diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/e_j0.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_j0.c | 212 |
1 files changed, 53 insertions, 159 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_j0.c b/sysdeps/ieee754/dbl-64/e_j0.c index 302df49d62..5ebf2056bf 100644 --- a/sysdeps/ieee754/dbl-64/e_j0.c +++ b/sysdeps/ieee754/dbl-64/e_j0.c @@ -13,10 +13,6 @@ for performance improvement on pipelined processors. */ -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $"; -#endif - /* __ieee754_j0(x), __ieee754_y0(x) * Bessel function of the first and second kinds of order zero. * Method -- j0(x): @@ -26,16 +22,16 @@ static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $"; * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) * for x in (2,inf) - * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) - * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) * as follow: * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) * = 1/sqrt(2) * (cos(x) + sin(x)) * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) * = 1/sqrt(2) * (sin(x) - cos(x)) - * (To avoid cancellation, use + * (To avoid cancellation, use * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - * to compute the worse one.) + * to compute the worse one.) * * 3 Special cases * j0(nan)= nan @@ -56,8 +52,8 @@ static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $"; * Note: For tiny x, U/V = u0 and j0(x)~1, hence * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) * 2. For x>=2. - * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) - * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) * by the method mentioned above. * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. */ @@ -65,22 +61,14 @@ static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $"; #include "math.h" #include "math_private.h" -#ifdef __STDC__ static double pzero(double), qzero(double); -#else -static double pzero(), qzero(); -#endif -#ifdef __STDC__ static const double -#else -static double -#endif -huge = 1e300, +huge = 1e300, one = 1.0, invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ - /* R0/S0 on [0, 2.00] */ + /* R0/S0 on [0, 2.00] */ R[] = {0.0, 0.0, 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ @@ -90,18 +78,10 @@ S[] = {0.0, 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ 1.16614003333790000205e-09}; /* 0x3E1408BC, 0xF4745D8F */ -#ifdef __STDC__ static const double zero = 0.0; -#else -static double zero = 0.0; -#endif -#ifdef __STDC__ - double __ieee754_j0(double x) -#else - double __ieee754_j0(x) - double x; -#endif +double +__ieee754_j0(double x) { double z, s,c,ss,cc,r,u,v,r1,r2,s1,s2,z2,z4; int32_t hx,ix; @@ -117,7 +97,7 @@ static double zero = 0.0; if(ix<0x7fe00000) { /* make sure x+x not overflow */ z = -__cos(x+x); if ((s*c)<zero) cc = z/ss; - else ss = z/cc; + else ss = z/cc; } /* * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) @@ -132,8 +112,8 @@ static double zero = 0.0; } if(ix<0x3f200000) { /* |x| < 2**-13 */ if(huge+x>one) { /* raise inexact if x != 0 */ - if(ix<0x3e400000) return one; /* |x|<2**-27 */ - else return one - 0.25*x*x; + if(ix<0x3e400000) return one; /* |x|<2**-27 */ + else return one - 0.25*x*x; } } z = x*x; @@ -155,12 +135,9 @@ static double zero = 0.0; return((one+u)*(one-u)+z*(r/s)); } } +strong_alias (__ieee754_j0, __j0_finite) -#ifdef __STDC__ static const double -#else -static double -#endif U[] = {-7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ @@ -173,52 +150,48 @@ V[] = {1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ 4.41110311332675467403e-10}; /* 0x3DFE5018, 0x3BD6D9EF */ -#ifdef __STDC__ - double __ieee754_y0(double x) -#else - double __ieee754_y0(x) - double x; -#endif +double +__ieee754_y0(double x) { double z, s,c,ss,cc,u,v,z2,z4,z6,u1,u2,u3,v1,v2; int32_t hx,ix,lx; EXTRACT_WORDS(hx,lx,x); - ix = 0x7fffffff&hx; + ix = 0x7fffffff&hx; /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf. */ if(ix>=0x7ff00000) return one/(x+x*x); - if((ix|lx)==0) return -HUGE_VAL+x; /* -inf and overflow exception. */ - if(hx<0) return zero/(zero*x); - 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. - */ + if((ix|lx)==0) return -HUGE_VAL+x; /* -inf and overflow exception. */ + if(hx<0) return zero/(zero*x); + 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. + */ __sincos (x, &s, &c); - ss = s-c; - cc = s+c; + 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<0x7fe00000) { /* make sure x+x not overflow */ - z = -__cos(x+x); - if ((s*c)<zero) cc = z/ss; - else ss = z/cc; - } - if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x); - else { - u = pzero(x); v = qzero(x); - z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x); - } - return z; + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = -__cos(x+x); + if ((s*c)<zero) cc = z/ss; + else ss = z/cc; + } + if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x); + } + return z; } if(ix<=0x3e400000) { /* x < 2**-27 */ return(U[0] + tpi*__ieee754_log(x)); @@ -238,21 +211,18 @@ V[] = {1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ #endif return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); } +strong_alias (__ieee754_y0, __y0_finite) /* 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) + * 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 + * S = 1 + pS0*s^2 + ... + pS4*s^10 * and * | pzero(x)-1-R/S | <= 2 ** ( -60.26) */ -#ifdef __STDC__ static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ @@ -260,11 +230,7 @@ static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ }; -#ifdef __STDC__ static const double pS8[5] = { -#else -static double pS8[5] = { -#endif 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ @@ -272,11 +238,7 @@ static double pS8[5] = { 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ }; -#ifdef __STDC__ static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ @@ -284,11 +246,7 @@ static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ }; -#ifdef __STDC__ static const double pS5[5] = { -#else -static double pS5[5] = { -#endif 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ @@ -296,11 +254,7 @@ static double pS5[5] = { 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ }; -#ifdef __STDC__ static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#else -static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ @@ -308,11 +262,7 @@ static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ }; -#ifdef __STDC__ static const double pS3[5] = { -#else -static double pS3[5] = { -#endif 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ @@ -320,11 +270,7 @@ static double pS3[5] = { 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ }; -#ifdef __STDC__ static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ @@ -332,11 +278,7 @@ static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ }; -#ifdef __STDC__ static const double pS2[5] = { -#else -static double pS2[5] = { -#endif 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ @@ -344,18 +286,10 @@ static double pS2[5] = { 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ }; -#ifdef __STDC__ - static double pzero(double x) -#else - static double pzero(x) - double x; -#endif +static double +pzero(double x) { -#ifdef __STDC__ const double *p,*q; -#else - double *p,*q; -#endif double z,r,s,z2,z4,r1,r2,r3,s1,s2,s3; int32_t ix; GET_HIGH_WORD(ix,x); @@ -385,17 +319,13 @@ static double pS2[5] = { /* 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)) + * 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 + * S = 1 + qS0*s^2 + ... + qS5*s^12 * and * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) */ -#ifdef __STDC__ static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ @@ -403,11 +333,7 @@ static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ }; -#ifdef __STDC__ static const double qS8[6] = { -#else -static double qS8[6] = { -#endif 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ @@ -416,11 +342,7 @@ static double qS8[6] = { -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ }; -#ifdef __STDC__ static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ @@ -428,11 +350,7 @@ static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ }; -#ifdef __STDC__ static const double qS5[6] = { -#else -static double qS5[6] = { -#endif 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ @@ -441,11 +359,7 @@ static double qS5[6] = { -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ }; -#ifdef __STDC__ static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#else -static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ @@ -453,11 +367,7 @@ static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ }; -#ifdef __STDC__ static const double qS3[6] = { -#else -static double qS3[6] = { -#endif 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ @@ -466,11 +376,7 @@ static double qS3[6] = { -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ }; -#ifdef __STDC__ static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ @@ -478,11 +384,7 @@ static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ }; -#ifdef __STDC__ static const double qS2[6] = { -#else -static double qS2[6] = { -#endif 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ @@ -491,18 +393,10 @@ static double qS2[6] = { -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ }; -#ifdef __STDC__ - static double qzero(double x) -#else - static double qzero(x) - double x; -#endif +static double +qzero(double x) { -#ifdef __STDC__ const double *p,*q; -#else - double *p,*q; -#endif double s,r,z,z2,z4,z6,r1,r2,r3,s1,s2,s3; int32_t ix; GET_HIGH_WORD(ix,x); |