diff options
| author | tijl <tijl@FreeBSD.org> | 2015-06-25 13:01:10 +0000 |
|---|---|---|
| committer | tijl <tijl@FreeBSD.org> | 2015-06-25 13:01:10 +0000 |
| commit | 95fcbd85e830ba474dede020a3b792ae31138e2b (patch) | |
| tree | a7fbd9fa2cff8aeacad80e2cea7c6a1651531374 /lib | |
| parent | 91e9d26e116c48b2b63d0153154f28797795a07f (diff) | |
| download | FreeBSD-src-95fcbd85e830ba474dede020a3b792ae31138e2b.zip FreeBSD-src-95fcbd85e830ba474dede020a3b792ae31138e2b.tar.gz | |
MFC r271651, r271719, r272138, r272457, r272845, r275476, r275518, r275614,
r275819, r276176, r278154, r278160, r278339, r279127, r279240, r279491,
r279493, r279856, r283032, r284423, r284426, r284427, r284428
Merge changes to libm from the past 9 months. This includes improvements
to the Bessel functions and adds the C99 function lgammal.
Diffstat (limited to 'lib')
43 files changed, 1297 insertions, 511 deletions
diff --git a/lib/msun/Makefile b/lib/msun/Makefile index 4473623..f34255f 100644 --- a/lib/msun/Makefile +++ b/lib/msun/Makefile @@ -98,6 +98,7 @@ COMMON_SRCS+= s_copysignl.c s_fabsl.c s_llrintl.c s_lrintl.c s_modfl.c # If long double != double use these; otherwise, we alias the double versions. COMMON_SRCS+= e_acoshl.c e_acosl.c e_asinl.c e_atan2l.c e_atanhl.c \ e_coshl.c e_fmodl.c e_hypotl.c \ + e_lgammal.c e_lgammal_r.c \ e_remainderl.c e_sinhl.c e_sqrtl.c \ invtrig.c k_cosl.c k_sinl.c k_tanl.c \ s_asinhl.c s_atanl.c s_cbrtl.c s_ceill.c s_cosl.c s_cprojl.c \ @@ -188,7 +189,8 @@ MLINKS+=ilogb.3 ilogbf.3 ilogb.3 ilogbl.3 \ ilogb.3 logb.3 ilogb.3 logbf.3 ilogb.3 logbl.3 MLINKS+=j0.3 j1.3 j0.3 jn.3 j0.3 y0.3 j0.3 y1.3 j0.3 y1f.3 j0.3 yn.3 MLINKS+=j0.3 j0f.3 j0.3 j1f.3 j0.3 jnf.3 j0.3 y0f.3 j0.3 ynf.3 -MLINKS+=lgamma.3 gamma.3 lgamma.3 gammaf.3 lgamma.3 lgammaf.3 \ +MLINKS+=lgamma.3 gamma.3 lgamma.3 gammaf.3 \ + lgamma.3 lgammaf.3 lgamma.3 lgammal.3 \ lgamma.3 tgamma.3 lgamma.3 tgammaf.3 MLINKS+=log.3 log10.3 log.3 log10f.3 log.3 log10l.3 \ log.3 log1p.3 log.3 log1pf.3 log.3 log1pl.3 \ diff --git a/lib/msun/Symbol.map b/lib/msun/Symbol.map index e53ca07..d5b7f46 100644 --- a/lib/msun/Symbol.map +++ b/lib/msun/Symbol.map @@ -269,6 +269,7 @@ FBSD_1.3 { erfl; expl; expm1l; + lgammal; log10l; log1pl; log2l; @@ -276,7 +277,11 @@ FBSD_1.3 { sinhl; tanhl; /* Implemented as weak aliases for imprecise versions */ - lgammal; powl; tgammal; }; + +/* First added in 11.0-CURRENT */ +FBSD_1.4 { + lgammal_r; +}; diff --git a/lib/msun/ld128/e_lgammal_r.c b/lib/msun/ld128/e_lgammal_r.c new file mode 100644 index 0000000..53d3af1 --- /dev/null +++ b/lib/msun/ld128/e_lgammal_r.c @@ -0,0 +1,330 @@ +/* @(#)e_lgamma_r.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +/* + * See e_lgamma_r.c for complete comments. + * + * Converted to long double by Steven G. Kargl. + */ + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" + +static const volatile double vzero = 0; + +static const double +zero= 0, +half= 0.5, +one = 1; + +static const long double +pi = 3.14159265358979323846264338327950288e+00L; +/* + * Domain y in [0x1p-119, 0.28], range ~[-1.4065e-36, 1.4065e-36]: + * |(lgamma(2 - y) + y / 2) / y - a(y)| < 2**-119.1 + */ +static const long double +a0 = 7.72156649015328606065120900824024296e-02L, +a1 = 3.22467033424113218236207583323018498e-01L, +a2 = 6.73523010531980951332460538330282217e-02L, +a3 = 2.05808084277845478790009252803463129e-02L, +a4 = 7.38555102867398526627292839296001626e-03L, +a5 = 2.89051033074152328576829509522483468e-03L, +a6 = 1.19275391170326097618357349881842913e-03L, +a7 = 5.09669524743042462515256340206203019e-04L, +a8 = 2.23154758453578096143609255559576017e-04L, +a9 = 9.94575127818397632126978731542755129e-05L, +a10 = 4.49262367375420471287545895027098145e-05L, +a11 = 2.05072127845117995426519671481628849e-05L, +a12 = 9.43948816959096748454087141447939513e-06L, +a13 = 4.37486780697359330303852050718287419e-06L, +a14 = 2.03920783892362558276037363847651809e-06L, +a15 = 9.55191070057967287877923073200324649e-07L, +a16 = 4.48993286185740853170657139487620560e-07L, +a17 = 2.13107543597620911675316728179563522e-07L, +a18 = 9.70745379855304499867546549551023473e-08L, +a19 = 5.61889970390290257926487734695402075e-08L, +a20 = 6.42739653024130071866684358960960951e-09L, +a21 = 3.34491062143649291746195612991870119e-08L, +a22 = -1.57068547394315223934653011440641472e-08L, +a23 = 1.30812825422415841213733487745200632e-08L; +/* + * Domain x in [tc-0.24, tc+0.28], range ~[-6.3201e-37, 6.3201e-37]: + * |(lgamma(x) - tf) - t(x - tc)| < 2**-120.3. + */ +static const long double +tc = 1.46163214496836234126265954232572133e+00L, +tf = -1.21486290535849608095514557177691584e-01L, +tt = 1.57061739945077675484237837992951704e-36L, +t0 = -1.99238329499314692728655623767019240e-36L, +t1 = -6.08453430711711404116887457663281416e-35L, +t2 = 4.83836122723810585213722380854828904e-01L, +t3 = -1.47587722994530702030955093950668275e-01L, +t4 = 6.46249402389127526561003464202671923e-02L, +t5 = -3.27885410884813055008502586863748063e-02L, +t6 = 1.79706751152103942928638276067164935e-02L, +t7 = -1.03142230366363872751602029672767978e-02L, +t8 = 6.10053602051788840313573150785080958e-03L, +t9 = -3.68456960831637325470641021892968954e-03L, +t10 = 2.25976482322181046611440855340968560e-03L, +t11 = -1.40225144590445082933490395950664961e-03L, +t12 = 8.78232634717681264035014878172485575e-04L, +t13 = -5.54194952796682301220684760591403899e-04L, +t14 = 3.51912956837848209220421213975000298e-04L, +t15 = -2.24653443695947456542669289367055542e-04L, +t16 = 1.44070395420840737695611929680511823e-04L, +t17 = -9.27609865550394140067059487518862512e-05L, +t18 = 5.99347334438437081412945428365433073e-05L, +t19 = -3.88458388854572825603964274134801009e-05L, +t20 = 2.52476631610328129217896436186551043e-05L, +t21 = -1.64508584981658692556994212457518536e-05L, +t22 = 1.07434583475987007495523340296173839e-05L, +t23 = -7.03070407519397260929482550448878399e-06L, +t24 = 4.60968590693753579648385629003100469e-06L, +t25 = -3.02765473778832036018438676945512661e-06L, +t26 = 1.99238771545503819972741288511303401e-06L, +t27 = -1.31281299822614084861868817951788579e-06L, +t28 = 8.60844432267399655055574642052370223e-07L, +t29 = -5.64535486432397413273248363550536374e-07L, +t30 = 3.99357783676275660934903139592727737e-07L, +t31 = -2.95849029193433121795495215869311610e-07L, +t32 = 1.37790144435073124976696250804940384e-07L; +/* + * Domain y in [-0.1, 0.232], range ~[-1.4046e-37, 1.4181e-37]: + * |(lgamma(1 + y) + 0.5 * y) / y - u(y) / v(y)| < 2**-122.8 + */ +static const long double +u0 = -7.72156649015328606065120900824024311e-02L, +u1 = 4.24082772271938167430983113242482656e-01L, +u2 = 2.96194003481457101058321977413332171e+00L, +u3 = 6.49503267711258043997790983071543710e+00L, +u4 = 7.40090051288150177152835698948644483e+00L, +u5 = 4.94698036296756044610805900340723464e+00L, +u6 = 2.00194224610796294762469550684947768e+00L, +u7 = 4.82073087750608895996915051568834949e-01L, +u8 = 6.46694052280506568192333848437585427e-02L, +u9 = 4.17685526755100259316625348933108810e-03L, +u10 = 9.06361003550314327144119307810053410e-05L, +v1 = 5.15937098592887275994320496999951947e+00L, +v2 = 1.14068418766251486777604403304717558e+01L, +v3 = 1.41164839437524744055723871839748489e+01L, +v4 = 1.07170702656179582805791063277960532e+01L, +v5 = 5.14448694179047879915042998453632434e+00L, +v6 = 1.55210088094585540637493826431170289e+00L, +v7 = 2.82975732849424562719893657416365673e-01L, +v8 = 2.86424622754753198010525786005443539e-02L, +v9 = 1.35364253570403771005922441442688978e-03L, +v10 = 1.91514173702398375346658943749580666e-05L, +v11 = -3.25364686890242327944584691466034268e-08L; +/* + * Domain x in (2, 3], range ~[-1.3341e-36, 1.3536e-36]: + * |(lgamma(y+2) - 0.5 * y) / y - s(y)/r(y)| < 2**-120.1 + * with y = x - 2. + */ +static const long double +s0 = -7.72156649015328606065120900824024297e-02L, +s1 = 1.23221687850916448903914170805852253e-01L, +s2 = 5.43673188699937239808255378293820020e-01L, +s3 = 6.31998137119005233383666791176301800e-01L, +s4 = 3.75885340179479850993811501596213763e-01L, +s5 = 1.31572908743275052623410195011261575e-01L, +s6 = 2.82528453299138685507186287149699749e-02L, +s7 = 3.70262021550340817867688714880797019e-03L, +s8 = 2.83374000312371199625774129290973648e-04L, +s9 = 1.15091830239148290758883505582343691e-05L, +s10 = 2.04203474281493971326506384646692446e-07L, +s11 = 9.79544198078992058548607407635645763e-10L, +r1 = 2.58037466655605285937112832039537492e+00L, +r2 = 2.86289413392776399262513849911531180e+00L, +r3 = 1.78691044735267497452847829579514367e+00L, +r4 = 6.89400381446725342846854215600008055e-01L, +r5 = 1.70135865462567955867134197595365343e-01L, +r6 = 2.68794816183964420375498986152766763e-02L, +r7 = 2.64617234244861832870088893332006679e-03L, +r8 = 1.52881761239180800640068128681725702e-04L, +r9 = 4.63264813762296029824851351257638558e-06L, +r10 = 5.89461519146957343083848967333671142e-08L, +r11 = 1.79027678176582527798327441636552968e-10L; +/* + * Domain z in [8, 0x1p70], range ~[-9.8214e-35, 9.8214e-35]: + * |lgamma(x) - (x - 0.5) * (log(x) - 1) - w(1/x)| < 2**-113.0 + */ +static const long double +w0 = 4.18938533204672741780329736405617738e-01L, +w1 = 8.33333333333333333333333333332852026e-02L, +w2 = -2.77777777777777777777777727810123528e-03L, +w3 = 7.93650793650793650791708939493907380e-04L, +w4 = -5.95238095238095234390450004444370959e-04L, +w5 = 8.41750841750837633887817658848845695e-04L, +w6 = -1.91752691752396849943172337347259743e-03L, +w7 = 6.41025640880333069429106541459015557e-03L, +w8 = -2.95506530801732133437990433080327074e-02L, +w9 = 1.79644237328444101596766586979576927e-01L, +w10 = -1.39240539108367641920172649259736394e+00L, +w11 = 1.33987701479007233325288857758641761e+01L, +w12 = -1.56363596431084279780966590116006255e+02L, +w13 = 2.14830978044410267201172332952040777e+03L, +w14 = -3.28636067474227378352761516589092334e+04L, +w15 = 5.06201257747865138432663574251462485e+05L, +w16 = -6.79720123352023636706247599728048344e+06L, +w17 = 6.57556601705472106989497289465949255e+07L, +w18 = -3.26229058141181783534257632389415580e+08L; + +static long double +sin_pil(long double x) +{ + volatile long double vz; + long double y,z; + uint64_t lx, n; + uint16_t hx; + + y = -x; + + vz = y+0x1.p112; + z = vz-0x1.p112; + if (z == y) + return zero; + + vz = y+0x1.p110; + EXTRACT_LDBL128_WORDS(hx,lx,n,vz); + z = vz-0x1.p110; + if (z > y) { + z -= 0.25; + n--; + } + n &= 7; + y = y - z + n * 0.25; + + switch (n) { + case 0: y = __kernel_sinl(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cosl(pi*(0.5-y),zero); break; + case 3: + case 4: y = __kernel_sinl(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cosl(pi*(y-1.5),zero); break; + default: y = __kernel_sinl(pi*(y-2.0),zero,0); break; + } + return -y; +} + +long double +lgammal_r(long double x, int *signgamp) +{ + long double nadj,p,p1,p2,p3,q,r,t,w,y,z; + uint64_t llx,lx; + int i; + uint16_t hx,ix; + + EXTRACT_LDBL128_WORDS(hx,lx,llx,x); + + /* purge +-Inf and NaNs */ + *signgamp = 1; + ix = hx&0x7fff; + if(ix==0x7fff) return x*x; + + /* purge +-0 and tiny arguments */ + *signgamp = 1-2*(hx>>15); + if(ix<0x3fff-116) { /* |x|<2**-(p+3), return -log(|x|) */ + if((ix|lx|llx)==0) + return one/vzero; + return -logl(fabsl(x)); + } + + /* purge negative integers and start evaluation for other x < 0 */ + if(hx&0x8000) { + *signgamp = 1; + if(ix>=0x3fff+112) /* |x|>=2**(p-1), must be -integer */ + return one/vzero; + t = sin_pil(x); + if(t==zero) return one/vzero; + nadj = logl(pi/fabsl(t*x)); + if(t<zero) *signgamp = -1; + x = -x; + } + + /* purge 1 and 2 */ + if((ix==0x3fff || ix==0x4000) && (lx|llx)==0) r = 0; + /* for x < 2.0 */ + else if(ix<0x4000) { + if(x<=8.9999961853027344e-01) { + r = -logl(x); + if(x>=7.3159980773925781e-01) {y = 1-x; i= 0;} + else if(x>=2.3163998126983643e-01) {y= x-(tc-1); i=1;} + else {y = x; i=2;} + } else { + r = 0; + if(x>=1.7316312789916992e+00) {y=2-x;i=0;} + else if(x>=1.2316322326660156e+00) {y=x-tc;i=1;} + else {y=x-1;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*(a10+z*(a12+z*(a14+z*(a16+ + z*(a18+z*(a20+z*a22)))))))))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*(a11+z*(a13+z*(a15+ + z*(a17+z*(a19+z*(a21+z*a23))))))))))); + p = y*p1+p2; + r += p-y/2; break; + case 1: + p = t0+y*t1+tt+y*y*(t2+y*(t3+y*(t4+y*(t5+y*(t6+y*(t7+y*(t8+ + y*(t9+y*(t10+y*(t11+y*(t12+y*(t13+y*(t14+y*(t15+y*(t16+ + y*(t17+y*(t18+y*(t19+y*(t20+y*(t21+y*(t22+y*(t23+ + y*(t24+y*(t25+y*(t26+y*(t27+y*(t28+y*(t29+y*(t30+ + y*(t31+y*t32)))))))))))))))))))))))))))))); + r += tf + p; break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*(u5+y*(u6+y*(u7+ + y*(u8+y*(u9+y*u10)))))))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*(v5+y*(v6+y*(v7+ + y*(v8+y*(v9+y*(v10+y*v11)))))))))); + r += p1/p2-y/2; + } + } + /* x < 8.0 */ + else if(ix<0x4002) { + i = x; + y = x-i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*(s6+y*(s7+y*(s8+ + y*(s9+y*(s10+y*s11))))))))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*(r6+y*(r7+y*(r8+ + y*(r9+y*(r10+y*r11)))))))))); + r = y/2+p/q; + z = 1; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+6); /* FALLTHRU */ + case 6: z *= (y+5); /* FALLTHRU */ + case 5: z *= (y+4); /* FALLTHRU */ + case 4: z *= (y+3); /* FALLTHRU */ + case 3: z *= (y+2); /* FALLTHRU */ + r += logl(z); break; + } + /* 8.0 <= x < 2**(p+3) */ + } else if (ix<0x3fff+116) { + t = logl(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*(w6+y*(w7+y*(w8+ + y*(w9+y*(w10+y*(w11+y*(w12+y*(w13+y*(w14+y*(w15+y*(w16+ + y*(w17+y*w18))))))))))))))))); + r = (x-half)*(t-one)+w; + /* 2**(p+3) <= x <= inf */ + } else + r = x*(logl(x)-1); + if(hx&0x8000) r = nadj - r; + return r; +} diff --git a/lib/msun/ld128/k_expl.h b/lib/msun/ld128/k_expl.h index a5668fd..e0a48fc 100644 --- a/lib/msun/ld128/k_expl.h +++ b/lib/msun/ld128/k_expl.h @@ -322,7 +322,7 @@ __ldexp_cexpl(long double complex z, int expt) scale2 = 1; SET_LDBL_EXPSIGN(scale1, BIAS + expt - half_expt); - return (cpackl(cos(y) * exp_x * scale1 * scale2, + return (CMPLXL(cos(y) * exp_x * scale1 * scale2, sinl(y) * exp_x * scale1 * scale2)); } #endif /* _COMPLEX_H */ diff --git a/lib/msun/ld80/e_lgammal_r.c b/lib/msun/ld80/e_lgammal_r.c new file mode 100644 index 0000000..1e65769 --- /dev/null +++ b/lib/msun/ld80/e_lgammal_r.c @@ -0,0 +1,358 @@ +/* @(#)e_lgamma_r.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +/* + * See e_lgamma_r.c for complete comments. + * + * Converted to long double by Steven G. Kargl. + */ + +#ifdef __i386__ +#include <ieeefp.h> +#endif + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" + +static const volatile double vzero = 0; + +static const double +zero= 0, +half= 0.5, +one = 1; + +static const union IEEEl2bits +piu = LD80C(0xc90fdaa22168c235, 1, 3.14159265358979323851e+00L); +#define pi (piu.e) +/* + * Domain y in [0x1p-70, 0.27], range ~[-4.5264e-22, 4.5264e-22]: + * |(lgamma(2 - y) + y / 2) / y - a(y)| < 2**-70.9 + */ +static const union IEEEl2bits +a0u = LD80C(0x9e233f1bed863d26, -4, 7.72156649015328606028e-02L), +a1u = LD80C(0xa51a6625307d3249, -2, 3.22467033424113218889e-01L), +a2u = LD80C(0x89f000d2abafda8c, -4, 6.73523010531979398946e-02L), +a3u = LD80C(0xa8991563eca75f26, -6, 2.05808084277991211934e-02L), +a4u = LD80C(0xf2027e10634ce6b6, -8, 7.38555102796070454026e-03L), +a5u = LD80C(0xbd6eb76dd22187f4, -9, 2.89051035162703932972e-03L), +a6u = LD80C(0x9c562ab05e0458ed, -10, 1.19275351624639999297e-03L), +a7u = LD80C(0x859baed93ee48e46, -11, 5.09674593842117925320e-04L), +a8u = LD80C(0xe9f28a4432949af2, -13, 2.23109648015769155122e-04L), +a9u = LD80C(0xd12ad0d9b93c6bb0, -14, 9.97387167479808509830e-05L), +a10u= LD80C(0xb7522643c78a219b, -15, 4.37071076331030136818e-05L), +a11u= LD80C(0xca024dcdece2cb79, -16, 2.40813493372040143061e-05L), +a12u= LD80C(0xbb90fb6968ebdbf9, -19, 2.79495621083634031729e-06L), +a13u= LD80C(0xba1c9ffeeae07b37, -17, 1.10931287015513924136e-05L); +#define a0 (a0u.e) +#define a1 (a1u.e) +#define a2 (a2u.e) +#define a3 (a3u.e) +#define a4 (a4u.e) +#define a5 (a5u.e) +#define a6 (a6u.e) +#define a7 (a7u.e) +#define a8 (a8u.e) +#define a9 (a9u.e) +#define a10 (a10u.e) +#define a11 (a11u.e) +#define a12 (a12u.e) +#define a13 (a13u.e) +/* + * Domain x in [tc-0.24, tc+0.28], range ~[-6.1205e-22, 6.1205e-22]: + * |(lgamma(x) - tf) - t(x - tc)| < 2**-70.5 + */ +static const union IEEEl2bits +tcu = LD80C(0xbb16c31ab5f1fb71, 0, 1.46163214496836234128e+00L), +tfu = LD80C(0xf8cdcde61c520e0f, -4, -1.21486290535849608093e-01L), +ttu = LD80C(0xd46ee54b27d4de99, -69, -2.81152980996018785880e-21L), +t0u = LD80C(0x80b9406556a62a6b, -68, 3.40728634996055147231e-21L), +t1u = LD80C(0xc7e9c6f6df3f8c39, -67, -1.05833162742737073665e-20L), +t2u = LD80C(0xf7b95e4771c55d51, -2, 4.83836122723810583532e-01L), +t3u = LD80C(0x97213c6e35e119ff, -3, -1.47587722994530691476e-01L), +t4u = LD80C(0x845a14a6a81dc94b, -4, 6.46249402389135358063e-02L), +t5u = LD80C(0x864d46fa89997796, -5, -3.27885410884846056084e-02L), +t6u = LD80C(0x93373cbd00297438, -6, 1.79706751150707171293e-02L), +t7u = LD80C(0xa8fcfca7eddc8d1d, -7, -1.03142230361450732547e-02L), +t8u = LD80C(0xc7e7015ff4bc45af, -8, 6.10053603296546099193e-03L), +t9u = LD80C(0xf178d2247adc5093, -9, -3.68456964904901200152e-03L), +t10u = LD80C(0x94188d58f12e5e9f, -9, 2.25976420273774583089e-03L), +t11u = LD80C(0xb7cbaef14e1406f1, -10, -1.40224943666225639823e-03L), +t12u = LD80C(0xe63a671e6704ea4d, -11, 8.78250640744776944887e-04L), +t13u = LD80C(0x914b6c9cae61783e, -11, -5.54255012657716808811e-04L), +t14u = LD80C(0xb858f5bdb79276fe, -12, 3.51614951536825927370e-04L), +t15u = LD80C(0xea73e744c34b9591, -13, -2.23591563824520112236e-04L), +t16u = LD80C(0x99aeabb0d67ba835, -13, 1.46562869351659194136e-04L), +t17u = LD80C(0xd7c6938325db2024, -14, -1.02889866046435680588e-04L), +t18u = LD80C(0xe24cb1e3b0474775, -15, 5.39540265505221957652e-05L); +#define tc (tcu.e) +#define tf (tfu.e) +#define tt (ttu.e) +#define t0 (t0u.e) +#define t1 (t1u.e) +#define t2 (t2u.e) +#define t3 (t3u.e) +#define t4 (t4u.e) +#define t5 (t5u.e) +#define t6 (t6u.e) +#define t7 (t7u.e) +#define t8 (t8u.e) +#define t9 (t9u.e) +#define t10 (t10u.e) +#define t11 (t11u.e) +#define t12 (t12u.e) +#define t13 (t13u.e) +#define t14 (t14u.e) +#define t15 (t15u.e) +#define t16 (t16u.e) +#define t17 (t17u.e) +#define t18 (t18u.e) +/* + * Domain y in [-0.1, 0.232], range ~[-8.1938e-22, 8.3815e-22]: + * |(lgamma(1 + y) + 0.5 * y) / y - u(y) / v(y)| < 2**-71.2 + */ +static const union IEEEl2bits +u0u = LD80C(0x9e233f1bed863d27, -4, -7.72156649015328606095e-02L), +u1u = LD80C(0x98280ee45e4ddd3d, -1, 5.94361239198682739769e-01L), +u2u = LD80C(0xe330c8ead4130733, 0, 1.77492629495841234275e+00L), +u3u = LD80C(0xd4a213f1a002ec52, 0, 1.66119622514818078064e+00L), +u4u = LD80C(0xa5a9ca6f5bc62163, -1, 6.47122051417476492989e-01L), +u5u = LD80C(0xc980e49cd5b019e6, -4, 9.83903751718671509455e-02L), +u6u = LD80C(0xff636a8bdce7025b, -9, 3.89691687802305743450e-03L), +v1u = LD80C(0xbd109c533a19fbf5, 1, 2.95413883330948556544e+00L), +v2u = LD80C(0xd295cbf96f31f099, 1, 3.29039286955665403176e+00L), +v3u = LD80C(0xdab8bcfee40496cb, 0, 1.70876276441416471410e+00L), +v4u = LD80C(0xd2f2dc3638567e9f, -2, 4.12009126299534668571e-01L), +v5u = LD80C(0xa07d9b0851070f41, -5, 3.91822868305682491442e-02L), +v6u = LD80C(0xe3cd8318f7adb2c4, -11, 8.68998648222144351114e-04L); +#define