Remove [jy][01n]f(). X/Open only standardizes the double versions.

include/openlibm_math.h

@@ -384,14 +384,6 @@ float	fminf(float, float) __pure2;
  * float versions of BSD math library entry points
  */
 #if __BSD_VISIBLE
-float	dremf(float, float);
-float	j0f(float);
-float	j1f(float);
-float	jnf(int, float);
-float	y0f(float);
-float	y1f(float);
-float	ynf(int, float);
-
 /*
  * Float versions of reentrant version of lgamma; passes signgam back by
  * reference as the second argument; user must allocate space for signgam.

src/Make.files

@@ -1,9 +1,8 @@
 $(CUR_SRCS) = common.c \
 	e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \
 	e_atan2.c e_atan2f.c e_atanh.c e_atanhf.c e_cosh.c e_coshf.c e_exp.c \
-	e_expf.c e_fmod.c e_fmodf.c \
-	e_hypot.c e_hypotf.c e_j0.c e_j0f.c e_j1.c e_j1f.c \
-	e_jn.c e_jnf.c e_lgamma.c e_lgamma_r.c e_lgammaf.c e_lgammaf_r.c \
+	e_expf.c e_fmod.c e_fmodf.c e_hypot.c e_hypotf.c e_j0.c e_j1.c \
+	e_jn.c e_lgamma.c e_lgamma_r.c e_lgammaf.c e_lgammaf_r.c \
 	e_lgammal.c e_log.c e_log10.c e_log10f.c e_log2.c e_log2f.c e_logf.c \
 	e_pow.c e_powf.c e_remainder.c e_remainderf.c \
 	e_rem_pio2.c e_rem_pio2f.c \

