diff options
Diffstat (limited to 'newlib/libm/mathfp/ef_j0.c')
-rw-r--r-- | newlib/libm/mathfp/ef_j0.c | 439 |
1 files changed, 0 insertions, 439 deletions
diff --git a/newlib/libm/mathfp/ef_j0.c b/newlib/libm/mathfp/ef_j0.c deleted file mode 100644 index e4cc108..0000000 --- a/newlib/libm/mathfp/ef_j0.c +++ /dev/null @@ -1,439 +0,0 @@ -/* 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 j0f(float x) -#else - float 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(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)); - } -} - -#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 y0f(float x) -#else - float 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(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*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*(j0f(x)*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; -} |