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Revert "Remove [jy][01n]f(). X/Open only standardizes the double versions."
This reverts commit 8c8693c.
1 parent 2af199e commit c29e8b1

7 files changed

Lines changed: 901 additions & 8 deletions

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‎include/openlibm_math.h‎

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Original file line numberDiff line numberDiff line change
@@ -387,6 +387,14 @@ float fminf(float, float) __pure2;
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* float versions of BSD math library entry points
388388
*/
389389
#if __BSD_VISIBLE
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float dremf(float, float);
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float j0f(float);
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float j1f(float);
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float jnf(int, float);
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float y0f(float);
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float y1f(float);
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float ynf(int, float);
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390398
/*
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* Float versions of reentrant version of lgamma; passes signgam back by
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* reference as the second argument; user must allocate space for signgam.

‎src/Make.files‎

Lines changed: 3 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -1,8 +1,9 @@
11
$(CUR_SRCS) = common.c \
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e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \
33
e_atan2.c e_atan2f.c e_atanh.c e_atanhf.c e_cosh.c e_coshf.c e_exp.c \
4-
e_expf.c e_fmod.c e_fmodf.c e_hypot.c e_hypotf.c e_j0.c e_j1.c \
5-
e_jn.c e_lgamma.c e_lgamma_r.c e_lgammaf.c e_lgammaf_r.c \
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e_expf.c e_fmod.c e_fmodf.c \
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e_hypot.c e_hypotf.c e_j0.c e_j0f.c e_j1.c e_j1f.c \
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e_jn.c e_jnf.c e_lgamma.c e_lgamma_r.c e_lgammaf.c e_lgammaf_r.c \
67
e_lgammal.c e_log.c e_log10.c e_log10f.c e_log2.c e_log2f.c e_logf.c \
78
e_pow.c e_powf.c e_remainder.c e_remainderf.c \
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e_rem_pio2.c e_rem_pio2f.c \