src/e_j0f.c

@@ -1,344 +0,0 @@
-/* e_j0f.c -- float version of e_j0.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
- */
-
-/*
- * ====================================================
- * 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 <assert.h>
-
-#include "cdefs-compat.h"
-//__FBSDID("$FreeBSD: src/lib/msun/src/e_j0f.c,v 1.8 2008/02/22 02:30:35 das Exp $");
-
-#include <openlibm_math.h>
-
-#include "math_private.h"
-
-static float pzerof(float), qzerof(float);
-
-static const float
-huge 	= 1e30,
-one	= 1.0,
-invsqrtpi=  5.6418961287e-01, /* 0x3f106ebb */
-tpi      =  6.3661974669e-01, /* 0x3f22f983 */
- 		/* R0/S0 on [0, 2.00] */
-R02  =  1.5625000000e-02, /* 0x3c800000 */
-R03  = -1.8997929874e-04, /* 0xb947352e */
-R04  =  1.8295404516e-06, /* 0x35f58e88 */
-R05  = -4.6183270541e-09, /* 0xb19eaf3c */
-S01  =  1.5619102865e-02, /* 0x3c7fe744 */
-S02  =  1.1692678527e-04, /* 0x38f53697 */
-S03  =  5.1354652442e-07, /* 0x3509daa6 */
-S04  =  1.1661400734e-09; /* 0x30a045e8 */
-
-static const float zero = 0.0;
-
-DLLEXPORT float
-__ieee754_j0f(float x)
-{
-	float z, s,c,ss,cc,r,u,v;
-	int32_t hx,ix;
-
-	GET_FLOAT_WORD(hx,x);
-	ix = hx&0x7fffffff;
-	if(ix>=0x7f800000) return one/(x*x);
-	x = fabsf(x);
-	if(ix >= 0x40000000) {	/* |x| >= 2.0 */
-		s = sinf(x);
-		c = cosf(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;
-		}
-	/*
-	 * 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>0x80000000) z = (invsqrtpi*cc)/sqrtf(x);
-		else {
-		    u = pzerof(x); v = qzerof(x);
-		    z = invsqrtpi*(u*cc-v*ss)/sqrtf(x);
-		}
-		return z;
-	}
-	if(ix<0x39000000) {	/* |x| < 2**-13 */
-	    if(huge+x>one) {	/* raise inexact if x != 0 */
-	        if(ix<0x32000000) return one;	/* |x|<2**-27 */
-	        else 	      return one - (float)0.25*x*x;
-	    }
-	}
-	z = x*x;
-	r =  z*(R02+z*(R03+z*(R04+z*R05)));
-	s =  one+z*(S01+z*(S02+z*(S03+z*S04)));
-	if(ix < 0x3F800000) {	/* |x| < 1.00 */
-	    return one + z*((float)-0.25+(r/s));
-	} else {
-	    u = (float)0.5*x;
-	    return((one+u)*(one-u)+z*(r/s));
-	}
-}
-
-static const float
-u00  = -7.3804296553e-02, /* 0xbd9726b5 */
-u01  =  1.7666645348e-01, /* 0x3e34e80d */
-u02  = -1.3818567619e-02, /* 0xbc626746 */
-u03  =  3.4745343146e-04, /* 0x39b62a69 */
-u04  = -3.8140706238e-06, /* 0xb67ff53c */
-u05  =  1.9559013964e-08, /* 0x32a802ba */
-u06  = -3.9820518410e-11, /* 0xae2f21eb */
-v01  =  1.2730483897e-02, /* 0x3c509385 */
-v02  =  7.6006865129e-05, /* 0x389f65e0 */
-v03  =  2.5915085189e-07, /* 0x348b216c */
-v04  =  4.4111031494e-10; /* 0x2ff280c2 */
-
-DLLEXPORT float
-__ieee754_y0f(float x)
-{
-	float z, s,c,ss,cc,u,v;
-	int32_t hx,ix;
-
-	GET_FLOAT_WORD(hx,x);
-        ix = 0x7fffffff&hx;
-    /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0  */
-	if(ix>=0x7f800000) return  one/(x+x*x);
-        if(ix==0) return -one/zero;
-        if(hx<0) return zero/zero;
-        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.
-         */
-                s = sinf(x);
-                c = cosf(x);
-                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<0x7f000000) {  /* make sure x+x not overflow */
-                    z = -cosf(x+x);
