Index: lib/msun/Makefile =================================================================== --- lib/msun/Makefile (revision 317529) +++ lib/msun/Makefile (working copy) @@ -59,6 +59,7 @@ s_asinh.c s_asinhf.c s_atan.c s_atanf.c s_carg.c s_cargf.c s_cargl.c \ s_cbrt.c s_cbrtf.c s_ceil.c s_ceilf.c \ s_copysign.c s_copysignf.c s_cos.c s_cosf.c \ + s_cospi.c s_cospif.c \ s_csqrt.c s_csqrtf.c s_erf.c s_erff.c \ s_exp2.c s_exp2f.c s_expm1.c s_expm1f.c s_fabsf.c s_fdim.c \ s_finite.c s_finitef.c \ @@ -74,7 +75,10 @@ s_rint.c s_rintf.c s_round.c s_roundf.c \ s_scalbln.c s_scalbn.c s_scalbnf.c s_signbit.c \ s_signgam.c s_significand.c s_significandf.c s_sin.c s_sinf.c \ - s_tan.c s_tanf.c s_tanh.c s_tanhf.c s_tgammaf.c s_trunc.c s_truncf.c \ + s_sinpi.c s_sinpif.c \ + s_tan.c s_tanf.c s_tanh.c s_tanhf.c \ + s_tanpi.c s_tanpif.c \ + s_tgammaf.c s_trunc.c s_truncf.c \ w_cabs.c w_cabsf.c w_drem.c w_dremf.c # Location of fpmath.h and _fpmath.h @@ -100,11 +104,16 @@ e_lgammal.c e_lgammal_r.c \ e_remainderl.c e_sinhl.c e_sqrtl.c \ invtrig.c k_cosl.c k_sinl.c k_tanl.c \ - s_asinhl.c s_atanl.c s_cbrtl.c s_ceill.c s_cosl.c s_cprojl.c \ + s_asinhl.c s_atanl.c s_cbrtl.c s_ceill.c s_cosl.c \ + s_cospil.c \ + s_cprojl.c \ s_csqrtl.c s_erfl.c s_exp2l.c s_expl.c s_floorl.c s_fmal.c \ s_fmaxl.c s_fminl.c s_frexpl.c s_logbl.c s_logl.c s_nanl.c \ s_nextafterl.c s_nexttoward.c s_remquol.c s_rintl.c s_roundl.c \ - s_scalbnl.c s_sinl.c s_tanhl.c s_tanl.c s_truncl.c w_cabsl.c + s_scalbnl.c s_sinl.c \ + s_sinpil.c \ + s_tanhl.c s_tanl.c \ + s_tanpil.c s_truncl.c w_cabsl.c .endif # C99 complex functions @@ -131,13 +140,19 @@ 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 copysign.3 cos.3 cosh.3 csqrt.3 erf.3 exp.3 fabs.3 fdim.3 \ + cimag.3 copysign.3 cos.3 cosh.3 \ + cospi.3 \ + csqrt.3 erf.3 exp.3 fabs.3 fdim.3 \ feclearexcept.3 feenableexcept.3 fegetenv.3 \ fegetround.3 fenv.3 floor.3 \ fma.3 fmax.3 fmod.3 hypot.3 ieee.3 ieee_test.3 ilogb.3 j0.3 \ 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 sinh.3 sqrt.3 tan.3 tanh.3 trunc.3 \ + round.3 scalbn.3 signbit.3 sin.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 @@ -166,6 +181,7 @@ 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+=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 MLINKS+=exp.3 expm1.3 exp.3 expm1f.3 exp.3 expm1l.3 exp.3 pow.3 exp.3 powf.3 \ @@ -216,10 +232,12 @@ MLINKS+=scalbn.3 scalbnf.3 scalbn.3 scalbnl.3 MLINKS+=sin.3 sinf.3 sin.3 sinl.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 Index: lib/msun/Symbol.map =================================================================== --- lib/msun/Symbol.map (revision 317529) +++ lib/msun/Symbol.map (working copy) @@ -294,4 +294,13 @@ casinl; catanl; catanhl; + cospi; + cospif; + cospil; + sinpi; + sinpif; + sinpil; + tanpi; + tanpif; + tanpil; }; Index: lib/msun/ld128/k_cospil.c =================================================================== --- lib/msun/ld128/k_cospil.c (nonexistent) +++ lib/msun/ld128/k_cospil.c (working copy) @@ -0,0 +1,73 @@ +/*- + * 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. + * + * FIXME: This has not been compiled nor has it been tested for accuracy. + * FIXME: This should use bit twiddling. + */ + +static const long double +c0 = 1, +c1hi = -4.93480220054467930941724549993807541e+00L, +c1lo = -1.61159244006703024615160135944400084e-34L, +c02 = 4.05871212641676821818501386202937963e+00L, +c03 = -1.33526276885458949587530478285057448e+00L, +c04 = 2.35330630358893204541879352772399571e-01L, +c05 = -2.58068913900140600125982936922503890e-02L, +c06 = 1.92957430940392304790328456072058283e-03L, +c07 = -1.04638104924845707113757250204498056e-04L, +c08 = 4.30306958703294680806457740580669010e-06L, +c09 = -1.38789524622131344829253970500107607e-07L, +c10 = 3.60473079732244660718578413933676910e-09L, +c11 = -7.70070692297072534641720608808474790e-11L, +c12 = 1.37684487309360112303144478033041762e-12L, +c13 = -2.07957304470476734518573046614539573e-14L; + +static inline long double +__kernel_cospi(long double x) +{ + union IEEEl2bits u; + long double c, chi, clo, x2, x2lo; + double x2hi; + + x2 = x * x; + + c = c09 + (c10 + (c11 + (c12 + c13 * x2) * x2) * x2) * x2; + c = c05 + (c06 + (c07 + (c08 + c * x2) * x2) * x2) * x2; + c = (c02 + (c03 + (c04 + c * x2) * x2) * x2) * x2 + c1hi; + + if (x2 < 0x1p-6) /* |x| < 0x1p-6 */ + return (c0 + c * x2); + + x2hi = x2; + x2lo = x2 - x2hi; + + c = clo * x2lo + chi * x2lo + clo * x2hi + (chi * x2hi + c0); + + return (c); +} Property changes on: lib/msun/ld128/k_cospil.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/ld128/k_sinpil.c =================================================================== --- lib/msun/ld128/k_sinpil.c (nonexistent) +++ lib/msun/ld128/k_sinpil.c (working copy) @@ -0,0 +1,73 @@ +/*- + * 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. + * + * FIXME: This has not been compiled nor has it been tested for accuracy. + * FIXME: This should use bit twiddling. + * + * Compute sinpi(x) = sin(pi*x) in the interval [0,0.25] + */ + +static const long double +s0lo = 3.14159265358979322702026593105983920e+00L, +s0md = 1.14423774522196636802274144823600323e-17L, +s0lo = -5.10459839933399352423791604618557491e-52L, +s01 = -5.16771278004997002924605251118356578e+00L, +s02 = 2.55016403987734544385617758369521912e+00L, +s03 = -5.99264529320792076887739383518724498e-01L, +s04 = 8.21458866111282287988023605285125252e-02L, +s05 = -7.37043094571435077725854643888422319e-03L, +s06 = 4.66302805767612564382677987452304496e-04L, +s07 = -2.19153534478302140522509092972929589e-05L, +s08 = 7.95205400147494466063630770553231865e-07L, +s09 = -2.29484289960219849488354905723109270e-08L, +s10 = 5.39266447760508581521426149354268607e-10L, +s11 = -1.05182947998557665557194979309998767e-11L, +s12 = 1.72036427603492093074818577722479034e-13L; + +static inline long double +__kernel_sinpi(long double x) +{ + union IEEEl2bits u; + long double hi, lo, sm, x2, xlo; + double xhi; + + /* Split x into high and low parts. */ + xhi = x; + xlo = x - xhi; + + x2 = x * x; + sm = x2 * (x2 * (x2 * (x2 * s12 + s11) + s10) + s09) + s08; + sm = x2 * (x2 * (x2 * (x2 * sm + s07) + s06) + s05) + s04; + sm = x2 * (x2 * (x2 * sm + s03) + s02) + s01; + lo = xlo * (x + xhi) * sm; + hi = sm * xhi * xhi; + lo = x * (lo + s0lo) + xlo * (s0hi + s0md) + x * hi; + + return (lo + xhi * s0md + xhi * s0hi); +} Property changes on: lib/msun/ld128/k_sinpil.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/ld128/s_cospil.c =================================================================== --- lib/msun/ld128/s_cospil.c (nonexistent) +++ lib/msun/ld128/s_cospil.c (working copy) @@ -0,0 +1,98 @@ +/*- + * 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" +#include "k_cospi.c" +#include "k_sinpi.c" + +static inline long double +__compute_cospil(long double x) +{ + + if (x < 0.5) { + if (x < 0.25) + return (__kernel_cospil(x)); + return (__kernel_sinpil(0.5 - x)); + } else { + if (x < 0.75) + return (-__kernel_sinpil(x - 0.5)); + return (-__kernel_cospil(1 - x)); + } +} + +long double +cospil(long double x) +{ + const double huge = 1e+300; + long double ax, xf; + uint32_t ix; + + ax = fabsl(x); + + if (ax < 1) { /* |x| < 1 */ + if (ax < 0x1p-60) { /* |x| < 0x1p-60 */ + if (huge + x > 0) + return (1); + } + if (ax == 0.5) + return (0); + return (__compute_cospil(ax)); + } + + if (ax < 0x1p112) { /* 1 <= |x| < 0x1p112 */ + + xf = floorl(ax); + + ax -= x; + if (ax == 0.5) + return (0); + + ax = ax == 0 ? 