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author	Martynas Venckus <martynas@cvs.openbsd.org>	2008-06-11 20:53:28 +0000
committer	Martynas Venckus <martynas@cvs.openbsd.org>	2008-06-11 20:53:28 +0000
commit	52b952ebc3ff31143605788b38d890798ea23055 (patch)
tree	110c2ad3877e4b59f6d3f44b7b0aea18a3c1efdb /lib
parent	61b9a28afee59294427e885ebdc5a1f9313d0388 (diff)

- on non-ieee, rename gamma to tgamma, the 'true' gamma

- make gamma an alias of lgamma - on ieee, add tgamma, based on gamma from non-ieee - fixes for tgamma/lgamma/exp/log, esp. special cases (some from freebsd); properly raise invalid fp operations on vax - also some general cleanup, ansification, man page (which was ok jmc@) - bump minor this makes some ports using tgamma possible; also consistifies behavior across openbsd/ieee and openbsd/non-ieee, and other operating systems much thanks sthen@, johan@, steven@, Simon Kuhnle, Wiktor Izdebski for testing ok millert@

Diffstat (limited to 'lib')

-rw-r--r--

lib/libm/Makefile

-rw-r--r--

lib/libm/man/lgamma.3

-rw-r--r--

lib/libm/noieee_src/n_exp.c

-rw-r--r--

lib/libm/noieee_src/n_lgamma.c

-rw-r--r--

lib/libm/noieee_src/n_log.c

-rw-r--r--

lib/libm/noieee_src/n_tgamma.c (renamed from lib/libm/noieee_src/n_gamma.c)

101

-rw-r--r--

lib/libm/shlib_version

-rw-r--r--

lib/libm/src/b_exp__D.c

126

-rw-r--r--

lib/libm/src/b_log__D.c

396

-rw-r--r--

lib/libm/src/b_tgamma.c

329

-rw-r--r--

lib/libm/src/math_private.h

11 files changed, 1082 insertions, 112 deletions

diff --git a/lib/libm/Makefile b/lib/libm/Makefile
index d8d787b3e40..e5d085f4b43 100644
--- a/lib/libm/Makefile
+++ b/lib/libm/Makefile

@@ -1,5 +1,5 @@

# $NetBSD: Makefile,v 1.28 1995/11/20 22:06:19 jtc Exp $

-# $OpenBSD: Makefile,v 1.43 2008/06/11 14:50:06 martynas Exp $

+# $OpenBSD: Makefile,v 1.44 2008/06/11 20:53:27 martynas Exp $

# @(#)Makefile 5.1beta 93/09/24

@@ -100,7 +100,8 @@ CFLAGS+= -D_MULTI_LIBM -D_POSIX_MODE

LIB= m

WANTLINT=

-COMMON_SRCS = e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \

+COMMON_SRCS = b_exp__D.c b_log__D.c b_tgamma.c \

+ e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \

e_atan2.c e_atan2f.c e_atanh.c e_atanhf.c e_cosh.c e_coshf.c e_exp.c \

e_expf.c e_fmod.c e_fmodf.c e_hypot.c e_hypotf.c e_j0.c e_j0f.c \

e_j1.c e_j1f.c e_jn.c e_jnf.c e_lgamma_r.c e_lgammaf_r.c e_log.c \

@@ -131,12 +132,12 @@ COMMON_SRCS = e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \

# math routines for non-IEEE architectures.

NOIEEE_SRCS = n_asincos.c n_acosh.c n_asinh.c n_atan.c n_atanh.c n_cosh.c \

- n_erf.c n_exp.c n_exp__E.c n_expm1.c n_floor.c n_fmod.c n_gamma.c \

+ n_erf.c n_exp.c n_exp__E.c n_expm1.c n_floor.c n_fmod.c n_tgamma.c \

n_lgamma.c n_j0.c n_j1.c n_jn.c n_log.c n_log10.c n_log1p.c \

n_log__L.c n_pow.c n_sinh.c n_tanh.c n_atan2.c n_cabs.c n_cbrt.c \

n_sqrt.c n_sincos.c n_tan.c n_argred.c n_support.c n_infnan.c \

n_round.c

# NetBSD's C library supplies these functions:

#COMMON_SRCS+= s_fabs.c s_frexp.c s_isinf.c s_isnan.c s_ldexp.c s_modf.c

@@ -173,7 +174,7 @@ MLINKS+=ieee.3 copysign.3 ieee.3 drem.3 ieee.3 finite.3 ieee.3 ilogb.3 \