-                    if ((s*c)<zero) cc = z/ss;
-                    else            ss = z/cc;
-                }
-                if(ix>0x80000000) z = (invsqrtpi*ss)/sqrtf(x);
-                else {
-                    u = pzerof(x); v = qzerof(x);
-                    z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
-                }
-                return z;
-	}
-	if(ix<=0x32000000) {	/* x < 2**-27 */
-	    return(u00 + tpi*__ieee754_logf(x));
-	}
-	z = x*x;
-	u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
-	v = one+z*(v01+z*(v02+z*(v03+z*v04)));
-	return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));
-}
-
-/* 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)
- * where  R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
- * 	  S = 1 + pS0*s^2 + ... + pS4*s^10
- * and
- *	| pzero(x)-1-R/S | <= 2  ** ( -60.26)
- */
-static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
-  0.0000000000e+00, /* 0x00000000 */
- -7.0312500000e-02, /* 0xbd900000 */
- -8.0816707611e+00, /* 0xc1014e86 */
- -2.5706311035e+02, /* 0xc3808814 */
- -2.4852163086e+03, /* 0xc51b5376 */
- -5.2530439453e+03, /* 0xc5a4285a */
-};
-static const float pS8[5] = {
-  1.1653436279e+02, /* 0x42e91198 */
-  3.8337448730e+03, /* 0x456f9beb */
-  4.0597855469e+04, /* 0x471e95db */
-  1.1675296875e+05, /* 0x47e4087c */
-  4.7627726562e+04, /* 0x473a0bba */
-};
-static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
- -1.1412546255e-11, /* 0xad48c58a */
- -7.0312492549e-02, /* 0xbd8fffff */
- -4.1596107483e+00, /* 0xc0851b88 */
- -6.7674766541e+01, /* 0xc287597b */
- -3.3123129272e+02, /* 0xc3a59d9b */
- -3.4643338013e+02, /* 0xc3ad3779 */
-};
-static const float pS5[5] = {
-  6.0753936768e+01, /* 0x42730408 */
-  1.0512523193e+03, /* 0x44836813 */
-  5.9789707031e+03, /* 0x45bad7c4 */
-  9.6254453125e+03, /* 0x461665c8 */
-  2.4060581055e+03, /* 0x451660ee */
-};
-
-static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
- -2.5470459075e-09, /* 0xb12f081b */
- -7.0311963558e-02, /* 0xbd8fffb8 */
- -2.4090321064e+00, /* 0xc01a2d95 */
- -2.1965976715e+01, /* 0xc1afba52 */
- -5.8079170227e+01, /* 0xc2685112 */
- -3.1447946548e+01, /* 0xc1fb9565 */
-};
-static const float pS3[5] = {
-  3.5856033325e+01, /* 0x420f6c94 */
-  3.6151397705e+02, /* 0x43b4c1ca */
-  1.1936077881e+03, /* 0x44953373 */
-  1.1279968262e+03, /* 0x448cffe6 */
-  1.7358093262e+02, /* 0x432d94b8 */
-};
-
-static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
- -8.8753431271e-08, /* 0xb3be98b7 */
- -7.0303097367e-02, /* 0xbd8ffb12 */
- -1.4507384300e+00, /* 0xbfb9b1cc */
- -7.6356959343e+00, /* 0xc0f4579f */
- -1.1193166733e+01, /* 0xc1331736 */
- -3.2336456776e+00, /* 0xc04ef40d */
-};
-static const float pS2[5] = {
-  2.2220300674e+01, /* 0x41b1c32d */
-  1.3620678711e+02, /* 0x430834f0 */
-  2.7047027588e+02, /* 0x43873c32 */
-  1.5387539673e+02, /* 0x4319e01a */
-  1.4657617569e+01, /* 0x416a859a */
-};
-
-	/* Note: This function is only called for ix>=0x40000000 (see above) */
-	static float pzerof(float x)
-{
-	const float *p,*q;
-	float z,r,s;
-	int32_t ix;
-	GET_FLOAT_WORD(ix,x);
-	ix &= 0x7fffffff;
-        assert(ix>=0x40000000 && ix<=0x48000000);