u0 (u0u.e) +#define u1 (u1u.e) +#define u2 (u2u.e) +#define u3 (u3u.e) +#define u4 (u4u.e) +#define u5 (u5u.e) +#define u6 (u6u.e) +#define v1 (v1u.e) +#define v2 (v2u.e) +#define v3 (v3u.e) +#define v4 (v4u.e) +#define v5 (v5u.e) +#define v6 (v6u.e) +/* + * Domain x in (2, 3], range ~[-3.3648e-22, 3.4416e-22]: + * |(lgamma(y+2) - 0.5 * y) / y - s(y)/r(y)| < 2**-72.3 + * with y = x - 2. + */ +static const union IEEEl2bits +s0u = LD80C(0x9e233f1bed863d27, -4, -7.72156649015328606095e-02L), +s1u = LD80C(0xd3ff0dcc7fa91f94, -3, 2.07027640921219389860e-01L), +s2u = LD80C(0xb2bb62782478ef31, -2, 3.49085881391362090549e-01L), +s3u = LD80C(0xb49f7438c4611a74, -3, 1.76389518704213357954e-01L), +s4u = LD80C(0x9a957008fa27ecf9, -5, 3.77401710862930008071e-02L), +s5u = LD80C(0xda9b389a6ca7a7ac, -9, 3.33566791452943399399e-03L), +s6u = LD80C(0xbc7a2263faf59c14, -14, 8.98728786745638844395e-05L), +r1u = LD80C(0xbf5cff5b11477d4d, 0, 1.49502555796294337722e+00L), +r2u = LD80C(0xd9aec89de08e3da6, -1, 8.50323236984473285866e-01L), +r3u = LD80C(0xeab7ae5057c443f9, -3, 2.29216312078225806131e-01L), +r4u = LD80C(0xf29707d9bd2b1e37, -6, 2.96130326586640089145e-02L), +r5u = LD80C(0xd376c2f09736c5a3, -10, 1.61334161411590662495e-03L), +r6u = LD80C(0xc985983d0cd34e3d, -16, 2.40232770710953450636e-05L), +r7u = LD80C(0xe5c7a4f7fc2ef13d, -25, -5.34997929289167573510e-08L); +#define s0 (s0u.e) +#define s1 (s1u.e) +#define s2 (s2u.e) +#define s3 (s3u.e) +#define s4 (s4u.e) +#define s5 (s5u.e) +#define s6 (s6u.e) +#define r1 (r1u.e) +#define r2 (r2u.e) +#define r3 (r3u.e) +#define r4 (r4u.e) +#define r5 (r5u.e) +#define r6 (r6u.e) +#define r7 (r7u.e) +/* + * Domain z in [8, 0x1p70], range ~[-3.0235e-22, 3.0563e-22]: + * |lgamma(x) - (x - 0.5) * (log(x) - 1) - w(1/x)| < 2**-71.7 + */ +static const union IEEEl2bits +w0u = LD80C(0xd67f1c864beb4a69, -2, 4.18938533204672741776e-01L), +w1u = LD80C(0xaaaaaaaaaaaaaaa1, -4, 8.33333333333333332678e-02L), +w2u = LD80C(0xb60b60b60b5491c9, -9, -2.77777777777760927870e-03L), +w3u = LD80C(0xd00d00cf58aede4c, -11, 7.93650793490637233668e-04L), +w4u = LD80C(0x9c09bf626783d4a5, -11, -5.95238023926039051268e-04L), +w5u = LD80C(0xdca7cadc5baa517b, -11, 8.41733700408000822962e-04L), +w6u = LD80C(0xfb060e361e1ffd07, -10, -1.91515849570245136604e-03L), +w7u = LD80C(0xcbd5101bb58d1f2b, -8, 6.22046743903262649294e-03L), +w8u = LD80C(0xad27a668d32c821b, -6, -2.11370706734662081843e-02L); +#define w0 (w0u.e) +#define w1 (w1u.e) +#define w2 (w2u.e) +#define w3 (w3u.e) +#define w4 (w4u.e) +#define w5 (w5u.e) +#define w6 (w6u.e) +#define w7 (w7u.e) +#define w8 (w8u.e) + +static long double +sin_pil(long double x) +{ + volatile long double vz; + long double y,z; + uint64_t n; + uint16_t hx; + + y = -x; + + vz = y+0x1p63; + z = vz-0x1p63; + if (z == y) + return zero; + + vz = y+0x1p61; + EXTRACT_LDBL80_WORDS(hx,n,vz); + z = vz-0x1p61; + if (z > y) { + z -= 0.25; /* adjust to round down */ + n--; + } + n &= 7; /* octant of y mod 2 */ + y = y - z + n * 0.25; /* y mod 2 */ + + switch (n) { + case 0: y = __kernel_sinl(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cosl(pi*(0.5-y),zero); break; + case 3: + case 4: y = __kernel_sinl(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cosl(pi*(y-1.5),zero); break; + default: y = __kernel_sinl(pi*(y-2.0),zero,0); break; + } + return -y; +} + +long double +lgammal_r(long double x, int *signgamp) +{ + long double nadj,p,p1,p2,p3,q,r,t,w,y,z; + uint64_t lx; + int i; + uint16_t hx,ix; + + EXTRACT_LDBL80_WORDS(hx,lx,x); + + /* purge +-Inf and NaNs */ + *signgamp = 1; + ix = hx&0x7fff; + if(ix==0x7fff) return x*x; + + ENTERI(); + + /* purge +-0 and tiny arguments */ + *signgamp = 1-2*(hx>>15); + if(ix<0x3fff-67) { /* |x|<2**-(p+3), return -log(|x|) */ + if((ix|lx)==0) + RETURNI(one/vzero); + RETURNI(-logl(fabsl(x))); + } + + /* purge negative integers and start evaluation for other x < 0 */ + if(hx&0x8000) { + *signgamp = 1; + if(ix>=0x3fff+63) /* |x|>=2**(p-1), must be -integer */ + RETURNI(one/vzero); + t = sin_pil(x); + if(t==zero) RETURNI(one/vzero); /* -integer */ + nadj = logl(pi/fabsl(t*x)); + if(t<zero) *signgamp = -1; + x = -x; + } + + /* purge 1 and 2 */ + if((ix==0x3fff || ix==0x4000) && lx==0x8000000000000000ULL) r = 0; + /* for x < 2.0 */ + else if(ix<0x4000) { + /* + * XXX Supposedly, one can use the following information to replace the + * XXX FP rational expressions. A similar approach is appropriate + * XXX for ld128, but one (may need?) needs to consider llx, too. + * + * 8.9999961853027344e-01 3ffe e666600000000000 + * 7.3159980773925781e-01 3ffe bb4a200000000000 + * 2.3163998126983643e-01 3ffc ed33080000000000 + * 1.7316312789916992e+00 3fff dda6180000000000 + * 1.2316322326660156e+00 3fff 9da6200000000000 + */ + if(x<8.9999961853027344e-01) { + r = -logl(x); + if(x>=7.3159980773925781e-01) {y = 1-x; i= 0;} + else if(x>=2.3163998126983643e-01) {y= x-(tc-1); i=1;} + else {y = x; i=2;} + } else { + r = 0; + if(x>=1.7316312789916992e+00) {y=2-x;i=0;} + else if(x>=1.2316322326660156e+00) {y=x-tc;i=1;} + else {y=x-1;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*(a10+z*a12))))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*(a11+z*a13)))))); + p = y*p1+p2; + r += p-y/2; break; + case 1: + p = t0+y*t1+tt+y*y*(t2+y*(t3+y*(t4+y*(t5+y*(t6+y*(t7+y*(t8+ + y*(t9+y*(t10+y*(t11+y*(t12+y*(t13+y*(t14+y*(t15+y*(t16+ + y*(t17+y*t18)))))))))))))))); + r += tf + p; break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*(u5+y*u6)))))); + p2 = 1+y*(v1+y*(v2+y*(v3+y*(v4+y*(v5+y*v6))))); + r += p1/p2-y/2; + } + } + /* x < 8.0 */ + else if(ix<0x4002) { + i = x; + y = x-i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = 1+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*(r6+y*r7)))))); + r = y/2+p/q; + z = 1; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+6); /* FALLTHRU */ + case 6: z *= (y+5); /* FALLTHRU */ + case 5: z *= (y+4); /* FALLTHRU */ + case 4: z *= (y+3); /* FALLTHRU */ + case 3: z *= (y+2); /* FALLTHRU */ + r += logl(z); break; + } + /* 8.0 <= x < 2**(p+3) */ + } else if (ix<0x3fff+67) { + t = logl(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*(w6+y*(w7+y*w8))))))); + r = (x-half)*(t-one)+w; + /* 2**(p+3) <= x <= inf */ + } else + r = x*(logl(x)-1); + if(hx&0x8000) r = nadj - r; + RETURNI(r); +} diff --git a/lib/msun/ld80/k_expl.h b/lib/msun/ld80/k_expl.h index ebfb9a8..9b081fa 100644 --- a/lib/msun/ld80/k_expl.h +++ b/lib/msun/ld80/k_expl.h @@ -299,7 +299,7 @@ __ldexp_cexpl(long double complex z, int expt) scale2 = 1; SET_LDBL_EXPSIGN(scale1, BIAS + expt - half_expt); - return (cpackl(cos(y) * exp_x * scale1 * scale2, + return (CMPLXL(cos(y) * exp_x * scale1 * scale2, sinl(y) * exp_x * scale1 * scale2)); } #endif /* _COMPLEX_H */ diff --git a/lib/msun/man/j0.3 b/lib/msun/man/j0.3 index 91849da..7e1b790 100644 --- a/lib/msun/man/j0.3 +++ b/lib/msun/man/j0.3 @@ -28,7 +28,7 @@ .\" from: @(#)j0.3 6.7 (Berkeley) 4/19/91 .\" $FreeBSD$ .\" -.Dd February 18, 2008 +.Dd March 10, 2015 .Dt J0 3 .Os .Sh NAME @@ -77,24 +77,17 @@ The functions .Fn j0 , .Fn j0f , -.Fn j1 +.Fn j1 , and .Fn j1f -compute the -.Em Bessel function of the first kind of the order -0 and the -.Em order -1, respectively, -for the -real value +compute the Bessel function of the first kind of orders +0 and 1 for the real value .Fa x ; the functions .Fn jn and .Fn jnf -compute the -.Em Bessel function of the first kind of the integer -.Em order +compute the Bessel function of the first kind of the integer order .Fa n for the real value .Fa x . @@ -105,13 +98,8 @@ The functions .Fn y1 , and .Fn y1f -compute the linearly independent -.Em Bessel function of the second kind of the order -0 and the -.Em order -1, respectively, -for the -positive +compute the linearly independent Bessel function of the second kind +of orders 0 and 1 for the positive .Em real value .Fa x ; @@ -119,9 +107,7 @@ the functions .Fn yn and .Fn ynf -compute the -.Em Bessel function of the second kind for the integer -.Em order +compute the Bessel function of the second kind for the integer order .Fa n for the positive .Em real @@ -141,11 +127,20 @@ and .Fn ynf . If .Fa x -is negative, these routines will generate an invalid exception and -return \*(Na. +is negative, including -\*(If, these routines will generate an invalid +exception and return \*(Na. +If +.Fa x +is \*(Pm0, these routines +will generate a divide-by-zero exception and return -\*(If. If .Fa x -is 0 or a sufficiently small positive number, these routines +is a sufficiently small positive number, then +.Fn y1 , +.Fn y1f , +.Fn yn , +and +.Fn ynf will generate an overflow exception and return -\*(If. .Sh SEE ALSO .Xr math 3 diff --git a/lib/msun/man/lgamma.3 b/lib/msun/man/lgamma.3 index ea6eb6f..d244722 100644 --- a/lib/msun/man/lgamma.3 +++ b/lib/msun/man/lgamma.3 @@ -28,7 +28,7 @@ .\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92 .\" $FreeBSD$ .