MLINKS+=logb.3 scalb.3

MLINKS+=logb.3 significand.3

MLINKS+=j0.3 j1.3 j0.3 jn.3 j0.3 y0.3 j0.3 y1.3 j0.3 yn.3

-MLINKS+=lgamma.3 gamma.3

+MLINKS+=lgamma.3 gamma.3 lgamma.3 tgamma.3 lgamma.3 tgammaf.3

MLINKS+=sqrt.3 cbrt.3

# float versions

diff --git a/lib/libm/man/lgamma.3 b/lib/libm/man/lgamma.3
index cc3f7411cdf..af12f5c50e6 100644
--- a/lib/libm/man/lgamma.3
+++ b/lib/libm/man/lgamma.3

@@ -1,4 +1,4 @@

-.\" $OpenBSD: lgamma.3,v 1.14 2007/05/31 19:19:35 jmc Exp $

+.\" $OpenBSD: lgamma.3,v 1.15 2008/06/11 20:53:27 martynas Exp $

.\"

@@ -28,12 +28,14 @@

.\"

.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92

.\"

-.Dd $Mdocdate: May 31 2007 $

+.Dd $Mdocdate: June 11 2008 $

.Dt LGAMMA 3

.Os

.Sh NAME

.Nm lgamma ,

-.Nm lgammaf

+.Nm lgammaf ,

+.Nm tgamma ,

+.Nm tgammaf

.Nd log gamma functions

.Sh SYNOPSIS

.Fd #include <math.h>

@@ -44,6 +46,10 @@

.Fn lgamma "double x"

.Ft float

.Fn lgammaf "float x"

+.Ft double

+.Fn tgamma "double x"

+.Ft float

+.Fn tgammaf "float x"

.Sh DESCRIPTION

.Fn lgamma x

.if t \{\

@@ -64,6 +70,23 @@ The

.Fn lgammaf

function is a single precision version of

.Fn lgamma .

+.Pp

+The

+.Fn tgamma x

+and

+.Fn tgammaf x

+functions return \(*G(x), with no effect on

+.Fa signgam .

+.Pp

+The

+.Fn gamma ,

+and

+.Fn gammaf

+are deprecated aliases for

+.Fn lgamma ,

+and

+.Fn lgammaf

+respectively.

.Sh IDIOSYNCRASIES

Do not use the expression

.Sq Li signgam\(**exp(lgamma(x))

@@ -76,11 +99,19 @@ lg = lgamma(x); g = signgam\(**exp(lg);

Only after

.Fn lgamma

has returned can signgam be correct.

+.Pp

+For arguments in its range,

+.Fn tgamma

+is preferred, as for positive arguments

+it is accurate to within one unit in the last place.

.Sh RETURN VALUES

.Fn lgamma

returns appropriate values unless an argument is out of range.

Overflow will occur for sufficiently large positive values, and

non-positive integers.

+For large non-integer negative values,

+.Fn tgamma

+will underflow.

On the

.Tn VAX ,

the reserved operator is returned,

@@ -91,8 +122,26 @@ is set to

.Sh SEE ALSO

.Xr infnan 3 ,

.Xr math 3

+.Sh STANDARDS

+The

+.Fn lgamma ,

+.Fn lgammaf ,

+.Fn tgamma ,

+and

+.Fn tgammaf

+functions are expected to conform to

+.St -isoC-99 .

.Sh HISTORY

The

.Fn lgamma

function appeared in

.Bx 4.3 .

