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, 53 insertions, 159 deletions

diff --git a/sysdeps/ieee754/dbl-64/e_j0.c b/sysdeps/ieee754/dbl-64/e_j0.c
index 302df49d62..5ebf2056bf 100644
--- a/sysdeps/ieee754/dbl-64/e_j0.c
+++ b/sysdeps/ieee754/dbl-64/e_j0.c
@@ -13,10 +13,6 @@
    for performance improvement on pipelined processors.
 */
 
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $";
-#endif
-
 /* __ieee754_j0(x), __ieee754_y0(x)
  * Bessel function of the first and second kinds of order zero.
  * Method -- j0(x):
@@ -26,16 +22,16 @@ static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $";
  *		j0(x) = 1-z/4+ z^2*R0/S0,  where z = x*x;
  *	   (precision:  |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
  *	   for x in (2,inf)
- * 		j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
- * 	   where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
+ *		j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
+ *	   where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
  *	   as follow:
  *		cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
  *			= 1/sqrt(2) * (cos(x) + sin(x))
  *		sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
  *			= 1/sqrt(2) * (sin(x) - cos(x))
- * 	   (To avoid cancellation, use
+ *	   (To avoid cancellation, use
  *		sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
- * 	    to compute the worse one.)
+ *	    to compute the worse one.)
  *
  *	3 Special cases
  *		j0(nan)= nan
@@ -56,8 +52,8 @@ static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $";
  *	   Note: For tiny x, U/V = u0 and j0(x)~1, hence
  *		y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
  *	2. For x>=2.
- * 		y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
- * 	   where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
+ *		y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
+ *	   where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
  *	   by the method mentioned above.
  *	3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
  */
@@ -65,22 +61,14 @@ static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $";
 #include "math.h"
 #include "math_private.h"
 
-#ifdef __STDC__
 static double pzero(double), qzero(double);
-#else
-static double pzero(), qzero();
-#endif
 
-#ifdef __STDC__
 static const double
-#else
-static double
-#endif
-huge 	= 1e300,
+huge	= 1e300,
 one	= 1.0,
 invsqrtpi=  5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
 tpi      =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
- 		/* R0/S0 on [0, 2.00] */
+		/* R0/S0 on [0, 2.00] */
 R[]  =  {0.0, 0.0, 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
  -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
   1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
@@ -90,18 +78,10 @@ S[]  =  {0.0, 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
   5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
   1.16614003333790000205e-09}; /* 0x3E1408BC, 0xF4745D8F */
 
-#ifdef __STDC__
 static const double zero = 0.0;
-#else
-static double zero = 0.0;
-#endif
 
-#ifdef __STDC__
-	double __ieee754_j0(double x)
-#else
-	double __ieee754_j0(x)
-	double x;
-#endif
+double
+__ieee754_j0(double x)
 {
 	double z, s,c,ss,cc,r,u,v,r1,r2,s1,s2,z2,z4;
 	int32_t hx,ix;
@@ -117,7 +97,7 @@ static double zero = 0.0;
 		if(ix<0x7fe00000) {  /* make sure x+x not overflow */
 		    z = -__cos(x+x);
 		    if ((s*c)<zero) cc = z/ss;
-		    else 	    ss = z/cc;
+		    else	    ss = z/cc;
 		}
 	/*
 	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
@@ -132,8 +112,8 @@ static double zero = 0.0;
 	}
 	if(ix<0x3f200000) {	/* |x| < 2**-13 */
 	    if(huge+x>one) {	/* raise inexact if x != 0 */
-	        if(ix<0x3e400000) return one;	/* |x|<2**-27 */
-	        else 	      return one - 0.25*x*x;
+		if(ix<0x3e400000) return one;	/* |x|<2**-27 */
+		else	      return one - 0.25*x*x;
 	    }
 	}
 	z = x*x;
@@ -155,12 +135,9 @@ static double zero = 0.0;
 	    return((one+u)*(one-u)+z*(r/s));
 	}
 }
+strong_alias (__ieee754_j0, __j0_finite)
 