-	if(ix>=0x41000000)     {p = pR8; q= pS8;}
-	else if(ix>=0x40f71c58){p = pR5; q= pS5;}
-	else if(ix>=0x4036db68){p = pR3; q= pS3;}
-	else                   {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 qzero is
- *	-1/8 s + 75/1024 s^3 - ..., where s = 1/x.
- * We approximate pzero by
- * 	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
- * and
- *	| qzero(x)/s +1.25-R/S | <= 2  ** ( -61.22)
- */
-static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
-  0.0000000000e+00, /* 0x00000000 */
-  7.3242187500e-02, /* 0x3d960000 */
-  1.1768206596e+01, /* 0x413c4a93 */
-  5.5767340088e+02, /* 0x440b6b19 */
-  8.8591972656e+03, /* 0x460a6cca */
-  3.7014625000e+04, /* 0x471096a0 */
-};
-static const float qS8[6] = {
-  1.6377603149e+02, /* 0x4323c6aa */
-  8.0983447266e+03, /* 0x45fd12c2 */
-  1.4253829688e+05, /* 0x480b3293 */
-  8.0330925000e+05, /* 0x49441ed4 */
-  8.4050156250e+05, /* 0x494d3359 */
- -3.4389928125e+05, /* 0xc8a7eb69 */
-};
-
-static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
-  1.8408595828e-11, /* 0x2da1ec79 */
-  7.3242180049e-02, /* 0x3d95ffff */
-  5.8356351852e+00, /* 0x40babd86 */
-  1.3511157227e+02, /* 0x43071c90 */
-  1.0272437744e+03, /* 0x448067cd */
-  1.9899779053e+03, /* 0x44f8bf4b */
-};
-static const float qS5[6] = {
-  8.2776611328e+01, /* 0x42a58da0 */
-  2.0778142090e+03, /* 0x4501dd07 */
-  1.8847289062e+04, /* 0x46933e94 */
-  5.6751113281e+04, /* 0x475daf1d */
-  3.5976753906e+04, /* 0x470c88c1 */
- -5.3543427734e+03, /* 0xc5a752be */
-};
-
-static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
-  4.3774099900e-09, /* 0x3196681b */
-  7.3241114616e-02, /* 0x3d95ff70 */
-  3.3442313671e+00, /* 0x405607e3 */
-  4.2621845245e+01, /* 0x422a7cc5 */
-  1.7080809021e+02, /* 0x432acedf */
-  1.6673394775e+02, /* 0x4326bbe4 */
-};
-static const float qS3[6] = {
-  4.8758872986e+01, /* 0x42430916 */
-  7.0968920898e+02, /* 0x44316c1c */
-  3.7041481934e+03, /* 0x4567825f */
-  6.4604252930e+03, /* 0x45c9e367 */
-  2.5163337402e+03, /* 0x451d4557 */
- -1.4924745178e+02, /* 0xc3153f59 */
-};
-
-static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
-  1.5044444979e-07, /* 0x342189db */
-  7.3223426938e-02, /* 0x3d95f62a */
-  1.9981917143e+00, /* 0x3fffc4bf */
-  1.4495602608e+01, /* 0x4167edfd */
-  3.1666231155e+01, /* 0x41fd5471 */
-  1.6252708435e+01, /* 0x4182058c */
-};
-static const float qS2[6] = {
-  3.0365585327e+01, /* 0x41f2ecb8 */
-  2.6934811401e+02, /* 0x4386ac8f */
-  8.4478375244e+02, /* 0x44533229 */
-  8.8293585205e+02, /* 0x445cbbe5 */
-  2.1266638184e+02, /* 0x4354aa98 */
- -5.3109550476e+00, /* 0xc0a9f358 */
-};
-
-	/* Note: This function is only called for ix>=0x40000000 (see above) */
-	static float qzerof(float x)
-{
-	const float *p,*q;
-	float s,r,z;
-	int32_t ix;
-	GET_FLOAT_WORD(ix,x);
-	ix &= 0x7fffffff;
-        assert(ix>=0x40000000 && ix<=0x48000000);
-	if(ix>=0x41000000)     {p = qR8; q= qS8;}
-	else if(ix>=0x40f71c58){p = qR5; q= qS5;}
-	else if(ix>=0x4036db68){p = qR3; q= qS3;}
-	else                   {p = qR2; q= qS2;}
-	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]+z*q[5])))));
-	return (-(float).125 + r/s)/x;
-}

