Optimize libm

libm is now somewhat integrated with gcc's -ffinite-math-only option
and lots of the wrapper functions have been optimized.

1 files changed, 65 insertions, 174 deletions

diff --git a/sysdeps/ieee754/flt-32/e_j1f.c b/sysdeps/ieee754/flt-32/e_j1f.c
index 71bb2515af..bb335a7403 100644
--- a/sysdeps/ieee754/flt-32/e_j1f.c
+++ b/sysdeps/ieee754/flt-32/e_j1f.c
@@ -13,24 +13,12 @@
  * ====================================================
  */
 
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: e_j1f.c,v 1.4 1995/05/10 20:45:31 jtc Exp $";
-#endif
-
 #include "math.h"
 #include "math_private.h"
 
-#ifdef __STDC__
 static float ponef(float), qonef(float);
-#else
-static float ponef(), qonef();
-#endif
 
-#ifdef __STDC__
 static const float
-#else
-static float
-#endif
 huge    = 1e30,
 one	= 1.0,
 invsqrtpi=  5.6418961287e-01, /* 0x3f106ebb */
@@ -46,25 +34,17 @@ s03  =  1.1771846857e-06, /* 0x359dffc2 */
 s04  =  5.0463624390e-09, /* 0x31ad6446 */
 s05  =  1.2354227016e-11; /* 0x2d59567e */
 
-#ifdef __STDC__
 static const float zero    = 0.0;
-#else
-static float zero    = 0.0;
-#endif
 
-#ifdef __STDC__
-	float __ieee754_j1f(float x)
-#else
-	float __ieee754_j1f(x)
-	float x;
-#endif
+float
+__ieee754_j1f(float x)
 {
 	float z, s,c,ss,cc,r,u,v,y;
 	int32_t hx,ix;
 
 	GET_FLOAT_WORD(hx,x);
 	ix = hx&0x7fffffff;
-	if(ix>=0x7f800000) return one/x;
+	if(__builtin_expect(ix>=0x7f800000, 0)) return one/x;
 	y = fabsf(x);
 	if(ix >= 0x40000000) {	/* |x| >= 2.0 */
 		__sincosf (y, &s, &c);
@@ -73,7 +53,7 @@ static float zero    = 0.0;
 		if(ix<0x7f000000) {  /* make sure y+y not overflow */
 		    z = __cosf(y+y);
 		    if ((s*c)>zero) cc = z/ss;
-		    else 	    ss = z/cc;
+		    else	    ss = z/cc;
 		}
 	/*
 	 * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
@@ -85,9 +65,9 @@ static float zero    = 0.0;
 		    z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(y);
 		}
 		if(hx<0) return -z;
-		else  	 return  z;
+		else	 return  z;
 	}
-	if(ix<0x32000000) {	/* |x|<2**-27 */
+	if(__builtin_expect(ix<0x32000000, 0)) {	/* |x|<2**-27 */
 	    if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */
 	}
 	z = x*x;
@@ -96,23 +76,16 @@ static float zero    = 0.0;
 	r *= x;
 	return(x*(float)0.5+r/s);
 }
+strong_alias (__ieee754_j1f, __j1f_finite)
 
-#ifdef __STDC__
 static const float U0[5] = {
-#else
-static float U0[5] = {
-#endif
  -1.9605709612e-01, /* 0xbe48c331 */
   5.0443872809e-02, /* 0x3d4e9e3c */
  -1.9125689287e-03, /* 0xbafaaf2a */
   2.3525259166e-05, /* 0x37c5581c */
  -9.1909917899e-08, /* 0xb3c56003 */
 };
-#ifdef __STDC__
 static const float V0[5] = {
-#else
-static float V0[5] = {
-#endif
   1.9916731864e-02, /* 0x3ca3286a */
   2.0255257550e-04, /* 0x3954644b */
   1.3560879779e-06, /* 0x35b602d4 */
@@ -120,73 +93,67 @@ static float V0[5] = {
   1.6655924903e-11, /* 0x2d9281cf */
 };
 
-#ifdef __STDC__
-	float __ieee754_y1f(float x)
-#else
-	float __ieee754_y1f(x)
-	float x;
-#endif
+float
+__ieee754_y1f(float x)
 {
 	float z, s,c,ss,cc,u,v;
 	int32_t hx,ix;
 
