Added atan implementation from uClibc
authorSam Lantinga <slouken@libsdl.org>
Sun, 29 Aug 2010 16:51:48 -0700
changeset 4873 67ad1c88dda0
parent 4872 231f8a1c5edd
child 4874 8288636b861d
Added atan implementation from uClibc
configure.in
include/SDL_config.h.in
include/SDL_stdinc.h
src/libm/math.h
src/libm/s_atan.c
--- a/configure.in	Sun Aug 29 16:28:04 2010 -0700
+++ b/configure.in	Sun Aug 29 16:51:48 2010 -0700
@@ -235,7 +235,7 @@
     AC_CHECK_FUNCS(malloc calloc realloc free getenv setenv putenv unsetenv qsort abs bcopy memset memcpy memmove strlen strlcpy strlcat strdup _strrev _strupr _strlwr strchr strrchr strstr itoa _ltoa _uitoa _ultoa strtol strtoul _i64toa _ui64toa strtoll strtoull atoi atof strcmp strncmp _stricmp strcasecmp _strnicmp strncasecmp sscanf snprintf vsnprintf sigaction setjmp nanosleep sysconf sysctlbyname)
 
     AC_CHECK_LIB(m, pow, [LIBS="$LIBS -lm"; EXTRA_LDFLAGS="$EXTRA_LDFLAGS -lm"])
-    AC_CHECK_FUNCS(atan2 ceil copysign cos cosf fabs floor log pow scalbn sin sinf sqrt)
+    AC_CHECK_FUNCS(atan atan2 ceil copysign cos cosf fabs floor log pow scalbn sin sinf sqrt)
 
     AC_CHECK_LIB(iconv, libiconv_open, [LIBS="$LIBS -liconv"; EXTRA_LDFLAGS="$EXTRA_LDFLAGS -liconv"])
     AC_CHECK_FUNCS(iconv)
--- a/include/SDL_config.h.in	Sun Aug 29 16:28:04 2010 -0700
+++ b/include/SDL_config.h.in	Sun Aug 29 16:51:48 2010 -0700
@@ -136,6 +136,7 @@
 #undef HAVE_SNPRINTF
 #undef HAVE_VSNPRINTF
 #undef HAVE_M_PI
+#undef HAVE_ATAN
 #undef HAVE_ATAN2
 #undef HAVE_CEIL
 #undef HAVE_COPYSIGN
--- a/include/SDL_stdinc.h	Sun Aug 29 16:28:04 2010 -0700
+++ b/include/SDL_stdinc.h	Sun Aug 29 16:51:48 2010 -0700
@@ -694,6 +694,12 @@
 #define M_PI    3.14159265358979323846264338327950288   /* pi */
 #endif
 
+#ifdef HAVE_ATAN
+#define SDL_atan        atan
+#else
+extern DECLSPEC double SDLCALL SDL_atan(double x);
+#endif
+
 #ifdef HAVE_ATAN2
 #define SDL_atan2       atan2
 #else
--- a/src/libm/math.h	Sun Aug 29 16:28:04 2010 -0700
+++ b/src/libm/math.h	Sun Aug 29 16:51:48 2010 -0700
@@ -24,6 +24,12 @@
 
 /* Math routines from uClibc: http://www.uclibc.org */
 
+#ifdef HAVE_ATAN
+#define atan            SDL_uclibc_atan
+#else
+#define atan            SDL_atan
+#endif
+
 #ifndef HAVE_ATAN2
 #define __ieee754_atan2 SDL_atan2
 #endif
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/libm/s_atan.c	Sun Aug 29 16:51:48 2010 -0700
@@ -0,0 +1,114 @@
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/* atan(x)
+ * Method
+ *   1. Reduce x to positive by atan(x) = -atan(-x).
+ *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
+ *      is further reduced to one of the following intervals and the
+ *      arctangent of t is evaluated by the corresponding formula:
+ *
+ *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
+ *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
+ *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
+ *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
+ *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double atanhi[] = {
+  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
+  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
+  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
+  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
+};
+
+static const double atanlo[] = {
+  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
+  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
+  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
+  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
+};
+
+static const double aT[] = {
+  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
+ -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
+  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
+ -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
+  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
+ -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
+  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
+ -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
+  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
+ -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
+  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
+};
+
+static const double
+one   = 1.0,
+huge   = 1.0e300;
+
+double atan(double x)
+{
+	double w,s1,s2,z;
+	int32_t ix,hx,id;
+
+	GET_HIGH_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
+	    u_int32_t low;
+	    GET_LOW_WORD(low,x);
+	    if(ix>0x7ff00000||
+		(ix==0x7ff00000&&(low!=0)))
+		return x+x;		/* NaN */
+	    if(hx>0) return  atanhi[3]+atanlo[3];
+	    else     return -atanhi[3]-atanlo[3];
+	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
+	    if (ix < 0x3e200000) {	/* |x| < 2^-29 */
+		if(huge+x>one) return x;	/* raise inexact */
+	    }
+	    id = -1;
+	} else {
+	x = fabs(x);
+	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
+	    if (ix < 0x3fe60000) {	/* 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 (ix < 0x40038000) {	/* |x| < 2.4375 */
+		id = 2; x  = (x-1.5)/(one+1.5*x);
+	    } else {			/* 2.4375 <= |x| < 2^66 */
+		id = 3; x  = -1.0/x;
+	    }
+	}}
+    /* end of argument reduction */
+	z = x*x;
+	w = z*z;
+    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
+	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
+	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
+	if (id<0) return x - x*(s1+s2);
+	else {
+	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
+	    return (hx<0)? -z:z;
+	}
+}
+libm_hidden_def(atan)