1 : __compute_cospil(ax); + + if (xf > 0x1p50) xf -= 0x1p50; + if (xf > 0x1p30) xf -= 0x1p30; + ix = (uint32_t)xf; + + return (ix & 1 ? -ax : ax); + } + + if (isinf(x) || isnan(x)) + return (x - x); + + /* + * |x| >= 0x1p112 is always an even integer, so return 1. + * FIXME: should this raise FE_INEXACT or FE_INVALID. + */ + return (1); +} Property changes on: lib/msun/ld128/s_cospil.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/ld128/s_sinpil.c =================================================================== --- lib/msun/ld128/s_sinpil.c (nonexistent) +++ lib/msun/ld128/s_sinpil.c (working copy) @@ -0,0 +1,100 @@ +/*- + * 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" +#include "k_cospil.c" +#include "k_sinpil.c" + +static const long double pihi = 3.14159265358979322702026593105983920e+00L; +static const long double pilo = 1.14423774522196636802434264184180742e-17L; + +static inline long double +__compute_sinpil(long double x) +{ + + if (x < 0.5) { + if (x <= 0.25) + return (__kernel_sinpil(x)); + return (__kernel_cospil(0.5 - x)); + } else { + if (x < 0.75) + return (__kernel_cospil(x - 0.5)); + return (__kernel_sinpil(1 - x)); + } +} + +long double +sinpi(long double x) +{ + long double ax, xf; + uint32_t ix; + + ax = fabsl(x); + + if (ax < 1) { /* |x| < 1 */ + if (ax < 0x1p-60) { /* |x| < 0x1p-60 */ + if (x == 0) + return (x); + return (pilo * x + pihi * x); + } + ax = __compute_sinpil(ax); + return (copysignl(ax, x)); + } + + if (ax < 0x1p112) { /* 1 <= |x| < 0x1p112 */ + + xf = floorl(ax); + + ax -= xf; + if (ax == 0) { + ax = 0; + } else { + ax = __compute_sinpil(ax); + if (xf > 0x1p50) xf -= 0x1p50; + if (xf > 0x1p30) xf -= 0x1p30; + ix = (uint32_t)xf; + if (ix & 1) ax = -ax; + } + return (copysignl(ax, x)); + } + + if (isinf(x) || isnan(x)) + return (x - x); + + /* + * |x| >= 0x1p112 is always an integer, so return +-0. + * FIXME: should this raise FE_INEXACT or FE_INVALID. + */ + return (copysignl(0, x)); +} Property changes on: lib/msun/ld128/s_sinpil.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/ld128/s_tanpil.c =================================================================== --- lib/msun/ld128/s_tanpil.c (nonexistent) +++ lib/msun/ld128/s_tanpil.c (working copy) @@ -0,0 +1,98 @@ +/*- + * 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. + * FIXME: This should use a polynomial approximation in [0,0.25], but the + * FIXME: increase in max ULP is probably small, so who cares. + */ + +#include "math.h" +#include "math_private.h" + +static const long double pihi = 3.14159265358979322702026593105983920e+00L; +static const long double pilo = 1.14423774522196636802434264184180742e-17L; + +static inline long double +__k_tanpi(long double x) +{ + + return (sinpil(x) / cospil(x)); +} + +static inline long double +__compute_tanpi(long double x) +{ + + return (x < 0.5 ? __k_tanpil(x) : -__k_tanpil(1 - x)); +} + +long double +tanpil(long double x) +{ + long double ax, xf; + uint32_t ix; + + ax = fabsl(ax); + + if (ax < 1) { /* |x| < 1 */ + if (ax < 0x1p-60) { /* |x| < 0x1p-60 */ + if (x == 0) + return (x); + return (pilo * x + pihi * x); + } + if (ax == 0.5) + return ((x - x) / (x - x)); + ax = __compute_tanpil(ax); + return (copysignl(ax, x)); + } + + if (ix < 0x1p112) { /* 1 <= |x| < 0x1p112 */ + + xf = floorl(ax); + + ax -= xf; + + if (ax == 0.5) + return ((x - x) / (x - x)); + + ax = ax == 0 ? 0 : __compute_tanpil(ax); + return (copysignl(ax, x)); + } + + /* x = +-inf or nan. */ + if (isinf(x) || isnan(x)) + return (x - x); + + /* + * |x| >= 0x1p53 is always an integer, so return +-0. + * FIXME: should this raise FE_INEXACT or FE_INVALID. + */ + return (copysignl(0, x)); +} Property changes on: lib/msun/ld128/s_tanpil.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/ld80/k_cospil.c =================================================================== --- lib/msun/ld80/k_cospil.c (nonexistent) +++ lib/msun/ld80/k_cospil.c (working copy) @@ -0,0 +1,78 @@ +/*- + * 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 const union IEEEl2bits +c1hiu = LD80C(0x9de9e64df22ef2d2, 2, -4.93480220054467930927e+00L), +c1lou = LD80C(0xadc4baf0dd791c3e, -63, -1.47187625629472133798e-19L), +c2u = LD80C(0x81e0f840dad61d9b, 2, 4.05871212641676821836e+00L); +#define c1hi (c1hiu.e) +#define c1lo (c1lou.e) +#define c2 (c2u.e) + +static const double +c3 = -1.3352627688545895e+00, /* 0xbff55d3c, 0x7e3cbffa */ +c4 = 2.3533063035889312e-01, /* 0x3fce1f50, 0x6891bab8 */ +c5 = -2.5806891390008115e-02, /* 0xbf9a6d1f, 0x2a2043da */ +c6 = 1.9295743091289794e-03, /* 0x3f5f9d38, 0xa362e3d1 */ +c7 = -1.0463809745687055e-04, /* 0xbf1b6e24, 0xd372e145 */ +c8 = 4.3029513401606985e-06, /* 0x3ed20c42, 0x4210907c */ +c9 = -1.3777927680211844e-07; /* 0xbe827e0f, 0x55d52bbb */ + +static const double c0 = 1; + +static inline long double +__kernel_cospil(long double x) +{ + long double c, chi, clo, x2hi, x2lo; + +#if HORNER + /* Horner's method. */ + long double x2; + x2 = x * x; + c = (c2 + (c3 + (c4 + (c5 + (c6 + (c7 + (c8 + c9 * x2) * x2) + * x2) * x2) * x2) * x2) * x2) * x2 + c1hi; +#else + /* Sort of Estrin's method. */ + long double x2, x4; + x2 = x * x; + x4 = x2 * x2; + c = ((c9 * x2 + c8) * x4 + (c7 * x2 + c6)) * x2 * x4 * x4 + + ((c5 * x2 + c4) * x4 + (c3 * x2 + c2)) * x2 + c1hi; +#endif + if (x2 < 0x1p-6) + return (c0 + c * x2); + x2hi =(float)x2; + x2lo = x2 - x2hi; + chi = (float)c; + clo = c - chi + c1lo; + c = clo * x2lo + chi * x2lo + clo * x2hi + (chi * x2hi + c0); + + return (c); +} Property changes on: lib/msun/ld80/k_cospil.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/ld80/k_sinpil.c =================================================================== --- lib/msun/ld80/k_sinpil.c (nonexistent) +++ lib/msun/ld80/k_sinpil.c (working copy) @@ -0,0 +1,78 @@ +/*- + * 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 const union IEEEl2bits +s0hiu = LD80C(0xc90fdaa200000000, 1, 3.14159265346825122833e+00L), +s0lou = LD80C(0x85a308d313167b73, -33, 1.21542010130121322891e-10L), +s1u = LD80C(0xa55de7312df295f5, 2, -5.16771278004997002909e+00L), +s2u = LD80C(0xa335e33bad570e85, 1, 2.55016403987734544098e+00L); + +#define s0hi (s0hiu.e) +#define s0lo (s0lou.e) +#define s1 (s1u.e) +#define s2 (s2u.e) + +static const double +s3 = -5.9926452932079166e-01, /* 0xbfe32d2c 0xce62bd82 */ +s4 = 8.2145886611090388e-02, /* 0x3fb50783 0x487edcdb */ +s5 = -7.3704309439650085e-03, /* 0xbf7e3074 0xfdc9c0c9 */ +s6 = 4.6630275825043123e-04, /* 0x3f3e8f43 0x18c2a7a0 */ +s7 = -2.1914601021339888e-05, /* 0xbef6faa7 0xea41adee */ +s8 = 7.8877623841310396e-07; /* 0x3eaa7789 0x4aacabad */ + +static inline long double +__kernel_sinpil(long double x) +{ + long double hi, lo, sm, xhi, xlo; + uint64_t lx; + uint16_t ix; + +#if HORNER + /* Horner's method. */ + long double x2; + x2 = x * x; + sm = x2 * (x2 * (x2 * (x2 * (x2 * (x2 * (x2 * s8 + s7) + s6) + + s5) + s4) + s3) + s2) + s1; +#else + /* Sort of Estrin's method. */ + long double a, b, x2, x4; + x2 = x * x; + x4 = x2 * x2; + sm = ((x2 * s8 + s7) * x4 + (x2 * s6 + s5)) * (x4 * x4) + + (x2 * s4 + s3) * x4 + x2 * s2 + s1; +#endif + xhi = (float)x; + xlo = x - xhi; + lo = xlo * (x + xhi) * sm; + hi = xhi * xhi * sm; + lo = x * lo + xlo * (s0hi + s0lo) + x * hi; + + return (lo + xhi * s0lo + xhi * s0hi); +} Property changes on: lib/msun/ld80/k_sinpil.