src/e_j1f.c

@@ -1,340 +0,0 @@
-/* e_j1f.c -- float version of e_j1.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
- */
-
-/*
- * ====================================================
- * 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 <assert.h>
-
-#include "cdefs-compat.h"
-//__FBSDID("$FreeBSD: src/lib/msun/src/e_j1f.c,v 1.8 2008/02/22 02:30:35 das Exp $");
-
-#include <openlibm_math.h>
-
-#include "math_private.h"
-
-static float ponef(float), qonef(float);
-
-static const float
-huge    = 1e30,
-one	= 1.0,
-invsqrtpi=  5.6418961287e-01, /* 0x3f106ebb */
-tpi      =  6.3661974669e-01, /* 0x3f22f983 */
-	/* R0/S0 on [0,2] */
-r00  = -6.2500000000e-02, /* 0xbd800000 */
-r01  =  1.4070566976e-03, /* 0x3ab86cfd */
-r02  = -1.5995563444e-05, /* 0xb7862e36 */
-r03  =  4.9672799207e-08, /* 0x335557d2 */
-s01  =  1.9153760746e-02, /* 0x3c9ce859 */
-s02  =  1.8594678841e-04, /* 0x3942fab6 */
-s03  =  1.1771846857e-06, /* 0x359dffc2 */
-s04  =  5.0463624390e-09, /* 0x31ad6446 */
-s05  =  1.2354227016e-11; /* 0x2d59567e */
-
-static const float zero    = 0.0;
-
-DLLEXPORT 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;
-	y = fabsf(x);
-	if(ix >= 0x40000000) {	/* |x| >= 2.0 */
-		s = sinf(y);
-		c = cosf(y);
-		ss = -s-c;
-		cc = s-c;
-		if(ix<0x7f000000) {  /* make sure y+y not overflow */
-		    z = cosf(y+y);
-		    if ((s*c)>zero) cc = z/ss;
-		    else 	    ss = z/cc;
-		}
-	/*
-	 * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
-	 * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
-	 */
-		if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(y);
-		else {
-		    u = ponef(y); v = qonef(y);
-		    z = invsqrtpi*(u*cc-v*ss)/sqrtf(y);
-		}
-		if(hx<0) return -z;
-		else  	 return  z;
-	}
-	if(ix<0x32000000) {	/* |x|<2**-27 */
-	    if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */
-	}
-	z = x*x;
-	r =  z*(r00+z*(r01+z*(r02+z*r03)));
-	s =  one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
-	r *= x;
-	return(x*(float)0.5+r/s);
-}
-
-static const float U0[5] = {
- -1.9605709612e-01, /* 0xbe48c331 */
-  5.0443872809e-02, /* 0x3d4e9e3c */
- -1.9125689287e-03, /* 0xbafaaf2a */
-  2.3525259166e-05, /* 0x37c5581c */
- -9.1909917899e-08, /* 0xb3c56003 */
-};
-static const float V0[5] = {
-  1.9916731864e-02, /* 0x3ca3286a */
-  2.0255257550e-04, /* 0x3954644b */
-  1.3560879779e-06, /* 0x35b602d4 */
-  6.2274145840e-09, /* 0x31d5f8eb */
-  1.6655924903e-11, /* 0x2d9281cf */
-};
-
-DLLEXPORT 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;
-    /* 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 -one/zero;
-        if(hx<0) return zero/zero;
-        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
-                s = sinf(x);
-                c = cosf(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)/sqrtf(x);
-                else {
-                    u = ponef(x); v = qonef(x);
-                    z = invsqrtpi*(u*ss+v*cc)/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));
-}
-
-/* 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)
- * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
- * 	  S = 1 + ps0*s^2 + ... + ps4*s^10
- * and
- *	| pone(x)-1-R/S | <= 2  ** ( -60.06)
- */
-
-static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
-  0.0000000000e+00, /* 0x00000000 */
-  1.1718750000e-01, /* 0x3df00000 */
-  1.3239480972e+01, /* 0x4153d4ea */
-  4.1205184937e+02, /* 0x43ce06a3 */
-  3.8747453613e+03, /* 0x45722bed */
-  7.9144794922e+03, /* 0x45f753d6 */
-};
-static const float ps8[5] = {
-  1.1420736694e+02, /* 0x42e46a2c */
-  3.6509309082e+03, /* 0x45642ee5 */
-  3.6956207031e+04, /* 0x47105c35 */
-  9.7602796875e+04, /* 0x47bea166 */
-  3.0804271484e+04, /* 0x46f0a88b */
-};
-
-static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
-  1.3199052094e-11, /* 0x2d68333f */
-  1.1718749255e-01, /* 0x3defffff */
-  6.8027510643e+00, /* 0x40d9b023 */
-  1.0830818176e+02, /* 0x42d89dca */
-  5.1763616943e+02, /* 0x440168b7 */
-  5.2871520996e+02, /* 0x44042dc6 */
-};
-static const float ps5[5] = {
-  5.9280597687e+01, /* 0x426d1f55 */
-  9.9140142822e+02, /* 0x4477d9b1 */
-  5.3532670898e+03, /* 0x45a74a23 */
-  7.8446904297e+03, /* 0x45f52586 */
-  1.5040468750e+03, /* 0x44bc0180 */
-};
-
-static const float pr3[6] = {
-  3.0250391081e-09, /* 0x314fe10d */
