Add implementations of acosl(), asinl(), atanl(), atan2l(),

and cargl().

Reviewed by:			bde
sparc64 testing resources from:	remko

10 files changed, 413 insertions, 0 deletions

diff --git a/lib/msun/src/e_acos.c b/lib/msun/src/e_acos.c
index 5b1b85a..1f6dca5 100644
--- a/lib/msun/src/e_acos.c
+++ b/lib/msun/src/e_acos.c
@@ -38,6 +38,8 @@ __FBSDID("$FreeBSD$");
  * Function needed: sqrt
  */
 
+#include <float.h>
+
 #include "math.h"
 #include "math_private.h"
 
@@ -103,3 +105,7 @@ __ieee754_acos(double x)
 	    return 2.0*(df+w);
 	}
 }
+
+#if LDBL_MANT_DIG == 53
+__weak_reference(acos, acosl);
+#endif
diff --git a/lib/msun/src/e_acosl.c b/lib/msun/src/e_acosl.c
new file mode 100644
index 0000000..4e9df52
--- /dev/null
+++ b/lib/msun/src/e_acosl.c
@@ -0,0 +1,77 @@
+
+/* @(#)e_acos.c 1.3 95/01/18 */
+/* FreeBSD: head/lib/msun/src/e_acos.c 176451 2008-02-22 02:30:36Z das */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * See comments in e_acos.c.
+ * Converted to long double by David Schultz <das@FreeBSD.ORG>.
+ */
+
+#include <float.h>
+
+#include "invtrig.h"
+#include "math.h"
+#include "math_private.h"
+
+static const long double
+one=  1.00000000000000000000e+00,
+pi =  3.14159265358979323846264338327950280e+00L;
+      
+long double
+acosl(long double x)
+{
+	union IEEEl2bits u;
+	long double z,p,q,r,w,s,c,df;
+	int16_t expsign, expt;
+	u.e = x;
+	expsign = u.xbits.expsign;
+	expt = expsign & 0x7fff;
+	if(expt >= BIAS) {	/* |x| >= 1 */
+	    if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) {
+		if (expsign>0) return 0.0;	/* acos(1) = 0  */
+		else return pi+2.0*pio2_lo;	/* acos(-1)= pi */
+	    }
+	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
+	}
+	if(expt<BIAS-1) {	/* |x| < 0.5 */
+	    if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/
+	    z = x*x;
+	    p = P(z);
+	    q = Q(z);
+	    r = p/q;
+	    return pio2_hi - (x - (pio2_lo-x*r));
+	} else  if (expsign<0) {	/* x < -0.5 */
+	    z = (one+x)*0.5;
+	    p = P(z);
+	    q = Q(z);
+	    s = sqrtl(z);
+	    r = p/q;
+	    w = r*s-pio2_lo;
+	    return pi - 2.0*(s+w);
+	} else {			/* x > 0.5 */
+	    z = (one-x)*0.5;
+	    s = sqrtl(z);
+	    u.e = s;
+	    u.bits.manl = 0;
+	    df = u.e;
+	    c  = (z-df*df)/(s+df);
+	    p = P(z);
+	    q = Q(z);
+	    r = p/q;
+	    w = r*s+c;
+	    return 2.0*(df+w);
+	}
+}
diff --git a/lib/msun/src/e_asin.c b/lib/msun/src/e_asin.c
index 149a533..4458604 100644
--- a/lib/msun/src/e_asin.c
+++ b/lib/msun/src/e_asin.c
@@ -44,6 +44,7 @@ __FBSDID("$FreeBSD$");
  *
  */
 
