diff options
| -rw-r--r-- | include/complex.h | 4 | ||||
| -rw-r--r-- | lib/libc/softfloat/bits64/softfloat-macros | 2 | ||||
| -rw-r--r-- | lib/msun/Makefile | 9 | ||||
| -rw-r--r-- | lib/msun/Symbol.map | 3 | ||||
| -rw-r--r-- | lib/msun/man/clog.3 | 103 | ||||
| -rw-r--r-- | lib/msun/man/complex.3 | 10 | ||||
| -rw-r--r-- | lib/msun/src/math_private.h | 6 | ||||
| -rw-r--r-- | lib/msun/src/s_clog.c | 155 | ||||
| -rw-r--r-- | lib/msun/src/s_clogf.c | 151 | ||||
| -rw-r--r-- | lib/msun/src/s_clogl.c | 168 |
10 files changed, 601 insertions, 10 deletions
diff --git a/include/complex.h b/include/complex.h index b502613c6acf..0f7228fad869 100644 --- a/include/complex.h +++ b/include/complex.h @@ -101,6 +101,10 @@ float complex cexpf(float complex); double cimag(double complex) __pure2; float cimagf(float complex) __pure2; long double cimagl(long double complex) __pure2; +double complex clog(double complex); +float complex clogf(float complex); +long double complex + clogl(long double complex); double complex conj(double complex) __pure2; float complex conjf(float complex) __pure2; long double complex diff --git a/lib/libc/softfloat/bits64/softfloat-macros b/lib/libc/softfloat/bits64/softfloat-macros index f4647def2bd4..7fedb0c348d0 100644 --- a/lib/libc/softfloat/bits64/softfloat-macros +++ b/lib/libc/softfloat/bits64/softfloat-macros @@ -157,7 +157,7 @@ INLINE void z0 = a0>>count; } else { - z1 = ( count < 64 ) ? ( a0>>( count & 63 ) ) : 0; + z1 = ( count < 128 ) ? ( a0>>( count & 63 ) ) : 0; z0 = 0; } *z1Ptr = z1; diff --git a/lib/msun/Makefile b/lib/msun/Makefile index ed9f96e61ae9..7f4283c01ed7 100644 --- a/lib/msun/Makefile +++ b/lib/msun/Makefile @@ -57,7 +57,7 @@ COMMON_SRCS= b_exp.c b_log.c b_tgamma.c \ k_cos.c k_cosf.c k_exp.c k_expf.c k_rem_pio2.c k_sin.c k_sinf.c \ 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_cbrt.c s_cbrtf.c s_ceil.c s_ceilf.c s_clog.c s_clogf.c \ s_copysign.c s_copysignf.c s_cos.c s_cosf.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 \ @@ -101,7 +101,8 @@ COMMON_SRCS+= catrigl.c \ 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_clogl.c s_cosl.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 \ @@ -133,7 +134,8 @@ INCS+= fenv.h math.h MAN= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 \ ceil.3 cacos.3 ccos.3 ccosh.3 cexp.3 \ - cimag.3 copysign.3 cos.3 cosh.3 csqrt.3 erf.3 exp.3 fabs.3 fdim.3 \ + cimag.3 clog.3 copysign.3 cos.3 cosh.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 \ @@ -166,6 +168,7 @@ MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.3 \ cimag.3 conj.3 cimag.3 conjf.3 cimag.3 conjl.3 \ cimag.3 cproj.3 cimag.3 cprojf.3 cimag.3 cprojl.3 \ cimag.3 creal.3 cimag.3 crealf.3 cimag.3 creall.3 +MLINKS+=clog.3 clogf.3 clog.3 clogl.3 MLINKS+=copysign.3 copysignf.3 copysign.3 copysignl.3 MLINKS+=cos.3 cosf.3 cos.3 cosl.3 MLINKS+=cosh.3 coshf.3 cosh.3 coshl.3 diff --git a/lib/msun/Symbol.map b/lib/msun/Symbol.map index f7d9e03d0f83..a9837f6c4d4e 100644 --- a/lib/msun/Symbol.map +++ b/lib/msun/Symbol.map @@ -294,6 +294,9 @@ FBSD_1.5 { casinl; catanl; catanhl; + clog; + clogf; + clogl; sincos; sincosf; sincosl; diff --git a/lib/msun/man/clog.3 b/lib/msun/man/clog.3 new file mode 100644 index 000000000000..0d23a845fb63 --- /dev/null +++ b/lib/msun/man/clog.3 @@ -0,0 +1,103 @@ +.