\" -.Dd January 14, 2005 +.Dd September 12, 2014 .Dt LGAMMA 3 .Os .Sh NAME @@ -36,6 +36,8 @@ .Nm lgamma_r , .Nm lgammaf , .Nm lgammaf_r , +.Nm lgammal , +.Nm lgammal_r , .Nm gamma , .Nm gamma_r , .Nm gammaf , @@ -58,6 +60,10 @@ .Fn lgammaf "float x" .Ft float .Fn lgammaf_r "float x" "int *signgamp" +.Ft "long double" +.Fn lgammal "long double x" +.Ft "long double" +.Fn lgammal_r "long double x" "int *signgamp" .Ft double .Fn gamma "double x" .Ft double @@ -66,14 +72,15 @@ .Fn gammaf "float x" .Ft float .Fn gammaf_r "float x" "int *signgamp" -.Ft double +.Ft "long double" .Fn tgamma "double x" .Ft float .Fn tgammaf "float x" .Sh DESCRIPTION -.Fn lgamma x +.Fn lgamma x , +.Fn lgammaf x , and -.Fn lgammaf x +.Fn lgammal x .if t \{\ return ln\||\(*G(x)| where .Bd -unfilled -offset indent @@ -87,13 +94,15 @@ The external integer .Fa signgam returns the sign of \(*G(x). .Pp -.Fn lgamma_r x signgamp +.Fn lgamma_r x signgamp , +.Fn lgammaf_r x signgamp , and -.Fn lgammaf_r x signgamp +.Fn lgammal_r x signgamp provide the same functionality as -.Fn lgamma x +.Fn lgamma x , +.Fn lgammaf x , and -.Fn lgammaf x +.Fn lgammal x , but the caller must provide an integer to store the sign of \(*G(x). .Pp The @@ -115,6 +124,7 @@ are deprecated aliases for and .Fn lgammaf_r , respectively. + .Sh IDIOSYNCRASIES Do not use the expression .Dq Li signgam\(**exp(lgamma(x)) @@ -139,14 +149,18 @@ Exponentiation of will lose up to 10 significant bits. .Sh RETURN VALUES .Fn gamma , -.Fn gamma_r , .Fn gammaf , +.Fn gammal , +.Fn gamma_r , .Fn gammaf_r , +.Fn gammal_r , .Fn lgamma , -.Fn lgamma_r , .Fn lgammaf , +.Fn lgammal , +.Fn lgamma_r , +.Fn lgammaf_r , and -.Fn lgammaf_r +.Fn lgammal_r return appropriate values unless an argument is out of range. Overflow will occur for sufficiently large positive values, and non-positive integers. @@ -159,6 +173,7 @@ will underflow. The .Fn lgamma , .Fn lgammaf , +.Fn lgammal , .Fn tgamma , and .Fn tgammaf diff --git a/lib/msun/src/catrig.c b/lib/msun/src/catrig.c index 200977c..c0f5f55 100644 --- a/lib/msun/src/catrig.c +++ b/lib/msun/src/catrig.c @@ -286,19 +286,19 @@ casinh(double complex z) if (isnan(x) || isnan(y)) { /* casinh(+-Inf + I*NaN) = +-Inf + I*NaN */ if (isinf(x)) - return (cpack(x, y + y)); + return (CMPLX(x, y + y)); /* casinh(NaN + I*+-Inf) = opt(+-)Inf + I*NaN */ if (isinf(y)) - return (cpack(y, x + x)); + return (CMPLX(y, x + x)); /* casinh(NaN + I*0) = NaN + I*0 */ if (y == 0) - return (cpack(x + x, y)); + return (CMPLX(x + x, y)); /* * All other cases involving NaN return NaN + I*NaN. * C99 leaves it optional whether to raise invalid if one of * the arguments is not NaN, so we opt not to raise it. */ - return (cpack(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); + return (CMPLX(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); } if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) { @@ -307,7 +307,7 @@ casinh(double complex z) w = clog_for_large_values(z) + m_ln2; else w = clog_for_large_values(-z) + m_ln2; - return (cpack(copysign(creal(w), x), copysign(cimag(w), y))); + return (CMPLX(copysign(creal(w), x), copysign(cimag(w), y))); } /* Avoid spuriously raising inexact for z = 0. */ @@ -325,7 +325,7 @@ casinh(double complex z) ry = asin(B); else ry = atan2(new_y, sqrt_A2my2); - return (cpack(copysign(rx, x), copysign(ry, y))); + return (CMPLX(copysign(rx, x), copysign(ry, y))); } /* @@ -335,9 +335,9 @@ casinh(double complex z) double complex casin(double complex z) { - double complex w = casinh(cpack(cimag(z), creal(z))); + double complex w = casinh(CMPLX(cimag(z), creal(z))); - return (cpack(cimag(w), creal(w))); + return (CMPLX(cimag(w), creal(w))); } /* @@ -370,19 +370,19 @@ cacos(double complex z) if (isnan(x) || isnan(y)) { /* cacos(+-Inf + I*NaN) = NaN + I*opt(-)Inf */ if (isinf(x)) - return (cpack(y + y, -INFINITY)); + return (CMPLX(y + y, -INFINITY)); /* cacos(NaN + I*+-Inf) = NaN + I*-+Inf */ if (isinf(y)) - return (cpack(x + x, -y)); + return (CMPLX(x + x, -y)); /* cacos(0 + I*NaN) = PI/2 + I*NaN with inexact */ if (x == 0) - return (cpack(pio2_hi + pio2_lo, y + y)); + return (CMPLX(pio2_hi + pio2_lo, y + y)); /* * All other cases involving NaN return NaN + I*NaN. * C99 leaves it optional whether to raise invalid if one of * the arguments is not NaN, so we opt not to raise it. */ - return (cpack(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); + return (CMPLX(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); } if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) { @@ -392,18 +392,18 @@ cacos(double complex z) ry = creal(w) + m_ln2; if (sy == 0) ry = -ry; - return (cpack(rx, ry)); + return (CMPLX(rx, ry)); } /* Avoid spuriously raising inexact for z = 1. */ if (x == 1 && y == 0) - return (cpack(0, -y)); + return (CMPLX(0, -y)); /* All remaining cases are inexact. */ raise_inexact(); if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4) - return (cpack(pio2_hi - (x - pio2_lo), -y)); + return (CMPLX(pio2_hi - (x - pio2_lo), -y)); do_hard_work(ay, ax, &ry, &B_is_usable, &B, &sqrt_A2mx2, &new_x); if (B_is_usable) { @@ -419,7 +419,7 @@ cacos(double complex z) } if (sy == 0) ry = -ry; - return (cpack(rx, ry)); + return (CMPLX(rx, ry)); } /* @@ -437,15 +437,15 @@ cacosh(double complex z) ry = cimag(w); /* cacosh(NaN + I*NaN) = NaN + I*NaN */ if (isnan(rx) && isnan(ry)) - return (cpack(ry, rx)); + return (CMPLX(ry, rx)); /* cacosh(NaN + I*+-Inf) = +Inf + I*NaN */ /* cacosh(+-Inf + I*NaN) = +Inf + I*NaN */ if (isnan(rx)) - return (cpack(fabs(ry), rx)); + return (CMPLX(fabs(ry), rx)); /* cacosh(0 + I*NaN) = NaN + I*NaN */ if (isnan(ry)) - return (cpack(ry, ry)); - return (cpack(fabs(ry), copysign(rx, cimag(z)))); + return (CMPLX(ry, ry)); + return (CMPLX(fabs(ry), copysign(rx, cimag(z)))); } /* @@ -475,16 +475,16 @@ clog_for_large_values(double complex z) * this method is still poor since it is uneccessarily slow. */ if (ax > DBL_MAX / 2) - return (cpack(log(hypot(x / m_e, y / m_e)) + 1, atan2(y, x))); + return (CMPLX(log(hypot(x / m_e, y / m_e)) + 1, atan2(y, x))); /* * Avoid overflow when x or y is large. Avoid underflow when x or * y is small. */ if (ax > QUARTER_SQRT_MAX || ay < SQRT_MIN) - return (cpack(log(hypot(x, y)), atan2(y, x))); + return (CMPLX(log(hypot(x, y)), atan2(y, x))); - return (cpack(log(ax * ax + ay * ay) / 2, atan2(y, x))); + return (CMPLX(log(ax * ax + ay * ay) / 2, atan2(y, x))); } /* @@ -575,30 +575,30 @@ catanh(double complex z) /* This helps handle many cases. */ if (y == 0 && ax <= 1) - return (cpack(atanh(x), y)); + return (CMPLX(atanh(x), y)); /* To ensure the same accuracy as atan(), and to filter out z = 0. */ if (x == 0) - return (cpack(x, atan(y))); + return (CMPLX(x, atan(y))); if (isnan(x) || isnan(y)) { /* catanh(+-Inf + I*NaN) = +-0 + I*NaN */ if (isinf(x)) - return (cpack(copysign(0, x), y + y)); + return (CMPLX(copysign(0, x), y + y)); /* catanh(NaN + I*+-Inf) = sign(NaN)0 + I*+-PI/2 */ if (isinf(y)) - return (cpack(copysign(0, x), + return (CMPLX(copysign(0, x), copysign(pio2_hi + pio2_lo, y))); /* * All other cases involving NaN return NaN + I*NaN. * C99 leaves it optional whether to raise invalid if one of * the arguments is not NaN, so we opt not to raise it. */ - return (cpack(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); + return (CMPLX(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); } if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) - return (cpack(real_part_reciprocal(x, y), + return (CMPLX(real_part_reciprocal(x, y), copysign(pio2_hi + pio2_lo, y))); if (ax < SQRT_3_EPSILON / 2 && ay < SQRT_3_EPSILON / 2) { @@ -623,7 +623,7 @@ catanh(double complex z) else ry = atan2(2 * ay, (1 - ax) * (1 + ax) - ay * ay) / 2; - return (cpack(copysign(rx, x), copysign(ry, y))); + return (CMPLX(copysign(rx, x), copysign(ry, y))); } /* @@ -633,7 +633,7 @@ catanh(double complex z) double complex catan(double complex z) { - double complex w = catanh(cpack(cimag(z), creal(z))); + double complex w = catanh(CMPLX(cimag(z), creal(z))); - return (cpack(cimag(w), creal(w))); + return (CMPLX(cimag(w), creal(w))); } diff --git a/lib/msun/src/catrigf.c b/lib/msun/src/catrigf.c index 08ebef7..ca84ce2 100644 --- a/lib/msun/src/catrigf.c +++ b/lib/msun/src/catrigf.c @@ -156,12 +156,12 @@ casinhf(float complex z) if (isnan(x) || isnan(y)) { if (isinf(x)) - return (cpackf(x, y + y)); + return (CMPLXF(x, y + y)); if (isinf(y)) - return (cpackf(y, x + x)); + return (CMPLXF(y, x + x)); if (y == 0) - return (cpackf(x + x, y)); - return (cpackf(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); + return (CMPLXF(x + x, y)); + return (CMPLXF(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); } if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) { @@ -169,7 +169,7 @@ casinhf(float complex z) w = clog_for_large_values(z) + m_ln2; else w = clog_for_large_values(-z) + m_ln2; - return (cpackf(copysignf(crealf(w), x), + return (CMPLXF(copysignf(crealf(w), x), copysignf(cimagf(w), y))); } @@ -186,15 +186,15 @@ casinhf(float complex z) ry = asinf(B); else ry = atan2f(new_y, sqrt_A2my2); - return (cpackf(copysignf(rx, x), copysignf(ry, y))); + return (CMPLXF(copysignf(rx, x), copysignf(ry, y))); } float complex casinf(float complex z) { - float complex w = casinhf(cpackf(cimagf(z), crealf(z))); + float complex w = casinhf(CMPLXF(cimagf(z), crealf(z))); - return (cpackf(cimagf(w), crealf(w))); + return (CMPLXF(cimagf(w), crealf(w))); } float complex @@ -214,12 +214,12 @@ cacosf(float complex z) if (isnan(x) || isnan(y)) { if (isinf(x)) - return (cpackf(y + y, -INFINITY)); + return (CMPLXF(y + y, -INFINITY)); if (isinf(y)) - return (cpackf(x + x, -y)); + return (CMPLXF(x + x, -y)); if (x == 0) - return (cpackf(pio2_hi + pio2_lo, y + y)); - return (cpackf(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); + return (CMPLXF(pio2_hi + pio2_lo, y + y)); + return (CMPLXF(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); } if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) { @@ -228,16 +228,16 @@ cacosf(float complex z) ry = crealf(w) + m_ln2; if (sy == 0) ry = -ry; - return (cpackf(rx, ry)); + return (CMPLXF(rx, ry)); } if (x == 1 && y == 0) - return (cpackf(0, -y)); + return (CMPLXF(0, -y)); raise_inexact(); if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4) - return (cpackf(pio2_hi - (x - pio2_lo), -y)); + return (CMPLXF(pio2_hi - (x - pio2_lo), -y)); do_hard_work(ay, ax, &ry, &B_is_usable, &B, &sqrt_A2mx2, &new_x); if (B_is_usable) { @@ -253,7 +253,7 @@ cacosf(float complex z) } if (sy == 0) ry = -ry; - return (cpackf(rx, ry)); + return (CMPLXF(rx, ry)); } float complex @@ -266,12 +266,12 @@ cacoshf(float complex z) rx = crealf(w); ry = cimagf(w); if (isnan(rx) && isnan(ry)) - return (cpackf(ry, rx)); + return (CMPLXF(ry, rx)); if (isnan(rx)) - return (cpackf(fabsf(ry), rx)); + return (CMPLXF(fabsf(ry), rx)); if (isnan(ry)) - return (cpackf(ry, ry)); - return (cpackf(fabsf(ry), copysignf(rx, cimagf(z)))); + return (CMPLXF(ry, ry)); + return (CMPLXF(fabsf(ry), copysignf(rx, cimagf(z)))); } static float complex @@ -291,13 +291,13 @@ clog_for_large_values(float complex z) } if (ax > FLT_MAX / 2) - return (cpackf(logf(hypotf(x / m_e, y / m_e)) + 1, + return (CMPLXF(logf(hypotf(x / m_e, y / m_e)) + 1, atan2f(y, x))); if (ax > QUARTER_SQRT_MAX || ay < SQRT_MIN) - return (cpackf(logf(hypotf(x, y)), atan2f(y, x))); + return (CMPLXF(logf(hypotf(x, y)), atan2f(y, x))); - return (cpackf(logf(ax * ax + ay * ay) / 2, atan2f(y, x))); + return (CMPLXF(logf(ax * ax + ay * ay) / 2, atan2f(y, x))); } static inline float @@ -346,22 +346,22 @@ catanhf(float complex z) ay = fabsf(y); if (y == 0 && ax <= 1) - return (cpackf(atanhf(x), y)); + return (CMPLXF(atanhf(x), y)); if (x == 0) - return (cpackf(x, atanf(y))); + return (CMPLXF(x, atanf(y))); if (isnan(x) || isnan(y)) { if (isinf(x)) - return (cpackf(copysignf(0, x), y + y)); + return (CMPLXF(copysignf(0, x), y + y)); if (isinf(y)) - return (cpackf(copysignf(0, x), + return (CMPLXF(copysignf(0, x), copysignf(pio2_hi + pio2_lo, y))); - return (cpackf(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); + return (CMPLXF(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); } if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) - return (cpackf(real_part_reciprocal(x, y), + return (CMPLXF(real_part_reciprocal(x, y), copysignf(pio2_hi + pio2_lo, y))); if (ax < SQRT_3_EPSILON / 2 && ay < SQRT_3_EPSILON / 2) { @@ -381,13 +381,13 @@ catanhf(float complex z) else ry = atan2f(2 * ay, (1 - ax) * (1 + ax) - ay * ay) / 2; - return (cpackf(copysignf(rx, x), copysignf(ry, y))); + return (CMPLXF(copysignf(rx, x), copysignf(ry, y))); } float complex catanf(float complex z) { - float complex w = catanhf(cpackf(cimagf(z), crealf(z))); + float complex w = catanhf(CMPLXF(cimagf(z), crealf(z))); - return (cpackf(cimagf(w), crealf(w))); + return (CMPLXF(cimagf(w), crealf(w))); } diff --git a/lib/msun/src/e_j0.c b/lib/msun/src/e_j0.c index 8320f25..a253ed1 100644 --- a/lib/msun/src/e_j0.c +++ b/lib/msun/src/e_j0.c @@ -62,7 +62,9 @@ __FBSDID("$FreeBSD$"); #include "math.h" #include "math_private.h" -static double pzero(double), qzero(double); +static __inline double pzero(double), qzero(double); + +static const volatile double vone = 1, vzero = 0; static const double huge = 1e300, @@ -115,7 +117,7 @@ __ieee754_j0(double x) 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; + else return one - x*x/4; } } z = x*x; @@ -150,10 +152,16 @@ __ieee754_y0(double x) EXTRACT_WORDS(hx,lx,x); ix = 0x7fffffff&hx; - /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ - if(ix>=0x7ff00000) return one/(x+x*x); - if((ix|lx)==0) return -one/zero; - if(hx<0) return zero/zero; + /* + * y0(NaN) = NaN. + * y0(Inf) = 0. + * y0(-Inf) = NaN and raise invalid exception. + */ + if(ix>=0x7ff00000) return vone/(x+x*x); + /* y0(+-0) = -inf and raise divide-by-zero exception. */ + if((ix|lx)==0) return -one/vzero; + /* y0(x<0) = NaN and raise invalid exception. */ + if(hx<0) return vzero/vzero; 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 @@ -268,7 +276,8 @@ static const double pS2[5] = { 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ }; - static double pzero(double x) +static __inline double +pzero(double x) { const double *p,*q; double z,r,s; @@ -278,7 +287,7 @@ static const double pS2[5] = { if(ix>=0x40200000) {p = pR8; q= pS8;} else if(ix>=0x40122E8B){p = pR5; q= pS5;} else if(ix>=0x4006DB6D){p = pR3; q= pS3;} - else if(ix>=0x40000000){p = pR2; q= pS2;} + else {p = pR2; q= pS2;} /* ix>=0x40000000 */ 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])))); @@ -363,7 +372,8 @@ static const double qS2[6] = { -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ }; - static double qzero(double x) +static __inline double +qzero(double x) { const double *p,*q; double s,r,z; @@ -373,7 +383,7 @@ static const double qS2[6] = { if(ix>=0x40200000) {p = qR8; q= qS8;} else if(ix>=0x40122E8B){p = qR5; q= qS5;} else if(ix>=0x4006DB6D){p = qR3; q= qS3;} - else if(ix>=0x40000000){p = qR2; q= qS2;} + else {p = qR2; q= qS2;} /* ix>=0x40000000 */ 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]))))); diff --git a/lib/msun/src/e_j0f.c b/lib/msun/src/e_j0f.c index c45faf3..3e2f7e8 100644 --- a/lib/msun/src/e_j0f.c +++ b/lib/msun/src/e_j0f.c @@ -16,10 +16,16 @@ #include <sys/cdefs.h> __FBSDID("$FreeBSD$"); +/* + * See e_j0.c for complete comments. + */ + #include "math.h" #include "math_private.h" -static float pzerof(float), qzerof(float); +static __inline float pzerof(float), qzerof(float); + +static const volatile float vone = 1, vzero = 0; static const float huge = 1e30, @@ -62,17 +68,17 @@ __ieee754_j0f(float x) * 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); + if(ix>0x58000000) z = (invsqrtpi*cc)/sqrtf(x); /* |x|>2**49 */ else { u = pzerof(x); v = qzerof(x); z = invsqrtpi*(u*cc-v*ss)/sqrtf(x); } return z; } - if(ix<0x39000000) { /* |x| < 2**-13 */ + if(ix<0x3b000000) { /* |x| < 2**-9 */ 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; + if(ix<0x39800000) return one; /* |x|<2**-12 */ + else return one - x*x/4; } } z = x*x; @@ -107,10 +113,9 @@ __ieee754_y0f(float x) 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>=0x7f800000) return vone/(x+x*x); + if(ix==0) return -one/vzero; + if(hx<0) return vzero/vzero; 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 @@ -136,14 +141,14 @@ __ieee754_y0f(float x) if ((s*c)<zero) cc = z/ss; else ss = z/cc; } - if(ix>0x80000000) z = (invsqrtpi*ss)/sqrtf(x); + if(ix>0x58000000) z = (invsqrtpi*ss)/sqrtf(x); /* |x|>2**49 */ else { u = pzerof(x); v = qzerof(x); z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); } return z; } - if(ix<=0x32000000) { /* x < 2**-27 */ + if(ix<=0x39000000) { /* x < 2**-13 */ return(u00 + tpi*__ieee754_logf(x)); } z = x*x; @@ -224,7 +229,8 @@ static const float pS2[5] = { 1.4657617569e+01, /* 0x416a859a */ }; - static float pzerof(float x) +static __inline float +pzerof(float x) { const float *p,*q; float z,r,s; @@ -232,9 +238,9 @@ static const float pS2[5] = { 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 if(ix>=0x40000000){p = pR2; q= pS2;} + else if(ix>=0x409173eb){p = pR5; q= pS5;} + else if(ix>=0x4036d917){p = pR3; q= pS3;} + else {p = pR2; q= pS2;} /* ix>=0x40000000 */ 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])))); @@ -319,7 +325,8 @@ static const float qS2[6] = { -5.3109550476e+00, /* 0xc0a9f358 */ }; - static float qzerof(float x) +static __inline float +qzerof(float x) { const float *p,*q; float s,r,z; @@ -327,9 +334,9 @@ static const float qS2[6] = { 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 if(ix>=0x40000000){p = qR2; q= qS2;} + else if(ix>=0x409173eb){p = qR5; q= qS5;} + else if(ix>=0x4036d917){p = qR3; q= qS3;} + else {p = qR2; q= qS2;} /* ix>=0x40000000 */ 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]))))); diff --git a/lib/msun/src/e_j1.c b/lib/msun/src/e_j1.c index 63800ad..74a7c69 100644 --- a/lib/msun/src/e_j1.c +++ b/lib/msun/src/e_j1.c @@ -62,7 +62,9 @@ __FBSDID("$FreeBSD$"); #include "math.h" #include "math_private.h" -static double pone(double), qone(double); +static __inline double pone(double), qone(double); + +static const volatile double vone = 1, vzero = 0; static const double huge = 1e300, @@ -147,10 +149,16 @@ __ieee754_y1(double x) EXTRACT_WORDS(hx,lx,x); ix = 0x7fffffff&hx; - /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ - if(ix>=0x7ff00000) return one/(x+x*x); - if((ix|lx)==0) return -one/zero; - if(hx<0) return zero/zero; + /* + * y1(NaN) = NaN. + * y1(Inf) = 0. + * y1(-Inf) = NaN and raise invalid exception. + */ + if(ix>=0x7ff00000) return vone/(x+x*x); + /* y1(+-0) = -inf and raise divide-by-zero exception. */ + if((ix|lx)==0) return -one/vzero; + /* y1(x<0) = NaN and raise invalid exception. */ + if(hx<0) return vzero/vzero; if(ix >= 0x40000000) { /* |x| >= 2.0 */ s = sin(x); c = cos(x); @@ -262,7 +270,8 @@ static const double ps2[5] = { 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ }; - static double pone(double x) +static __inline double +pone(double x) { const double *p,*q; double z,r,s; @@ -272,7 +281,7 @@ static const double ps2[5] = { if(ix>=0x40200000) {p = pr8; q= ps8;} else if(ix>=0x40122E8B){p = pr5; q= ps5;} else if(ix>=0x4006DB6D){p = pr3; q= ps3;} - else if(ix>=0x40000000){p = pr2; q= ps2;} + else {p = pr2; q= ps2;} /* ix>=0x40000000 */ 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])))); @@ -358,7 +367,8 @@ static const double qs2[6] = { -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ }; - static double qone(double x) +static __inline double +qone(double x) { const double *p,*q; double s,r,z; @@ -368,7 +378,7 @@ static const double qs2[6] = { if(ix>=0x40200000) {p = qr8; q= qs8;} else if(ix>=0x40122E8B){p = qr5; q= qs5;} else if(ix>=0x4006DB6D){p = qr3; q= qs3;} - else if(ix>=0x40000000){p = qr2; q= qs2;} + else {p = qr2; q= qs2;} /* ix>=0x40000000 */ 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]))))); diff --git a/lib/msun/src/e_j1f.c b/lib/msun/src/e_j1f.c index 88e2d83..ec7f381 100644 --- a/lib/msun/src/e_j1f.c +++ b/lib/msun/src/e_j1f.c @@ -16,10 +16,16 @@ #include <sys/cdefs.h> __FBSDID("$FreeBSD$"); +/* + * See