diff options
Diffstat (limited to 'lib/mlibc/options/ansi/musl-generic-math/j0f.c')
| -rw-r--r-- | lib/mlibc/options/ansi/musl-generic-math/j0f.c | 314 |
1 files changed, 0 insertions, 314 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/j0f.c b/lib/mlibc/options/ansi/musl-generic-math/j0f.c deleted file mode 100644 index fab554a..0000000 --- a/lib/mlibc/options/ansi/musl-generic-math/j0f.c +++ /dev/null @@ -1,314 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_j0f.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. - * ==================================================== - */ - -#define _GNU_SOURCE -#include "libm.h" - -static float pzerof(float), qzerof(float); - -static const float -invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */ -tpi = 6.3661974669e-01; /* 0x3f22f983 */ - -static float common(uint32_t ix, float x, int y0) -{ - float z,s,c,ss,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) - */ - s = sinf(x); - c = cosf(x); - if (y0) - c = -c; - cc = s+c; - if (ix < 0x7f000000) { - ss = s-c; - z = -cosf(2*x); - if (s*c < 0) - cc = z/ss; - else - ss = z/cc; - if (ix < 0x58800000) { - if (y0) - ss = -ss; - cc = pzerof(x)*cc-qzerof(x)*ss; - } - } - return invsqrtpi*cc/sqrtf(x); -} - -/* R0/S0 on [0, 2.00] */ -static const float -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 */ - -float j0f(float x) -{ - float z,r,s; - uint32_t ix; - - GET_FLOAT_WORD(ix, x); - ix &= 0x7fffffff; - if (ix >= 0x7f800000) - return 1/(x*x); - x = fabsf(x); - - if (ix >= 0x40000000) { /* |x| >= 2 */ - /* large ulp error near zeros */ - return common(ix, x, 0); - } - if (ix >= 0x3a000000) { /* |x| >= 2**-11 */ - /* up to 4ulp error near 2 */ - z = x*x; - r = z*(R02+z*(R03+z*(R04+z*R05))); - s = 1+z*(S01+z*(S02+z*(S03+z*S04))); - return (1+x/2)*(1-x/2) + z*(r/s); - } - if (ix >= 0x21800000) /* |x| >= 2**-60 */ - x = 0.25f*x*x; - return 1 - x; -} - -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 */ - -float y0f(float x) -{ - float z,u,v; - uint32_t ix; - - GET_FLOAT_WORD(ix, x); - if ((ix & 0x7fffffff) == 0) - return -1/0.0f; - if (ix>>31) - return 0/0.0f; - if (ix >= 0x7f800000) - return 1/x; - if (ix >= 0x40000000) { /* |x| >= 2.0 */ - /* large ulp error near zeros */ - return common(ix,x,1); - } - if (ix >= 0x39000000) { /* x >= 2**-13 */ - /* large ulp error at x ~= 0.89 */ - z = x*x; - u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); - v = 1+z*(v01+z*(v02+z*(v03+z*v04))); - return u/v + tpi*(j0f(x)*logf(x)); - } - return u00 + tpi*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 */ -}; - -static float pzerof(float x) -{ - const float *p,*q; - float_t z,r,s; - uint32_t ix; - - GET_FLOAT_WORD(ix, x); - ix &= 0x7fffffff; - if (ix >= 0x41000000){p = pR8; q = pS8;} - else if (ix >= 0x409173eb){p = pR5; q = pS5;} - else if (ix >= 0x4036d917){p = pR3; q = pS3;} - else /*ix >= 0x40000000*/ {p = pR2; q = pS2;} - z = 1.0f/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); - return 1.0f + 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 */ -}; - -static float qzerof(float x) -{ - const float *p,*q; - float_t s,r,z; - uint32_t ix; - - GET_FLOAT_WORD(ix, x); - ix &= 0x7fffffff; - if (ix >= 0x41000000){p = qR8; q = qS8;} - else if (ix >= 0x409173eb){p = qR5; q = qS5;} - else if (ix >= 0x4036d917){p = qR3; q = qS3;} - else /*ix >= 0x40000000*/ {p = qR2; q = qS2;} - z = 1.0f/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); - return (-.125f + r/s)/x; -} |