0,0 → 1,439 |
/* ef_j0.c -- float version of e_j0.c. |
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
*/ |
|
/* |
* ==================================================== |
* 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 "fdlibm.h" |
|
#ifdef __STDC__ |
static float pzerof(float), qzerof(float); |
#else |
static float pzerof(), qzerof(); |
#endif |
|
#ifdef __STDC__ |
static const float |
#else |
static float |
#endif |
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 */ |
|
#ifdef __STDC__ |
static const float zero = 0.0; |
#else |
static float zero = 0.0; |
#endif |
|
#ifdef __STDC__ |
float __ieee754_j0f(float x) |
#else |
float __ieee754_j0f(x) |
float x; |
#endif |
{ |
float z, s,c,ss,cc,r,u,v; |
__int32_t hx,ix; |
|
GET_FLOAT_WORD(hx,x); |
ix = hx&0x7fffffff; |
if(!FLT_UWORD_IS_FINITE(ix)) 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<=FLT_UWORD_HALF_MAX) { /* 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)/__ieee754_sqrtf(x); |
else { |
u = pzerof(x); v = qzerof(x); |
z = invsqrtpi*(u*cc-v*ss)/__ieee754_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)); |
} |
} |
|
#ifdef __STDC__ |
static const float |
#else |
static float |
#endif |
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 */ |
|
#ifdef __STDC__ |
float __ieee754_y0f(float x) |
#else |
float __ieee754_y0f(x) |
float x; |
#endif |
{ |
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(!FLT_UWORD_IS_FINITE(ix)) return one/(x+x*x); |
if(FLT_UWORD_IS_ZERO(ix)) 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<=FLT_UWORD_HALF_MAX) { /* 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)/__ieee754_sqrtf(x); |
else { |
u = pzerof(x); v = qzerof(x); |
z = invsqrtpi*(u*ss+v*cc)/__ieee754_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) |
*/ |
#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 */ |
-7.0312500000e-02, /* 0xbd900000 */ |
-8.0816707611e+00, /* 0xc1014e86 */ |
-2.5706311035e+02, /* 0xc3808814 */ |
-2.4852163086e+03, /* 0xc51b5376 */ |
-5.2530439453e+03, /* 0xc5a4285a */ |
}; |
#ifdef __STDC__ |
static const float pS8[5] = { |
#else |
static float pS8[5] = { |
#endif |
1.1653436279e+02, /* 0x42e91198 */ |
3.8337448730e+03, /* 0x456f9beb */ |
4.0597855469e+04, /* 0x471e95db */ |
1.1675296875e+05, /* 0x47e4087c */ |
4.7627726562e+04, /* 0x473a0bba */ |
}; |
#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 |
-1.1412546255e-11, /* 0xad48c58a */ |
-7.0312492549e-02, /* 0xbd8fffff */ |
-4.1596107483e+00, /* 0xc0851b88 */ |
-6.7674766541e+01, /* 0xc287597b */ |
-3.3123129272e+02, /* 0xc3a59d9b */ |
-3.4643338013e+02, /* 0xc3ad3779 */ |
}; |
#ifdef __STDC__ |
static const float pS5[5] = { |
#else |
static float pS5[5] = { |
#endif |
6.0753936768e+01, /* 0x42730408 */ |
1.0512523193e+03, /* 0x44836813 */ |
5.9789707031e+03, /* 0x45bad7c4 */ |
9.6254453125e+03, /* 0x461665c8 */ |
2.4060581055e+03, /* 0x451660ee */ |
}; |
|
#ifdef __STDC__ |
static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
#else |
static float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
#endif |
-2.5470459075e-09, /* 0xb12f081b */ |
-7.0311963558e-02, /* 0xbd8fffb8 */ |
-2.4090321064e+00, /* 0xc01a2d95 */ |
-2.1965976715e+01, /* 0xc1afba52 */ |
-5.8079170227e+01, /* 0xc2685112 */ |
-3.1447946548e+01, /* 0xc1fb9565 */ |
}; |
#ifdef __STDC__ |
static const float pS3[5] = { |
#else |
static float pS3[5] = { |
#endif |
3.5856033325e+01, /* 0x420f6c94 */ |
3.6151397705e+02, /* 0x43b4c1ca */ |
1.1936077881e+03, /* 0x44953373 */ |
1.1279968262e+03, /* 0x448cffe6 */ |
1.7358093262e+02, /* 0x432d94b8 */ |
}; |
|
#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 |
-8.8753431271e-08, /* 0xb3be98b7 */ |
