / vzero); + + /* + * |x| >= 0x1p63 is always an integer, so return +-0. + */ + RETURNI(copysignl(0, x)); +} diff --git a/lib/msun/ld80/s_tanpil.c b/lib/msun/ld80/s_tanpil.c new file mode 100644 index 000000000000..02451e562025 --- /dev/null +++ b/lib/msun/ld80/s_tanpil.c @@ -0,0 +1,139 @@ +/*- + * Copyright (c) 2017 Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: *** 1464 LINES SKIPPED ***
