FreeBSD Bugzilla – Attachment 181622 Details for
Bug 218514
[LIBM] implementations of sinpi[fl], cospi[fl], and tanpi[fl]
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[patch]
patch
sinpi.diff (text/plain), 95.50 KB, created by
sgk
on 2017-04-09 22:04:34 UTC
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sgk
Created:
2017-04-09 22:04:34 UTC
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95.50 KB
patch
obsolete
>Index: Makefile >=================================================================== >--- Makefile (revision 316585) >+++ Makefile (working copy) >@@ -58,7 +58,7 @@ > k_tan.c k_tanf.c \ > 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_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 \ >@@ -73,8 +73,11 @@ > s_nexttowardf.c s_remquo.c s_remquof.c \ > 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_signgam.c s_significand.c s_significandf.c s_sin.c \ >+ s_sinf.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 +103,14 @@ > 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 +137,15 @@ > > 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 +174,7 @@ > 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 +225,12 @@ > 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 <src.opts.mk> >Index: Symbol.map >=================================================================== >--- Symbol.map (revision 316585) >+++ Symbol.map (working copy) >@@ -294,4 +294,13 @@ > casinl; > catanl; > catanhl; >+ cospi; >+ cospif; >+ cospil; >+ sinpi; >+ sinpif; >+ sinpil; >+ tanpi; >+ tanpif; >+ tanpil; > }; >Index: ld128/k_cospil.c >=================================================================== >--- ld128/k_cospil.c (nonexistent) >+++ ld128/k_cospil.c (working copy) >@@ -0,0 +1,79 @@ >+/*- >+ * 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, x2hi, x2lo; >+ >+ 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); >+ >+ u.e = x2; >+ u.bits.manl = 0; >+ x2hi = u.e; >+ x2lo = x2 - x2hi; >+ >+ u.e = c; >+ u.bits.manl = 0; >+ chi = u.e; >+ clo = c - chi + c1lo; >+ >+ c = clo * x2lo + chi * x2lo + clo * x2hi + (chi * x2hi + c0); >+ >+ return (c); >+} > >Property changes on: 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: ld128/k_sinpil.c >=================================================================== >--- ld128/k_sinpil.c (nonexistent) >+++ ld128/k_sinpil.c (working copy) >@@ -0,0 +1,74 @@ >+/*- >+ * 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, xhi, xlo; >+ >+ /* Split x into high and low parts. */ >+ u.e = x; >+ u.bits.manl = 0; >+ xhi = u.e; >+ 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 = xhi * xhi * sm; >+ lo = x * (lo + s0lo) + xlo * (s0hi + s0md) + x * hi; >+ >+ return (lo + xhi * s0md + xhi * s0hi); >+} > >Property changes on: 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: ld128/s_cospil.c >=================================================================== >--- ld128/s_cospil.c (nonexistent) >+++ ld128/s_cospil.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. >+ * >+ * 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 (ix < 0x1p-60) { /* |x| < 0x1p-60 */ >+ if (huge * x == 0) >+ return (1); >+ 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: 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: ld128/s_sinpil.c >=================================================================== >--- ld128/s_sinpil.c (nonexistent) >+++ 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: 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: ld128/s_tanpil.c >=================================================================== >--- ld128/s_tanpil.c (nonexistent) >+++ 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| < 0x1p52 */ >+ >+ 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: 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: ld80/k_cospil.c >=================================================================== >--- ld80/k_cospil.c (nonexistent) >+++ ld80/k_cospil.c (working copy) >@@ -0,0 +1,75 @@ >+/*- >+ * 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, x2, x2hi, x2lo; >+ uint64_t lx; >+ uint16_t ix; >+ >+ x2 = x * x; >+ c = (c2 + (c3 + (c4 + (c5 + (c6 + (c7 + (c8 + c9 * x2) * x2) >+ * x2) * x2) * x2) * x2) * x2) * x2 + c1hi; >+ >+ EXTRACT_LDBL80_WORDS(ix, lx, x2); >+ if (ix < 0x3ff9) /* |x| < 0x1p-6 */ >+ return (c0 + c * x2); >+ >+ INSERT_LDBL80_WORDS(x2hi, ix, (lx >> 32) << 32); >+ x2lo = x2 - x2hi; >+ >+ EXTRACT_LDBL80_WORDS(ix, lx, c); >+ INSERT_LDBL80_WORDS(chi, ix, (lx >> 40) << 40); >+ clo = c - chi + c1lo; >+ >+ c = clo * x2lo + chi * x2lo + clo * x2hi + (chi * x2hi + c0); >+ >+ return (c); >+} > >Property changes on: 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: ld80/k_sinpil.c >=================================================================== >--- ld80/k_sinpil.c (nonexistent) >+++ ld80/k_sinpil.c (working copy) >@@ -0,0 +1,71 @@ >+/*- >+ * 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), >+s0mdu = LD80C(0xbe32e3e32bca9d07, -98, -4.68876217131824210625e-30L), >+s1u = LD80C(0xa55de7312df295f5, 2, -5.16771278004997002909e+00L), >+s2u = LD80C(0xa335e33bad570e85, 1, 2.55016403987734544098e+00L); >+ >+#define s0hi (s0hiu.e) >+#define s0md (s0mdu.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, x2, xhi, xlo; >+ uint64_t lx; >+ uint16_t ix; >+ >+ EXTRACT_LDBL80_WORDS(ix, lx, x); >+ INSERT_LDBL80_WORDS(xhi, ix, (lx >> 32) << 32); >+ xlo = x - xhi; >+ >+ x2 = x * x; >+ sm = x2 * (x2 * (x2 * (x2 * (x2 * (x2 * (x2 * s8 + s7) + s6) >+ + s5) + s4) + s3) + s2) + s1; >+ lo = xlo * (x + xhi) * sm; >+ hi = xhi * xhi * sm; >+ lo = x * (lo + s0lo) + xlo * (s0hi + s0md) + x * hi; >+ >+ return (lo + xhi * s0md + xhi * s0hi); >+} > >Property changes on: 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: ld80/s_cospil.c >=================================================================== >--- ld80/s_cospil.c (nonexistent) >+++ ld80/s_cospil.c (working copy) >@@ -0,0 +1,116 @@ >+/*- >+ * Copyright (c) 2017 Steven G. Kargl >+ * All rights reserved. >+ * >+ * Redistribution and use in source and binary forms, with or without >+ * modification, are permitted provided that the following conditions >+ * are met: >+ * 1. Redistributions of source code must retain the above copyright >+ * notice unmodified, this list of conditions, and the following >+ * disclaimer. >+ * 2. Redistributions in binary form must reproduce the above copyright >+ * notice, this list of conditions and the following disclaimer in the >+ * documentation and/or other materials provided with the distribution. >+ * >+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR >+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES >+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. >+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, >+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT >+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, >+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY >+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT >+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF >+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. >+ */ >+ >+/* >+ * See ../src/s_cospi.c for implementation details. >+ */ >+ >+#ifdef __i386__ >+#include <ieeefp.h> >+#endif >+#include <stdint.h> >+ >+#include "fpmath.h" >+#include "math.h" >+#include "math_private.h" >+#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) >+{ >+ 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); >+ 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) >+ return (x - x); >+ >+ /* >+ * |x| >= 0x1p52 is always an even integer, so return 1. >+ * FIXME: should this raise FE_INEXACT or FE_INVALID. >+ */ >+ return (1); >+} > >Property