[liba] Add hypot in math.h header

liba/Makefile

@@ -34,12 +34,11 @@ objs += $(addprefix liba/src/external/openbsd/, \
   e_acoshf.o \
   e_asinf.o \
   e_atanhf.o \
-  e_atan2.o \
   e_atan2f.o \
   e_coshf.o \
   e_expf.o \
-  e_fmod.o \
   e_fmodf.o \
+  e_hypotf.o \
   e_lgammaf_r.o \
   e_log10f.o \
   e_log2.o \
@@ -85,8 +84,11 @@ objs += $(addprefix liba/src/external/openbsd/, \
   e_acosh.o \
   e_asin.o \
   e_atanh.o \
+  e_atan2.o \
   e_cosh.o \
   e_exp.o \
+  e_fmod.o \
+  e_hypot.o \
   e_lgamma_r.o \
   e_log.o \
   e_log10.o \

liba/include/math.h

@@ -60,6 +60,7 @@ float fabsf(float x);
 float floorf(float x);
 float fmodf(float x, float y);
 float frexpf(float x, int *eptr);
+float hypotf(float x, float y);
 float ldexpf(float x, int n);
 float lgammaf(float x);
 float lgammaf_r(float x, int *signgamp);
@@ -97,6 +98,7 @@ double fabs(double x);
 double floor(double x);
 double fmod(double x, double y);
 double frexp(double x, int *eptr);
+double hypot(double x, double y);
 double lgamma(double x);
 double lgamma_r(double x, int *signgamp);
 double log(double x);

liba/src/external/openbsd/e_hypot.c

@@ -0,0 +1,120 @@
+/* @(#)e_hypot.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/* hypot(x,y)
+ *
+ * Method :                  
+ *	If (assume round-to-nearest) z=x*x+y*y 
+ *	has error less than sqrt(2)/2 ulp, than 
+ *	sqrt(z) has error less than 1 ulp (exercise).
+ *
+ *	So, compute sqrt(x*x+y*y) with some care as 
+ *	follows to get the error below 1 ulp:
+ *
+ *	Assume x>y>0;
+ *	(if possible, set rounding to round-to-nearest)
+ *	1. if x > 2y  use
+ *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
+ *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else
+ *	2. if x <= 2y use
+ *		t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
+ *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 
+ *	yy1= y with lower 32 bits chopped, y2 = y-yy1.
+ *		
+ *	NOTE: scaling may be necessary if some argument is too 
+ *	      large or too tiny
+ *
+ * Special cases:
+ *	hypot(x,y) is INF if x or y is +INF or -INF; else
+ *	hypot(x,y) is NAN if x or y is NAN.
+ *
+ * Accuracy:
+ * 	hypot(x,y) returns sqrt(x^2+y^2) with error less 
+ * 	than 1 ulps (units in the last place) 
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+double
+hypot(double x, double y)
+{
+	double a=x,b=y,t1,t2,yy1,y2,w;
+	int32_t j,k,ha,hb;
+
+	GET_HIGH_WORD(ha,x);
+	ha &= 0x7fffffff;
+	GET_HIGH_WORD(hb,y);
+	hb &= 0x7fffffff;
+	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
+	SET_HIGH_WORD(a,ha);	/* a <- |a| */
+	SET_HIGH_WORD(b,hb);	/* b <- |b| */
+	if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
+	k=0;
+	if(ha > 0x5f300000) {	/* a>2**500 */
+	   if(ha >= 0x7ff00000) {	/* Inf or NaN */
+	       u_int32_t low;
+	       w = a+b;			/* for sNaN */
+	       GET_LOW_WORD(low,a);
+	       if(((ha&0xfffff)|low)==0) w = a;
+	       GET_LOW_WORD(low,b);
+	       if(((hb^0x7ff00000)|low)==0) w = b;
+	       return w;
+	   }
+	   /* scale a and b by 2**-600 */
+	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
+	   SET_HIGH_WORD(a,ha);
+	   SET_HIGH_WORD(b,hb);
+	}
+	if(hb < 0x20b00000) {	/* b < 2**-500 */
+	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */	
+	        u_int32_t low;
+		GET_LOW_WORD(low,b);
+		if((hb|low)==0) return a;
+		t1=0;
+		SET_HIGH_WORD(t1,0x7fd00000);	/* t1=2^1022 */
+		b *= t1;
+		a *= t1;
+		k -= 1022;
+	    } else {		/* scale a and b by 2^600 */
+	        ha += 0x25800000; 	/* a *= 2^600 */
+		hb += 0x25800000;	/* b *= 2^600 */
+		k -= 600;
+		SET_HIGH_WORD(a,ha);
+		SET_HIGH_WORD(b,hb);
+	    }
+	}
+    /* medium size a and b */
+	w = a-b;
+	if (w>b) {
+	    t1 = 0;
+	    SET_HIGH_WORD(t1,ha);
+	    t2 = a-t1;
+	    w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
+	} else {
+	    a  = a+a;
+	    yy1 = 0;
+	    SET_HIGH_WORD(yy1,hb);
+	    y2 = b - yy1;
+	    t1 = 0;
+	    SET_HIGH_WORD(t1,ha+0x00100000);
+	    t2 = a - t1;
+	    w  = sqrt(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
+	}
+	if(k!=0) {
+	    u_int32_t high;
+	    t1 = 1.0;
+	    GET_HIGH_WORD(high,t1);
+	    SET_HIGH_WORD(t1,high+(k<<20));
+	    return t1*w;
+	} else return w;
+}