-  1.1718686670e-01, /* 0x3defffab */
-  3.9329774380e+00, /* 0x407bb5e7 */
-  3.5119403839e+01, /* 0x420c7a45 */
-  9.1055007935e+01, /* 0x42b61c2a */
-  4.8559066772e+01, /* 0x42423c7c */
-};
-static const float ps3[5] = {
-  3.4791309357e+01, /* 0x420b2a4d */
-  3.3676245117e+02, /* 0x43a86198 */
-  1.0468714600e+03, /* 0x4482dbe3 */
-  8.9081134033e+02, /* 0x445eb3ed */
-  1.0378793335e+02, /* 0x42cf936c */
-};
-
-static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
-  1.0771083225e-07, /* 0x33e74ea8 */
-  1.1717621982e-01, /* 0x3deffa16 */
-  2.3685150146e+00, /* 0x401795c0 */
-  1.2242610931e+01, /* 0x4143e1bc */
-  1.7693971634e+01, /* 0x418d8d41 */
-  5.0735230446e+00, /* 0x40a25a4d */
-};
-static const float ps2[5] = {
-  2.1436485291e+01, /* 0x41ab7dec */
-  1.2529022980e+02, /* 0x42fa9499 */
-  2.3227647400e+02, /* 0x436846c7 */
-  1.1767937469e+02, /* 0x42eb5bd7 */
-  8.3646392822e+00, /* 0x4105d590 */
-};
-
-	/* Note: This function is only called for ix>=0x40000000 (see above) */
-	static float ponef(float x)
-{
-	const float *p,*q;
-	float z,r,s;
-        int32_t ix;
-	GET_FLOAT_WORD(ix,x);
-	ix &= 0x7fffffff;
-        assert(ix>=0x40000000 && ix<=0x48000000);
-        if(ix>=0x41000000)     {p = pr8; q= ps8;}
-        else if(ix>=0x40f71c58){p = pr5; q= ps5;}
-        else if(ix>=0x4036db68){p = pr3; q= ps3;}
-        else                   {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))
- * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
- * 	  S = 1 + qs1*s^2 + ... + qs6*s^12
- * and
- *	| qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
- */
-
-static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
-  0.0000000000e+00, /* 0x00000000 */
- -1.0253906250e-01, /* 0xbdd20000 */
- -1.6271753311e+01, /* 0xc1822c8d */
- -7.5960174561e+02, /* 0xc43de683 */
- -1.1849806641e+04, /* 0xc639273a */
- -4.8438511719e+04, /* 0xc73d3683 */
-};
-static const float qs8[6] = {
-  1.6139537048e+02, /* 0x43216537 */
-  7.8253862305e+03, /* 0x45f48b17 */
-  1.3387534375e+05, /* 0x4802bcd6 */
-  7.1965775000e+05, /* 0x492fb29c */
-  6.6660125000e+05, /* 0x4922be94 */
- -2.9449025000e+05, /* 0xc88fcb48 */
-};
-
-static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
- -2.0897993405e-11, /* 0xadb7d219 */
- -1.0253904760e-01, /* 0xbdd1fffe */
- -8.0564479828e+00, /* 0xc100e736 */
- -1.8366960144e+02, /* 0xc337ab6b */
- -1.3731937256e+03, /* 0xc4aba633 */
- -2.6124443359e+03, /* 0xc523471c */
-};
-static const float qs5[6] = {
-  8.1276550293e+01, /* 0x42a28d98 */
-  1.9917987061e+03, /* 0x44f8f98f */
-  1.7468484375e+04, /* 0x468878f8 */
-  4.9851425781e+04, /* 0x4742bb6d */
-  2.7948074219e+04, /* 0x46da5826 */
- -4.7191835938e+03, /* 0xc5937978 */
-};
-
-static const float qr3[6] = {
- -5.0783124372e-09, /* 0xb1ae7d4f */
- -1.0253783315e-01, /* 0xbdd1ff5b */
- -4.6101160049e+00, /* 0xc0938612 */
- -5.7847221375e+01, /* 0xc267638e */
- -2.2824453735e+02, /* 0xc3643e9a */
- -2.1921012878e+02, /* 0xc35b35cb */
-};
-static const float qs3[6] = {
-  4.7665153503e+01, /* 0x423ea91e */
-  6.7386511230e+02, /* 0x4428775e */
-  3.3801528320e+03, /* 0x45534272 */
-  5.5477290039e+03, /* 0x45ad5dd5 */
-  1.9031191406e+03, /* 0x44ede3d0 */
- -1.3520118713e+02, /* 0xc3073381 */
-};
-
-static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
- -1.7838172539e-07, /* 0xb43f8932 */
- -1.0251704603e-01, /* 0xbdd1f475 */
- -2.7522056103e+00, /* 0xc0302423 */
- -1.9663616180e+01, /* 0xc19d4f16 */
- -4.2325313568e+01, /* 0xc2294d1f */
- -2.1371921539e+01, /* 0xc1aaf9b2 */
-};
-static const float qs2[6] = {
-  2.9533363342e+01, /* 0x41ec4454 */
-  2.5298155212e+02, /* 0x437cfb47 */
-  7.5750280762e+02, /* 0x443d602e */
-  7.3939318848e+02, /* 0x4438d92a */
-  1.5594900513e+02, /* 0x431bf2f2 */
- -4.9594988823e+00, /* 0xc09eb437 */
-};
-
-	/* Note: This function is only called for ix>=0x40000000 (see above) */
-	static float qonef(float x)
-{
-	const float *p,*q;
-	float  s,r,z;
-	int32_t ix;
-	GET_FLOAT_WORD(ix,x);
-	ix &= 0x7fffffff;
-        assert(ix>=0x40000000 && ix<=0x48000000);
-	if(ix>=0x40200000)     {p = qr8; q= qs8;}
-	else if(ix>=0x40f71c58){p = qr5; q= qs5;}
-	else if(ix>=0x4036db68){p = qr3; q= qs3;}
-	else                   {p = qr2; q= qs2;}
-	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]+z*q[5])))));
-	return ((float).375 + r/s)/x;
-}