e_j1.c for complete comments. + */ + #include "math.h" #include "math_private.h" -static float ponef(float), qonef(float); +static __inline float ponef(float), qonef(float); + +static const volatile float vone = 1, vzero = 0; static const float huge = 1e30, @@ -63,7 +69,7 @@ __ieee754_j1f(float x) * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) */ - if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(y); + if(ix>0x58000000) z = (invsqrtpi*cc)/sqrtf(y); /* |x|>2**49 */ else { u = ponef(y); v = qonef(y); z = invsqrtpi*(u*cc-v*ss)/sqrtf(y); @@ -71,7 +77,7 @@ __ieee754_j1f(float x) if(hx<0) return -z; else return z; } - if(ix<0x32000000) { /* |x|<2**-27 */ + if(ix<0x39000000) { /* |x|<2**-13 */ if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */ } z = x*x; @@ -104,10 +110,9 @@ __ieee754_y1f(float x) GET_FLOAT_WORD(hx,x); ix = 0x7fffffff&hx; - /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(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>=0x7f800000) return vone/(x+x*x); + if(ix==0) return -one/vzero; + if(hx<0) return vzero/vzero; if(ix >= 0x40000000) { /* |x| >= 2.0 */ s = sinf(x); c = cosf(x); @@ -129,14 +134,14 @@ __ieee754_y1f(float x) * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) * to compute the worse one. */ - if(ix>0x48000000) z = (invsqrtpi*ss)/sqrtf(x); + if(ix>0x58000000) z = (invsqrtpi*ss)/sqrtf(x); /* |x|>2**49 */ else { u = ponef(x); v = qonef(x); z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); } return z; } - if(ix<=0x24800000) { /* x < 2**-54 */ + if(ix<=0x33000000) { /* x < 2**-25 */ return(-tpi/x); } z = x*x; @@ -219,7 +224,8 @@ static const float ps2[5] = { 8.3646392822e+00, /* 0x4105d590 */ }; - static float ponef(float x) +static __inline float +ponef(float x) { const float *p,*q; float z,r,s; @@ -227,9 +233,9 @@ static const float ps2[5] = { 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 if(ix>=0x40000000){p = pr2; q= ps2;} + else if(ix>=0x409173eb){p = pr5; q= ps5;} + else if(ix>=0x4036d917){p = pr3; q= ps3;} + else {p = pr2; q= ps2;} /* ix>=0x40000000 */ 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])))); @@ -315,17 +321,18 @@ static const float qs2[6] = { -4.9594988823e+00, /* 0xc09eb437 */ }; - static float qonef(float x) +static __inline float +qonef(float x) { const float *p,*q; float s,r,z; int32_t ix; GET_FLOAT_WORD(ix,x); ix &= 0x7fffffff; - if(ix>=0x40200000) {p = qr8; q= qs8;} - else if(ix>=0x40f71c58){p = qr5; q= qs5;} - else if(ix>=0x4036db68){p = qr3; q= qs3;} - else if(ix>=0x40000000){p = qr2; q= qs2;} + if(ix>=0x41000000) {p = qr8; q= qs8;} + else if(ix>=0x409173eb){p = qr5; q= qs5;} + else if(ix>=0x4036d917){p = qr3; q= qs3;} + else {p = qr2; q= qs2;} /* ix>=0x40000000 */ 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]))))); diff --git a/lib/msun/src/e_jn.c b/lib/msun/src/e_jn.c index 8b0bc62..eefd4ff 100644 --- a/lib/msun/src/e_jn.c +++ b/lib/msun/src/e_jn.c @@ -43,6 +43,8 @@ __FBSDID("$FreeBSD$"); #include "math.h" #include "math_private.h" +static const volatile double vone = 1, vzero = 0; + static const double invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ @@ -220,10 +222,12 @@ __ieee754_yn(int n, double x) EXTRACT_WORDS(hx,lx,x); ix = 0x7fffffff&hx; - /* if Y(n,NaN) is NaN */ + /* yn(n,NaN) = NaN */ if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; - if((ix|lx)==0) return -one/zero; - if(hx<0) return zero/zero; + /* yn(n,+-0) = -inf and raise divide-by-zero exception. */ + if((ix|lx)==0) return -one/vzero; + /* yn(n,x<0) = NaN and raise invalid exception. */ + if(hx<0) return vzero/vzero; sign = 1; if(n<0){ n = -n; diff --git a/lib/msun/src/e_jnf.c b/lib/msun/src/e_jnf.c index f564aec..965feeb 100644 --- a/lib/msun/src/e_jnf.c +++ b/lib/msun/src/e_jnf.c @@ -16,9 +16,15 @@ #include <sys/cdefs.h> __FBSDID("$FreeBSD$"); +/* + * See e_jn.c for complete comments. + */ + #include "math.h" #include "math_private.h" +static const volatile float vone = 1, vzero = 0; + static const float two = 2.0000000000e+00, /* 0x40000000 */ one = 1.0000000000e+00; /* 0x3F800000 */ @@ -172,10 +178,9 @@ __ieee754_ynf(int n, float x) GET_FLOAT_WORD(hx,x); ix = 0x7fffffff&hx; - /* if Y(n,NaN) is NaN */ if(ix>0x7f800000) return x+x; - if(ix==0) return -one/zero; - if(hx<0) return zero/zero; + if(ix==0) return -one/vzero; + if(hx<0) return vzero/vzero; sign = 1; if(n<0){ n = -n; diff --git a/lib/msun/src/e_lgamma.c b/lib/msun/src/e_lgamma.c index 4674d9b..43f5175 100644 --- a/lib/msun/src/e_lgamma.c +++ b/lib/msun/src/e_lgamma.c @@ -21,6 +21,8 @@ __FBSDID("$FreeBSD$"); * Method: call __ieee754_lgamma_r */ +#include <float.h> + #include "math.h" #include "math_private.h" @@ -31,3 +33,7 @@ __ieee754_lgamma(double x) { return __ieee754_lgamma_r(x,&signgam); } + +#if (LDBL_MANT_DIG == 53) +__weak_reference(lgamma, lgammal); +#endif diff --git a/lib/msun/src/e_lgamma_r.c b/lib/msun/src/e_lgamma_r.c index 7a95ea4..be70767 100644 --- a/lib/msun/src/e_lgamma_r.c +++ b/lib/msun/src/e_lgamma_r.c @@ -1,4 +1,3 @@ - /* @(#)e_lgamma_r.c 1.3 95/01/18 */ /* * ==================================================== @@ -6,22 +5,21 @@ * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== - * */ #include <sys/cdefs.h> __FBSDID("$FreeBSD$"); /* __ieee754_lgamma_r(x, signgamp) - * Reentrant version of the logarithm of the Gamma function - * with user provide pointer for the sign of Gamma(x). + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). * * Method: * 1. Argument Reduction for 0 < x <= 8 - * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may * reduce x to a number in [1.5,2.5] by * lgamma(1+s) = log(s) + lgamma(s) * for example, @@ -59,20 +57,20 @@ __FBSDID("$FreeBSD$"); * by * 3 5 11 * w = w0 + w1*z + w2*z + w3*z + ... + w6*z - * where + * where * |w - f(z)| < 2**-58.74 - * + * * 4. For negative x, since (G is gamma function) * -x*G(-x)*G(x) = pi/sin(pi*x), * we have * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 - * Hence, for x<0, signgam = sign(sin(pi*x)) and + * Hence, for x<0, signgam = sign(sin(pi*x)) and * lgamma(x) = log(|Gamma(x)|) * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); - * Note: one should avoid compute pi*(-x) directly in the + * Note: one should avoid compute pi*(-x) directly in the * computation of sin(pi*(-x)). - * + * * 5. Special Cases * lgamma(2+s) ~ s*(1-Euler) for tiny s * lgamma(1) = lgamma(2) = 0 @@ -80,9 +78,10 @@ __FBSDID("$FreeBSD$"); * lgamma(0) = lgamma(neg.integer) = inf and raise divide-by-zero * lgamma(inf) = inf * lgamma(-inf) = inf (bug for bug compatible with C99!?) - * */ +#include <float.h> + #include "math.h" #include "math_private.h" @@ -187,9 +186,9 @@ sin_pi(double x) switch (n) { case 0: y = __kernel_sin(pi*y,zero,0); break; - case 1: + case 1: case 2: y = __kernel_cos(pi*(0.5-y),zero); break; - case 3: + case 3: case 4: y = __kernel_sin(pi*(one-y),zero,0); break; case 5: case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; @@ -202,24 +201,28 @@ sin_pi(double x) double __ieee754_lgamma_r(double x, int *signgamp) { - double t,y,z,nadj,p,p1,p2,p3,q,r,w; + double nadj,p,p1,p2,p3,q,r,t,w,y,z; int32_t hx; int i,ix,lx; EXTRACT_WORDS(hx,lx,x); - /* purge off +-inf, NaN, +-0, tiny and negative arguments */ + /* purge +-Inf and NaNs */ *signgamp = 1; ix = hx&0x7fffffff; if(ix>=0x7ff00000) return x*x; - if((ix|lx)==0) return one/vzero; - if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */ - if(hx<0) { - *signgamp = -1; - return -__ieee754_log(-x); - } else return -__ieee754_log(x); + + /* purge +-0 and tiny arguments */ + *signgamp = 1-2*((uint32_t)hx>>31); + if(ix<0x3c700000) { /* |x|<2**-56, return -log(|x|) */ + if((ix|lx)==0) + return one/vzero; + return -__ieee754_log(fabs(x)); } + + /* purge negative integers and start evaluation for other x < 0 */ if(hx<0) { + *signgamp = 1; if(ix>=0x43300000) /* |x|>=2**52, must be -integer */ return one/vzero; t = sin_pi(x); @@ -229,7 +232,7 @@ __ieee754_lgamma_r(double x, int *signgamp) x = -x; } - /* purge off 1 and 2 */ + /* purge 1 and 2 */ if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0; /* for x < 2.0 */ else if(ix<0x40000000) { @@ -250,7 +253,7 @@ __ieee754_lgamma_r(double x, int *signgamp) p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); p = y*p1+p2; - r += (p-0.5*y); break; + r += p-y/2; break; case 1: z = y*y; w = z*y; @@ -258,38 +261,43 @@ __ieee754_lgamma_r(double x, int *signgamp) p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); p = z*p1-(tt-w*(p2+y*p3)); - r += (tf + p); break; - case 2: + r += tf + p; break; + case 2: p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); - r += (-0.5*y + p1/p2); + r += p1/p2-y/2; } } - else if(ix<0x40200000) { /* x < 8.0 */ - i = (int)x; - y = x-(double)i; + /* x < 8.0 */ + else if(ix<0x40200000) { + i = x; + y = x-i; p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); - r = half*y+p/q; + r = y/2+p/q; z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ switch(i) { - case 7: z *= (y+6.0); /* FALLTHRU */ - case 6: z *= (y+5.0); /* FALLTHRU */ - case 5: z *= (y+4.0); /* FALLTHRU */ - case 4: z *= (y+3.0); /* FALLTHRU */ - case 3: z *= (y+2.0); /* FALLTHRU */ + case 7: z *= (y+6); /* FALLTHRU */ + case 6: z *= (y+5); /* FALLTHRU */ + case 5: z *= (y+4); /* FALLTHRU */ + case 4: z *= (y+3); /* FALLTHRU */ + case 3: z *= (y+2); /* FALLTHRU */ r += __ieee754_log(z); break; } - /* 8.0 <= x < 2**58 */ - } else if (ix < 0x43900000) { + /* 8.0 <= x < 2**56 */ + } else if (ix < 0x43700000) { t = __ieee754_log(x); z = one/x; y = z*z; w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); r = (x-half)*(t-one)+w; - } else - /* 2**58 <= x <= inf */ + } else + /* 2**56 <= x <= inf */ r = x*(__ieee754_log(x)-one); if(hx<0) r = nadj - r; return r; } + +#if (LDBL_MANT_DIG == 53) +__weak_reference(lgamma_r, lgammal_r); +#endif diff --git a/lib/msun/src/e_lgammaf_r.c b/lib/msun/src/e_lgammaf_r.c index 9a7ab39..9084e18 100644 --- a/lib/msun/src/e_lgammaf_r.c +++ b/lib/msun/src/e_lgammaf_r.c @@ -1,5 +1,6 @@ /* e_lgammaf_r.c -- float version of e_lgamma_r.c. * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Conversion to float fixed By Steven G. Kargl. */ /* @@ -22,72 +23,63 @@ __FBSDID("$FreeBSD$"); static const volatile float vzero = 0; static const float -zero= 0.0000000000e+00, -half= 5.0000000000e-01, /* 0x3f000000 */ -one = 1.0000000000e+00, /* 0x3f800000 */ +zero= 0, +half= 0.5, +one = 1, pi = 3.1415927410e+00, /* 0x40490fdb */ -a0 = 7.7215664089e-02, /* 0x3d9e233f */ -a1 = 3.2246702909e-01, /* 0x3ea51a66 */ -a2 = 6.7352302372e-02, /* 0x3d89f001 */ -a3 = 2.0580807701e-02, /* 0x3ca89915 */ -a4 = 7.3855509982e-03, /* 0x3bf2027e */ -a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ -a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ -a7 = 5.1006977446e-04, /* 0x3a05b634 */ -a8 = 2.2086278477e-04, /* 0x39679767 */ -a9 = 1.0801156895e-04, /* 0x38e28445 */ -a10 = 2.5214456400e-05, /* 0x37d383a2 */ -a11 = 4.4864096708e-05, /* 0x383c2c75 */ -tc = 1.4616321325e+00, /* 0x3fbb16c3 */ -tf = -1.2148628384e-01, /* 0xbdf8cdcd */ -/* tt = -(tail of tf) */ -tt = 6.6971006518e-09, /* 0x31e61c52 */ -t0 = 4.8383611441e-01, /* 0x3ef7b95e */ -t1 = -1.4758771658e-01, /* 0xbe17213c */ -t2 = 6.4624942839e-02, /* 0x3d845a15 */ -t3 = -3.2788541168e-02, /* 0xbd064d47 */ -t4 = 1.7970675603e-02, /* 0x3c93373d */ -t5 = -1.0314224288e-02, /* 0xbc28fcfe */ -t6 = 6.1005386524e-03, /* 0x3bc7e707 */ -t7 = -3.6845202558e-03, /* 0xbb7177fe */ -t8 = 2.2596477065e-03, /* 0x3b141699 */ -t9 = -1.4034647029e-03, /* 0xbab7f476 */ -t10 = 8.8108185446e-04, /* 0x3a66f867 */ -t11 = -5.3859531181e-04, /* 0xba0d3085 */ -t12 = 3.1563205994e-04, /* 0x39a57b6b */ -t13 = -3.1275415677e-04, /* 0xb9a3f927 */ -t14 = 3.3552918467e-04, /* 0x39afe9f7 */ -u0 = -7.7215664089e-02, /* 0xbd9e233f */ -u1 = 6.3282704353e-01, /* 0x3f2200f4 */ -u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ -u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ -u4 = 2.2896373272e-01, /* 0x3e6a7578 */ -u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ -v1 = 2.4559779167e+00, /* 0x401d2ebe */ -v2 = 2.1284897327e+00, /* 0x4008392d */ -v3 = 7.6928514242e-01, /* 0x3f44efdf */ -v4 = 1.0422264785e-01, /* 0x3dd572af */ -v5 = 3.2170924824e-03, /* 0x3b52d5db */ -s0 = -7.7215664089e-02, /* 0xbd9e233f */ -s1 = 2.1498242021e-01, /* 0x3e5c245a */ -s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ -s3 = 1.4635047317e-01, /* 0x3e15dce6 */ -s4 = 2.6642270386e-02, /* 0x3cda40e4 */ -s5 = 1.8402845599e-03, /* 0x3af135b4 */ -s6 = 3.1947532989e-05, /* 0x3805ff67 */ -r1 = 1.3920053244e+00, /* 0x3fb22d3b */ -r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ -r3 = 1.7193385959e-01, /* 0x3e300f6e */ -r4 = 1.8645919859e-02, /* 0x3c98bf54 */ -r5 = 7.7794247773e-04, /* 0x3a4beed6 */ -r6 = 7.3266842264e-06, /* 0x36f5d7bd */ -w0 = 4.1893854737e-01, /* 0x3ed67f1d */ -w1 = 8.3333335817e-02, /* 0x3daaaaab */ -w2 = -2.7777778450e-03, /* 0xbb360b61 */ -w3 = 7.9365057172e-04, /* 0x3a500cfd */ -w4 = -5.9518753551e-04, /* 0xba1c065c */ -w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ -w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ +/* + * Domain y in [0x1p-27, 0.27], range ~[-3.4599e-10, 3.4590e-10]: + * |(lgamma(2 - y) + 0.5 * y) / y - a(y)| < 2**-31.4 + */ +a0 = 7.72156641e-02, /* 0x3d9e233f */ +a1 = 3.22467119e-01, /* 0x3ea51a69 */ +a2 = 6.73484802e-02, /* 0x3d89ee00 */ +a3 = 2.06395667e-02, /* 0x3ca9144f */ +a4 = 6.98275631e-03, /* 0x3be4cf9b */ +a5 = 4.11768444e-03, /* 0x3b86eda4 */ +/* + * Domain x in [tc-0.24, tc+0.28], range ~[-5.6577e-10, 5.5677e-10]: + * |(lgamma(x) - tf) - t(x - tc)| < 2**-30.8. + */ +tc = 1.46163213e+00, /* 0x3fbb16c3 */ +tf = -1.21486291e-01, /* 0xbdf8cdce */ +t0 = -2.94064460e-11, /* 0xae0154b7 */ +t1 = -2.35939837e-08, /* 0xb2caabb8 */ +t2 = 4.83836412e-01, /* 0x3ef7b968 */ +t3 = -1.47586212e-01, /* 0xbe1720d7 */ +t4 = 6.46013096e-02, /* 0x3d844db1 */ +t5 = -3.28450352e-02, /* 0xbd068884 */ +t6 = 1.86483748e-02, /* 0x3c98c47a */ +t7 = -9.89206228e-03, /* 0xbc221251 */ +/* + * Domain y in [-0.1, 0.232], range ~[-8.4931e-10, 8.7794e-10]: + * |(lgamma(1 + y) + 0.5 * y) / y - u(y) / v(y)| < 2**-31.2 + */ +u0 = -7.72156641e-02, /* 0xbd9e233f */ +u1 = 7.36789703e-01, /* 0x3f3c9e40 */ +u2 = 4.95649040e-01, /* 0x3efdc5b6 */ +v1 = 1.10958421e+00, /* 0x3f8e06db */ +v2 = 2.10598111e-01, /* 0x3e57a708 */ +v3 = -1.02995494e-02, /* 0xbc28bf71 */ +/* + * Domain x in (2, 3], range ~[-5.5189e-11, 5.2317e-11]: + * |(lgamma(y+2) - 0.5 * y) / y - s(y)/r(y)| < 2**-35.0 + * with y = x - 2. + */ +s0 = -7.72156641e-02, /* 0xbd9e233f */ +s1 = 2.69987404e-01, /* 0x3e8a3bca */ +s2 = 1.42851010e-01, /* 0x3e124789 */ +s3 = 1.19389519e-02, /* 0x3c439b98 */ +r1 = 6.79650068e-01, /* 0x3f2dfd8c */ +r2 = 1.16058730e-01, /* 0x3dedb033 */ +r3 = 3.75673687e-03, /* 0x3b763396 */ +/* + * Domain z in [8, 0x1p24], range ~[-1.2640e-09, 1.2640e-09]: + * |lgamma(x) - (x - 0.5) * (log(x) - 1) - w(1/x)| < 2**-29.6. + */ +w0 = 4.18938547e-01, /* 0x3ed67f1d */ +w1 = 8.33332464e-02, /* 0x3daaaa9f */ +w2 = -2.76129087e-03; /* 0xbb34f6c6 */ static float sin_pif(float x) @@ -130,25 +122,29 @@ sin_pif(float x) float __ieee754_lgammaf_r(float x, int *signgamp) { - float t,y,z,nadj,p,p1,p2,p3,q,r,w; + float nadj,p,p1,p2,p3,q,r,t,w,y,z; int32_t hx; int i,ix; GET_FLOAT_WORD(hx,x); - /* purge off +-inf, NaN, +-0, tiny and negative arguments */ + /* purge +-Inf and NaNs */ *signgamp = 1; ix = hx&0x7fffffff; if(ix>=0x7f800000) return x*x; - if(ix==0) return one/vzero; - if(ix<0x35000000) { /* |x|<2**-21, return -log(|x|) */ - if(hx<0) { - *signgamp = -1; - return -__ieee754_logf(-x); - } else return -__ieee754_logf(x); + + /* purge +-0 and tiny arguments */ + *signgamp = 1-2*((uint32_t)hx>>31); + if(ix<0x32000000) { /* |x|<2**-27, return -log(|x|) */ + if(ix==0) + return one/vzero; + return -__ieee754_logf(fabsf(x)); } + + /* purge negative integers and start evaluation for other x < 0 */ if(hx<0) { - if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ + *signgamp = 1; + if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ return one/vzero; t = sin_pif(x); if(t==zero) return one/vzero; /* -integer */ @@ -157,7 +153,7 @@ __ieee754_lgammaf_r(float x, int *signgamp) x = -x; } - /* purge off 1 and 2 */ + /* purge 1 and 2 */ if (ix==0x3f800000||ix==0x40000000) r = 0; /* for x < 2.0 */ else if(ix<0x40000000) { @@ -168,55 +164,51 @@ __ieee754_lgammaf_r(float x, int *signgamp) else {y = x; i=2;} } else { r = zero; - if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ + if(ix>=0x3fdda618) {y=2-x;i=0;} /* [1.7316,2] */ else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ else {y=x-one;i=2;} } switch(i) { case 0: z = y*y; - p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); - p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p1 = a0+z*(a2+z*a4); + p2 = z*(a1+z*(a3+z*a5)); p = y*p1+p2; - r += (p-(float)0.5*y); break; + r += p-y/2; break; case 1: - z = y*y; - w = z*y; - p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ - p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); - p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); - p = z*p1-(tt-w*(p2+y*p3)); - r += (tf + p); break; + p = t0+y*t1+y*y*(t2+y*(t3+y*(t4+y*(t5+y*(t6+y*t7))))); + r += tf + p; break; case 2: - p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); - p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); - r += (-(float)0.5*y + p1/p2); + p1 = y*(u0+y*(u1+y*u2)); + p2 = one+y*(v1+y*(v2+y*v3)); + r += p1/p2-y/2; } } - else if(ix<0x41000000) { /* x < 8.0 */ - i = (int)x; - y = x-(float)i; - p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); - q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); - r = half*y+p/q; + /* x < 8.0 */ + else if(ix<0x41000000) { + i = x; + y = x-i; + p = y*(s0+y*(s1+y*(s2+y*s3))); + q = one+y*(r1+y*(r2+y*r3)); + r = y/2+p/q; z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ switch(i) { - case 7: z *= (y+(float)6.0); /* FALLTHRU */ - case 6: z *= (y+(float)5.0); /* FALLTHRU */ - case 5: z *= (y+(float)4.0); /* FALLTHRU */ - case 4: z *= (y+(float)3.0); /* FALLTHRU */ - case 3: z *= (y+(float)2.0); /* FALLTHRU */ + case 7: z *= (y+6); /* FALLTHRU */ + case 6: z *= (y+5); /* FALLTHRU */ + case 5: z *= (y+4); /* FALLTHRU */ + case 4: z *= (y+3); /* FALLTHRU */ + case 3: z *= (y+2); /* FALLTHRU */ r += __ieee754_logf(z); break; } - /* 8.0 <= x < 2**58 */ - } else if (ix < 0x5c800000) { + /* 8.0 <= x < 2**27 */ + } else if (ix < 0x4d000000) { t = __ieee754_logf(x); z = one/x; y = z*z; - w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + w = w0+z*(w1+y*w2); r = (x-half)*(t-one)+w; } else - /* 2**58 <= x <= inf */ + /* 2**27 <= x <= inf */ r = x*(__ieee754_logf(x)-one); if(hx<0) r = nadj - r; return r; diff --git a/lib/msun/src/e_lgammal.c b/lib/msun/src/e_lgammal.c new file mode 100644 index 0000000..ebc2fc7 --- /dev/null +++ b/lib/msun/src/e_lgammal.c @@ -0,0 +1,25 @@ +/* @(#)e_lgamma.