changes on: 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: ld80/s_sinpil.c >=================================================================== >--- ld80/s_sinpil.c (nonexistent) >+++ ld80/s_sinpil.c (working copy) >@@ -0,0 +1,120 @@ >+/*- >+ * Copyright (c) 2017 Steven G. Kargl >+ * All rights reserved. >+ * >+ * Redistribution and use in source and binary forms, with or without >+ * modification, are permitted provided that the following conditions >+ * are met: >+ * 1. Redistributions of source code must retain the above copyright >+ * notice unmodified, this list of conditions, and the following >+ * disclaimer. >+ * 2. Redistributions in binary form must reproduce the above copyright >+ * notice, this list of conditions and the following disclaimer in the >+ * documentation and/or other materials provided with the distribution. >+ * >+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR >+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES >+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. >+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, >+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT >+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, >+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY >+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT >+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF >+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. >+ */ >+ >+/* >+ * See ../src/s_sinpi.c for implementation details. >+ */ >+ >+#ifdef __i386__ >+#include <ieeefp.h> >+#endif >+#include <stdint.h> >+ >+#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) >+{ >+ 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(x - x); >+ >+ /* >+ * |x| >= 0x1p63 is always an integer, so return +-0. >+ * FIXME: should this raise FE_INEXACT or FE_INVALID. >+ */ >+ RETURNI(copysignl(0, x)); >+} > >Property changes on: 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: ld80/s_tanpil.c >=================================================================== >--- ld80/s_tanpil.c (nonexistent) >+++ ld80/s_tanpil.c (working copy) >@@ -0,0 +1,180 @@ >+/*- >+ * 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 <ieeefp.h> >+#endif >+#include <stdint.h> >+ >+#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, x2, xhi, xlo; >+ uint64_t lx; >+ uint16_t ix; >+ >+ EXTRACT_LDBL80_WORDS(ix, lx, x); >+ INSERT_LDBL80_WORDS(xhi, ix, (lx >> 32) << 32); >+ xlo = x - xhi; >+ xlo *= (xlo + xhi + xhi); >+ xhi *= xhi; >+ x2 = x * x; >+ >+ if (x < 0.25) { >+ t = x2 * (x2 * (x2 * (x2 * t20 + t19) + t18) + t17) + t16; >+ t = x2 * (x2 * (x2 * (x2 * t + t15) + t14) + t13) + t12; >+ t = x2 * (x2 * (x2 * (x2 * t + t11) + t10) + t09) + t08; >+ t = x2 * (x2 * (x2 * (x2 * t + t07) + t06) + t05) + t04; >+ 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_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) >+{ >+ 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(x - x); >+ >+ /* >+ * |x| >= 0x1p53 is always an integer, so return +-0. >+ * FIXME: should this raise FE_INEXACT or FE_INVALID. >+ */ >+ RETURNI(copysignl(0, x)); >+} > >Property changes on: 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: man/cospi.3 >=================================================================== >--- man/cospi.3 (nonexistent) >+++ man/cospi.3 (working copy) >@@ -0,0 +1,111 @@ >+.\" Copyright (c) 2017 Steven G. Kargl <kargl@FreeBSD.org> >+.\" 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: 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: man/sinpi.3 >=================================================================== >--- man/sinpi.3 (nonexistent) >+++ man/sinpi.3 (working copy) >@@ -0,0 +1,102 @@ >+.\" Copyright (c) 2017 Steven G. Kargl <kargl@FreeBSD.org> >+.