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/ld80/s_cospil.c =================================================================== --- lib/msun/ld80/s_cospil.c (nonexistent) +++ lib/msun/ld80/s_cospil.c (working copy) @@ -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_cospi.c for implementation details. + */ + +#ifdef __i386__ +#include +#endif +#include + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" +#include "k_cospil.c" +#include "k_sinpil.c" + +static inline long double +__compute_cospil(long double x) +{ + + if (x < 0.5) { + if (x < 0.25) + return (__kernel_cospil(x)); + return (__kernel_sinpil(0.5 - x)); + } else { + if (x < 0.75) + return (-__kernel_sinpil(x - 0.5)); + return (-__kernel_cospil(1 - x)); + } +} + +long double +cospil(long double x) +{ + volatile static const double vzero = 0; + const double huge = 1e+300; + long double ax; + uint32_t j0; + uint64_t lx; + 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 < 0x3fdd) { /* |x| < 0x1p-34 */ + if (huge + x > 0) + RETURNI(1); + } + if (ix == 0x3ffe && lx == 0x8000000000000000ull) + RETURNI(0); + RETURNI(__compute_cospil(ax)); + } + + 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 { + uint64_t m = (uint64_t)-1 >> (j0 + 1); + if (lx & m) lx &= ~m; + } + INSERT_LDBL80_WORDS(x, ix, lx); + + ax -= x; + if (ax == 0.5) + RETURNI(0); + + ax = ax == 0 ? 1 : __compute_cospil(ax); + + if (j0 > 40) x -= 0x1p40; + if (j0 > 30) x -= 0x1p30; + j0 = (uint32_t)x; + + return (j0 & 1 ? -ax : ax); + } + + if (ix >= 0x7fff) + RETURNI(vzero / vzero); + + /* + * |x| >= 0x1p63 is always an even integer, so return 1. + * FIXME: should this raise FE_INEXACT or FE_INVALID. + */ + if (ax + 1 > 1) + ax = 1; + return (ax); +} Property changes on: lib/msun/ld80/s_cospil.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/ld80/s_sinpil.c =================================================================== --- lib/msun/ld80/s_sinpil.c (nonexistent) +++ lib/msun/ld80/s_sinpil.c (working copy) @@ -0,0 +1,123 @@ +/*- + * 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 +#endif +#include + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" +#include "k_cospil.c" +#include "k_sinpil.c" + +static inline long double +__compute_sinpil(long double x) +{ + + if (x <= 0.5) { + if (x <= 0.25) + return (__kernel_sinpil(x)); + return (__kernel_cospil(0.5 - x)); + } else { + if (x <= 0.75) + return (__kernel_cospil(x - 0.5)); + return (__kernel_sinpil(1 - x)); + } +} + +static const double pihi = 3.1415926814079285e+00; /* 0x400921fb 0x58000000 */ +static const double pilo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */ + +long double +sinpil(long double x) +{ + volatile static const double vzero = 0; + long double ax; + uint32_t j0; + uint64_t lx; + 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 < 0x3fdc) { /* |x| < 0x1p-35 */ + if (x == 0) + RETURNI(x); + INSERT_LDBL80_WORDS(ax, hx, (lx >> 32) << 32); + x -= ax; + RETURNI(pilo * x + pihi * x + pilo * ax + pihi * ax); + } + ax = __compute_sinpil(ax); + RETURNI((hx & 0x8000) ? -ax : ax); + } + + 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 { + uint64_t m = (uint64_t)-1 >> (j0 + 1); + if (lx & m) lx &= ~m; + } + INSERT_LDBL80_WORDS(x, ix, lx); + + ax -= x; + if (ax == 0) { + ax = 0; + } else { + ax = __compute_sinpil(ax); + if (j0 > 40) x -= 0x1p40; + if (j0 > 30) x -= 0x1p30; + j0 = (uint32_t)x; + if (j0 & 1) ax = -ax; + } + RETURNI((hx & 0x8000) ? -ax : ax); + } + + /* x = +-inf or nan. */ + if (ix >= 0x7fff) + RETURNI(vzero / vzero); + + /* + * |x| >= 0x1p63 is always an integer, so return +-0. + * FIXME: should this raise FE_INEXACT or FE_INVALID. + */ + if (ax + 1 > 1) + ax = copysignl(0, x); + RETURNI(ax); +} Property changes on: lib/msun/ld80/s_sinpil.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/ld80/s_tanpil.c =================================================================== --- lib/msun/ld80/s_tanpil.c (nonexistent) +++ lib/msun/ld80/s_tanpil.c (working copy) @@ -0,0 +1,195 @@ +/*- + * 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. + */ + +#ifdef __i386__ +#include +#endif +#include + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" +#include "k_cospil.c" +#include "k_sinpil.c" + +static const double pihi = 3.1415926814079285e+00; /* 0x400921fb 0x58000000 */ +static const double pilo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */ + +static const union IEEEl2bits +t00hiu = LD80C(0xc90fdaa22168c235, 1, 3.14159265358979323851e+00L), +t00lou = LD80C(0xecdfa9e9520ede79, -65, -5.01599541779735313611e-20L), +t01hiu = LD80C(0xa55de7312df295f5, 3, 1.03354255600999400582e+01L), +t01lou = LD80C(0x8d51cc1ca8412de2, -62, 2.39404580332694307957e-19L), +t02hiu = LD80C(0xa335e33bad570ec7, 5, 4.08026246380375272847e+01L), +t02lou = LD80C(0xe72db1e59703a7ba, -60, -1.56652642070969805771e-18L), +t03u = LD80C(0xa2fffcda474ac1d3, 7, 1.62999951975255277944e+02L), +t04u = LD80C(0xa2fa3971d7988829, 9, 6.51909756145994949750e+02L), +t05u = LD80C(0xa2f99792aec80f33, 11, 2.60759950512193695427e+03L), +t06u = LD80C(0xa2f985abafb74d99, 13, 1.04303805377441052764e+04L), +t07u = LD80C(0xa2f983819a4712aa, 15, 4.17215136963294523085e+04L); +#define t00 (t00hiu.e) +#define t00lo (t00lou.e) +#define t01 (t01hiu.e) +#define t01lo (t01lou.e) +#define t02 (t02hiu.e) +#define t02lo (t02lou.e) +#define t03 (t03u.e) +#define t04 (t04u.e) +#define t05 (t05u.e) +#define t06 (t06u.e) +#define t07 (t07u.e) + +static const double +t08 = 1.6688612339742415e+05, /* 0x41045f30, 0xfcb7c9e9 */ +t09 = 6.6753884815733030e+05, /* 0x41245f25, 0xb241ad77 */ +t10 = 2.6704954502371075e+06, /* 0x41445fcf, 0xb9a15e9a */ +t11 = 1.0666012381827524e+07, /* 0x41645803, 0x8c37ee5b */ +t12 = 4.3253268125143178e+07, /* 0x41849ff0, 0xa1004b11 */ +t13 = 1.5587209092892912e+08, /* 0x41a294d6, 0xb5db9c99 */ +t14 = 1.0162479548145952e+09, /* 0x41ce495b, 0x496844a8 */ +t15 = -2.9808831901354914e+09, /* 0xc1e63595, 0x5ec455f2 */ +t16 = 8.5833091951381027e+10, /* 0x4233fc0d, 0x0b6f618b */ +t17 = -6.8395913998321326e+11, /* 0xc263e7e4, 0x87d1e6d3 */ +t18 = 5.1641660627562871e+12, /* 0x4292c981, 0x228a9126 */ +t19 = -2.1258706455671141e+13, /* 0xc2b355ad, 0xa58c7724 */ +t20 = 5.2041706779955102e+13; /* 0x42c7aa73, 0xb91a998d */ + +static inline long double +__kernel_tanpil(long double x) +{ + long double t, xhi, xlo; + uint64_t lx; + uint16_t ix; + + xhi = (float)x; + xlo = x - xhi; + xlo *= (xlo + xhi + xhi); + xhi *= xhi; + + if (x < 0.25) { +#if HORNER + long double a, b, c, x2; + x2 = xlo + xhi; + a = x2 * (x2 * (x2 * (x2 * t20 + t19) + t18) + t17) + t16; + b = x2 * (x2 * (x2 * (x2 * a + t15) + t14) + t13) + t12; + c = x2 * (x2 * (x2 * (x2 * b + t11) + t10) + t09) + t08; + t = x2 * (x2 * (x2 * (x2 * c + t07) + t06) + t05); +#else + long double d, x2, x4; + double a, b, c, d2, d4; + d2 = x2 = xlo + xhi; + d4 = x4 = x2 * x2; + a = ((d2 * t20 + t19) * d4 + (d2 * t18 + t17)) * d4; + b = ((d2 * t16 + t15) * d4 + (d2 * t14 + t13)); + c = ((d2 * t12 + t11) * d4 + (d2 * t10 + t09)); + d = ((x2 * t08 + t07) * x4 + (x2 * t06 + t05)); + t = (((a * d4 + b) * (x4 * x4) + c) * (x4 * x4) + d) * x2; +#endif + t = t02lo + x2 * (x2 * (t + t04) + t03) + t02; + t = t01lo + xlo * t + xhi * t + t01; + t = t00lo + xlo * t + xhi * t + t00; + return (t * x); + } else if (x > 0.25) { + x = 0.5 - x; + t = __kernel_cospil(x) / __kernel_sinpil(x); + } else + t = 1; + return (t); +} + +static inline long double +__compute_tanpil(long double x) +{ + + return (x < 0.5 ? __kernel_tanpil(x) : -__kernel_tanpil(1 - x)); +} + +long double +tanpil(long double x) +{ + volatile static const double vzero = 0; + long double ax; + uint32_t j0; + uint64_t lx; + 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 < 0x3fdd) { /* |x| < 0x1p-34 */ + if (x == 0) + RETURNI(x); + INSERT_LDBL80_WORDS(ax, ix, (lx >> 32) << 32); + x -= ax; + RETURNI(pilo * x + pihi * x + pilo * ax + pihi * ax); + } + if (ix == 0x3ffe && lx == 0x8000000000000000ull) + RETURNI((x - x) / (x - x)); + ax = __compute_tanpil(ax); + RETURNI((hx & 0x8000) ? -ax : ax); + } + + 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 { + uint64_t m = (uint64_t)-1 >> (j0 + 1); + if (lx & m) lx &= ~m; + } + INSERT_LDBL80_WORDS(x, ix, lx); + + ax -= x; + + if (ax == 0.5) + RETURNI((x - x) / (x - x)); + + ax = ax == 0 ? 0 : __compute_tanpil(ax); + RETURNI((hx & 0x8000) ? -ax : ax); + } + + /* x = +-inf or nan. */ + if (ix >= 0x7fff) + RETURNI(vzero / vzero); + + /* + * |x| >= 0x1p63 is always an integer, so return +-0. + * FIXME: should this raise FE_INEXACT or FE_INVALID. + */ + if (ax + 1 > 1) + ax = copysignl(0, x); + RETURNI(ax); +} Property changes on: lib/msun/ld80/s_tanpil.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/man/cospi.3 =================================================================== --- lib/msun/man/cospi.3 (nonexistent) +++ lib/msun/man/cospi.3 (working copy) @@ -0,0 +1,111 @@ +.\" 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, 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 REGENTS AND CONTRIBUTORS ``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 REGENTS OR CONTRIBUTORS 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. +.\" +.\" $FreeBSD$ +.\" +.Dd April 1, 2017 +.Dt COSPI 3 +.Os +.Sh NAME +.Nm cospi , +.Nm cospif , +.Nm cospil +.Nd half\(encycle cosine functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn cospi "double x" +.Ft float +.Fn cospif "float x" +.Ft long double +.Fn cospil "long double x" +.Sh DESCRIPTION +The +.Fn cospi , +.Fn cospif , +and +.Fn cospil +functions compute the cosine of +.Fa "\(*p \(mu x" . +and measure angles in half-cycles. +.Sh RETURN VALUES +The +.Fn cospi , +.Fn cospif , +and +.Fn cospil +functions returns +.Fn cos "\(*p \(mu x" . +If \*(Bax\*(Ba \*(Ge 2^(p - 1) +where p is the floating\(enpoint precision of +.Ar x , +then the returned value is 1 and it has no significance. +.Sh SPECIAL VALUES +.Bl -tag +.It +.Fn cospi \*(Pm0 +returns 1. +.It +.Fn cospi \*(Pmn/2 +returns 0 for positive integers +.Ar n . +.It +.Fn cospi n +returns 1 for even integers +.Ar n . +.It +.Fn cospi n +returns \-1 for odd integers +.Ar n . +.It +.Fn cospi \*(Pm\(if +return an \*(Na and raises an FE_INVALID exception. +.It +.Fn cospi \*(Na +return an \*(Na and raises an FE_INVALID exception. +.El +.Sh SEE ALSO +.Xr cos 3 , +.Xr fenv 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinpi 3 , +.Xr tan 3 , +.Xr tanpi 3 +.Sh AUTHORS +The half\(encycle trignometric functions were written by +.An Steven G. Kargl Aq Mt kargl@FreeBSD.org . +.Sh STANDARDS +These functions conform to +IEEE Std 754\(tm\(en2008 , +\(dqIEEE Standard for Floating-Point Arithmetic\(dq +and to +ISO/IEC TS 18661-4 , +\(dqInformation technology \(em Programming languages, their environments, +and system software interfaces \(em Floating\(enpoint extensions for +C\(dq \(em Part 4: Supplementary functions. + + Property changes on: lib/msun/man/cospi.3 ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/man/sinpi.3 =================================================================== --- lib/msun/man/sinpi.3 (nonexistent) +++ lib/msun/man/sinpi.3 (working copy) @@ -0,0 +1,102 @@ +.\" 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, 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 REGENTS AND CONTRIBUTORS ``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 REGENTS OR CONTRIBUTORS 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. +.\" +.\" $FreeBSD$ +.\" +.Dd April 1, 2017 +.Dt SINPI 3 +.Os +.Sh NAME +.Nm sinpi , +.Nm sinpif , +.Nm sinpil +.Nd half\(encycle sine functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn sinpi "double x" +.Ft float +.Fn sinpif "float x" +.Ft long double +.Fn sinpil "long double x" +.Sh DESCRIPTION +The +.Fn sinpi , +.Fn sinpif , +and +.Fn sinpil +functions compute the sine of +.Fa "\(*p \(mu x" . +and measure angles in half-cycles. +.Sh RETURN VALUES +The +.Fn sinpi , +.Fn sinpif , +and +.Fn sinpil +functions returns +.Fn sin "\(*p \(mu x" . +If \*(Bax\*(Ba \*(Ge 2^(p - 1) +where p is the floating\(enpoint precision of +.Ar x , +then the returned value is \*(Pm0 and it has no significance. +.Sh SPECIAL VALUES +.Bl -tag +.It +.Fn sinpi \*(Pm0 +returns \*(Pm0. +.It +.Fn sinpi \*(Pmn +returns \*(Pm0 for positive integers +.Ar n . +.It +.Fn sinpi \*(Pm\(if +return an \*(Na and raises an FE_INVALID exception. +.It +.Fn sinpi \*(Na +return an \*(Na and raises an FE_INVALID exception. +.El +.Sh SEE ALSO +.Xr cos 3 , +.Xr cospi 3 , +.Xr fenv 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr tan 3 , +.Xr tanpi 3 +.Sh AUTHORS +The half\(encycle trignometric functions were written by +.An Steven G. Kargl Aq Mt kargl@FreeBSD.org . +.Sh STANDARDS +These functions conform to +IEEE Std 754\(tm\(en2008 , +\(dqIEEE Standard for Floating-Point Arithmetic\(dq +and to +ISO/IEC TS 18661-4 , +\(dqInformation technology \(em Programming languages, their environments, +and system software interfaces \(em Floating\(enpoint extensions for +C\(dq \(em Part 4: Supplementary functions. + Property changes on: lib/msun/man/sinpi.3 ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/man/tanpi.3 =================================================================== --- lib/msun/man/tanpi.3 (nonexistent) +++ lib/msun/man/tanpi.3 (working copy) @@ -0,0 +1,106 @@ +.\" 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, 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 REGENTS AND CONTRIBUTORS ``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 REGENTS OR CONTRIBUTORS 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. +.\" +.\" $FreeBSD$ +.