+The

+.Fn tgamma

+function appeared in

+.Ox 4.4 ,

+which is based on the

+.Fn gamma

+function that appeared in

+.Bx 4.4

+as a function to compute \(*G(x).

diff --git a/lib/libm/noieee_src/n_exp.c b/lib/libm/noieee_src/n_exp.c
index e1fef84bc1b..a51696b58d6 100644
--- a/lib/libm/noieee_src/n_exp.c
+++ b/lib/libm/noieee_src/n_exp.c

@@ -1,4 +1,4 @@

-/* $NetBSD: n_exp.c,v 1.1 1995/10/10 23:36:44 ragge Exp $ */

+/* $OpenBSD: n_exp.c,v 1.5 2008/06/11 20:53:27 martynas Exp $ */

@@ -35,21 +35,21 @@ static char sccsid[] = "@(#)exp.c 8.1 (Berkeley) 6/4/93";

/* EXP(X)

* RETURN THE EXPONENTIAL OF X

* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)

- * CODED IN C BY K.C. NG, 1/19/85;

+ * CODED IN C BY K.C. NG, 1/19/85;

* REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.

* Required system supported functions:

- * scalbn(x,n)

- * copysign(x,y)

+ * scalbn(x,n)

+ * copysign(x,y)

* finite(x)

* Method:

- * 1. Argument Reduction: given the input x, find r and integer k such

+ * 1. Argument Reduction: given the input x, find r and integer k such

* that

- * x = k*ln2 + r, |r| <= 0.5*ln2 .

+ * x = k*ln2 + r, |r| <= 0.5*ln2 .

* r will be represented as r := z+c for better accuracy.

- * 2. Compute exp(r) by

+ * 2. Compute exp(r) by

* exp(r) = 1 + r + r*R1/(2-R1),

* where

@@ -111,10 +111,9 @@ ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2)

ic(lntiny,-7.5137154372698068983E2, 9, -1.77AF8EBEAE354)

ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)

-double exp(x)

-double x;

+double exp(double x)

{

- double z,hi,lo,c;

+ double z, hi, lo, c;

int k;

#if !defined(__vax__)&&!defined(tahoe)

@@ -140,7 +139,7 @@ double x;

}

/* end of x > lntiny */

- else

+ else

/* exp(-big#) underflows to zero */

if(finite(x)) return(scalbn(1.0,-5000));

@@ -149,17 +148,16 @@ double x;

}

/* end of x < lnhuge */

- else

+ else

/* exp(INF) is INF, exp(+big#) overflows to INF */

return( finite(x) ? scalbn(1.0,5000) : x);

}

/* returns exp(r = x + c) for |c| < |x| with no overlap. */

-double __exp__D(x, c)

-double x, c;

+double __exp__D(double x, double c)

{

- double z,hi,lo, t;

+ double z, hi, lo;

int k;

#if !defined(__vax__)&&!defined(tahoe)

@@ -185,7 +183,7 @@ double x, c;

}

/* end of x > lntiny */

- else

+ else

/* exp(-big#) underflows to zero */

if(finite(x)) return(scalbn(1.0,-5000));

@@ -194,7 +192,7 @@ double x, c;

}

/* end of x < lnhuge */

- else

+ else

/* exp(INF) is INF, exp(+big#) overflows to INF */

return( finite(x) ? scalbn(1.0,5000) : x);

}

diff --git a/lib/libm/noieee_src/n_lgamma.c b/lib/libm/noieee_src/n_lgamma.c
index 5eaed3d2f34..c874e8c6ba5 100644
--- a/lib/libm/noieee_src/n_lgamma.c
+++ b/lib/libm/noieee_src/n_lgamma.c

@@ -1,4 +1,4 @@

-/* $NetBSD: n_lgamma.c,v 1.1 1995/10/10 23:36:56 ragge Exp $ */

+/* $OpenBSD: n_lgamma.c,v 1.4 2008/06/11 20:53:27 martynas Exp $ */

/*-

@@ -53,7 +53,7 @@ static char sccsid[] = "@(#)lgamma.c 8.2 (Berkeley) 11/30/93";

* x > 6:

* Use the asymptotic expansion (Stirling's Formula)

* 0 < x < 6:

- * Use gamma(x+1) = x*gamma(x) for argument reduction.

+ * Use tgamma(x+1) = x*tgamma(x) for argument reduction.