\" 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: 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: man/tanpi.3 >=================================================================== >--- man/tanpi.3 (nonexistent) >+++ man/tanpi.3 (working copy) >@@ -0,0 +1,106 @@ >+.\" Copyright (c) 2017 Steven G. Kargl <kargl@FreeBSD.org> >+.\" 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: 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: src/k_cospi.c >=================================================================== >--- src/k_cospi.c (nonexistent) >+++ src/k_cospi.c (working copy) >@@ -0,0 +1,94 @@ >+/*- >+ * 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. The Remes algorithm used MPFR with a working >+ * precision of 30 times that of the target precision (e.g., for 53-bit >+ * precision MPFR computed f(x) with 1590-bit precision). If |x| < 0x1p-6, >+ * the polynomial can be summed using a Horner's method. If |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 (Horner's method) >+ * cospi(x) = c0 + x2 * C(x2) (Fused multiply add) >+ * >+ * On an Intel(R) Core(TM)2 Duo CPU T7250, limited testing in the >+ * interval [0x1p-28,0.25] gave >+ * >+ * a = 2.4885199032723904e-01 >+ * cospi(a) = 7.0965241314283167e-01, (0x3fe6b578 0xfa3f3aec) >+ * cos(pi*a) = 7.0965241314283156e-01, (0x3fe6b578 0xfa3f3aeb) >+ * >+ * MAX ULP: 0.88903717 >+ * Total tested: 134217727 >+ * 0.8 < ULP <= 0.9: 31605 >+ * 0.7 < ULP <= 0.8: 382675 >+ * 0.6 < ULP <= 0.7: 1367966 >+ */ >+ >+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, x2, x2hi, x2lo; >+ uint32_t hx, lx; >+ >+ x2 = x * x; >+ c = (c2 + (c3 + (c4 + (c5 + (c6 + c7 * x2) * x2) * x2) * x2) >+ * x2) * x2 + c1hi; >+ >+ EXTRACT_WORDS(hx, lx, x2); >+ if (hx < 0x3f900000) /* |x| < 0x1p-6 */ >+ return (c0 + c * x2); >+ >+ INSERT_WORDS(x2hi, hx, 0); >+ x2lo = x2 - x2hi; >+ >+ EXTRACT_WORDS(hx, lx, c); >+ INSERT_WORDS(chi, hx, 0); >+ clo = c - chi + c1lo; >+ >+ c = clo * x2lo + chi * x2lo + clo * x2hi + (chi * x2hi + c0); >+ >+ return (c); >+} > >Property changes on: 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: src/k_cospif.c >=================================================================== >--- src/k_cospif.c (nonexistent) >+++ src/k_cospif.c (working copy) >@@ -0,0 +1,62 @@ >+/*- >+ * 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: 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: src/k_sinpi.c >=================================================================== >--- src/k_sinpi.c (nonexistent) >+++ src/k_sinpi.c (working copy) >@@ -0,0 +1,91 @@ >+/*- >+ * 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. The Remes algorithm used MPFR with a working >+ * precision of 30 times that of the target precision (e.g., for 53-bit >+ * precision MPFR computed f(x) with 1590-bit precision). 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 (Horner's method) >+ * 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. >+ * >+ * On an Intel(R) Core(TM)2 Duo CPU T7250, limited testing in the >+ * interval [0x1p-28,0.25] gave >+ * >+ * a = 2.4959746748209000e-01 >+ * sinpi(a) = 7.0621201359586339e-01 (0x3fe69949 0xefcdf824) >+ * sin(pi*a) = 7.0621201359586350e-01 (0x3fe69949 0xefcdf825) >+ * >+ * MAX ULP: 0.82844596 >+ * Total tested: 134217727 >+ * 0.8 < ULP <= 0.9: 13 >+ * 0.7 < ULP <= 0.8: 9062 >+ * 0.6 < ULP <= 0.7: 181394 >+ */ >+ >+static const double >+s0hi = 3.1415926218032837e+00, /* 0x400921fb 0x50000000 */ >+s0md = 3.1786509547050787e-08, /* 0x3e6110b4 0x611a5f14 */ >+s0lo = 1.6590549662519743e-24, /* 0x3b000b9f 0x030b40fc */ >+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, x2, xhi, xlo; >+ uint32_t hx, lx; >+ >+ EXTRACT_WORDS(hx, lx, x); >+ INSERT_WORDS(xhi, hx, 0); >+ xlo = x - xhi; >+ >+ x2 = x * x; >+ sm = x2 * (x2 * (x2 * (x2 * (x2 * (x2 * s7 + s6) + s5) + s4) + s3) >+ + s2) + s1; >+ lo = xlo * (x + xhi) * sm; >+ hi = xhi * xhi * sm; >+ lo = x * (lo + s0lo) + xlo * (s0hi + s0md) + x * hi; >+ >+ return (lo + xhi * s0md + xhi * s0hi); >+} > >Property changes on: 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: src/k_sinpif.c >=================================================================== >--- src/k_sinpif.c (nonexistent) >+++ src/k_sinpif.c (working copy) >@@ -0,0 +1,57 @@ >+/*- >+ * 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 */ >+s0md = 9.67653585e-04f, /* 0x3a7daa22 */ >+s0lo = -8.43987033e-12f, /* 0xad1479cc */ >+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 + s0lo) + xlo * (s0hi + s0md) + x * hi; >+ >+ return (lo + xhi * s0md + xhi * s0hi); >+} > >Property changes on: 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: src/math.h >=================================================================== >--- src/math.h (revision 316585) >+++ 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: src/s_cospi.c >=================================================================== >--- src/s_cospi.c (nonexistent) >+++ src/s_cospi.c (working copy) >@@ -0,0 +1,144 @@ >+/*- >+ * 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 for sinpi(x) and cospi(x) 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 0 <= r < 1 is a remainder. With >+ * the given domain, a simplified inline j0 = 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) >+{ >+ 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); >+ 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 (x - x); >+ >+ /* >+ * |x| >= 0x1p52 is always an even integer, so return 1. >+ * FIXME: should this raise FE_INEXACT or FE_INVALID. >+ */ >+ return (1); >+} >+ >+#if LDBL_MANT_DIG == 53 >+__weak_reference(cospi, cospil); >+#endif > >Property changes on: 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: src/s_cospif.c >=================================================================== >--- src/s_cospif.c (nonexistent) >+++ src/s_cospif.c (working copy) >@@ -0,0 +1,96 @@ >+/*- >+ * 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) >+{ >+ 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 (x - x); >+ >+ /* >+ * |x| >= 0x1p23 is always an even integer, so return 1. >+ * FIXME: should this raise FE_INEXACT or FE_INVALID. >+ */ >+ return (1); >+} > >Property changes on: 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: src/s_sinpi.c >=================================================================== >--- src/s_sinpi.c (nonexistent) >+++ src/s_sinpi.c (working copy) >@@ -0,0 +1,151 @@ >+/*- >+ * 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 a max ULP less than >+ * 0.67, 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 for sinpi(x) and cospi(x) 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 0 <= r < 1 is a remainder. With >+ * the given domain, a simplified inline j0 = 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) >+{ >+ 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 (x - x); >+ >+ /* >+ * |x| >= 0x1p52 is always an integer, so return +-0. >+ * FIXME: should this raise FE_INEXACT or FE_INVALID. >+ */ >+ return (copysign(0, x)); >+} >+ >+#if LDBL_MANT_DIG == 53 >+__weak_reference(sinpi, sinpil); >+#endif > >Property changes on: 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: src/s_sinpif.c >=================================================================== >--- src/s_sinpif.c (nonexistent) >+++ src/s_sinpif.c (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 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) >+{ >+ 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 (x - x); >+ >+ /* >+ * |x| >= 0x1p23 is always an integer, so return +-0. >+ * FIXME: should this raise FE_INEXACT or FE_INVALID. >+ */ >+ return (copysignf(0, x)); >+} > >Property changes on: 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: src/s_tanpi.c >=================================================================== >--- src/s_tanpi.c (nonexistent) >+++ src/s_tanpi.c (working copy) >@@ -0,0 +1,240 @@ >+/*- >+ * 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 a max ULP less than >+ * 0.59, 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 >+ * tan in terms of sin and cos. 