\" +.Dd April 1, 2017 +.Dt TANPI 3 +.Os +.Sh NAME +.Nm tanpi , +.Nm tanpif , +.Nm tanpil +.Nd half\(encycle tangent functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn tanpi "double x" +.Ft float +.Fn tanpif "float x" +.Ft long double +.Fn tanpil "long double x" +.Sh DESCRIPTION +The +.Fn tanpi , +.Fn tanpif , +and +.Fn tanpil +functions compute the tangent of +.Fa "\(*p \(mu x" +and measure angles in half-cycles. +.Sh RETURN VALUES +The +.Fn tanpi , +.Fn tanpif , +and +.Fn tanpil +functions returns +.Fn tan "\(*p \(mu x" . +If \*(Bax\*(Ba \*(Ge 2^(p - 1) +where p is the floating\(enpoint precision of +.Ar x , +then the returned value is \*(Pm0 and it has no significance. +.Sh SPECIAL VALUES +.Bl -tag +.It +.Fn tanpi \*(Pm0 +returns \*(Pm0. +.It +.Fn tanpi \*(Pmn +returns \*(Pm0 for positive integers +.Ar n . +.It +.Fn tanpi \*(Pmn/2 +returns \*(Na for n > 0 and raises an FE_INVALID exception. +.It +.Fn tanpi \*(Pm\(if +return an \*(Na and raises an FE_INVALID exception. +.It +.Fn tanpi \*(Na +return an \*(Na and raises an FE_INVALID exception. +.El +.Sh SEE ALSO +.Xr cos 3 , +.Xr cospi 3 , +.Xr fenv 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinpi 3 , +.Xr tan 3 , +.Sh AUTHORS +The half\(encycle trignometric functions were written by +.An Steven G. Kargl Aq Mt kargl@FreeBSD.org . +.Sh STANDARDS +These functions conform to +IEEE Std 754\(tm\(en2008 , +\(dqIEEE Standard for Floating-Point Arithmetic\(dq +and to +ISO/IEC TS 18661-4 , +\(dqInformation technology \(em Programming languages, their environments, +and system software interfaces \(em Floating\(enpoint extensions for +C\(dq \(em Part 4: Supplementary functions. + + Property changes on: lib/msun/man/tanpi.3 ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/src/k_cospi.c =================================================================== --- lib/msun/src/k_cospi.c (nonexistent) +++ lib/msun/src/k_cospi.c (working copy) @@ -0,0 +1,83 @@ +/*- + * 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. + */ + +/* + * Compute cospi(x) = cos(pi*x) via a polynomial approximation. Coefficients + * were determined for the following function: + * + * f(x) = ((cos(pi*x) - 1) / (x*x)) = c1 + c2*x**2 + c3*x**4 + ... + * + * with an Remes algorithm. If |x*x| < 0x1p-6, the polynomial can be summed + * using a Horner's method. If |x*x| exceeds 0x1p-6, then to accumulate the + * result with sufficient accuracy the c1 coefficient and final + * multiplications needed to be handled specially. + * + * x2 = x * x + * C(x2) = c1hi + c2*x2 + c3*x2**2 + ... + * = c1hi + (c2 + (c3 ...) * x2) * x2 + * cospi(x) = c0 + x2 * C(x2) + */ + +static const double +c0 = 1.0000000000000000e+00, /* 0x3ff00000 0x00000000 */ +c1hi = -4.9348022005446790e+00, /* 0xc013bd3c 0xc9be45de */ +c1lo = -3.1132368291465357e-16, /* 0xbcb66ee8 0x86887579 */ +c2 = 4.0587121264167649e+00, /* 0x40103c1f 0x081b5ac0 */ +c3 = -1.3352627688538099e+00, /* 0xbff55d3c 0x7e3cb243 */ +c4 = 2.3533063028402096e-01, /* 0x3fce1f50 0x68689166 */ +c5 = -2.5806887965588832e-02, /* 0xbf9a6d1e 0xef4b8280 */ +c6 = 1.9294938875092037e-03, /* 0x3f5f9ce2 0x49428066 */ +c7 = -1.0370089699114971e-04; /* 0xbf1b2f3f 0xd835d4fe */ + +static inline double +__kernel_cospi(double x) +{ + double c, chi, clo, x2hi, x2lo; +#if HORNER + /* Horner's method. */ + double x2; + x2 = x * x; + c = (c2 + (c3 + (c4 + (c5 + (c6 + c7 * x2) * x2) * x2) * x2) + * x2) * x2 + c1hi; +#else + /* Sort of Estrin's method. */ + double x2, x4; + x2 = x * x; + x4 = x2 * x2; + c = (c5 + c6 * x2 + c7 * x4) * (x4 * x4) + + (c2 + c3 * x2 + c4 * x4) * x2 + c1hi; +#endif + if (x2 < 0x1p-6) + return (c0 + c * x2); + + x2hi = (float)x2; + x2lo = x2 - x2hi; + chi = (float)c; + clo = c - chi + c1lo; + c = clo * x2lo + (chi * x2lo + clo * x2hi) + (chi * x2hi + c0); + + return (c); +} Property changes on: lib/msun/src/k_cospi.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/src/k_cospif.c =================================================================== --- lib/msun/src/k_cospif.c (nonexistent) +++ lib/msun/src/k_cospif.c (working copy) @@ -0,0 +1,60 @@ +/*- + * 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 const float +c0 = 1.00000000e+00f, /* 0x3fc00000 */ +c1hi = -4.93480206e+00f, /* 0xc09de9e6 0xb418a08d */ +c1lo = -1.42145112e-07f, /* 0xc09de9e6 0xb418a08d */ +c2 = 4.05871058e+00f, /* 0x4081e0f5 0xb1fc37ea */ +c3 = -1.33513784e+00f, /* 0xbfaae5cc 0xb375e792 */ +c4 = 2.32126340e-01f; /* 0x3e6db287 0x31daa25f */ + +static inline float +__kernel_cospif(float x) +{ + float c, chi, clo, x2, x2hi, x2lo; + uint32_t ix; + + x2 = x * x; + c = (c2 + (c3 + c4 * x2) * x2) * x2 + c1hi; + + GET_FLOAT_WORD(ix, x2); + if (ix < 0x3c800000) /* |x2| < 0x1p-6 */ + return (c0 + c * x2); + + SET_FLOAT_WORD(x2hi, (ix >> 14) << 14); + x2lo = x2 - x2hi; + GET_FLOAT_WORD(ix, c); + SET_FLOAT_WORD(chi, (ix >> 14) << 14); + clo = c - chi + c1lo; + c = clo * x2lo + chi * x2lo + clo * x2hi + (chi * x2hi + c0); + + return (c); +} Property changes on: lib/msun/src/k_cospif.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/src/k_sinpi.c =================================================================== --- lib/msun/src/k_sinpi.c (nonexistent) +++ lib/msun/src/k_sinpi.c (working copy) @@ -0,0 +1,84 @@ +/*- + * 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. + */ + +/* + * Compute sinpi(x) = sin(pi*x) via a polynomial approximation. Coefficients + * were determined for the following function: + * + * f(x) = sin(pi*x) / x = s0 + s1*x**2 + s2*x**4 + ... + * + * with an Remes algorithm. To accumulate the result with sufficient + * accuracy the s0 coefficient and final multiplications needed to be + * handled specially. + * + * x2 = x * x + * S(x2) = s1 + s2*x2 + s3*x2**2 + ... + * = s1 + (s2 + (s3 ...) * x2) * x2 + * sinpi(x) = x * (s0 + x2 * S(x2)) + * + * The final multiplications and additions in the above expression for + * sinpi(x) are done in an extra precision arithmetic. + */ + +static const double +s0hi = 3.1415926218032837e+00, /* 0x400921fb 0x50000000 */ +s0lo = 3.1786509547050787e-08, /* 0x3e6110b4 0x611a5f14 */ +s1 = -5.1677127800499703e+00, /* 0xc014abbc 0xe625be53 */ +s2 = 2.5501640398773415e+00, /* 0x400466bc 0x6775aad9 */ +s3 = -5.9926452932029806e-01, /* 0xbfe32d2c 0xce62ac24 */ +s4 = 8.2145886580065136e-02, /* 0x3fb50783 0x485cc006 */ +s5 = -7.3704298849218506e-03, /* 0xbf7e3074 0xb502de6a */ +s6 = 4.6628273194622205e-04, /* 0x3f3e8eed 0x159b24d7 */ +s7 = -2.1717412527405332e-05; /* 0xbef6c5b9 0x3995dfbe */ + +static inline double +__kernel_sinpi(double x) +{ + double hi, lo, sm, xhi, xlo; + uint32_t hx, lx; +#if HORNER + double x2; + /* Horner's method. */ + x2 = x * x; + sm = x2 * (x2 * (x2 * (x2 * (x2 * (x2 * s7 + s6) + s5) + s4) + s3) + + s2) + s1; +#else + double x2, x4; + /* Sort of Estrin's method. */ + x2 = x * x; + x4 = x2 * x2; + sm = (s5 + s6 * x2 + s7 * x4) * (x4 * x4) + + (s2 + s3 * x2 + s4 * x4) * x2 + s1; +#endif + EXTRACT_WORDS(hx, lx, x); + INSERT_WORDS(xhi, hx, 0); + xlo = x - xhi; + lo = xlo * (x + xhi) * sm; + hi = xhi * xhi * sm; + lo = x * lo + xlo * (s0hi + s0lo) + x * hi; + + return (lo + xhi * s0lo + xhi * s0hi); +} Property changes on: lib/msun/src/k_sinpi.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/src/k_sinpif.c =================================================================== --- lib/msun/src/k_sinpif.c (nonexistent) +++ lib/msun/src/k_sinpif.c (working copy) @@ -0,0 +1,56 @@ +/*- + * 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 const float +s0hi = 3.14062500e+00f, /* 0x40490000 */ +s0lo = 9.67653585e-04f, /* 0x3a7daa22 */ +s1 = -5.16771269e+00f, /* 0xc0a55de7 */ +s2 = 2.55016255e+00f, /* 0x402335dd */ +s3 = -5.99202096e-01f, /* 0xbf19654f */ +s4 = 8.10018554e-02f; /* 0x3da5e44d */ + +static inline float +__kernel_sinpif(float x) +{ + float hi, lo, sm, x2, xhi, xlo; + uint32_t ix; + + GET_FLOAT_WORD(ix, x); + SET_FLOAT_WORD(xhi, (ix >> 14) << 14); + xlo = x - xhi; + + x2 = x * x; + sm = x2 * (x2 * (x2 * s4 + s3) + s2) + s1; + lo = xlo * (x + xhi) * sm; + hi = xhi * xhi * sm; + lo = x * lo + xlo * (s0hi + s0lo) + x * hi; + + return (lo + xhi * s0lo + xhi * s0hi); +} Property changes on: lib/msun/src/k_sinpif.