[liba] Add openbsd implemenation of acos and asin

Change-Id: Ifc455f4e758e7c9fd936439b988bf4faf8affe4b

liba/Makefile

@@ -19,6 +19,8 @@ objs += $(addprefix liba/src/, \
 
 objs += $(addprefix liba/src/external/openbsd/, \
   a_atanf.o \
+  e_acosf.o \
+  e_asinf.o \
   e_expf.o \
   e_lgammaf_r.o \
   e_log10f.o \

liba/include/math.h

@@ -21,6 +21,8 @@ int isinff(float x);
 int isnanf(float x);
 #define isnan(x) isnanf(x)
 
+float acosf(float x);
+float asinf(float x);
 float atanf(float x);
 float ceilf(float x);
 float copysignf(float x, float y);

liba/src/external/openbsd/e_acosf.c

@@ -0,0 +1,77 @@
+/* e_acosf.c -- float version of e_acos.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * 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 "math.h"
+#include "math_private.h"
+
+static const float 
+one =  1.0000000000e+00, /* 0x3F800000 */
+pi =  3.1415925026e+00, /* 0x40490fda */
+pio2_hi =  1.5707962513e+00, /* 0x3fc90fda */
+pio2_lo =  7.5497894159e-08, /* 0x33a22168 */
+pS0 =  1.6666667163e-01, /* 0x3e2aaaab */
+pS1 = -3.2556581497e-01, /* 0xbea6b090 */
+pS2 =  2.0121252537e-01, /* 0x3e4e0aa8 */
+pS3 = -4.0055535734e-02, /* 0xbd241146 */
+pS4 =  7.9153501429e-04, /* 0x3a4f7f04 */
+pS5 =  3.4793309169e-05, /* 0x3811ef08 */
+qS1 = -2.4033949375e+00, /* 0xc019d139 */
+qS2 =  2.0209457874e+00, /* 0x4001572d */
+qS3 = -6.8828397989e-01, /* 0xbf303361 */
+qS4 =  7.7038154006e-02; /* 0x3d9dc62e */
+
+float
+acosf(float x)
+{
+	float z,p,q,r,w,s,c,df;
+	int32_t hx,ix;
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix==0x3f800000) {		/* |x|==1 */
+	    if(hx>0) return 0.0;	/* acos(1) = 0  */
+	    else return pi+(float)2.0*pio2_lo;	/* acos(-1)= pi */
+	} else if(ix>0x3f800000) {	/* |x| >= 1 */
+	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
+	}
+	if(ix<0x3f000000) {	/* |x| < 0.5 */
+	    if(ix<=0x23000000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
+	    z = x*x;
+	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	    r = p/q;
+	    return pio2_hi - (x - (pio2_lo-x*r));
+	} else  if (hx<0) {		/* x < -0.5 */
+	    z = (one+x)*(float)0.5;
+	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	    s = sqrtf(z);
+	    r = p/q;
+	    w = r*s-pio2_lo;
+	    return pi - (float)2.0*(s+w);
+	} else {			/* x > 0.5 */
+	    int32_t idf;
+	    z = (one-x)*(float)0.5;
+	    s = sqrtf(z);
+	    df = s;
+	    GET_FLOAT_WORD(idf,df);
+	    SET_FLOAT_WORD(df,idf&0xfffff000);
+	    c  = (z-df*df)/(s+df);
+	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	    r = p/q;
+	    w = r*s+c;
+	    return (float)2.0*(df+w);
+	}
+}

liba/src/external/openbsd/e_asinf.c

@@ -0,0 +1,80 @@
+/* e_asinf.c -- float version of e_asin.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * 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 "math.h"
+#include "math_private.h"
+
+static const float 
+one =  1.0000000000e+00, /* 0x3F800000 */
+huge =  1.000e+30,
+pio2_hi =  1.5707962513e+00, /* 0x3fc90fda */
+pio2_lo =  7.5497894159e-08, /* 0x33a22168 */
+pio4_hi =  7.8539818525e-01, /* 0x3f490fdb */
+	/* coefficient for R(x^2) */
+pS0 =  1.6666667163e-01, /* 0x3e2aaaab */
+pS1 = -3.2556581497e-01, /* 0xbea6b090 */
+pS2 =  2.0121252537e-01, /* 0x3e4e0aa8 */
+pS3 = -4.0055535734e-02, /* 0xbd241146 */
+pS4 =  7.9153501429e-04, /* 0x3a4f7f04 */
+pS5 =  3.4793309169e-05, /* 0x3811ef08 */
+qS1 = -2.4033949375e+00, /* 0xc019d139 */
+qS2 =  2.0209457874e+00, /* 0x4001572d */
+qS3 = -6.8828397989e-01, /* 0xbf303361 */
+qS4 =  7.7038154006e-02; /* 0x3d9dc62e */
+
+float
+asinf(float x)
+{
+	float t,w,p,q,c,r,s;
+	int32_t hx,ix;
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix==0x3f800000) {
+		/* asin(1)=+-pi/2 with inexact */
+	    return x*pio2_hi+x*pio2_lo;	
+	} else if(ix> 0x3f800000) {	/* |x|>= 1 */
+	    return (x-x)/(x-x);		/* asin(|x|>1) is NaN */   
+	} else if (ix<0x3f000000) {	/* |x|<0.5 */
+	    if(ix<0x32000000) {		/* if |x| < 2**-27 */
+		if(huge+x>one) return x;/* return x with inexact if x!=0*/
+	    }
+	    t = x*x;
+	    p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
+	    q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
+	    w = p/q;
+	    return x+x*w;
+	}
+	/* 1> |x|>= 0.5 */
+	w = one-fabsf(x);
+	t = w*(float)0.5;
+	p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
+	q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
+	s = sqrtf(t);
+	if(ix>=0x3F79999A) { 	/* if |x| > 0.975 */
+	    w = p/q;
+	    t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
+	} else {
+	    int32_t iw;
+	    w  = s;
+	    GET_FLOAT_WORD(iw,w);
+	    SET_FLOAT_WORD(w,iw&0xfffff000);
+	    c  = (t-w*w)/(s+w);
+	    r  = p/q;
+	    p  = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
+	    q  = pio4_hi-(float)2.0*w;
+	    t  = pio4_hi-(p-q);
+	}    
+	if(hx>0) return t; else return -t;    
+}