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 0 <= r < 1 is a remainder. With >+ * the given domain, a simplified inline j0 = floor(x) is used. >+ * >+ * tanpi(x) = tan(pi*(j0+r)) >+ * tan(pi*j0) + tan(pi*r) >+ * = ---------------------------- >+ * 1 - tan(pi*j0) * tan(pi*r) >+ * = tanpi(r) >+ * >+ * 4. For |x| >= 0x1p(P-1), |x| is integral and tanpi(x) = copysign(0,x). >+ * >+ * 5. Special cases: >+ * >+ * tanpif(+-0) = +-0 >+ * tanpif(+-n) = +-0, for positive integers n. >+ * tanpif(+-n+1/4) = +-1, for positive integers n. >+ * tanpif(+-n+1/2) = NaN, for positive integers n. >+ * tanpif(+-inf) = nan. Raises the "invalid" floating-point exception. >+ * tanpif(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. The Remes algorithm used MPFR with a working >+ * precision of 30 times that of the target precision (e.g., for 53-bit >+ * precision MPFR computed f(x) with 1590-bit precision). 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 (Horner's method) >+ * 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. >+ * >+ * On an Intel(R) Core(TM)2 Duo CPU T7250, limited testing in the >+ * interval [0x1p-28,0.25] gave >+ * >+ * a = 2.4250162020325661e-01 >+ * tanpi(a) = 9.5396227802027667e-01 (0x3fee86db 0xe636df37) >+ * tan(pi*a) = 9.5396227802027678e-01 (0x3fee86db 0xe636df38) >+ * >+ * MAX ULP: 1.37582114 >+ * Total tested: 134217727 >+ * 1.0 < ULP : 309144 >+ * 0.9 < ULP <= 1.0: 1047636 >+ * 0.8 < ULP <= 0.9: 2732819 >+ * 0.7 < ULP <= 0.8: 5491591 >+ * 0.6 < ULP <= 0.7: 8639239 >+ * >+ * In the interval [0.25,0.48], limited testing finds >+ * >+ * a = 4.1875240078199505e-01 >+ * tanpi(a) = 3.8323217592887793e+00 (0x400ea898 0x4f7f27eb) >+ * tan(pi*a) = 3.8323217592887784e+00 (0x400ea898 0x4f7f27e9) >+ * >+ * MAX ULP: 2.01127812 >+ * Total tested: 134217727 >+ * 1.0 < ULP : 5702704 >+ * 0.9 < ULP <= 1.0: 3602502 >+ * 0.8 < ULP <= 0.9: 5207602 >+ * 0.7 < ULP <= 0.8: 7173276 >+ * 0.6 < ULP <= 0.7: 9449882 >+ */ >+ >+#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, x2, xhi, xlo; >+ uint32_t hx, lx; >+ >+ if (x < 0.25) { >+ x2 = x * x; >+ t = x2 * (x2 * (x2 * (t15 + x2 * t16) + t14) + t13) + t12; >+ t = x2 * (x2 * (x2 * (x2 * t + t11) + t10) + t09) + t08; >+ t = x2 * (x2 * (x2 * (x2 * t + t07) + t06) + t05) + t04; >+ >+ 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) >+{ >+ 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 (x - x); >+ >+ /* >+ * |x| >= 0x1p53 is always an integer, so return +-0. >+ * FIXME: should this raise FE_INEXACT or FE_INVALID. >+ */ >+ return (copysign(0, x)); >+} >+ >+#if LDBL_MANT_DIG == 53 >+__weak_reference(tanpi, tanpil); >+#endif > >Property changes on: 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: src/s_tanpif.c >=================================================================== >--- src/s_tanpif.c (nonexistent) >+++ src/s_tanpif.c (working copy) >@@ -0,0 +1,138 @@ >+/*- >+ * 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) { /* 0 <= |x| < 0.25 */ >+ x2 = x * x; >+ t = t3lo + x2 * (t4 + x2 * (t5 + x2 * (t6 + x2 * (t7 >+ + x2 * t8)))) + 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) { /* 0.25 < |x| < 0.5 */ >+ 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) >+{ >+ 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 (x - x); >+ >+ /* >+ * |x| >= 0x1p23 is always an integer, so return +-0. >+ * FIXME: should this raise FE_INEXACT or FE_INVALID. >+ */ >+ return (copysignf(0, x)); >+} > >Property changes on: 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
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