-#ifdef __STDC__
 static const double
-#else
-static double
-#endif
 U[]  = {-7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
   1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
  -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
@@ -173,52 +150,48 @@ V[]  =  {1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
   2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
   4.41110311332675467403e-10}; /* 0x3DFE5018, 0x3BD6D9EF */
 
-#ifdef __STDC__
-	double __ieee754_y0(double x)
-#else
-	double __ieee754_y0(x)
-	double x;
-#endif
+double
+__ieee754_y0(double x)
 {
 	double z, s,c,ss,cc,u,v,z2,z4,z6,u1,u2,u3,v1,v2;
 	int32_t hx,ix,lx;
 
 	EXTRACT_WORDS(hx,lx,x);
-        ix = 0x7fffffff&hx;
+	ix = 0x7fffffff&hx;
     /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf.  */
 	if(ix>=0x7ff00000) return  one/(x+x*x);
-        if((ix|lx)==0) return -HUGE_VAL+x; /* -inf and overflow exception.  */
-        if(hx<0) return zero/(zero*x);
-        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
-        /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
-         * where x0 = x-pi/4
-         *      Better formula:
-         *              cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
-         *                      =  1/sqrt(2) * (sin(x) + cos(x))
-         *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
-         *                      =  1/sqrt(2) * (sin(x) - cos(x))
-         * To avoid cancellation, use
-         *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
-         * to compute the worse one.
-         */
+	if((ix|lx)==0) return -HUGE_VAL+x; /* -inf and overflow exception.  */
+	if(hx<0) return zero/(zero*x);
+	if(ix >= 0x40000000) {  /* |x| >= 2.0 */
+	/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
+	 * where x0 = x-pi/4
+	 *      Better formula:
+	 *              cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
+	 *                      =  1/sqrt(2) * (sin(x) + cos(x))
+	 *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+	 *                      =  1/sqrt(2) * (sin(x) - cos(x))
+	 * To avoid cancellation, use
+	 *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+	 * to compute the worse one.
+	 */
 		__sincos (x, &s, &c);
-                ss = s-c;
-                cc = s+c;
+		ss = s-c;
+		cc = s+c;
 	/*
 	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
 	 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
 	 */
-                if(ix<0x7fe00000) {  /* make sure x+x not overflow */
-                    z = -__cos(x+x);
-                    if ((s*c)<zero) cc = z/ss;
-                    else            ss = z/cc;
-                }
-                if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
-                else {
-                    u = pzero(x); v = qzero(x);
-                    z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
-                }
-                return z;
+		if(ix<0x7fe00000) {  /* make sure x+x not overflow */
+		    z = -__cos(x+x);
+		    if ((s*c)<zero) cc = z/ss;
+		    else            ss = z/cc;
+		}
+		if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
+		else {
+		    u = pzero(x); v = qzero(x);
+		    z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
+		}
+		return z;
 	}
 	if(ix<=0x3e400000) {	/* x < 2**-27 */
 	    return(U[0] + tpi*__ieee754_log(x));
@@ -238,21 +211,18 @@ V[]  =  {1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
 #endif
 	return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
 }
+strong_alias (__ieee754_y0, __y0_finite)
 
 /* The asymptotic expansions of pzero is
  *	1 - 9/128 s^2 + 11025/98304 s^4 - ...,	where s = 1/x.
  * For x >= 2, We approximate pzero by
- * 	pzero(x) = 1 + (R/S)
+ *	pzero(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
  *	| pzero(x)-1-R/S | <= 2  ** ( -60.26)
  */
-#ifdef __STDC__
 static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
-#else
-static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
-#endif
   0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
  -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
@@ -260,11 +230,7 @@ static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
  -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
 };
-#ifdef __STDC__
 static const double pS8[5] = {
-#else
-static double pS8[5] = {
-#endif
   1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
   3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
   4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
@@ -272,11 +238,7 @@ static double pS8[5] = {
   4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
 };
 
-#ifdef __STDC__
 static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
-#else
-static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
-#endif
  -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
  -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
  -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
@@ -284,11 +246,7 @@ static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
  -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
 };
-#ifdef __STDC__
 static const double pS5[5] = {
-#else
-static double pS5[5] = {
-#endif
   6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
   1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
   5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
@@ -296,11 +254,7 @@ static double pS5[5] = {
   2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
 };
 