 	GET_FLOAT_WORD(hx,x);
-        ix = 0x7fffffff&hx;
+	ix = 0x7fffffff&hx;
     /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
-	if(ix>=0x7f800000) return  one/(x+x*x);
-        if(ix==0) return -HUGE_VALF+x;  /* -inf and overflow exception.  */
-        if(hx<0) return zero/(zero*x);
-        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
+	if(__builtin_expect(ix>=0x7f800000, 0)) return  one/(x+x*x);
+	if(__builtin_expect(ix==0, 0))
+		return -HUGE_VALF+x;  /* -inf and overflow exception.  */
+	if(__builtin_expect(hx<0, 0)) return zero/(zero*x);
+	if(ix >= 0x40000000) {  /* |x| >= 2.0 */
 		__sincosf (x, &s, &c);
-                ss = -s-c;
-                cc = s-c;
-                if(ix<0x7f000000) {  /* make sure x+x not overflow */
-                    z = __cosf(x+x);
-                    if ((s*c)>zero) cc = z/ss;
-                    else            ss = z/cc;
-                }
-        /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
-         * where x0 = x-3pi/4
-         *      Better formula:
-         *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
-         *                      =  1/sqrt(2) * (sin(x) - cos(x))
-         *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
-         *                      = -1/sqrt(2) * (cos(x) + sin(x))
-         * To avoid cancellation, use
-         *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
-         * to compute the worse one.
-         */
-                if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
-                else {
-                    u = ponef(x); v = qonef(x);
-                    z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
-                }
-                return z;
-        }
-        if(ix<=0x24800000) {    /* x < 2**-54 */
-            return(-tpi/x);
-        }
-        z = x*x;
-        u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
-        v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
-        return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x));
+		ss = -s-c;
+		cc = s-c;
+		if(ix<0x7f000000) {  /* make sure x+x not overflow */
+		    z = __cosf(x+x);
+		    if ((s*c)>zero) cc = z/ss;
+		    else            ss = z/cc;
+		}
+	/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
+	 * where x0 = x-3pi/4
+	 *      Better formula:
+	 *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
+	 *                      =  1/sqrt(2) * (sin(x) - cos(x))
+	 *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+	 *                      = -1/sqrt(2) * (cos(x) + sin(x))
+	 * To avoid cancellation, use
+	 *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+	 * to compute the worse one.
+	 */
+		if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x);
+		else {
+		    u = ponef(x); v = qonef(x);
+		    z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);
+		}
+		return z;
+	}
+	if(__builtin_expect(ix<=0x24800000, 0)) {    /* x < 2**-54 */
+	    return(-tpi/x);
+	}
+	z = x*x;
+	u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
+	v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
+	return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x));
 }
+strong_alias (__ieee754_y1f, __y1f_finite)
 
 /* For x >= 8, the asymptotic expansions of pone is
  *	1 + 15/128 s^2 - 4725/2^15 s^4 - ...,	where s = 1/x.
  * We approximate pone by
- * 	pone(x) = 1 + (R/S)
+ *	pone(x) = 1 + (R/S)
  * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
- * 	  S = 1 + ps0*s^2 + ... + ps4*s^10
+ *	  S = 1 + ps0*s^2 + ... + ps4*s^10
  * and
  *	| pone(x)-1-R/S | <= 2  ** ( -60.06)
  */
 
-#ifdef __STDC__
 static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
-#else
-static float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
-#endif
   0.0000000000e+00, /* 0x00000000 */
   1.1718750000e-01, /* 0x3df00000 */
   1.3239480972e+01, /* 0x4153d4ea */
@@ -194,11 +161,7 @@ static float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
   3.8747453613e+03, /* 0x45722bed */
   7.9144794922e+03, /* 0x45f753d6 */
 };
-#ifdef __STDC__
 static const float ps8[5] = {
-#else
-static float ps8[5] = {
-#endif
   1.1420736694e+02, /* 0x42e46a2c */
   3.6509309082e+03, /* 0x45642ee5 */
   3.6956207031e+04, /* 0x47105c35 */
@@ -206,11 +169,7 @@ static float ps8[5] = {
   3.0804271484e+04, /* 0x46f0a88b */
 };
 