‎src/e_j0f.c‎

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,344 @@
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/* e_j0f.c -- float version of e_j0.c.
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3+
*/
4+
5+
/*
6+
* ====================================================
7+
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8+
*
9+
* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <assert.h>
17+
18+
#include "cdefs-compat.h"
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//__FBSDID("$FreeBSD: src/lib/msun/src/e_j0f.c,v 1.8 2008/02/22 02:30:35 das Exp $");
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#include <openlibm_math.h>
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#include "math_private.h"
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static float pzerof(float), qzerof(float);
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static const float
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huge = 1e30,
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one = 1.0,
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invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
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tpi = 6.3661974669e-01, /* 0x3f22f983 */
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/* R0/S0 on [0, 2.00] */
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R02 = 1.5625000000e-02, /* 0x3c800000 */
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R03 = -1.8997929874e-04, /* 0xb947352e */
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R04 = 1.8295404516e-06, /* 0x35f58e88 */
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R05 = -4.6183270541e-09, /* 0xb19eaf3c */
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S01 = 1.5619102865e-02, /* 0x3c7fe744 */
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S02 = 1.1692678527e-04, /* 0x38f53697 */
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S03 = 5.1354652442e-07, /* 0x3509daa6 */
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S04 = 1.1661400734e-09; /* 0x30a045e8 */
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static const float zero = 0.0;
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DLLEXPORT float
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__ieee754_j0f(float x)
46+
{
47+
float z, s,c,ss,cc,r,u,v;
48+
int32_t hx,ix;
49+
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GET_FLOAT_WORD(hx,x);
51+
ix = hx&0x7fffffff;
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if(ix>=0x7f800000) return one/(x*x);
53+
x = fabsf(x);
54+
if(ix >= 0x40000000) { /* |x| >= 2.0 */
55+
s = sinf(x);
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c = cosf(x);
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ss = s-c;
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cc = s+c;
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if(ix<0x7f000000) { /* make sure x+x not overflow */
60+
z = -cosf(x+x);
61+
if ((s*c)<zero) cc = z/ss;
62+
else ss = z/cc;
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}
64+
/*
65+
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
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* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
67+
*/
68+
if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(x);
69+
else {
70+
u = pzerof(x); v = qzerof(x);
71+
z = invsqrtpi*(u*cc-v*ss)/sqrtf(x);
72+
}
73+
return z;
74+
}
75+
if(ix<0x39000000) { /* |x| < 2**-13 */
76+
if(huge+x>one) { /* raise inexact if x != 0 */
77+
if(ix<0x32000000) return one; /* |x|<2**-27 */
78+
else return one - (float)0.25*x*x;
79+
}
80+
}
81+
z = x*x;
82+
r = z*(R02+z*(R03+z*(R04+z*R05)));
83+
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
84+
if(ix < 0x3F800000) { /* |x| < 1.00 */
85+
return one + z*((float)-0.25+(r/s));
86+
} else {
87+
u = (float)0.5*x;
88+
return((one+u)*(one-u)+z*(r/s));
89+
}
90+
}
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static const float
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u00 = -7.3804296553e-02, /* 0xbd9726b5 */
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u01 = 1.7666645348e-01, /* 0x3e34e80d */
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u02 = -1.3818567619e-02, /* 0xbc626746 */
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u03 = 3.4745343146e-04, /* 0x39b62a69 */
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u04 = -3.8140706238e-06, /* 0xb67ff53c */
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u05 = 1.9559013964e-08, /* 0x32a802ba */
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u06 = -3.9820518410e-11, /* 0xae2f21eb */
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v01 = 1.2730483897e-02, /* 0x3c509385 */
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v02 = 7.6006865129e-05, /* 0x389f65e0 */
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v03 = 2.5915085189e-07, /* 0x348b216c */
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v04 = 4.4111031494e-10; /* 0x2ff280c2 */
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DLLEXPORT float