* Use rational approximation in

* the range 1.2, 2.5

* Two approximations are used, one centered at the

@@ -66,12 +66,12 @@ static char sccsid[] = "@(#)lgamma.c 8.2 (Berkeley) 11/30/93";

* non-positive integer returns +Inf.

* NaN returns NaN

-static int endian;

#if defined(__vax__) || defined(tahoe)

#define _IEEE 0

/* double and float have same size exponent field */

#define TRUNC(x) x = (double) (float) (x)

#else

+static int endian;

#define _IEEE 1

#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000

#define infnan(x) 0.0

@@ -80,16 +80,16 @@ static int endian;

static double small_lgam(double);

static double large_lgam(double);

static double neg_lgam(double);

-static double zero = 0.0, one = 1.0;

-int signgam;

+static const double one = 1.0;

+extern int signgam;

#define UNDERFL (1e-1020 * 1e-1020)

#define LEFT (1.0 - (x0 + .25))

#define RIGHT (x0 - .218)

-/* Constants for approximation in [1.244,1.712]

-*/

+ * Constants for approximation in [1.244,1.712]

+ */

#define x0 0.461632144968362356785

#define x0_lo -.000000000000000015522348162858676890521

#define a0_hi -0.12148629128932952880859

@@ -141,7 +141,9 @@ lgamma(double x)

double r;

signgam = 1;

+#if _IEEE

endian = ((*(int *) &one)) ? 1 : 0;

+#endif

if (!finite(x))

if (_IEEE)

@@ -161,11 +163,33 @@ lgamma(double x)

return (neg_lgam(x));

}

+float

+lgammaf(float x)

+ return lgamma(x);

+/*

+ * The gamma() function performs identically to lgamma(), including

+ * the use of signgam.

+ */

+double

+gamma(double x)

+ return lgamma(x);

+float

+gammaf(float x)

+ return lgammaf(x);

static double

large_lgam(double x)

{

double z, p, x1;

- int i;

struct Double t, u, v;

u = __log__D(x);

u.a -= 1.0;

@@ -266,8 +290,7 @@ static double

neg_lgam(double x)

{

int xi;

- double y, z, one = 1.0, zero = 0.0;

- extern double gamma();

+ double y, z, zero = 0.0;

/* avoid destructive cancellation as much as possible */

if (x > -170) {

@@ -277,7 +300,7 @@ neg_lgam(double x)

return(one/zero);

else

return(infnan(ERANGE));

- y = gamma(x);

+ y = tgamma(x);

if (y < 0)

y = -y, signgam = -1;

return (log(y));

diff --git a/lib/libm/noieee_src/n_log.c b/lib/libm/noieee_src/n_log.c
index ac367f72429..04f4a22bacc 100644
--- a/lib/libm/noieee_src/n_log.c
+++ b/lib/libm/noieee_src/n_log.c

@@ -1,4 +1,4 @@

-/* $NetBSD: n_log.c,v 1.1 1995/10/10 23:36:57 ragge Exp $ */

+/* $OpenBSD: n_log.c,v 1.4 2008/06/11 20:53:27 martynas Exp $ */

@@ -93,12 +93,12 @@ static char sccsid[] = "@(#)log.c 8.2 (Berkeley) 11/30/93";

* Values for log(F) were generated using error < 10^-57 absolute

* with the bc -l package.

-static double A1 = .08333333333333178827;

-static double A2 = .01250000000377174923;

-static double A3 = .002232139987919447809;

-static double A4 = .0004348877777076145742;

+static const double A1 = .08333333333333178827;

+static const double A2 = .01250000000377174923;

+static const double A3 = .002232139987919447809;

+static const double A4 = .0004348877777076145742;

-static double logF_head[N+1] = {

+static const double logF_head[N+1] = {

0.,

.007782140442060381246,

.015504186535963526694,

@@ -230,7 +230,7 @@ static double logF_head[N+1] = {

.693147180560117703862

};

-static double logF_tail[N+1] = {

+static const double logF_tail[N+1] = {

0.,

-.00000000000000543229938420049,

.00000000000000172745674997061,

@@ -363,11 +363,7 @@ static double logF_tail[N+1] = {

};

double

-#ifdef _ANSI_SOURCE

log(double x)

-#else

-log(x) double x;

-#endif

{

int m, j;

double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0;

@@ -388,7 +384,7 @@ log(x) double x;

return (x+x);

else

return (infnan(ERANGE));

/* Argument reduction: 1 <= g < 2; x/2^m = g; */

/* y = F*(1 + f/F) for |f| <= 2^-8 */

@@ -435,17 +431,13 @@ log(x) double x;

* Extra precision variant, returning struct {double a, b;};

- * log(x) = a+b to 63 bits, with a is rounded to 26 bits.