+#include <float.h>
 
 #include "math.h"
 #include "math_private.h"
@@ -110,3 +111,7 @@ __ieee754_asin(double x)
 	}    
 	if(hx>0) return t; else return -t;    
 }
+
+#if LDBL_MANT_DIG == 53
+__weak_reference(asin, asinl);
+#endif
diff --git a/lib/msun/src/e_asinl.c b/lib/msun/src/e_asinl.c
new file mode 100644
index 0000000..ee7f5af
--- /dev/null
+++ b/lib/msun/src/e_asinl.c
@@ -0,0 +1,77 @@
+
+/* @(#)e_asin.c 1.3 95/01/18 */
+/* FreeBSD: head/lib/msun/src/e_asin.c 176451 2008-02-22 02:30:36Z das */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * See comments in e_asin.c.
+ * Converted to long double by David Schultz <das@FreeBSD.ORG>.
+ */
+
+#include <float.h>
+
+#include "invtrig.h"
+#include "math.h"
+#include "math_private.h"
+
+static const long double
+one =  1.00000000000000000000e+00,
+huge = 1.000e+300;
+
+long double
+asinl(long double x)
+{
+	union IEEEl2bits u;
+	long double t=0.0,w,p,q,c,r,s;
+	int16_t expsign, expt;
+	u.e = x;
+	expsign = u.xbits.expsign;
+	expt = expsign & 0x7fff;
+	if(expt >= BIAS) {		/* |x|>= 1 */
+		if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0)
+		    /* asin(1)=+-pi/2 with inexact */
+		    return x*pio2_hi+x*pio2_lo;	
+	    return (x-x)/(x-x);		/* asin(|x|>1) is NaN */   
+	} else if (expt<BIAS-1) {	/* |x|<0.5 */
+	    if(expt<ASIN_LINEAR) {	/* if |x| is small, asinl(x)=x */
+		if(huge+x>one) return x;/* return x with inexact if x!=0*/
+	    } else 
+		t = x*x;
+	        p = P(t);
+	        q = Q(t);
+		w = p/q;
+		return x+x*w;
+	}
+	/* 1> |x|>= 0.5 */
+	w = one-fabsl(x);
+	t = w*0.5;
+	p = P(t);
+	q = Q(t);
+	s = sqrtl(t);
+	if(u.bits.manh>=THRESH) { 	/* if |x| is close to 1 */
+	    w = p/q;
+	    t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
+	} else {
+	    u.e = s;
+	    u.bits.manl = 0;
+	    w = u.e;
+	    c  = (t-w*w)/(s+w);
+	    r  = p/q;
+	    p  = 2.0*s*r-(pio2_lo-2.0*c);
+	    q  = pio4_hi-2.0*w;
+	    t  = pio4_hi-(p-q);
+	}    
+	if(expsign>0) return t; else return -t;    
+}
diff --git a/lib/msun/src/e_atan2.c b/lib/msun/src/e_atan2.c
index ba0b618..399822a 100644
--- a/lib/msun/src/e_atan2.c
+++ b/lib/msun/src/e_atan2.c
@@ -42,6 +42,8 @@ __FBSDID("$FreeBSD$");
  * to produce the hexadecimal values shown.
  */
 
+#include <float.h>
+
 #include "math.h"
 #include "math_private.h"
 
@@ -123,3 +125,7 @@ __ieee754_atan2(double y, double x)
 	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
 	}
 }
+
+#if LDBL_MANT_DIG == 53
+__weak_reference(atan2, atan2l);
+#endif
diff --git a/lib/msun/src/e_atan2l.c b/lib/msun/src/e_atan2l.c
new file mode 100644
index 0000000..8368bbf
--- /dev/null
+++ b/lib/msun/src/e_atan2l.c
@@ -0,0 +1,107 @@
+
+/* @(#)e_atan2.c 1.3 95/01/18 */
+/* FreeBSD: head/lib/msun/src/e_atan2.c 176451 2008-02-22 02:30:36Z das */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ *
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * See comments in e_atan2.c.
+ * Converted to long double by David Schultz <das@FreeBSD.ORG>.
+ */
+
+#include <float.h>
+
+#include "invtrig.h"
+#include "math.h"
+#include "math_private.h"
+
+static volatile long double
+tiny  = 1.0e-300;
+static const long double
+zero  = 0.0,
+pi = 3.14159265358979323846264338327950280e+00L;
+
+long double
+atan2l(long double y, long double x)
+{
+	union IEEEl2bits ux, uy;
+	long double z;
+	int32_t k,m;
+	int16_t exptx, expsignx, expty, expsigny;
+
+	uy.e = y;
+	expsigny = uy.xbits.expsign;
+	expty = expsigny & 0x7fff;
+	ux.e = x;
+	expsignx = ux.xbits.expsign;
+	exptx = expsignx & 0x7fff;
+
+	if ((exptx==BIAS+LDBL_MAX_EXP &&
+	     ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) ||	/* x is NaN */
+	    (expty==BIAS+LDBL_MAX_EXP &&
+	     ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0))	/* y is NaN */
+	    return x+y;
+	if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
+	    return atanl(y);					/* x=1.0 */
+	m = ((expsigny>>15)&1)|((expsignx>>14)&2);	/* 2*sign(x)+sign(y) */
+
+    /* when y = 0 */
+	if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
+	    switch(m) {
+		case 0: 
+		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
+		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
+		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
+	    }
+	}
+    /* when x = 0 */
+	if(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
+	    return (expsigny<0)?  -pio2_hi-tiny: pio2_hi+tiny;
+
+    /* when x is INF */
+	if(exptx==BIAS+LDBL_MAX_EXP) {
+	    if(expty==BIAS+LDBL_MAX_EXP) {
+		switch(m) {
+		    case 0: return  pio2_hi*0.5+tiny;/* atan(+INF,+INF) */
+		    case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */
+		    case 2: return  1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/
+		    case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/
+		}
+	    } else {
+		switch(m) {
+		    case 0: return  zero  ;	/* atan(+...,+INF) */
+		    case 1: return -zero  ;	/* atan(-...,+INF) */
+		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
+		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
+		}
+	    }
+	}
+    /* when y is INF */
+	if(expty==BIAS+LDBL_MAX_EXP)
+	    return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
+
+    /* compute y/x */
+	k = expty-exptx;
+	if(k > LDBL_MANT_DIG+2) z=pio2_hi+pio2_lo;	/* |y/x| huge */
+	else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; 	/* |y/x| tiny, x<0 */
+	else z=atanl(fabsl(y/x));		/* safe to do y/x */
+	switch (m) {
+	    case 0: return       z  ;	/* atan(+,+) */
+	    case 1: return      -z  ;	/* atan(-,+) */
+	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
+	    default: /* case 3 */
+	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
+	}
+}
diff --git a/lib/msun/src/math.h b/lib/msun/src/math.h
index 97d1a58..374f95f 100644
--- a/lib/msun/src/math.h
+++ b/lib/msun/src/math.h
@@ -394,12 +394,18 @@ float	significandf(float);
 #if __ISO_C_VISIBLE >= 1999
 #if 0
 long double	acoshl(long double);
+#endif
 long double	acosl(long double);
+#if 0
 long double	asinhl(long double);
+#endif
 long double	asinl(long double);
 long double	atan2l(long double, long double);
+#if 0
 long double	atanhl(long double);
+#endif
 long double	atanl(long double);
+#if 0
 long double	cbrtl(long double);
 #endif
 long double	ceill(long double);
diff --git a/lib/msun/src/s_atan.c b/lib/msun/src/s_atan.c
index 01e7bea..24daed5 100644
--- a/lib/msun/src/s_atan.c
+++ b/lib/msun/src/s_atan.c
@@ -33,6 +33,8 @@ __FBSDID("$FreeBSD$");
  * to produce the hexadecimal values shown.
  */
 