106+
__ieee754_y0f(float x)
107+
{
108+
float z, s,c,ss,cc,u,v;
109+
int32_t hx,ix;
110+
111+
GET_FLOAT_WORD(hx,x);
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ix = 0x7fffffff&hx;
113+
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
114+
if(ix>=0x7f800000) return one/(x+x*x);
115+
if(ix==0) return -one/zero;
116+
if(hx<0) return zero/zero;
117+
if(ix >= 0x40000000) { /* |x| >= 2.0 */
118+
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
119+
* where x0 = x-pi/4
120+
* Better formula:
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* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
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* = 1/sqrt(2) * (sin(x) + cos(x))
123+
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
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* = 1/sqrt(2) * (sin(x) - cos(x))
125+
* To avoid cancellation, use
126+
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
127+
* to compute the worse one.
128+
*/
129+
s = sinf(x);
130+
c = cosf(x);
131+
ss = s-c;
132+
cc = s+c;
133+
/*
134+
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
135+
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
136+
*/
137+
if(ix<0x7f000000) { /* make sure x+x not overflow */
138+
z = -cosf(x+x);
139+
if ((s*c)<zero) cc = z/ss;
140+
else ss = z/cc;
141+
}
142+
if(ix>0x80000000) z = (invsqrtpi*ss)/sqrtf(x);
143+
else {
144+
u = pzerof(x); v = qzerof(x);
145+
z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
146+
}
147+
return z;
148+
}
149+
if(ix<=0x32000000) { /* x < 2**-27 */
150+
return(u00 + tpi*__ieee754_logf(x));
151+
}
152+
z = x*x;
153+
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
154+
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
155+
return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));
156+
}
157+
158+
/* The asymptotic expansions of pzero is
159+
* 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
160+
* For x >= 2, We approximate pzero by
161+
* pzero(x) = 1 + (R/S)
162+
* where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
163+
* S = 1 + pS0*s^2 + ... + pS4*s^10
164+
* and
165+
* | pzero(x)-1-R/S | <= 2 ** ( -60.26)
166+
*/
167+
static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
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0.0000000000e+00, /* 0x00000000 */
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-7.0312500000e-02, /* 0xbd900000 */
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-8.0816707611e+00, /* 0xc1014e86 */
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-2.5706311035e+02, /* 0xc3808814 */
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-2.4852163086e+03, /* 0xc51b5376 */
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-5.2530439453e+03, /* 0xc5a4285a */
174+
};
175+
static const float pS8[5] = {
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1.1653436279e+02, /* 0x42e91198 */
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3.8337448730e+03, /* 0x456f9beb */
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4.0597855469e+04, /* 0x471e95db */
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1.1675296875e+05, /* 0x47e4087c */
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4.7627726562e+04, /* 0x473a0bba */
181+
};
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static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
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-1.1412546255e-11, /* 0xad48c58a */
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-7.0312492549e-02, /* 0xbd8fffff */
185+
-4.1596107483e+00, /* 0xc0851b88 */
186+
-6.7674766541e+01, /* 0xc287597b */
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-3.3123129272e+02, /* 0xc3a59d9b */
188+
-3.4643338013e+02, /* 0xc3ad3779 */
189+
};
190+
static const float pS5[5] = {
191+
6.0753936768e+01, /* 0x42730408 */
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1.0512523193e+03, /* 0x44836813 */
193+
5.9789707031e+03, /* 0x45bad7c4 */
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9.6254453125e+03, /* 0x461665c8 */
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2.4060581055e+03, /* 0x451660ee */
196+
};
197+
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static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
199+
-2.5470459075e-09, /* 0xb12f081b */
200+
-7.0311963558e-02, /* 0xbd8fffb8 */
201+
-2.4090321064e+00, /* 0xc01a2d95 */
202+
-2.1965976715e+01, /* 0xc1afba52 */
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-5.8079170227e+01, /* 0xc2685112 */
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-3.1447946548e+01, /* 0xc1fb9565 */
205+
};
206+
static const float pS3[5] = {
207+
3.5856033325e+01, /* 0x420f6c94 */
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3.6151397705e+02, /* 0x43b4c1ca */
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1.1936077881e+03, /* 0x44953373 */
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1.1279968262e+03, /* 0x448cffe6 */
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1.7358093262e+02, /* 0x432d94b8 */