+ * log(x) = a+b to 63 bits, with a rounded to 26 bits.

struct Double

-#ifdef _ANSI_SOURCE

__log__D(double x)

-#else

-__log__D(x) double x;

-#endif

{

int m, j;

- double F, f, g, q, u, v, u2, one = 1.0;

+ double F, f, g, q, u, v, u2;

volatile double u1;

struct Double r;

diff --git a/lib/libm/noieee_src/n_gamma.c b/lib/libm/noieee_src/n_tgamma.c
index cce478274c7..de9ff444733 100644
--- a/lib/libm/noieee_src/n_gamma.c
+++ b/lib/libm/noieee_src/n_tgamma.c

@@ -1,4 +1,4 @@

-/* $NetBSD: n_gamma.c,v 1.1 1995/10/10 23:36:50 ragge Exp $ */

+/* $OpenBSD: n_tgamma.c,v 1.1 2008/06/11 20:53:27 martynas Exp $ */

/*-

@@ -45,7 +45,7 @@ static char sccsid[] = "@(#)gamma.c 8.1 (Berkeley) 6/4/93";

/* METHOD:

* x < 0: Use reflection formula, G(x) = pi/(sin(pi*x)*x*G(x))

- * At negative integers, return +Inf, and set errno.

+ * At negative integers, return +Inf and raise overflow.

* x < 6.5:

* Use argument reduction G(x+1) = xG(x) to reach the

@@ -62,11 +62,15 @@ static char sccsid[] = "@(#)gamma.c 8.1 (Berkeley) 6/4/93";

* avoid premature round-off.

* Special values:

- * non-positive integer: Set overflow trap; return +Inf;

- * x > 171.63: Set overflow trap; return +Inf;

- * NaN: Set invalid trap; return NaN

+ * -Inf: return 0 and raise invalid;

+ * negative integer: return +Inf and raise overflow;

+ * other x ~< -177.79: return 0 and raise underflow;

+ * +-0: return +Inf and raise overflow;

+ * finite x ~> 171.63: return +Inf and raise div-by-0;

+ * +Inf: return +Inf and raise div-by-0;

+ * NaN: return 0 and raise invalid.

- * Accuracy: Gamma(x) is accurate to within

+ * Accuracy: tgamma(x) is accurate to within

* x > 0: error provably < 0.9ulp.

* Maximum observed in 1,000,000 trials was .87ulp.

* x < 0:

@@ -118,7 +122,7 @@ static struct Double ratfun_gam(double, double);

#define Pa7 -1.44705562421428915453880392761e-02

static const double zero = 0., one = 1.0, tiny = 1e-300;

-static int endian;

* TRUNC sets trailing bits in a floating-point number to zero.

* is a temporary variable.

@@ -127,21 +131,26 @@ static int endian;

#define _IEEE 0

#define TRUNC(x) x = (double) (float) (x)

#else

+static int endian;

#define _IEEE 1

#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000

#define infnan(x) 0.0

#endif

double

-gamma(x)

- double x;

+tgamma(double x)

{

struct Double u;

+#if _IEEE

endian = (*(int *) &one) ? 1 : 0;

+#endif

if (x >= 6) {

if(x > 171.63)

- return(one/zero);

+ if (_IEEE)

+ return (x/zero);

+ else

+ return (infnan(ERANGE));

u = large_gam(x);

return(__exp__D(u.a, u.b));

} else if (x >= 1.0 + LEFT + x0)

@@ -149,28 +158,43 @@ gamma(x)

else if (x > 1.e-17)

return (smaller_gam(x));

else if (x > -1.e-17) {

- if (x == 0.0)