src/e_jnf.c

@@ -1,200 +0,0 @@
-/* e_jnf.c -- float version of e_jn.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
- */
-
-/*
- * ====================================================
- * 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 "cdefs-compat.h"
-//__FBSDID("$FreeBSD: src/lib/msun/src/e_jnf.c,v 1.11 2010/11/13 10:54:10 uqs Exp $");
-
-#include <openlibm_math.h>
-
-#include "math_private.h"
-
-static const float
-two   =  2.0000000000e+00, /* 0x40000000 */
-one   =  1.0000000000e+00; /* 0x3F800000 */
-
-static const float zero  =  0.0000000000e+00;
-
-DLLEXPORT float
-__ieee754_jnf(int n, float x)
-{
-	int32_t i,hx,ix, sgn;
-	float a, b, temp, di;
-	float z, w;
-
-    /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
-     * Thus, J(-n,x) = J(n,-x)
-     */
-	GET_FLOAT_WORD(hx,x);
-	ix = 0x7fffffff&hx;
-    /* if J(n,NaN) is NaN */
-	if(ix>0x7f800000) return x+x;
-	if(n<0){
-		n = -n;
-		x = -x;
-		hx ^= 0x80000000;
-	}
-	if(n==0) return(__ieee754_j0f(x));
-	if(n==1) return(__ieee754_j1f(x));
-	sgn = (n&1)&(hx>>31);	/* even n -- 0, odd n -- sign(x) */
-	x = fabsf(x);
-	if(ix==0||ix>=0x7f800000) 	/* if x is 0 or inf */
-	    b = zero;
-	else if((float)n<=x) {
-		/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
-	    a = __ieee754_j0f(x);
-	    b = __ieee754_j1f(x);
-	    for(i=1;i<n;i++){
-		temp = b;
-		b = b*((float)(i+i)/x) - a; /* avoid underflow */
-		a = temp;
-	    }
-	} else {
-	    if(ix<0x30800000) {	/* x < 2**-29 */
-    /* x is tiny, return the first Taylor expansion of J(n,x)
-     * J(n,x) = 1/n!*(x/2)^n  - ...
-     */
-		if(n>33)	/* underflow */
-		    b = zero;
-		else {
-		    temp = x*(float)0.5; b = temp;
-		    for (a=one,i=2;i<=n;i++) {
-			a *= (float)i;		/* a = n! */
-			b *= temp;		/* b = (x/2)^n */
-		    }
-		    b = b/a;
-		}
-	    } else {
-		/* use backward recurrence */
-		/* 			x      x^2      x^2
-		 *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
-		 *			2n  - 2(n+1) - 2(n+2)
-		 *
-		 * 			1      1        1
-		 *  (for large x)   =  ----  ------   ------   .....
-		 *			2n   2(n+1)   2(n+2)
-		 *			-- - ------ - ------ -
-		 *			 x     x         x
-		 *
-		 * Let w = 2n/x and h=2/x, then the above quotient
-		 * is equal to the continued fraction:
-		 *		    1
-		 *	= -----------------------
-		 *		       1
-		 *	   w - -----------------
-		 *			  1
-		 * 	        w+h - ---------
-		 *		       w+2h - ...
-		 *
-		 * To determine how many terms needed, let
-		 * Q(0) = w, Q(1) = w(w+h) - 1,
-		 * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
-		 * When Q(k) > 1e4	good for single
-		 * When Q(k) > 1e9	good for double
-		 * When Q(k) > 1e17	good for quadruple
-		 */
-	    /* determine k */
-		float t,v;
-		float q0,q1,h,tmp; int32_t k,m;
-		w  = (n+n)/(float)x; h = (float)2.0/(float)x;
-		q0 = w;  z = w+h; q1 = w*z - (float)1.0; k=1;
-		while(q1<(float)1.0e9) {
-			k += 1; z += h;
-			tmp = z*q1 - q0;
-			q0 = q1;
-			q1 = tmp;
-		}
-		m = n+n;
-		for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
-		a = t;
-		b = one;
-		/*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
-		 *  Hence, if n*(log(2n/x)) > ...
-		 *  single 8.8722839355e+01
-		 *  double 7.09782712893383973096e+02
-		 *  long double 1.1356523406294143949491931077970765006170e+04
-		 *  then recurrent value may overflow and the result is
-		 *  likely underflow to zero
-		 */
-		tmp = n;
-		v = two/x;
-		tmp = tmp*__ieee754_logf(fabsf(v*tmp));
-		if(tmp<(float)8.8721679688e+01) {
-	    	    for(i=n-1,di=(float)(i+i);i>0;i--){
-		        temp = b;
-			b *= di;
-			b  = b/x - a;
-		        a = temp;
-			di -= two;
-	     	    }
-		} else {
-	    	    for(i=n-1,di=(float)(i+i);i>0;i--){
-		        temp = b;
-			b *= di;
-			b  = b/x - a;
-		        a = temp;
-			di -= two;
-		    /* scale b to avoid spurious overflow */
-			if(b>(float)1e10) {
-			    a /= b;
-			    t /= b;
-			    b  = one;
-			}
-	     	    }
-		}
-		z = __ieee754_j0f(x);
-		w = __ieee754_j1f(x);
-		if (fabsf(z) >= fabsf(w))
-		    b = (t*z/b);
-		else
-		    b = (t*w/a);
-	    }
-	}
-	if(sgn==1) return -b; else return b;
-}
-
-DLLEXPORT float
-__ieee754_ynf(int n, float x)
-{
-	int32_t i,hx,ix,ib;
-	int32_t sign;
-	float a, b, temp;
-
-	GET_FLOAT_WORD(hx,x);
-	ix = 0x7fffffff&hx;
-    /* if Y(n,NaN) is NaN */
-	if(ix>0x7f800000) return x+x;
-	if(ix==0) return -one/zero;
-	if(hx<0) return zero/zero;
-	sign = 1;
-	if(n<0){
-		n = -n;
-		sign = 1 - ((n&1)<<1);
-	}
-	if(n==0) return(__ieee754_y0f(x));
-	if(n==1) return(sign*__ieee754_y1f(x));
-	if(ix==0x7f800000) return zero;
-
-	a = __ieee754_y0f(x);
-	b = __ieee754_y1f(x);
-	/* quit if b is -inf */
-	GET_FLOAT_WORD(ib,b);
-	for(i=1;i<n&&ib!=0xff800000;i++){
-	    temp = b;
-	    b = ((float)(i+i)/x)*b - a;
-	    GET_FLOAT_WORD(ib,b);
-	    a = temp;
-	}
-	if(sign>0) return b; else return -b;
-}