-7.0303097367e-02, /* 0xbd8ffb12 */ |
-1.4507384300e+00, /* 0xbfb9b1cc */ |
-7.6356959343e+00, /* 0xc0f4579f */ |
-1.1193166733e+01, /* 0xc1331736 */ |
-3.2336456776e+00, /* 0xc04ef40d */ |
}; |
#ifdef __STDC__ |
static const float pS2[5] = { |
#else |
static float pS2[5] = { |
#endif |
2.2220300674e+01, /* 0x41b1c32d */ |
1.3620678711e+02, /* 0x430834f0 */ |
2.7047027588e+02, /* 0x43873c32 */ |
1.5387539673e+02, /* 0x4319e01a */ |
1.4657617569e+01, /* 0x416a859a */ |
}; |
|
#ifdef __STDC__ |
static float pzerof(float x) |
#else |
static float pzerof(x) |
float x; |
#endif |
{ |
#ifdef __STDC__ |
const float *p,*q; |
#else |
float *p,*q; |
#endif |
float z,r,s; |
__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 {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 qzero 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) |
*/ |
#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 */ |
7.3242187500e-02, /* 0x3d960000 */ |
1.1768206596e+01, /* 0x413c4a93 */ |
5.5767340088e+02, /* 0x440b6b19 */ |
8.8591972656e+03, /* 0x460a6cca */ |
3.7014625000e+04, /* 0x471096a0 */ |
}; |
#ifdef __STDC__ |
static const float qS8[6] = { |
#else |
static float qS8[6] = { |
#endif |
1.6377603149e+02, /* 0x4323c6aa */ |
8.0983447266e+03, /* 0x45fd12c2 */ |
1.4253829688e+05, /* 0x480b3293 */ |
8.0330925000e+05, /* 0x49441ed4 */ |
8.4050156250e+05, /* 0x494d3359 */ |
-3.4389928125e+05, /* 0xc8a7eb69 */ |
}; |
|
#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 |
1.8408595828e-11, /* 0x2da1ec79 */ |
7.3242180049e-02, /* 0x3d95ffff */ |
5.8356351852e+00, /* 0x40babd86 */ |
1.3511157227e+02, /* 0x43071c90 */ |
1.0272437744e+03, /* 0x448067cd */ |
1.9899779053e+03, /* 0x44f8bf4b */ |
}; |
#ifdef __STDC__ |
static const float qS5[6] = { |
#else |
static float qS5[6] = { |
#endif |
8.2776611328e+01, /* 0x42a58da0 */ |
2.0778142090e+03, /* 0x4501dd07 */ |
1.8847289062e+04, /* 0x46933e94 */ |
5.6751113281e+04, /* 0x475daf1d */ |
3.5976753906e+04, /* 0x470c88c1 */ |
-5.3543427734e+03, /* 0xc5a752be */ |
}; |
|
#ifdef __STDC__ |
static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
#else |
static float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
#endif |
4.3774099900e-09, /* 0x3196681b */ |
7.3241114616e-02, /* 0x3d95ff70 */ |
3.3442313671e+00, /* 0x405607e3 */ |
4.2621845245e+01, /* 0x422a7cc5 */ |
1.7080809021e+02, /* 0x432acedf */ |
1.6673394775e+02, /* 0x4326bbe4 */ |
}; |
#ifdef __STDC__ |
static const float qS3[6] = { |
#else |
static float qS3[6] = { |
#endif |
4.8758872986e+01, /* 0x42430916 */ |
7.0968920898e+02, /* 0x44316c1c */ |
3.7041481934e+03, /* 0x4567825f */ |
6.4604252930e+03, /* 0x45c9e367 */ |
2.5163337402e+03, /* 0x451d4557 */ |
-1.4924745178e+02, /* 0xc3153f59 */ |
}; |
|
#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 |
1.5044444979e-07, /* 0x342189db */ |
7.3223426938e-02, /* 0x3d95f62a */ |
1.9981917143e+00, /* 0x3fffc4bf */ |
1.4495602608e+01, /* 0x4167edfd */ |
3.1666231155e+01, /* 0x41fd5471 */ |
1.6252708435e+01, /* 0x4182058c */ |
}; |
#ifdef __STDC__ |
static const float qS2[6] = { |
#else |
static float qS2[6] = { |
#endif |
3.0365585327e+01, /* 0x41f2ecb8 */ |
2.6934811401e+02, /* 0x4386ac8f */ |
8.4478375244e+02, /* 0x44533229 */ |
8.8293585205e+02, /* 0x445cbbe5 */ |
2.1266638184e+02, /* 0x4354aa98 */ |
-5.3109550476e+00, /* 0xc0a9f358 */ |
}; |
|
#ifdef __STDC__ |
static float qzerof(float x) |
#else |
static float qzerof(x) |
float x; |
#endif |
{ |
#ifdef __STDC__ |
const float *p,*q; |
#else |
float *p,*q; |
#endif |
float s,r,z; |
__int32_t ix; |
GET_FLOAT_WORD(ix,x); |
ix &= 0x7fffffff; |
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; |
} |