212+
};
213+
214+
static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
215+
-8.8753431271e-08, /* 0xb3be98b7 */
216+
-7.0303097367e-02, /* 0xbd8ffb12 */
217+
-1.4507384300e+00, /* 0xbfb9b1cc */
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-7.6356959343e+00, /* 0xc0f4579f */
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-1.1193166733e+01, /* 0xc1331736 */
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-3.2336456776e+00, /* 0xc04ef40d */
221+
};
222+
static const float pS2[5] = {
223+
2.2220300674e+01, /* 0x41b1c32d */
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1.3620678711e+02, /* 0x430834f0 */
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2.7047027588e+02, /* 0x43873c32 */
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1.5387539673e+02, /* 0x4319e01a */
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1.4657617569e+01, /* 0x416a859a */
228+
};
229+
230+
/* Note: This function is only called for ix>=0x40000000 (see above) */
231+
static float pzerof(float x)
232+
{
233+
const float *p,*q;
234+
float z,r,s;
235+
int32_t ix;
236+
GET_FLOAT_WORD(ix,x);
237+
ix &= 0x7fffffff;
238+
assert(ix>=0x40000000 && ix<=0x48000000);
239+
if(ix>=0x41000000) {p = pR8; q= pS8;}
240+
else if(ix>=0x40f71c58){p = pR5; q= pS5;}
241+
else if(ix>=0x4036db68){p = pR3; q= pS3;}
242+
else {p = pR2; q= pS2;}
243+
z = one/(x*x);
244+
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
245+
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
246+
return one+ r/s;
247+
}
248+
249+
250+
/* For x >= 8, the asymptotic expansions of qzero is
251+
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
252+
* We approximate pzero by
253+
* qzero(x) = s*(-1.25 + (R/S))
254+
* where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
255+
* S = 1 + qS0*s^2 + ... + qS5*s^12
256+
* and
257+
* | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
258+
*/
259+
static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
260+
0.0000000000e+00, /* 0x00000000 */
261+
7.3242187500e-02, /* 0x3d960000 */
262+
1.1768206596e+01, /* 0x413c4a93 */
263+
5.5767340088e+02, /* 0x440b6b19 */
264+
8.8591972656e+03, /* 0x460a6cca */
265+
3.7014625000e+04, /* 0x471096a0 */
266+
};
267+
static const float qS8[6] = {
268+
1.6377603149e+02, /* 0x4323c6aa */
269+
8.0983447266e+03, /* 0x45fd12c2 */
270+
1.4253829688e+05, /* 0x480b3293 */
271+
8.0330925000e+05, /* 0x49441ed4 */
272+
8.4050156250e+05, /* 0x494d3359 */
273+
-3.4389928125e+05, /* 0xc8a7eb69 */
274+
};
275+
276+
static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
277+
1.8408595828e-11, /* 0x2da1ec79 */
278+
7.3242180049e-02, /* 0x3d95ffff */
279+
5.8356351852e+00, /* 0x40babd86 */
280+
1.3511157227e+02, /* 0x43071c90 */
281+
1.0272437744e+03, /* 0x448067cd */
282+
1.9899779053e+03, /* 0x44f8bf4b */
283+
};
284+
static const float qS5[6] = {
285+
8.2776611328e+01, /* 0x42a58da0 */
286+
2.0778142090e+03, /* 0x4501dd07 */
287+
1.8847289062e+04, /* 0x46933e94 */
288+
5.6751113281e+04, /* 0x475daf1d */
289+
3.5976753906e+04, /* 0x470c88c1 */
290+
-5.3543427734e+03, /* 0xc5a752be */
291+
};
292+
293+
static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
294+
4.3774099900e-09, /* 0x3196681b */
295+
7.3241114616e-02, /* 0x3d95ff70 */
296+
3.3442313671e+00, /* 0x405607e3 */
297+
4.2621845245e+01, /* 0x422a7cc5 */
298+
1.7080809021e+02, /* 0x432acedf */
299+
1.6673394775e+02, /* 0x4326bbe4 */
300+
};
301+
static const float qS3[6] = {
302+
4.8758872986e+01, /* 0x42430916 */
303+
7.0968920898e+02, /* 0x44316c1c */
304+
3.7041481934e+03, /* 0x4567825f */
305+
6.4604252930e+03, /* 0x45c9e367 */
306+
2.5163337402e+03, /* 0x451d4557 */
307+
-1.4924745178e+02, /* 0xc3153f59 */
308+
};
309+
310+
static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
311+
1.5044444979e-07, /* 0x342189db */
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7.3223426938e-02, /* 0x3d95f62a */
313+
1.9981917143e+00, /* 0x3fffc4bf */
314+
1.4495602608e+01, /* 0x4167edfd */
315+
3.1666231155e+01, /* 0x41fd5471 */
316+
1.6252708435e+01, /* 0x4182058c */
317+
};
318+
static const float qS2[6] = {
319+
3.0365585327e+01, /* 0x41f2ecb8 */
320+
2.6934811401e+02, /* 0x4386ac8f */
321+
8.4478375244e+02, /* 0x44533229 */
322+
8.8293585205e+02, /* 0x445cbbe5 */
323+
2.1266638184e+02, /* 0x4354aa98 */
324+
-5.3109550476e+00, /* 0xc0a9f358 */
325+
};
326+
327+
/* Note: This function is only called for ix>=0x40000000 (see above) */
328+
static float qzerof(float x)
329+
{
330+
const float *p,*q;
331+
float s,r,z;
332+
int32_t ix;
333+
GET_FLOAT_WORD(ix,x);
334+
ix &= 0x7fffffff;
335+
assert(ix>=0x40000000 && ix<=0x48000000);
336+
if(ix>=0x41000000) {p = qR8; q= qS8;}
337+
else if(ix>=0x40f71c58){p = qR5; q= qS5;}
338+
else if(ix>=0x4036db68){p = qR3; q= qS3;}
339+
else {p = qR2; q= qS2;}
340+
z = one/(x*x);
341+
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
342+
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
343+
return (-(float).125 + r/s)/x;
344+
}

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