src/math_private.h

@@ -308,12 +308,6 @@ irint(double x)
 #define	__ieee754_log2f log2f
 #define	__ieee754_sinhf	sinhf
 #define	__ieee754_hypotf hypotf
-#define	__ieee754_j0f	j0f
-#define	__ieee754_j1f	j1f
-#define	__ieee754_y0f	y0f
-#define	__ieee754_y1f	y1f
-#define	__ieee754_jnf	jnf
-#define	__ieee754_ynf	ynf
 #define	__ieee754_remainderf remainderf
 
 /* fdlibm kernel function */

test/libm-test.c

@@ -2918,6 +2918,7 @@ isnormal_test (void)
   print_max_error ("isnormal", 0, 0);
 }
 
+#ifdef TEST_DOUBLE
 static void
 j0_test (void)
 {
@@ -3055,6 +3056,7 @@ jn_test (void)
 
   print_max_error ("jn", DELTAjn, 0);
 }
+#endif
 
 
 static void
@@ -4121,6 +4123,7 @@ trunc_test (void)
   print_max_error ("trunc", 0, 0);
 }
 
+#ifdef TEST_DOUBLE
 static void
 y0_test (void)
 {
@@ -4256,6 +4259,7 @@ yn_test (void)
   print_max_error ("yn", DELTAyn, 0);
 
 }
+#endif
 
 
 
@@ -4534,6 +4538,7 @@ main (int argc, char **argv)
   ctanh_test ();
 #endif
 
+#ifdef TEST_DOUBLE
   /* Bessel functions:  */
   j0_test ();
   j1_test ();
@@ -4541,6 +4546,7 @@ main (int argc, char **argv)
   y0_test ();
   y1_test ();
   yn_test ();
+#endif
 
   if (output_ulps)
     fclose (ulps_file);