liba/src/external/openbsd/e_hypotf.c

@@ -0,0 +1,79 @@
+/* e_hypotf.c -- float version of e_hypot.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"
+
+float
+hypotf(float x, float y)
+{
+	float a=x,b=y,t1,t2,yy1,y2,w;
+	int32_t j,k,ha,hb;
+
+	GET_FLOAT_WORD(ha,x);
+	ha &= 0x7fffffff;
+	GET_FLOAT_WORD(hb,y);
+	hb &= 0x7fffffff;
+	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
+	SET_FLOAT_WORD(a,ha);	/* a <- |a| */
+	SET_FLOAT_WORD(b,hb);	/* b <- |b| */
+	if((ha-hb)>0xf000000) {return a+b;} /* x/y > 2**30 */
+	k=0;
+	if(ha > 0x58800000) {	/* a>2**50 */
+	   if(ha >= 0x7f800000) {	/* Inf or NaN */
+	       w = a+b;			/* for sNaN */
+	       if(ha == 0x7f800000) w = a;
+	       if(hb == 0x7f800000) w = b;
+	       return w;
+	   }
+	   /* scale a and b by 2**-60 */
+	   ha -= 0x5d800000; hb -= 0x5d800000;	k += 60;
+	   SET_FLOAT_WORD(a,ha);
+	   SET_FLOAT_WORD(b,hb);
+	}
+	if(hb < 0x26800000) {	/* b < 2**-50 */
+	    if(hb <= 0x007fffff) {	/* subnormal b or 0 */	
+	        if(hb==0) return a;
+		SET_FLOAT_WORD(t1,0x3f000000);	/* t1=2^126 */
+		b *= t1;
+		a *= t1;
+		k -= 126;
+	    } else {		/* scale a and b by 2^60 */
+	        ha += 0x5d800000; 	/* a *= 2^60 */
+		hb += 0x5d800000;	/* b *= 2^60 */
+		k -= 60;
+		SET_FLOAT_WORD(a,ha);
+		SET_FLOAT_WORD(b,hb);
+	    }
+	}
+    /* medium size a and b */
+	w = a-b;
+	if (w>b) {
+	    SET_FLOAT_WORD(t1,ha&0xfffff000);
+	    t2 = a-t1;
+	    w  = sqrtf(t1*t1-(b*(-b)-t2*(a+t1)));
+	} else {
+	    a  = a+a;
+	    SET_FLOAT_WORD(yy1,hb&0xfffff000);
+	    y2 = b - yy1;
+	    SET_FLOAT_WORD(t1,ha+0x00800000);
+	    t2 = a - t1;
+	    w  = sqrtf(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
+	}
+	if(k!=0) {
+	    SET_FLOAT_WORD(t1,0x3f800000+(k<<23));
+	    return t1*w;
+	} else return w;
+}

libaxx/include/cmath

@@ -25,6 +25,7 @@
 #undef fabsf
 #undef floorf
 #undef fmodf
+#undef hypotf
 #undef lgammaf
 #undef lgammaf_r
 #undef log1pf
@@ -57,6 +58,7 @@
 #undef expm1
 #undef fabs
 #undef floor
+#undef hypot
 #undef lgamma
 #undef lgamma_r
 #undef log1p
@@ -104,6 +106,8 @@ static inline double floor(double x) { return __builtin_floor(x); }
 static inline float floor(float x) { return __builtin_floorf(x); }
 static inline int fpclassify(double x) { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x); }
 static inline int fpclassify(float x) { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x); }
+static inline double hypot(double x, double y) { return __builtin_hypot(x, y); }
+static inline float hypotf(float x, float y) { return __builtin_hypotf(x, y); }
 static inline bool isfinite(double x) { return __builtin_isfinite(x); }
 static inline bool isfinite(float x) { return __builtin_isfinite(x); }
 static inline bool isinf(double x) { return __builtin_isinf(x); }