-#ifdef __STDC__
 static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
-#else
-static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
-#endif
  -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
  -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
  -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
@@ -308,11 +262,7 @@ static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
  -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
  -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
 };
-#ifdef __STDC__
 static const double pS3[5] = {
-#else
-static double pS3[5] = {
-#endif
   3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
   3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
   1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
@@ -320,11 +270,7 @@ static double pS3[5] = {
   1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
 };
 
-#ifdef __STDC__
 static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
-#else
-static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
-#endif
  -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
  -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
  -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
@@ -332,11 +278,7 @@ static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
  -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
 };
-#ifdef __STDC__
 static const double pS2[5] = {
-#else
-static double pS2[5] = {
-#endif
   2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
   1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
   2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
@@ -344,18 +286,10 @@ static double pS2[5] = {
   1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
 };
 
-#ifdef __STDC__
-	static double pzero(double x)
-#else
-	static double pzero(x)
-	double x;
-#endif
+static double
+pzero(double x)
 {
-#ifdef __STDC__
 	const double *p,*q;
-#else
-	double *p,*q;
-#endif
 	double z,r,s,z2,z4,r1,r2,r3,s1,s2,s3;
 	int32_t ix;
 	GET_HIGH_WORD(ix,x);
@@ -385,17 +319,13 @@ static double pS2[5] = {
 /* For x >= 8, the asymptotic expansions of qzero is
  *	-1/8 s + 75/1024 s^3 - ..., where s = 1/x.
  * We approximate pzero by
- * 	qzero(x) = s*(-1.25 + (R/S))
+ *	qzero(x) = s*(-1.25 + (R/S))
  * where  R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
- * 	  S = 1 + qS0*s^2 + ... + qS5*s^12
+ *	  S = 1 + qS0*s^2 + ... + qS5*s^12
  * and
  *	| qzero(x)/s +1.25-R/S | <= 2  ** ( -61.22)
  */
-#ifdef __STDC__
 static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
-#else
-static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
-#endif
   0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
   7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
   1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
@@ -403,11 +333,7 @@ static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
   8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
   3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
 };
-#ifdef __STDC__
 static const double qS8[6] = {
-#else
-static double qS8[6] = {
-#endif
   1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
   8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
   1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
@@ -416,11 +342,7 @@ static double qS8[6] = {
  -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
 };
 
-#ifdef __STDC__
 static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
-#else
-static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
-#endif
   1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
   7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
   5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
@@ -428,11 +350,7 @@ static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
   1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
   1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
 };
-#ifdef __STDC__
 static const double qS5[6] = {
-#else
-static double qS5[6] = {
-#endif
   8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
   2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
   1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
@@ -441,11 +359,7 @@ static double qS5[6] = {
  -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
 };
 
-#ifdef __STDC__
 static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
-#else
-static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
-#endif
   4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
   7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
   3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
@@ -453,11 +367,7 @@ static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
   1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
   1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
 };
-#ifdef __STDC__
 static const double qS3[6] = {
-#else
-static double qS3[6] = {
-#endif
   4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
   7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
   3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
@@ -466,11 +376,7 @@ static double qS3[6] = {
  -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
 };
 
-#ifdef __STDC__
 static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
-#else
-static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
-#endif
   1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
   7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
   1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
@@ -478,11 +384,7 @@ static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
   3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
   1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
 };
-#ifdef __STDC__
 static const double qS2[6] = {
-#else
-static double qS2[6] = {
-#endif
   3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
   2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
   8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
@@ -491,18 +393,10 @@ static double qS2[6] = {
  -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
 };
 
-#ifdef __STDC__
-	static double qzero(double x)
-#else
-	static double qzero(x)
-	double x;
-#endif
+static double
+qzero(double x)
 {
-#ifdef __STDC__
 	const double *p,*q;
-#else
-	double *p,*q;
-#endif
 	double s,r,z,z2,z4,z6,r1,r2,r3,s1,s2,s3;
 	int32_t ix;
 	GET_HIGH_WORD(ix,x);