- if (!_IEEE) return (infnan(ERANGE));

- else return (one/x);

- one+1e-20; /* Raise inexact flag. */

+ if (x == 0.0) {

+ if (!_IEEE)

+ return (infnan(ERANGE));

+ } else {

+ u.a = one - tiny; /* raise inexact */

+ }

return (one/x);

} else if (!finite(x)) {

if (_IEEE) /* x = NaN, -Inf */

- return (x*x);

+ return (x - x);

else

return (infnan(EDOM));

} else

return (neg_gam(x));

}

+/*

+ * We simply call tgamma() rather than bloating the math library

+ * with a float-optimized version of it. The reason is that tgammaf()

+ * is essentially useless, since the function is superexponential

+ * and floats have very limited range. -- das@freebsd.org

+ */

+float

+tgammaf(float x)

+ return tgamma(x);

* Accurate to max(ulp(1/128) absolute, 2^-66 relative) error.

static struct Double

-large_gam(x)

- double x;

+large_gam(double x)

{

double z, p;

- int i;

struct Double t, u, v;

z = one/(x*x);

@@ -191,15 +215,16 @@ large_gam(x)

u.b += lns2pi_hi; u.b += t.b;

return (u);

}

* Good to < 1 ulp. (provably .90 ulp; .87 ulp on 1,000,000 runs.)

* It also has correct monotonicity.

static double

-small_gam(x)

- double x;

+small_gam(double x)

{

- double y, ym1, t, x1;

+ double y, ym1, t;

struct Double yy, r;

y = x - one;

ym1 = y - one;

@@ -220,18 +245,19 @@ small_gam(x)

TRUNC(r.a);

r.b += (t - r.a);

}

- /* Return r*gamma(y). */

+ /* Return r*tgamma(y). */

yy = ratfun_gam(y - x0, 0);

y = r.b*(yy.a + yy.b) + r.a*yy.b;

y += yy.a*r.a;

return (y);

}

* Good on (0, 1+x0+LEFT]. Accurate to 1ulp.

static double

-smaller_gam(x)

- double x;

+smaller_gam(double x)

{

double t, d;

struct Double r, xx;

@@ -255,14 +281,14 @@ smaller_gam(x)

r.a -= d*xx.a; r.a -= d*xx.b; r.a += r.b;

return (d + r.a/x);

}

* returns (z+c)^2 * P(z)/Q(z) + a0

static struct Double

-ratfun_gam(z, c)

- double z, c;

+ratfun_gam(double z, double c)

{

- int i;

double p, q;

struct Double r, t;

@@ -287,21 +313,22 @@ ratfun_gam(z, c)

}

static double

-neg_gam(x)

- double x;

+neg_gam(double x)

{

int sgn = 1;

struct Double lg, lsine;

double y, z;

- y = floor(x + .5);

+ y = ceil(x);

if (y == x) /* Negative integer. */

- if(!_IEEE)

- return (infnan(ERANGE));

+ if (_IEEE)

+ return ((x - x) / zero);

else

- return (one/zero);

- z = fabs(x - y);

- y = .5*ceil(x);

+ return (infnan(ERANGE));

+ z = y - x;

+ if (z > 0.5)

+ z = one - z;

+ y = 0.5 * y;

if (y == ceil(y))

sgn = -1;

if (z < .25)

@@ -325,9 +352,9 @@ neg_gam(x)

}

y = one-x;

if (one-y == x)

- y = gamma(y);

+ y = tgamma(y);

else /* 1-x is inexact */

- y = -x*gamma(-x);

+ y = -x*tgamma(-x);

if (sgn < 0) y = -y;

return (M_PI / (y*z));

}

diff --git a/lib/libm/shlib_version b/lib/libm/shlib_version
index b363be4447c..c87e1c60d46 100644
--- a/lib/libm/shlib_version
+++ b/lib/libm/shlib_version

@@ -1,2 +1,2 @@

major=2

-minor=3

+minor=4

diff --git a/lib/libm/src/b_exp__D.c b/lib/libm/src/b_exp__D.c
new file mode 100644
index 00000000000..18f4452d7d5
--- /dev/null
+++ b/lib/libm/src/b_exp__D.c

@@ -0,0 +1,126 @@

+/* $OpenBSD: b_exp__D.c,v 1.1 2008/06/11 20:53:27 martynas Exp $ */

+/*

+ *

+ * 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.