\" 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 AUTHOR 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 AUTHOR 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 February 13, 2017 +.Dt CLOG 3 +.Os +.Sh NAME +.Nm clog , +.Nm clogf , +and +.Nm clogl +.Nd complex natural logrithm functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In complex.h +.Ft double complex +.Fn clog "double complex z" +.Ft float complex +.Fn clogf "float complex z" +.Ft long double complex +.Fn clogl "long double complex z" +.Sh DESCRIPTION +The +.Fn clog , +.Fn clogf , +and +.Fn clogl +functions compute the complex natural logrithm of +.Fa z . +with a branch cut along the negative real axis . +.Sh RETURN VALUES +The +.Fn clog +function returns the complex natural logarithm value, in the +range of a strip mathematically unbounded along the real axis and in +the interval [-I* \*(Pi , +I* \*(Pi ] along the imaginary axis. +The function satisfies the relationship: +.Fo clog +.Fn conj "z" Fc += +.Fo conj +.Fn clog "z" Fc . +.Pp + +.\" Table is formatted for an 80-column xterm. +.Bl -column ".Sy +\*(If + I*\*(Na" ".Sy Return value" ".Sy Divide-by-zero exception" +.It Sy Argument Ta Sy Return value Ta Sy Comment +.It -0 + I*0 Ta -\*(If + I*\*(Pi Ta Divide-by-zero exception +.It Ta Ta raised +.It +0 + I*0 Ta -\*(If + I*0 Ta Divide by zero exception +.It Ta Ta raised +.It x + I*\*(If Ta +\*(If + I*\*(Pi/2 Ta For finite x +.It x + I*\*(Na Ta \*(Na + I*\*(Na Ta Optionally raises invalid +.It Ta Ta floating-point exception +.It Ta Ta for finite x +.It -\*(If + I*y Ta +\*(If + I*\*(Pi Ta For finite positive-signed y +.It +\*(If + I*y Ta +\*(If + I*0 Ta For finite positive-signed y +.It -\*(If + I*\*(If Ta +\*(If + I*3\*(Pi/4 +.It +\*(If + I*\*(If Ta +\*(If + I*\*(Pi/4 +.It \*(Pm\*(If + I*\*(Na Ta +\*(If + I*\*(Na +.It \*(Na + I*y Ta \*(Na + I*\*(Na Ta Optionally raises invalid +.It Ta Ta floating-point exception +.It Ta Ta for finite y +.It \*(Na + I*\*(If Ta +\*(If + I*\*(Na +.It \*(Na + I*\*(Na Ta \*(Na + I*\*(Na +.El + +.Sh SEE ALSO +.Xr complex 3 , +.Xr log 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn clog , +.Fn cexpf , +and +.Fn clogl +functions conform to +.St -isoC-99 . diff --git a/lib/msun/man/complex.3 b/lib/msun/man/complex.3 index d2864944cf00..436c7e6fc889 100644 --- a/lib/msun/man/complex.3 +++ b/lib/msun/man/complex.3 @@ -24,7 +24,7 @@ .\" .\" $FreeBSD$ .\" -.Dd October 17, 2011 +.Dd May 13, 2018 .Dt COMPLEX 3 .Os .Sh NAME @@ -77,6 +77,10 @@ csqrt complex square root .Cl cexp exponential base e .El +.Ss Natural logrithm Function +.Cl +clog natural logrithm +.El .\" Section 7.3.9 of ISO C99 standard .Ss Manipulation Functions .Cl @@ -117,8 +121,6 @@ The functions described here conform to .St -isoC-99 . .Sh BUGS -The logarithmic functions -.Fn clog -and the power functions +The power functions .Fn cpow are not implemented. diff --git a/lib/msun/src/math_private.h b/lib/msun/src/math_private.h index 74879027dba4..7f81381a2423 100644 --- a/lib/msun/src/math_private.h +++ b/lib/msun/src/math_private.h @@ -294,8 +294,9 @@ do { \ /* Support switching the mode to FP_PE if necessary. */ #if defined(__i386__) && !defined(NO_FPSETPREC) -#define ENTERI() \ - long double __retval; \ +#define ENTERI() ENTERIT(long double) +#define ENTERIT(returntype) \ + returntype __retval; \ fp_prec_t __oprec; \ \ if ((__oprec = fpgetprec()) != FP_PE) \ @@ -318,6 +319,7 @@ do { \ } while (0) #else #define ENTERI() +#define ENTERIT(x) #define RETURNI(x) RETURNF(x) #define ENTERV() #define RETURNV() return diff --git a/lib/msun/src/s_clog.c b/lib/msun/src/s_clog.c new file mode 100644 index 000000000000..8150fa7f8bce --- /dev/null +++ b/lib/msun/src/s_clog.c @@ -0,0 +1,155 @@ +/*- + * Copyright (c) 2013 Bruce D. Evans + * 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. + */ + +#include <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +#include <complex.h> +#include <float.h> + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" + +#define MANT_DIG DBL_MANT_DIG +#define MAX_EXP DBL_MAX_EXP +#define MIN_EXP DBL_MIN_EXP + +static const double +ln2_hi = 6.9314718055829871e-1, /* 0x162e42fefa0000.0p-53 */ +ln2_lo = 1.6465949582897082e-12; /* 0x1cf79abc9e3b3a.0p-92 */ + +double complex +clog(double complex z) +{ + double_t ax, ax2h, ax2l, axh, axl, ay, ay2h, ay2l, ayh, ayl, sh, sl, t; + double x, y, v; + uint32_t hax, hay; + int kx, ky; + + x = creal(z); + y = cimag(z); + v = atan2(y, x); + + ax = fabs(x); + ay = fabs(y); + if (ax < ay) { + t = ax; + ax = ay; + ay = t; + } + + GET_HIGH_WORD(hax, ax); + kx = (hax >> 20) - 1023; + GET_HIGH_WORD(hay, ay); + ky = (hay >> 20) - 1023; + + /* Handle NaNs and Infs using the general formula. */ + if (kx == MAX_EXP || ky == MAX_EXP) + return (CMPLX(log(hypot(x, y)), v)); + + /* Avoid spurious underflow, and reduce inaccuracies when ax is 1. */ + if (ax == 1) { + if (ky < (MIN_EXP - 1) / 2) + return (CMPLX((ay / 2) * ay, v)); + return (CMPLX(log1p(ay * ay) / 2, v)); + } + + /* Avoid underflow when ax is not small. Also handle zero args. */ + if (kx - ky > MANT_DIG || ay == 0) + return (CMPLX(log(ax), v)); + + /* Avoid overflow. */ + if (kx >= MAX_EXP - 1) + return (CMPLX(log(hypot(x * 0x1p-1022, y * 0x1p-1022)) + + (MAX_EXP - 2) * ln2_lo + (MAX_EXP - 2) * ln2_hi, v)); + if (kx >= (MAX_EXP - 1) / 2) + return (CMPLX(log(hypot(x, y)), v)); + + /* Reduce inaccuracies and avoid underflow when ax is denormal. */ + if (kx <= MIN_EXP - 2) + return (CMPLX(log(hypot(x * 0x1p1023, y * 0x1p1023)) + + (MIN_EXP - 2) * ln2_lo + (MIN_EXP - 2) * ln2_hi, v)); + + /* Avoid remaining underflows (when ax is small but not denormal). */ + if (ky < (MIN_EXP - 1) / 2 + MANT_DIG) + return (CMPLX(log(hypot(x, y)), v)); + + /* Calculate ax*ax and ay*ay exactly using Dekker's algorithm. */ + t = (double)(ax * (0x1p27 + 1)); + axh = (double)(ax - t) + t; + axl = ax - axh; + ax2h = ax * ax; + ax2l = axh * axh - ax2h + 2 * axh * axl + axl * axl; + t = (double)(ay * (0x1p27 + 1)); + ayh = (double)(ay - t) + t; + ayl = ay - ayh; + ay2h = ay * ay; + ay2l = ayh * ayh - ay2h + 2 * ayh * ayl + ayl * ayl; + + /* + * When log(|z|) is far from 1, accuracy in calculating the sum + * of the squares is not very important since log() reduces + * inaccuracies. We depended on this to use the general + * formula when log(|z|) is very far from 1. When log(|z|) is + * moderately far from 1, we go through the extra-precision + * calculations to reduce branches and gain a little accuracy. + * + * When |z| is near 1, we subtract 1 and use log1p() and don't + * leave it to log() to subtract 1, since we gain at least 1 