+#include <float.h>
+
 #include "math.h"
 #include "math_private.h"
 
@@ -116,3 +118,7 @@ atan(double x)
 	    return (hx<0)? -z:z;
 	}
 }
+
+#if LDBL_MANT_DIG == 53
+__weak_reference(atan, atanl);
+#endif
diff --git a/lib/msun/src/s_atanl.c b/lib/msun/src/s_atanl.c
new file mode 100644
index 0000000..ff29c3c
--- /dev/null
+++ b/lib/msun/src/s_atanl.c
@@ -0,0 +1,85 @@
+/* @(#)s_atan.c 5.1 93/09/24 */
+/* FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * See comments in s_atan.c.
+ * Converted to long double by David Schultz <das@FreeBSD.ORG>.
+ */
+
+#include <float.h>
+
+#include "invtrig.h"
+#include "math.h"
+#include "math_private.h"
+
+static const long double
+one   = 1.0,
+huge   = 1.0e300;
+
+long double
+atanl(long double x)
+{
+	union IEEEl2bits u;
+	long double w,s1,s2,z;
+	int id;
+	int16_t expsign, expt;
+	int32_t expman;
+
+	u.e = x;
+	expsign = u.xbits.expsign;
+	expt = expsign & 0x7fff;
+	if(expt >= ATAN_CONST) {	/* if |x| is large, atan(x)~=pi/2 */
+	    if(expt == BIAS + LDBL_MAX_EXP &&
+	       ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0)
+		return x+x;		/* NaN */
+	    if(expsign>0) return  atanhi[3]+atanlo[3];
+	    else     return -atanhi[3]-atanlo[3];
+	}
+	/* Extract the exponent and the first few bits of the mantissa. */
+	/* XXX There should be a more convenient way to do this. */
+	expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
+	if (expman < ((BIAS - 2) << 8) + 0xc0) {	/* |x| < 0.4375 */
+	    if (expt < ATAN_LINEAR) {	/* if |x| is small, atanl(x)~=x */
+		if(huge+x>one) return x;	/* raise inexact */
+	    }
+	    id = -1;
+	} else {
+	x = fabsl(x);
+	if (expman < (BIAS << 8) + 0x30) {		/* |x| < 1.1875 */
+	    if (expman < ((BIAS - 1) << 8) + 0x60) {	/* 7/16 <=|x|<11/16 */
+		id = 0; x = (2.0*x-one)/(2.0+x);
+	    } else {			/* 11/16<=|x|< 19/16 */
+		id = 1; x  = (x-one)/(x+one);
+	    }
+	} else {
+	    if (expman < ((BIAS + 1) << 8) + 0x38) {	/* |x| < 2.4375 */
+		id = 2; x  = (x-1.5)/(one+1.5*x);
+	    } else {			/* 2.4375 <= |x| < 2^ATAN_CONST */
+		id = 3; x  = -1.0/x;
+	    }
+	}}
+    /* end of argument reduction */
+	z = x*x;
+	w = z*z;
+    /* break sum aT[i]z**(i+1) into odd and even poly */
+	s1 = z*T_even(w);
+	s2 = w*T_odd(w);
+	if (id<0) return x - x*(s1+s2);
+	else {
+	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
+	    return (expsign<0)? -z:z;
+	}
+}
diff --git a/lib/msun/src/s_cargl.c b/lib/msun/src/s_cargl.c
new file mode 100644
index 0000000..0555083
--- /dev/null
+++ b/lib/msun/src/s_cargl.c
@@ -0,0 +1,38 @@
+/*-
+ * Copyright (c) 2005-2008 David Schultz <das@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.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <complex.h>
+#include <math.h>
+
+long double
+cargl(long double complex z)
+{
+
+	return (atan2l(cimagl(z), creall(z)));
+}