-#ifdef __STDC__
 static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
-#else
-static float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
-#endif
   1.3199052094e-11, /* 0x2d68333f */
   1.1718749255e-01, /* 0x3defffff */
   6.8027510643e+00, /* 0x40d9b023 */
@@ -218,11 +177,7 @@ static float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
   5.1763616943e+02, /* 0x440168b7 */
   5.2871520996e+02, /* 0x44042dc6 */
 };
-#ifdef __STDC__
 static const float ps5[5] = {
-#else
-static float ps5[5] = {
-#endif
   5.9280597687e+01, /* 0x426d1f55 */
   9.9140142822e+02, /* 0x4477d9b1 */
   5.3532670898e+03, /* 0x45a74a23 */
@@ -230,11 +185,7 @@ static float ps5[5] = {
   1.5040468750e+03, /* 0x44bc0180 */
 };
 
-#ifdef __STDC__
 static const float pr3[6] = {
-#else
-static float pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
-#endif
   3.0250391081e-09, /* 0x314fe10d */
   1.1718686670e-01, /* 0x3defffab */
   3.9329774380e+00, /* 0x407bb5e7 */
@@ -242,11 +193,7 @@ static float pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
   9.1055007935e+01, /* 0x42b61c2a */
   4.8559066772e+01, /* 0x42423c7c */
 };
-#ifdef __STDC__
 static const float ps3[5] = {
-#else
-static float ps3[5] = {
-#endif
   3.4791309357e+01, /* 0x420b2a4d */
   3.3676245117e+02, /* 0x43a86198 */
   1.0468714600e+03, /* 0x4482dbe3 */
@@ -254,11 +201,7 @@ static float ps3[5] = {
   1.0378793335e+02, /* 0x42cf936c */
 };
 
-#ifdef __STDC__
 static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
-#else
-static float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
-#endif
   1.0771083225e-07, /* 0x33e74ea8 */
   1.1717621982e-01, /* 0x3deffa16 */
   2.3685150146e+00, /* 0x401795c0 */
@@ -266,11 +209,7 @@ static float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
   1.7693971634e+01, /* 0x418d8d41 */
   5.0735230446e+00, /* 0x40a25a4d */
 };
-#ifdef __STDC__
 static const float ps2[5] = {
-#else
-static float ps2[5] = {
-#endif
   2.1436485291e+01, /* 0x41ab7dec */
   1.2529022980e+02, /* 0x42fa9499 */
   2.3227647400e+02, /* 0x436846c7 */
@@ -278,48 +217,36 @@ static float ps2[5] = {
   8.3646392822e+00, /* 0x4105d590 */
 };
 
-#ifdef __STDC__
-	static float ponef(float x)
-#else
-	static float ponef(x)
-	float x;
-#endif
+static float
+ponef(float x)
 {
-#ifdef __STDC__
 	const float *p,*q;
-#else
-	float *p,*q;
-#endif
 	float z,r,s;
-        int32_t ix;
+	int32_t ix;
 	GET_FLOAT_WORD(ix,x);
 	ix &= 0x7fffffff;
-        if(ix>=0x41000000)     {p = pr8; q= ps8;}
-        else if(ix>=0x40f71c58){p = pr5; q= ps5;}
-        else if(ix>=0x4036db68){p = pr3; q= ps3;}
-        else if(ix>=0x40000000){p = pr2; q= ps2;}
-        z = one/(x*x);
-        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
-        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
-        return one+ r/s;
+	if(ix>=0x41000000)     {p = pr8; q= ps8;}
+	else if(ix>=0x40f71c58){p = pr5; q= ps5;}
+	else if(ix>=0x4036db68){p = pr3; q= ps3;}
+	else if(ix>=0x40000000){p = pr2; q= ps2;}
+	z = one/(x*x);
+	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
+	return one+ r/s;
 }
 