bit + * of accuracy in this way. + * + * When |z| is very near 1, subtracting 1 can cancel almost + * 3*MANT_DIG bits. We arrange that subtracting 1 is exact in + * doubled precision, and then do the rest of the calculation + * in sloppy doubled precision. Although large cancellations + * often lose lots of accuracy, here the final result is exact + * in doubled precision if the large calculation occurs (because + * then it is exact in tripled precision and the cancellation + * removes enough bits to fit in doubled precision). Thus the + * result is accurate in sloppy doubled precision, and the only + * significant loss of accuracy is when it is summed and passed + * to log1p(). + */ + sh = ax2h; + sl = ay2h; + _2sumF(sh, sl); + if (sh < 0.5 || sh >= 3) + return (CMPLX(log(ay2l + ax2l + sl + sh) / 2, v)); + sh -= 1; + _2sum(sh, sl); + _2sum(ax2l, ay2l); + /* Briggs-Kahan algorithm (except we discard the final low term): */ + _2sum(sh, ax2l); + _2sum(sl, ay2l); + t = ax2l + sl; + _2sumF(sh, t); + return (CMPLX(log1p(ay2l + t + sh) / 2, v)); +} + +#if (LDBL_MANT_DIG == 53) +__weak_reference(clog, clogl); +#endif diff --git a/lib/msun/src/s_clogf.c b/lib/msun/src/s_clogf.c new file mode 100644 index 000000000000..19a94453ea37 --- /dev/null +++ b/lib/msun/src/s_clogf.c @@ -0,0 +1,151 @@ +/*- + * Copyright (c) 2013 Bruce D. Evans + * 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. + */ + +#include <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +#include <complex.h> +#include <float.h> + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" + +#define MANT_DIG FLT_MANT_DIG +#define MAX_EXP FLT_MAX_EXP +#define MIN_EXP FLT_MIN_EXP + +static const float +ln2f_hi = 6.9314575195e-1, /* 0xb17200.0p-24 */ +ln2f_lo = 1.4286067653e-6; /* 0xbfbe8e.0p-43 */ + +float complex +clogf(float complex z) +{ + float_t ax, ax2h, ax2l, axh, axl, ay, ay2h, ay2l, ayh, ayl, sh, sl, t; + float x, y, v; + uint32_t hax, hay; + int kx, ky; + + x = crealf(z); + y = cimagf(z); + v = atan2f(y, x); + + ax = fabsf(x); + ay = fabsf(y); + if (ax < ay) { + t = ax; + ax = ay; + ay = t; + } + + GET_FLOAT_WORD(hax, ax); + kx = (hax >> 23) - 127; + GET_FLOAT_WORD(hay, ay); + ky = (hay >> 23) - 127; + + /* Handle NaNs and Infs using the general formula. */ + if (kx == MAX_EXP || ky == MAX_EXP) + return (CMPLXF(logf(hypotf(x, y)), v)); + + /* Avoid spurious underflow, and reduce inaccuracies when ax is 1. */ + if (hax == 0x3f800000) { + if (ky < (MIN_EXP - 1) / 2) + return (CMPLXF((ay / 2) * ay, v)); + return (CMPLXF(log1pf(ay * ay) / 2, v)); + } + + /* Avoid underflow when ax is not small. Also handle zero args. */ + if (kx - ky > MANT_DIG || hay == 0) + return (CMPLXF(logf(ax), v)); + + /* Avoid overflow. */ + if (kx >= MAX_EXP - 1) + return (CMPLXF(logf(hypotf(x * 0x1p-126F, y * 0x1p-126F)) + + (MAX_EXP - 2) * ln2f_lo + (MAX_EXP - 2) * ln2f_hi, v)); + if (kx >= (MAX_EXP - 1) / 2) + return (CMPLXF(logf(hypotf(x, y)), v)); + + /* Reduce inaccuracies and avoid underflow when ax is denormal. */ + if (kx <= MIN_EXP - 2) + return (CMPLXF(logf(hypotf(x * 0x1p127F, y * 0x1p127F)) + + (MIN_EXP - 2) * ln2f_lo + (MIN_EXP - 2) * ln2f_hi, v)); + + /* Avoid remaining underflows (when ax is small but not denormal). */ + if (ky < (MIN_EXP - 1) / 2 + MANT_DIG) + return (CMPLXF(logf(hypotf(x, y)), v)); + + /* Calculate