+ * 3. Neither the name of the University nor the names of its contributors

+ * may be used to endorse or promote products derived from this software

+ * without specific prior written permission.

+ *

+ * 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.

+ */

+#ifndef lint

+static char sccsid[] = "@(#)exp.c 8.1 (Berkeley) 6/4/93";

+#endif /* not lint */

+/* EXP(X)

+ * RETURN THE EXPONENTIAL OF X

+ * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)

+ * CODED IN C BY K.C. NG, 1/19/85;

+ * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.

+ *

+ * Required system supported functions:

+ * scalb(x,n)

+ * copysign(x,y)

+ * finite(x)

+ *

+ * Method:

+ * 1. Argument Reduction: given the input x, find r and integer k such

+ * that

+ * x = k*ln2 + r, |r| <= 0.5*ln2 .

+ * r will be represented as r := z+c for better accuracy.

+ *

+ * 2. Compute exp(r) by

+ *

+ * exp(r) = 1 + r + r*R1/(2-R1),

+ * where

+ * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).

+ *

+ * 3. exp(x) = 2^k * exp(r) .

+ *

+ * Special cases:

+ * exp(INF) is INF, exp(NaN) is NaN;

+ * exp(-INF)= 0;

+ * for finite argument, only exp(0)=1 is exact.

+ *

+ * Accuracy:

+ * exp(x) returns the exponential of x nearly rounded. In a test run

+ * with 1,156,000 random arguments on a VAX, the maximum observed

+ * error was 0.869 ulps (units in the last place).

+ */

+#include "math.h"

+#include "math_private.h"

+const static double p1 = 0x1.555555555553ep-3;

+const static double p2 = -0x1.6c16c16bebd93p-9;

+const static double p3 = 0x1.1566aaf25de2cp-14;

+const static double p4 = -0x1.bbd41c5d26bf1p-20;

+const static double p5 = 0x1.6376972bea4d0p-25;

+const static double ln2hi = 0x1.62e42fee00000p-1;

+const static double ln2lo = 0x1.a39ef35793c76p-33;

+const static double lnhuge = 0x1.6602b15b7ecf2p9;

+const static double lntiny = -0x1.77af8ebeae354p9;

+const static double invln2 = 0x1.71547652b82fep0;

+/* returns exp(r = x + c) for |c| < |x| with no overlap. */

+double __exp__D(double x, double c)

+ double z, hi, lo;

+ int k;

+ if (x != x) /* x is NaN */

+ return(x);

+ if ( x <= lnhuge ) {

+ if ( x >= lntiny ) {

+ /* argument reduction : x --> x - k*ln2 */

+ z = invln2*x;

+ k = z + copysign(.5, x);

+ /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */

+ hi=(x-k*ln2hi); /* Exact. */

+ x= hi - (lo = k*ln2lo-c);

+ /* return 2^k*[1+x+x*c/(2+c)] */

+ z=x*x;

+ c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));

+ c = (x*c)/(2.0-c);

+ return scalb(1.+(hi-(lo - c)), k);

+ }

+ /* end of x > lntiny */

+ else

+ /* exp(-big#) underflows to zero */

+ if(finite(x)) return(scalb(1.0,-5000));

+ /* exp(-INF) is zero */

+ else return(0.0);

+ }

+ /* end of x < lnhuge */

+ else

+ /* exp(INF) is INF, exp(+big#) overflows to INF */

+ return( finite(x) ? scalb(1.0,5000) : x);

diff --git a/lib/libm/src/b_log__D.c b/lib/libm/src/b_log__D.c
new file mode 100644
index 00000000000..4c862a7b9d4
--- /dev/null
+++ b/lib/libm/src/b_log__D.c

@@ -0,0 +1,396 @@

+/* $OpenBSD: b_log__D.c,v 1.1 2008/06/11 20:53:27 martynas Exp $ */