 
 /* For x >= 8, the asymptotic expansions of qone is
  *	3/8 s - 105/1024 s^3 - ..., where s = 1/x.
  * We approximate pone by
- * 	qone(x) = s*(0.375 + (R/S))
+ *	qone(x) = s*(0.375 + (R/S))
  * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
- * 	  S = 1 + qs1*s^2 + ... + qs6*s^12
+ *	  S = 1 + qs1*s^2 + ... + qs6*s^12
  * and
  *	| qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
  */
 
-#ifdef __STDC__
 static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
-#else
-static float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
-#endif
   0.0000000000e+00, /* 0x00000000 */
  -1.0253906250e-01, /* 0xbdd20000 */
  -1.6271753311e+01, /* 0xc1822c8d */
@@ -327,11 +254,7 @@ static float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  -1.1849806641e+04, /* 0xc639273a */
  -4.8438511719e+04, /* 0xc73d3683 */
 };
-#ifdef __STDC__
 static const float qs8[6] = {
-#else
-static float qs8[6] = {
-#endif
   1.6139537048e+02, /* 0x43216537 */
   7.8253862305e+03, /* 0x45f48b17 */
   1.3387534375e+05, /* 0x4802bcd6 */
@@ -340,11 +263,7 @@ static float qs8[6] = {
  -2.9449025000e+05, /* 0xc88fcb48 */
 };
 
-#ifdef __STDC__
 static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
-#else
-static float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
-#endif
  -2.0897993405e-11, /* 0xadb7d219 */
  -1.0253904760e-01, /* 0xbdd1fffe */
  -8.0564479828e+00, /* 0xc100e736 */
@@ -352,11 +271,7 @@ static float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  -1.3731937256e+03, /* 0xc4aba633 */
  -2.6124443359e+03, /* 0xc523471c */
 };
-#ifdef __STDC__
 static const float qs5[6] = {
-#else
-static float qs5[6] = {
-#endif
   8.1276550293e+01, /* 0x42a28d98 */
   1.9917987061e+03, /* 0x44f8f98f */
   1.7468484375e+04, /* 0x468878f8 */
@@ -365,11 +280,7 @@ static float qs5[6] = {
  -4.7191835938e+03, /* 0xc5937978 */
 };
 
-#ifdef __STDC__
 static const float qr3[6] = {
-#else
-static float qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
-#endif
  -5.0783124372e-09, /* 0xb1ae7d4f */
  -1.0253783315e-01, /* 0xbdd1ff5b */
  -4.6101160049e+00, /* 0xc0938612 */
@@ -377,11 +288,7 @@ static float qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
  -2.2824453735e+02, /* 0xc3643e9a */
  -2.1921012878e+02, /* 0xc35b35cb */
 };
-#ifdef __STDC__
 static const float qs3[6] = {
-#else
-static float qs3[6] = {
-#endif
   4.7665153503e+01, /* 0x423ea91e */
   6.7386511230e+02, /* 0x4428775e */
   3.3801528320e+03, /* 0x45534272 */
@@ -390,11 +297,7 @@ static float qs3[6] = {
  -1.3520118713e+02, /* 0xc3073381 */
 };
 
-#ifdef __STDC__
 static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
-#else
-static float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
-#endif
  -1.7838172539e-07, /* 0xb43f8932 */
  -1.0251704603e-01, /* 0xbdd1f475 */
  -2.7522056103e+00, /* 0xc0302423 */
@@ -402,11 +305,7 @@ static float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  -4.2325313568e+01, /* 0xc2294d1f */
  -2.1371921539e+01, /* 0xc1aaf9b2 */
 };
-#ifdef __STDC__
 static const float qs2[6] = {
-#else
-static float qs2[6] = {
-#endif
   2.9533363342e+01, /* 0x41ec4454 */
   2.5298155212e+02, /* 0x437cfb47 */
   7.5750280762e+02, /* 0x443d602e */
@@ -415,18 +314,10 @@ static float qs2[6] = {
  -4.9594988823e+00, /* 0xc09eb437 */
 };
 
-#ifdef __STDC__
-	static float qonef(float x)
-#else
-	static float qonef(x)
-	float x;
-#endif
+static float
+qonef(float x)
 {
-#ifdef __STDC__
 	const float *p,*q;
-#else
-	float *p,*q;
-#endif
 	float  s,r,z;
 	int32_t ix;
 	GET_FLOAT_WORD(ix,x);