ax*ax and ay*ay exactly using Dekker's algorithm. */ + t = (float)(ax * (0x1p12F + 1)); + axh = (float)(ax - t) + t; + axl = ax - axh; + ax2h = ax * ax; + ax2l = axh * axh - ax2h + 2 * axh * axl + axl * axl; + t = (float)(ay * (0x1p12F + 1)); + ayh = (float)(ay - t) + t; + ayl = ay - ayh; + ay2h = ay * ay; + ay2l = ayh * ayh - ay2h + 2 * ayh * ayl + ayl * ayl; + + /* + * When log(|z|) is far from 1, accuracy in calculating the sum + * of the squares is not very important since log() reduces + * inaccuracies. We depended on this to use the general + * formula when log(|z|) is very far from 1. When log(|z|) is + * moderately far from 1, we go through the extra-precision + * calculations to reduce branches and gain a little accuracy. + * + * When |z| is near 1, we subtract 1 and use log1p() and don't + * leave it to log() to subtract 1, since we gain at least 1 bit + * of accuracy in this way. + * + * When |z| is very near 1, subtracting 1 can cancel almost + * 3*MANT_DIG bits. We arrange that subtracting 1 is exact in + * doubled precision, and then do the rest of the calculation + * in sloppy doubled precision. Although large cancellations + * often lose lots of accuracy, here the final result is exact + * in doubled precision if the large calculation occurs (because + * then it is exact in tripled precision and the cancellation + * removes enough bits to fit in doubled precision). Thus the + * result is accurate in sloppy doubled precision, and the only + * significant loss of accuracy is when it is summed and passed + * to log1p(). + */ + sh = ax2h; + sl = ay2h; + _2sumF(sh, sl); + if (sh < 0.5F || sh >= 3) + return (CMPLXF(logf(ay2l + ax2l + sl + sh) / 2, v)); + sh -= 1; + _2sum(sh, sl); + _2sum(ax2l, ay2l); + /* Briggs-Kahan algorithm (except we discard the final low term): */ + _2sum(sh, ax2l); + _2sum(sl, ay2l); + t = ax2l + sl; + _2sumF(sh, t); + return (CMPLXF(log1pf(ay2l + t + sh) / 2, v)); +} diff --git a/lib/msun/src/s_clogl.c b/lib/msun/src/s_clogl.c new file mode 100644 index 000000000000..e59a1377afd8 --- /dev/null +++ b/lib/msun/src/s_clogl.c @@ -0,0 +1,168 @@ +/*- + * Copyright (c) 2013 Bruce D. Evans + * 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. + */ + +#include <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +#include <complex.h> +#include <float.h> +#ifdef __i386__ +#include <ieeefp.h> +#endif + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" + +#define MANT_DIG LDBL_MANT_DIG +#define MAX_EXP LDBL_MAX_EXP +#define MIN_EXP LDBL_MIN_EXP + +static const double +ln2_hi = 6.9314718055829871e-1; /* 0x162e42fefa0000.0p-53 */ + +#if LDBL_MANT_DIG == 64 +#define MULT_REDUX 0x1p32 /* exponent MANT_DIG / 2 rounded up */ +static const double +ln2l_lo = 1.6465949582897082e-12; /* 0x1cf79abc9e3b3a.0p-92 */ +#elif LDBL_MANT_DIG == 113 +#define MULT_REDUX 0x1p57 +static const long double +ln2l_lo = 1.64659495828970812809844307550013433e-12L; /* 0x1cf79abc9e3b39803f2f6af40f343.0p-152L */ +#else +#error "Unsupported long double format" +#endif + +long double complex +clogl(long double complex z) +{ + long double ax, ax2h, ax2l, axh, axl, ay, ay2h, ay2l, ayh, ayl; + long double sh, sl, t; + long double x, y, v; + uint16_t hax, hay; + int kx, ky; + + ENTERIT(long double complex); + + x = creall(z); + y = cimagl(z); + v = atan2l(y, x); + + ax = fabsl(x); + ay = fabsl(y); + if (ax < ay) { + t = ax; + ax = ay; + ay = t; + } + + GET_LDBL_EXPSIGN(hax, ax); + kx = hax - 16383; + GET_LDBL_EXPSIGN(hay, ay); + ky = hay - 16383; + + /* Handle NaNs and Infs using the general formula. */ + if (kx == MAX_EXP || ky == MAX_EXP) + RETURNI(CMPLXL(logl(hypotl(x, y)), v)); + + /* Avoid spurious underflow, and reduce inaccuracies when ax is 1. */ + if (ax == 1) { + if (ky < (MIN_EXP - 1) / 2) + RETURNI(CMPLXL((ay / 2) * ay, v)); + RETURNI(CMPLXL(log1pl(ay * ay) / 2, v)); + } + + /* Avoid underflow when ax is not small. Also handle zero args. */ + if (kx - ky > MANT_DIG || ay == 0) + RETURNI(CMPLXL(logl(ax), v)); + + /* Avoid overflow. */ + if (kx >= MAX_EXP - 1) + RETURNI(CMPLXL(logl(hypotl(x * 0x1p-16382L, y * 0x1p-16382L)) + + (MAX_EXP - 2) * ln2l_lo + (MAX_EXP - 2) * ln2_hi, v)); + if (kx >= (MAX_EXP - 1) / 2) + RETURNI(CMPLXL(logl(hypotl(x, y)), v)); + + /* Reduce inaccuracies and avoid underflow when ax is denormal. */ + if (kx <= MIN_EXP - 2) + RETURNI(CMPLXL(logl(hypotl(x * 0x1p16383L, y * 0x1p16383L)) + + (MIN_EXP - 2) * ln2l_lo + (MIN_EXP - 2) * ln2_hi, v)); + + /* Avoid remaining underflows (when ax is small but not denormal). */ + if (ky < (MIN_EXP - 1) / 2 + MANT_DIG) + RETURNI(CMPLXL(logl(hypotl(x, y)), v)); + + /* Calculate ax*ax and ay*ay exactly using Dekker's algorithm. */ + t = (long double)(ax * (MULT_REDUX + 1)); + axh = (long double)(ax - t) + t; + axl = ax - axh; + ax2h = ax * ax; + ax2l = axh * axh - ax2h + 2 * axh * axl + axl * axl; + t = (long double)(ay * (MULT_REDUX + 1)); + ayh = (long double)(ay - t) + t; + ayl = ay - ayh; + ay2h = ay * ay; + ay2l = ayh * ayh - ay2h + 2 * ayh * ayl + ayl * ayl; + + /* + * When log(|z|) is far from 1, accuracy in calculating the sum + * of the squares is not very important since log() reduces + * inaccuracies. We depended on this to use the general + * formula when log(|z|) is very far from 1. When log(|z|) is + * moderately far from 1, we go through the extra-precision + * calculations to reduce branches and gain a little accuracy. + * + * When |z| is near 1, we subtract 1 and use log1p() and don't + * leave it to log() to subtract 1, since we gain at least 1 bit + * of accuracy in this way. + * + * When |z| is very near 1, subtracting 1 can cancel almost + * 3*MANT_DIG bits. We arrange that subtracting 1 is exact in + * doubled precision, and then do the rest of the calculation + * in sloppy doubled precision. Although large cancellations + * often lose lots of accuracy, here the final result is exact + * in doubled precision if the large calculation occurs (because + * then it is exact in tripled precision and the cancellation + * removes enough bits to fit in doubled precision). Thus the + * result is accurate in sloppy doubled precision, and the only + * significant loss of accuracy is when it is summed and passed + * to log1p(). + */ + sh = ax2h; + sl = ay2h; + _2sumF(sh, sl); + if (sh < 0.5 || sh >= 3) + RETURNI(CMPLXL(logl(ay2l + ax2l + sl + sh) / 2, v)); + sh -= 1; + _2sum(sh, sl); + _2sum(ax2l, ay2l); + /* Briggs-Kahan algorithm (except we discard the final low term): */ + _2sum(sh, ax2l); + _2sum(sl, ay2l); + t = ax2l + sl; + _2sumF(sh, t); + RETURNI(CMPLXL(log1pl(ay2l + t + sh) / 2, v)); +} |