Use only double precision for "kernel" tanf (except for returning float).

This is a minor interface change.  The function is renamed from
__kernel_tanf() to __kernel_tandf() so that misues of it will cause
link errors and not crashes.

This version is a routine translation with no special optimizations
for accuracy or efficiency.  It gives an unimportant increase in
accuracy, from ~0.9 ulps to 0.5285 ulps.  Almost all of the error is
from the minimax polynomial (~0.03 ulps and the final rounding step
(< 0.5 ulps).  It gives strange differences in efficiency in the -5
to +10% range, with -O1 fairly consistently becoming faster and -O2
slower on AXP and A64 with gcc-3.3 and gcc-3.4.

lib/msun/src/k_tanf.c

@@ -21,35 +21,32 @@ static char rcsid[] = "$FreeBSD$";
 #include "math.h"
 #include "math_private.h"
 
-static const float
-pio4  =  7.8539812565e-01, /* 0x3f490fda */
-pio4lo=  3.7748947079e-08, /* 0x33222168 */
-/* |tan(x)/x - t(x)| < 2**-29.2 (~[-1.73e-09, 1.724e-09]). */
+static const double
+pio4 = M_PI_4,
+/* |tan(x)/x - t(x)| < 2**-29.1 (~[-1.72e-09, 1.719e-09]). */
 T[] =  {
-  0xaaaaa3.0p-25,		/* 0.33333310485 */
-  0x888b06.0p-26,		/* 0.13334283238 */
-  0xdc84c8.0p-28,		/* 0.053837567568 */
-  0xb9d8f1.0p-29,		/* 0.022686453536 */
-  0xcfe632.0p-31,		/* 0.0063445800915 */
-  0xeaf97e.0p-31,		/* 0.0071708550677 */
+  0x1555545f8b54d0.0p-54,	/* 0.333333104424423432022 */
+  0x111160cdc2c9af.0p-55,	/* 0.133342838734802765499 */
+  0x1b9097e5693cd0.0p-57,	/* 0.0538375346701457369036 */
+  0x173b2333895b6f.0p-58,	/* 0.0226865291791357691353 */
+  0x19fcb197e825ab.0p-60,	/* 0.00634450313965243938713 */
+  0x1d5f3701b44a27.0p-60,	/* 0.00717088210082520490646 */
 };
 
 #ifdef INLINE_KERNEL_TANF
 extern inline
 #endif
 float
-__kernel_tanf(float x, float y, int iy)
+__kernel_tandf(double x, int iy)
 {
-	float z,r,v,w,s;
+	double z,r,v,w,s;
 	int32_t ix,hx;
 
 	GET_FLOAT_WORD(hx,x);
 	ix = hx&0x7fffffff;
 	if(ix>=0x3f2ca140) { 			/* |x|>=0.67434 */
-	    if(hx<0) {x = -x; y = -y;}
-	    z = pio4-x;
-	    w = pio4lo-y;
-	    x = z+w; y = 0.0;
+	    if(hx<0) {x = -x;}
+	    x = pio4-x;
 	}
 	z	=  x*x;
 	w 	=  z*z;
@@ -60,13 +57,13 @@ __kernel_tanf(float x, float y, int iy)
 	r = T[1]+w*(T[3]+w*T[5]);
 	v = z*(T[2]+w*T[4]);
 	s = z*x;
-	r = y + z*(s*(r+v)+y);
+	r = z*s*(r+v);
 	r += T[0]*s;
 	w = x+r;
 	if(ix>=0x3f2ca140) {
-	    v = (float)iy;
-	    return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
+	    v = (double)iy;
+	    return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
 	}
 	if(iy==1) return w;
-	else return -1.0/((double)x+r);
+	else return -1.0/w;
 }

lib/msun/src/math_private.h

@@ -266,7 +266,7 @@ int	__kernel_rem_pio2(double*,double*,int,int,int,const int*);
 int	__ieee754_rem_pio2f(float,float*);
 float	__kernel_sinf(float,float,int);
 float	__kernel_cosf(float,float);
-float	__kernel_tanf(float,float,int);
+float	__kernel_tandf(double,int);
 int	__kernel_rem_pio2f(float*,float*,int,int,int,const int*);
 
 #endif /* !_MATH_PRIVATE_H_ */

lib/msun/src/s_tanf.c

@@ -29,12 +29,6 @@ t2pio2 = 2*M_PI_2,			/* 0x400921FB, 0x54442D18 */
 t3pio2 = 3*M_PI_2,			/* 0x4012D97C, 0x7F3321D2 */
 t4pio2 = 4*M_PI_2;			/* 0x401921FB, 0x54442D18 */
 
-static inline float
-__kernel_tandf(double x, int iy)
-{
-	return __kernel_tanf((float)x, x - (float)x, iy);
-}
-
 float
 tanf(float x)
 {
@@ -47,7 +41,7 @@ tanf(float x)
 	if(ix <= 0x3f490fda) {		/* |x| ~<= pi/4 */
 	    if(ix<0x39800000)		/* |x| < 2**-12 */
 		if(((int)x)==0) return x;	/* x with inexact if x != 0 */
-	    return __kernel_tanf(x,0.0,1);
+	    return __kernel_tandf(x,1);
 	}
 	if(ix<=0x407b53d1) {		/* |x| ~<= 5*pi/4 */
 	    if(ix<=0x4016cbe3)		/* |x| ~<= 3pi/4 */
@@ -69,6 +63,6 @@ tanf(float x)
 	else {
 	    n = __ieee754_rem_pio2f(x,y);
 	    /* integer parameter: 1 -- n even; -1 -- n odd */
-	    return __kernel_tanf(y[0],y[1],1-((n&1)<<1));
+	    return __kernel_tandf((double)y[0]+y[1],1-((n&1)<<1));
 	}
 }