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/src/math.h =================================================================== --- lib/msun/src/math.h (revision 317529) +++ lib/msun/src/math.h (working copy) @@ -500,6 +500,15 @@ #if __BSD_VISIBLE long double lgammal_r(long double, int *); +double cospi(double); +float cospif(float); +long double cospil(long double); +double sinpi(double); +float sinpif(float); +long double sinpil(long double); +double tanpi(double); +float tanpif(float); +long double tanpil(long double); #endif __END_DECLS Index: lib/msun/src/s_cospi.c =================================================================== --- lib/msun/src/s_cospi.c (nonexistent) +++ lib/msun/src/s_cospi.c (working copy) @@ -0,0 +1,147 @@ +/*- + * 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. + */ + +/** + * cospi(x) computes cos(pi*x) without multiplication by pi (almost). First, + * note that cospi(-x) = cospi(x), so the algorithm considers only |x|. The + * method used depends on the magnitude of x. + * + * 1. For small |x|, cospi(x) = 1 with FE_INEXACT raised where a sloppy + * threshold is used. The threshold is |x| < 0x1pN with N = -(P/2+M). + * P is the precision of the floating-point type and M = 3 or 4. + * + * 2. For |x| < 1, argument reduction is not required and cospi(x) is + * computed by polynomial approximations in the the interval [0,0.25]. + * See k_sinpi.c and k_cospi.c for the details for these polynomial + * approximations. + * + * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where + * |x| = j0 + r with j0 an integer and the remainder r statisfies + * 0 <= r < 1. With the given domain, a simplified inline floor(x) + * is used. + * + * cospi(x) = cos(pi*(j0+r)) + * = cos(pi*j0) * cos(pi*r) - sin(pi*j0) * sin(pi*r) + * = cos(pi*j0) * cos(pi*r) + * = +-cospi(r) + * + * If j0 is even, then cos(pi*j0) = 1. If j0 is odd, then cos(pi*j0) = -1. + * cospi(r) is then computed via polynomial approximation. + * + * 4. For |x| >= 0x1p(P-1), |x| is integral and cospi(x) = 1. + * + * 5. Special cases: + * + * cospi(+-0) = 1. + * cospi(n.5) = 0 for n an integer. + * cospi(+-inf) = nan. Raises the "invalid" floating-point exception. + * cospi(nan) = nan. Raises the "invalid" floating-point exception. + */ + +#include "math.h" +#include "math_private.h" +#include "k_cospi.c" +#include "k_sinpi.c" + +/* + * To compute cospi(x) for 0 < x < 1, use trignometric identities to map + * cospi(x) into the [0,0.25] quadrant of sinpi(r) or cospi(r). + */ +static inline double +__compute_cospi(double x) +{ + + if (x < 0.5) { + if (x < 0.25) + return (__kernel_cospi(x)); + return (__kernel_sinpi(0.5 - x)); + } else { + if (x < 0.75) + return (-__kernel_sinpi(x - 0.5)); + return (-__kernel_cospi(1 - x)); + } +} + +double +cospi(double x) +{ + volatile static const double vzero = 0; + static const double huge = 1e+300; + double ax; + uint32_t hx, ix, j0, lx; + + EXTRACT_WORDS(hx, lx, x); + ix = hx & 0x7fffffff; + INSERT_WORDS(ax, ix, lx); + + if (ix < 0x3ff00000) { /* |x| < 1 */ + if (ix < 0x3e200000) { /* |x| < 0x1p-29 */ + if (huge + x > 0) + return (1); + } + if ((ix | lx) == 0x3fe00000) + return (0); + return (__compute_cospi(ax)); + } + + if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */ + /* Determine integer part of ax. */ + j0 = ((ix >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) { + ix &= ~(0x000fffff >> j0); + lx = 0; + } else { + lx &= ~((uint32_t)0xffffffff >> (j0 - 20)); + } + INSERT_WORDS(x, ix, lx); + + ax -= x; + if (ax == 0.5) + return (0); + + ax = ax == 0 ? 1 : __compute_cospi(ax); + + if (j0 > 30) x -= 0x1p30; + j0 = (uint32_t)x; + + return (j0 & 1 ? -ax : ax); + } + + if (ix >= 0x7f800000) + return (vzero / vzero); + + /* + * |x| >= 0x1p52 is always an even integer, so return 1. + * FIXME: should this raise FE_INEXACT or FE_INVALID? + */ + if (ax + 1 > 1) + ax = 1; + return (ax); +} + +#if LDBL_MANT_DIG == 53 +__weak_reference(cospi, cospil); +#endif Property changes on: lib/msun/src/s_cospi.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/src/s_cospif.c =================================================================== --- lib/msun/src/s_cospif.c (nonexistent) +++ lib/msun/src/s_cospif.c (working copy) @@ -0,0 +1,99 @@ +/*- + * 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. + */ + +#include "math.h" +#include "math_private.h" +#include "k_cospif.c" +#include "k_sinpif.c" + +static inline float +__compute_cospif(float x) +{ + + if (x <= 0.5f) { + if (x <= 0.25f) + return (__kernel_cospif(x)); + return (__kernel_sinpif(0.5f - x)); + } else { + if (x <= 0.75f) + return (-__kernel_sinpif(x - 0.5f)); + return (-__kernel_cospif(1 - x)); + } +} + +float +cospif(float x) +{ + volatile static const float vzero = 0; + static const float huge = 1e30; + float ax; + uint32_t ix, j0; + + GET_FLOAT_WORD(ix, x); + ix = ix & 0x7fffffff; + SET_FLOAT_WORD(ax, ix); + + if (ix < 0x3f800000) { /* |x| < 1 */ + if (ix < 0x39000000) { /* |x| < 0x1p-13 */ + if (huge + ax > 0) /* Raise inexact iff != 0. */ + return (1); + } + return (__compute_cospif(ax)); + } + + if (ix < 0x4b000000) { /* 1 <= |x| < 0x1p23 */ + /* Determine integer part of ax. */ + j0 = ((ix >> 23) & 0xff) - 0x7f; + ix &= ~(0x007fffff >> j0); + SET_FLOAT_WORD(x, ix); + + ax -= x; + if (ax == 0.5f) + return (0); + + ax = ax == 0 ? 1 : __compute_cospif(ax); + + ix = (uint32_t)x; + + return (ix & 1 ? -ax : ax); + } + + /* x = +-inf or nan. */ + if (ix >= 0x7f800000) + return (vzero / vzero); + + /* + * |x| >= 0x1p23 is always an even integer, so return 1. + * FIXME: should this raise FE_INEXACT or FE_INVALID. + */ + if (ax + 1 > 1) + ax = 1; + return (ax); +} Property changes on: lib/msun/src/s_cospif.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/src/s_sinpi.c =================================================================== --- lib/msun/src/s_sinpi.c (nonexistent) +++ lib/msun/src/s_sinpi.c (working copy) @@ -0,0 +1,154 @@ +/*- + * 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. + */ + +/** + * sinpi(x) computes sin(pi*x) without multiplication by pi (almost). First, + * note that sinpi(-x) = -sinpi(x), so the algorithm considers only |x| and + * includes reflection symmetry by considering the sign of x on output. The + * method used depends on the magnitude of x. + * + * 1. For small |x|, sinpi(x) = pi * x where a sloppy threshold is used. The + * threshold is |x| < 0x1pN with N = -(P/2+M). P is the precision of the + * floating-point type and M = 3 or 4. To achieve high accuracy, pi is + * decomposed into high and low parts with the high part containing a + * number of trailing zero bits. x is also split into high and low parts. + * + * 2. For |x| < 1, argument reduction is not required and sinpi(x) is + * computed by polynomial approximations in the the interval [0,0.25]. + * See k_sinpi.c and k_cospi.c for the details for these polynomial + * approximations. + * + * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where + * |x| = j0 + r with j0 an integer and the remainder r satisifies + * 0 <= r < 1. With the given domain, a simplified inline floor(x) + * is used. + * + * sinpi(x) = sin(pi*(j0+r)) + * = sin(pi*j0) * cos(pi*r) + cos(pi*j0) * sin(pi*r) + * = cos(pi*j0) * sin(pi*r) + * = +-sinpi(r) + * + * If j0 is even, then cos(pi*j0) = 1. If j0 is odd, then cos(pi*j0) = -1. + * sinpi(r) is then computed via polynomial approximation. + * + * 4. For |x| >= 0x1p(P-1), |x| is integral and sinpi(x) = copysign(0,x). + * + * 5. Special cases: + * + * sinpi(+-0) = +-0 + * sinpi(+-n) = +-0, for positive integers n. + * sinpi(+-inf) = nan. Raises the "invalid" floating-point exception. + * sinpi(nan) = nan. Raises the "invalid" floating-point exception. + */ + +#include "math.h" +#include "math_private.h" +#include "k_cospi.c" +#include "k_sinpi.c" + +static const double pihi = 3.1415926814079285e+00; /* 0x400921fb 0x58000000 */ +static const double pilo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */ + +/* + * To compute sinpi(x) for 0 < x < 1, use trignometric identities to map + * sinpi(x) into the [0,0.25] quadrant of sinpi(r) or cospi(r). + */ +static inline double +__compute_sinpi(double x) +{ + + if (x < 0.5) { + if (x < 0.25) + return (__kernel_sinpi(x)); + return (__kernel_cospi(0.5 - x)); + } else { + if (x < 0.75) + return (__kernel_cospi(x - 0.5)); + return (__kernel_sinpi(1 - x)); + } +} + +double +sinpi(double x) +{ + volatile static const double vzero = 0; + double ax; + uint32_t hx, ix, j0, lx; + + EXTRACT_WORDS(hx, lx, x); + ix = hx & 0x7fffffff; + INSERT_WORDS(ax, ix, lx); + + if (ix < 0x3ff00000) { /* |x| < 1 */ + if (ix < 0x3e300000) { /* |x| < 0x1p-28 */ + if (x == 0) + return (x); + INSERT_WORDS(ax, hx, 0); + x -= ax; + return (pilo * x + pihi * x + pilo * ax + pihi * ax); + } + ax = __compute_sinpi(ax); + return ((hx & 0x80000000) ? -ax : ax); + } + + if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */ + /* Determine integer part of ax. */ + j0 = ((ix >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) { + ix &= ~(0x000fffff >> j0); + lx = 0; + } else { + lx &= ~((uint32_t)0xffffffff >> (j0 - 20)); + } + INSERT_WORDS(x, ix, lx); + + ax -= x; + if (ax == 0) { + ax = 0; + } else { + ax = __compute_sinpi(ax); + if (j0 > 30) x -= 0x1p30; + lx = (uint32_t)x; + if (lx & 1) ax = -ax; + } + return ((hx & 0x80000000) ? -ax : ax); + } + + if (ix >= 0x7f800000) + return (vzero / vzero); + + /* + * |x| >= 0x1p52 is always an integer, so return +-0. + * FIXME: should this raise FE_INEXACT or FE_INVALID? + */ + if (ax + 1 > 1) + ax = copysign(0, x); + return (ax); +} + +#if LDBL_MANT_DIG == 53 +__weak_reference(sinpi, sinpil); +#endif Property changes on: lib/msun/src/s_sinpi.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/src/s_sinpif.c =================================================================== --- lib/msun/src/s_sinpif.c (nonexistent) +++ lib/msun/src/s_sinpif.c (working copy) @@ -0,0 +1,105 @@ +/*- + * 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. + */ + +#include "math.h" +#include "math_private.h" +#include "k_cospif.c" +#include "k_sinpif.c" + +static inline float +__compute_sinpif(float x) +{ + + if (x <= 0.5f) { + if (x <= 0.25f) + return (__kernel_sinpif(x)); + return (__kernel_cospif(0.5f - x)); + } else { + if (x <= 0.75f) + return (__kernel_cospif(x - 0.5f)); + return (__kernel_sinpif(1 - x)); + } +} + +static const float pihi = 3.14160156e+00f; /* 0x40491000 */ +static const float pilo = -8.90890988e-06f; /* 0xb715777a */ + +float +sinpif(float x) +{ + volatile static const float vzero = 0; + float ax; + uint32_t hx, ix, j0; + + GET_FLOAT_WORD(hx, x); + ix = hx & 0x7fffffff; + SET_FLOAT_WORD(ax, ix); + + if (ix < 0x3f800000) { /* |x| < 1 */ + if (ix < 0x38000000) { /* |x| < 0x1p-15 */ + if (x == 0) + return (x); + SET_FLOAT_WORD(ax, (hx >> 13) << 13); + x -= ax; + return (pilo * x + pihi * x + pilo * ax + pihi * ax); + } + ax = __compute_sinpif(ax); + return ((hx & 0x80000000) ? -ax : ax); + } + + if (ix < 0x4b000000) { /* 1 <= |x| < 0x1p23 */ + /* Determine integer part of ax. */ + j0 = ((ix >> 23) & 0xff) - 0x7f; + ix &= ~(0x007fffff >> j0); + SET_FLOAT_WORD(x, ix); + + ax -= x; + if (ax == 0) { + ax = 0; + } else { + ix = (uint32_t)x; + ax = __compute_sinpif(ax); + if (ix & 1) ax = -ax; + } + return ((hx & 0x80000000) ? -ax : ax); + } + + /* x = +-inf or nan. */ + if (ix >= 0x7f800000) + return (vzero / vzero); + + /* + * |x| >= 0x1p23 is always an integer, so return +-0. + * FIXME: should this raise FE_INEXACT or FE_INVALID? + */ + if (ax + 1 > 1) + ax = copysignf(0, x); + return (ax); +} Property changes on: lib/msun/src/s_sinpif.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/src/s_tanpi.c =================================================================== --- lib/msun/src/s_tanpi.c (nonexistent) +++ lib/msun/src/s_tanpi.c (working copy) @@ -0,0 +1,224 @@ +/*- + * 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. + */ + +/** + * tanpi(x) computes tan(pi*x) without multiplication by pi (almost). First, + * note that tanpi(-x) = -tanpi(x), so the algorithm considers only |x| and + * includes reflection symmetry by considering the sign of x on output. The + * method used depends on the magnitude of x. + * + * 1. For small |x|, tanpi(x) = pi * x where a sloppy threshold is used. The + * threshold is |x| < 0x1pN with N = -(P/2+M). P is the precision of the + * floating-point type and M = 3 or 4. To achieve high accuracy, pi is + * decomposed into high and low parts with the high part containing a + * number of trailing zero bits. x is also split into high and low parts. + * + * 2. For |x| < 1, argument reduction is not required and tanpi(x) is + * computed by either a polynomial approximation or the definition of + * tanpi in terms of sinpi and cospi. For |x| in [0,0.25), a polynomial + * approximation is used. For |x| in (0.25, 0.5], tanpi(x) is computed + * by tanpi(x) = cospi(0.5 - x) / sinpi(0.5 - x). + * + * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where + * |x| = j0 + r with j0 an integer and the remainder r satisfies + * 0 <= r < 1. With the given domain, a simplified inline floor(x) + * is used. + * tan(pi*j0) + tan(pi*r) + * tanpi(x) = tan(pi*(j0+r)) = ---------------------------- = tanpi(r) + * 1 - tan(pi*j0) * tan(pi*r) + * + * 4. For |x| >= 0x1p(P-1), |x| is integral and tanpi(x) = copysign(0,x). + * + * 5. Special cases: + * + * tanpi(+-0) = +-0 + * tanpi(+-n) = +-0, for positive integers n. + * tanpi(+-n+1/4) = +-1, for positive integers n. + * tanpi(+-n+1/2) = NaN, for positive integers n. + * tanpi(+-inf) = nan. Raises the "invalid" floating-point exception. + * tanpi(nan) = nan. Raises the "invalid" floating-point exception. + * + * Compute tanpi(x) = tan(pi*x) via a polynomial approximation. Coefficients + * were determined for the following function: + * + * f(x) = tan(pi*x) / x = t0 + t1*x**2 + t2*x**4 + ... + * + * with an Remes algorithm. To accumulate the result with sufficient accuracy, + * the t0, t1, and t2 coefficients and final multiplications and additions + * needed to be handled specially. + * + * x2 = x * x + * T(x2) = t3 + t4*x2 + t5*x2**2 + ... + * = t3 + (t4 + (t5 ...) * x2) * x2 + * tanpi(x) = x * (t0 + x2*(t1 + x2*(t2 + x2*T(x2)))) + * + * The final multiplications and additions in the above expression for + * tanpi(x) are done in an extra precision arithmetic. + */ + +#include "math.h" +#include "math_private.h" +#include "k_cospi.c" +#include "k_sinpi.c" + +static const double pihi = 3.1415926814079285e+00; /* 0x400921fb 0x58000000 */ +static const double pilo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */ + +static const double +t00 = 3.1415926535897931e+00, /* 0x400921fb 0x54442d18 */ +t00lo = 1.2267625636978282e-16, /* 0x3ca1adf4 0x7b8ee56b */ +t01 = 1.0335425560099939e+01, /* 0x4024abbc 0xe625be52 */ +t01lo = -6.0289590484334045e-16, /* 0xbcc5b8bb 0xb4f3d850 */ +t02 = 4.0802624638040442e+01, /* 0x404466bc 0x6775ac7c */ +t02lo = -3.1181465177803440e-15, /* 0xbcec15f4 0xd355f491 */ +t03 = 1.6299995197351416e+02, /* 0x40645fff 0x9b47fa0c */ +t04 = 6.5190975669363422e+02, /* 0x40845f47 0x2e8473cf */ +t05 = 2.6075994007466215e+03, /* 0x40a45f32 0xe4a797e0 */ +t06 = 1.0430393632420044e+04, /* 0x40c45f32 0x628c115e */ +t07 = 4.1720374420664804e+04, /* 0x40e45f0b 0xfb410bc9 */ +t08 = 1.6695720713150888e+05, /* 0x41046169 0xa8349085 */ +t09 = 6.6429163117898861e+05, /* 0x412445c7 0x4329e474 */ +t10 = 2.7802499382503941e+06, /* 0x4145362c 0xf81896c3 */ +t11 = 7.9185101944778729e+06, /* 0x415e34eb 0x8c725352 */ +t12 = 9.3691291294289947e+07, /* 0x41965676 0x6d2d5a58 */ +t13 = -5.0585651903137898e+08, /* 0xc1be26c2 0x07080874 */ +t14 = 6.8772398519624548e+09, /* 0x41f99ea5 0xa2bf6637 */ +t15 = -3.3094464588263161e+10, /* 0xc21ed255 0xd1310d7a */ +t16 = 1.1673794006564838e+11; /* 0x423b2e1f 0x9a61a5fc */ + +static inline double +__kernel_tanpi(double x) +{ + double hi, lo, t, xhi, xlo; + uint32_t hx, lx; + + if (x < 0.25) { +#if HORNER + double x2; + /* Horner's method. */ + x2 = x * x; + t = x2 * (x2 * (x2 * (x2 * (x2 * (x2 * (x2 * (x2 * (x2 * (x2 + * (x2 * (x2 * t16 + t15) + t14) + t13) + t12) + t11) + + t10) + t09) + t08) + t07) + t06) + t05) + t04; +#else + double a, b, c, d, x2, x4, x6; + /* Sort of Estrin's method. */ + x2 = x * x; + x4 = x2 * x2; + x6 = x4 * x2; + a = (t16 * x4 + t15 * x2 + t14) * x6; + b = (t13 * x4 + t12 * x2 + t11); + c = (t10 * x4 + t09 * x2 + t08) * x6; + d = (t07 * x4 + t06 * x2 + t05); + t = (a + b) * x6 * (x4 * x4) + (c + d) * x2 + t04; +#endif + + EXTRACT_WORDS(hx, lx, x); + INSERT_WORDS(xhi, hx, 0); + xlo = x - xhi; + xlo *= (xlo + xhi + xhi); + xhi *= xhi; + + t = t02lo + x2 * (x2 * t + t03) + t02; + t = t01lo + xlo * t + xhi * t + t01; + t = t00lo + xlo * t + xhi * t + t00; + return (t * x); + } else if (x > 0.25) { + x = 0.5 - x; + t = __kernel_cospi(x) / __kernel_sinpi(x); + } else + t = 1; + return (t); +} + +static inline double +__compute_tanpi(double x) +{ + + return (x < 0.5 ? __kernel_tanpi(x) : -__kernel_tanpi(1 - x)); +} + +double +tanpi(double x) +{ + volatile static const double vzero = 0; + double ax; + uint32_t hx, ix, j0, lx; + + EXTRACT_WORDS(hx, lx, x); + ix = hx & 0x7fffffff; + INSERT_WORDS(ax, ix, lx); + + if (ix < 0x3ff00000) { /* |x| < 1 */ + if (ix < 0x3e200000) { /* |x| < 0x1p-29 */ + if (x == 0) + return (x); + INSERT_WORDS(ax, hx, 0); + x -= ax; + return (pilo * x + pihi * x + pilo * ax + pihi * ax); + } + if (ix == 0x3fe00000 && !lx) + return ((x - x) / (x - x)); + ax = __compute_tanpi(ax); + return ((hx & 0x80000000) ? -ax : ax); + } + + if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */ + /* Determine integer part of ax. */ + j0 = ((ix >> 20) & 0x7ff) - 0x3ff; + if (j0 < 20) { + ix &= ~(0x000fffff >> j0); + lx = 0; + } else { + lx &= ~(((uint32_t)(0xffffffff)) >> (j0 - 20)); + } + INSERT_WORDS(x,ix,lx); + + ax -= x; + + if (ax == 0.5) + return ((x - x) / (x - x)); + + ax = ax == 0 ? 0 : __compute_tanpi(ax); + return ((hx & 0x80000000) ? -ax : ax); + } + + /* x = +-inf or nan. */ + if (ix >= 0x7f800000) + return (vzero / vzero); + + /* + * |x| >= 0x1p52 is always an integer, so return +-0. + * FIXME: should this raise FE_INEXACT or FE_INVALID? + */ + if (ax + 1 > 1) + ax = copysign(0, x); + return (ax); +} + +#if LDBL_MANT_DIG == 53 +__weak_reference(tanpi, tanpil); +#endif Property changes on: lib/msun/src/s_tanpi.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: lib/msun/src/s_tanpif.c =================================================================== --- lib/msun/src/s_tanpif.c (nonexistent) +++ lib/msun/src/s_tanpif.c (working copy) @@ -0,0 +1,141 @@ +/*- + * 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. + */ + +#include "math.h" +#include "math_private.h" +#include "k_cospif.c" +#include "k_sinpif.c" + +static const float pihi = 3.14160156e+00f; /* 0x40491000 */ +static const float pilo = -8.90890988e-06f; /* 0xb715777a */ + +static const float +t0 = 3.14159274e+00f, /* 0x40490fdb */ +t0lo = -8.71231194e-08f, /* 0xb3bb1871 */ +t1 = 1.03354244e+01f, /* 0x41255de6 */ +t1lo = 3.83117083e-07f, /* 0x34cdaf36 */ +t2 = 4.08029366e+01f, /* 0x42233635 */ +t2lo = -1.28256147e-07f, /* 0xb409b6c8 */ +t3 = 1.62950455e+02f, /* 0x4322f351 */ +t3lo = 4.45962769e-06f, /* 0x3695a3e9 */ +t4 = 6.55820984e+02f, /* 0x4423f48b */ +t5 = 2.43586987e+03f, /* 0x45183deb */ +t6 = 1.47717539e+04f, /* 0x4666cf04 */ +t7 = -1.96741250e+04f, /* 0xc699b440 */ +t8 = 5.87398688e+05f; /* 0x490f686b */ + +static inline float +__kernel_tanpif(float x) +{ + float hi, lo, t, x2, xhi, xlo; + uint32_t ix; + + if (x < 0.25f) { + x2 = x * x; + t = t3lo + x2 * (x2 * (x2 * (x2 * (x2 * t8 + t7) + t6) + t5) + + t4) + t3; + + GET_FLOAT_WORD(ix, x); + SET_FLOAT_WORD(xhi, (ix >> 14) << 14); + xlo = x - xhi; + xlo *= (xlo + xhi + xhi); + xhi *= xhi; + + t = t2lo + xlo * t + xhi * t + t2; + t = t1lo + xlo * t + xhi * t + t1; + t = t0lo + xlo * t + xhi * t + t0; + t *= x; + } else if (x > 0.25f) { + x = 0.5f - x; + t = __kernel_cospif(x) / __kernel_sinpif(x); + } else + t = 1; + return (t); +} + +static inline float +__compute_tanpif(float x) +{ + + return (x < 0.5f ? __kernel_tanpif(x) : -__kernel_tanpif(1 - x)); +} + +float +tanpif(float x) +{ + volatile static const float vzero = 0; + float ax; + uint32_t hx, ix, j0; + + GET_FLOAT_WORD(hx, x); + ix = hx & 0x7fffffff; + SET_FLOAT_WORD(ax, ix); + + if (ix < 0x3f800000) { /* |x| < 1 */ + if (ix < 0x38800000) { /* |x| < 0x1p-14 */ + if (x == 0) + return (x); + SET_FLOAT_WORD(ax, (hx >> 13) << 13); + x -= ax; + return (pilo * x + pihi * x + pilo * ax + pihi * ax); + } + if (ix == 0x3f000000) + return ((x - x) / (x - x)); + ax = __compute_tanpif(ax); + return ((hx & 0x80000000) ? -ax : ax); + } + + if (ix < 0x4b000000) { /* 1 <= |x| < 0x1p23 */ + /* Determine integer part of ax. */ + j0 = ((ix >> 23) & 0xff) - 0x7f; + ix &= ~(0x007fffff >> j0); + SET_FLOAT_WORD(x, ix); + + ax -= x; + + if (ax == 0.5f) + return ((x - x) / (x - x)); + + ax = ax == 0 ? 0 : __compute_tanpif(ax); + return ((hx & 0x80000000) ? -ax : ax); + } + + /* x = +-inf or nan. */ + if (ix >= 0x7f800000) + return (vzero / vzero); + + /* + * |x| >= 0x1p23 is always an integer, so return +-0. + * FIXME: should this raise FE_INEXACT or FE_INVALID. + */ + if (ax + 1 > 1) + ax = copysignf(0, x); + return (ax); +} Property changes on: lib/msun/src/s_tanpif.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property