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +#include "math.h" +#include "math_private.h" + +extern int signgam; + +long double +lgammal(long double x) +{ + return lgammal_r(x,&signgam); +} diff --git a/lib/msun/src/imprecise.c b/lib/msun/src/imprecise.c index 92fb2d0..08cd239 100644 --- a/lib/msun/src/imprecise.c +++ b/lib/msun/src/imprecise.c @@ -60,5 +60,4 @@ DECLARE_WEAK(powl); long double imprecise_ ## f ## l(long double v) { return f(v); }\ DECLARE_WEAK(f ## l) -DECLARE_IMPRECISE(lgamma); DECLARE_IMPRECISE(tgamma); diff --git a/lib/msun/src/k_exp.c b/lib/msun/src/k_exp.c index f592f69..ecef54c 100644 --- a/lib/msun/src/k_exp.c +++ b/lib/msun/src/k_exp.c @@ -103,6 +103,6 @@ __ldexp_cexp(double complex z, int expt) half_expt = expt - half_expt; INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0); - return (cpack(cos(y) * exp_x * scale1 * scale2, + return (CMPLX(cos(y) * exp_x * scale1 * scale2, sin(y) * exp_x * scale1 * scale2)); } diff --git a/lib/msun/src/k_expf.c b/lib/msun/src/k_expf.c index 548a008..f8c254d 100644 --- a/lib/msun/src/k_expf.c +++ b/lib/msun/src/k_expf.c @@ -82,6 +82,6 @@ __ldexp_cexpf(float complex z, int expt) half_expt = expt - half_expt; SET_FLOAT_WORD(scale2, (0x7f + half_expt) << 23); - return (cpackf(cosf(y) * exp_x * scale1 * scale2, + return (CMPLXF(cosf(y) * exp_x * scale1 * scale2, sinf(y) * exp_x * scale1 * scale2)); } diff --git a/lib/msun/src/math.h b/lib/msun/src/math.h index 3ab76f8..be8240a 100644 --- a/lib/msun/src/math.h +++ b/lib/msun/src/math.h @@ -500,8 +500,12 @@ long double tanhl(long double); long double tanl(long double); long double tgammal(long double); long double truncl(long double); - #endif /* __ISO_C_VISIBLE >= 1999 */ + +#if __BSD_VISIBLE +long double lgammal_r(long double, int *); +#endif + __END_DECLS #endif /* !_MATH_H_ */ diff --git a/lib/msun/src/math_private.h b/lib/msun/src/math_private.h index 8af2c65..afaf201 100644 --- a/lib/msun/src/math_private.h +++ b/lib/msun/src/math_private.h @@ -454,9 +454,15 @@ typedef union { * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product. * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted * to -0.0+I*0.0. + * + * The C11 standard introduced the macros CMPLX(), CMPLXF() and CMPLXL() + * to construct complex values. Compilers that conform to the C99 + * standard require the following functions to avoid the above issues. */ + +#ifndef CMPLXF static __inline float complex -cpackf(float x, float y) +CMPLXF(float x, float y) { float_complex z; @@ -464,9 +470,11 @@ cpackf(float x, float y) IMAGPART(z) = y; return (z.f); } +#endif +#ifndef CMPLX static __inline double complex -cpack(double x, double y) +CMPLX(double x, double y) { double_complex z; @@ -474,9 +482,11 @@ cpack(double x, double y) IMAGPART(z) = y; return (z.f); } +#endif +#ifndef CMPLXL static __inline long double complex -cpackl(long double x, long double y) +CMPLXL(long double x, long double y) { long_double_complex z; @@ -484,6 +494,8 @@ cpackl(long double x, long double y) IMAGPART(z) = y; return (z.f); } +#endif + #endif /* _COMPLEX_H */ #ifdef __GNUCLIKE_ASM diff --git a/lib/msun/src/s_ccosh.c b/lib/msun/src/s_ccosh.c index 9ea962b..2843198 100644 --- a/lib/msun/src/s_ccosh.c +++ b/lib/msun/src/s_ccosh.c @@ -32,6 +32,8 @@ * * Exceptional values are noted in the comments within the source code. * These values and the return value were taken from n1124.pdf. + * The sign of the result for some exceptional values is unspecified but + * must satisfy both cosh(conj(z)) == conj(cosh(z)) and cosh(-z) == cosh(z). */ #include <sys/cdefs.h> @@ -62,49 +64,48 @@ ccosh(double complex z) /* Handle the nearly-non-exceptional cases where x and y are finite. */ if (ix < 0x7ff00000 && iy < 0x7ff00000) { if ((iy | ly) == 0) - return (cpack(cosh(x), x * y)); - if (ix < 0x40360000) /* small x: normal case */ - return (cpack(cosh(x) * cos(y), sinh(x) * sin(y))); + return (CMPLX(cosh(x), x * y)); + if (ix < 0x40360000) /* |x| < 22: normal case */ + return (CMPLX(cosh(x) * cos(y), sinh(x) * sin(y))); /* |x| >= 22, so cosh(x) ~= exp(|x|) */ if (ix < 0x40862e42) { /* x < 710: exp(|x|) won't overflow */ h = exp(fabs(x)) * 0.5; - return (cpack(h * cos(y), copysign(h, x) * sin(y))); + return (CMPLX(h * cos(y), copysign(h, x) * sin(y))); } else if (ix < 0x4096bbaa) { /* x < 1455: scale to avoid overflow */ - z = __ldexp_cexp(cpack(fabs(x), y), -1); - return (cpack(creal(z), cimag(z) * copysign(1, x))); + z = __ldexp_cexp(CMPLX(fabs(x), y), -1); + return (CMPLX(creal(z), cimag(z) * copysign(1, x))); } else { /* x >= 1455: the result always overflows */ h = huge * x; - return (cpack(h * h * cos(y), h * sin(y))); + return (CMPLX(h * h * cos(y), h * sin(y))); } } /* - * cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0. - * The sign of 0 in the result is unspecified. Choice = normally - * the same as dNaN. Raise the invalid floating-point exception. + * cosh(+-0 +- I Inf) = dNaN + I (+-)(+-)0. + * The sign of 0 in the result is unspecified. Choice = product + * of the signs of the argument. Raise the invalid floating-point + * exception. * - * cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0. - * The sign of 0 in the result is unspecified. Choice = normally - * the same as d(NaN). + * cosh(+-0 +- I NaN) = d(NaN) + I (+-)(+-)0. + * The sign of 0 in the result is unspecified. Choice = product + * of the signs of the argument. */ - if ((ix | lx) == 0 && iy >= 0x7ff00000) - return (cpack(y - y, copysign(0, x * (y - y)))); + if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */ + return (CMPLX(y - y, x * copysign(0, y))); /* * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0. * - * cosh(NaN +- I 0) = d(NaN) + I sign(d(NaN, +-0))0. - * The sign of 0 in the result is unspecified. + * cosh(NaN +- I 0) = d(NaN) + I (+-)(+-)0. + * The sign of 0 in the result is unspecified. Choice = product + * of the signs of the argument. */ - if ((iy | ly) == 0 && ix >= 0x7ff00000) { - if (((hx & 0xfffff) | lx) == 0) - return (cpack(x * x, copysign(0, x) * y)); - return (cpack(x * x, copysign(0, (x + x) * y))); - } + if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */ + return (CMPLX(x * x, copysign(0, x) * y)); /* * cosh(x +- I Inf) = dNaN + I dNaN. @@ -114,8 +115,8 @@ ccosh(double complex z) * Optionally raises the invalid floating-point exception for finite * nonzero x. Choice = don't raise (except for signaling NaNs). */ - if (ix < 0x7ff00000 && iy >= 0x7ff00000) - return (cpack(y - y, x * (y - y))); + if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */ + return (CMPLX(y - y, x * (y - y))); /* * cosh(+-Inf + I NaN) = +Inf + I d(NaN). @@ -126,10 +127,10 @@ ccosh(double complex z) * * cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y) */ - if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { + if (ix == 0x7ff00000 && lx == 0) { if (iy >= 0x7ff00000) - return (cpack(x * x, x * (y - y))); - return (cpack((x * x) * cos(y), x * sin(y))); + return (CMPLX(INFINITY, x * (y - y))); + return (CMPLX(INFINITY * cos(y), x * sin(y))); } /* @@ -143,7 +144,7 @@ ccosh(double complex z) * Optionally raises the invalid floating-point exception for finite * nonzero y. Choice = don't raise (except for signaling NaNs). */ - return (cpack((x * x) * (y - y), (x + x) * (y - y))); + return (CMPLX((x * x) * (y - y), (x + x) * (y - y))); } double complex @@ -151,5 +152,5 @@ ccos(double complex z) { /* ccos(z) = ccosh(I * z) */ - return (ccosh(cpack(-cimag(z), creal(z)))); + return (ccosh(CMPLX(-cimag(z), creal(z)))); } diff --git a/lib/msun/src/s_ccoshf.c b/lib/msun/src/s_ccoshf.c index 1de9ad4..eeed92f 100644 --- a/lib/msun/src/s_ccoshf.c +++ b/lib/msun/src/s_ccoshf.c @@ -25,7 +25,7 @@ */ /* - * Hyperbolic cosine of a complex argument. See s_ccosh.c for details. + * Float version of ccosh(). See s_ccosh.c for details. */ #include <sys/cdefs.h> @@ -55,50 +55,47 @@ ccoshf(float complex z) if (ix < 0x7f800000 && iy < 0x7f800000) { if (iy == 0) - return (cpackf(coshf(x), x * y)); - if (ix < 0x41100000) /* small x: normal case */ - return (cpackf(coshf(x) * cosf(y), sinhf(x) * sinf(y))); + return (CMPLXF(coshf(x), x * y)); + if (ix < 0x41100000) /* |x| < 9: normal case */ + return (CMPLXF(coshf(x) * cosf(y), sinhf(x) * sinf(y))); /* |x| >= 9, so cosh(x) ~= exp(|x|) */ if (ix < 0x42b17218) { /* x < 88.7: expf(|x|) won't overflow */ - h = expf(fabsf(x)) * 0.5f; - return (cpackf(h * cosf(y), copysignf(h, x) * sinf(y))); + h = expf(fabsf(x)) * 0.5F; + return (CMPLXF(h * cosf(y), copysignf(h, x) * sinf(y))); } else if (ix < 0x4340b1e7) { /* x < 192.7: scale to avoid overflow */ - z = __ldexp_cexpf(cpackf(fabsf(x), y), -1); - return (cpackf(crealf(z), cimagf(z) * copysignf(1, x))); + z = __ldexp_cexpf(CMPLXF(fabsf(x), y), -1); + return (CMPLXF(crealf(z), cimagf(z) * copysignf(1, x))); } else { /* x >= 192.7: the result always overflows */ h = huge * x; - return (cpackf(h * h * cosf(y), h * sinf(y))); + return (CMPLXF(h * h * cosf(y), h * sinf(y))); } } - if (ix == 0 && iy >= 0x7f800000) - return (cpackf(y - y, copysignf(0, x * (y - y)))); + if (ix == 0) /* && iy >= 0x7f800000 */ + return (CMPLXF(y - y, x * copysignf(0, y))); - if (iy == 0 && ix >= 0x7f800000) { - if ((hx & 0x7fffff) == 0) - return (cpackf(x * x, copysignf(0, x) * y)); - return (cpackf(x * x, copysignf(0, (x + x) * y))); - } + if (iy == 0) /* && ix >= 0x7f800000 */ + return (CMPLXF(x * x, copysignf(0, x) * y)); - if (ix < 0x7f800000 && iy >= 0x7f800000) - return (cpackf(y - y, x * (y - y))); + if (ix < 0x7f800000) /* && iy >= 0x7f800000 */ + return (CMPLXF(y - y, x * (y - y))); - if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) { + if (ix == 0x7f800000) { if (iy >= 0x7f800000) - return (cpackf(x * x, x * (y - y))); - return (cpackf((x * x) * cosf(y), x * sinf(y))); + return (CMPLXF(INFINITY, x * (y - y))); + return (CMPLXF(INFINITY * cosf(y), x * sinf(y))); } - return (cpackf((x * x) * (y - y), (x + x) * (y - y))); + return (CMPLXF((x * x) * (y - y), (x + x) * (y - y))); } float complex ccosf(float complex z) { - return (ccoshf(cpackf(-cimagf(z), crealf(z)))); + return (ccoshf(CMPLXF(-cimagf(z), crealf(z)))); } diff --git a/lib/msun/src/s_cexp.c b/lib/msun/src/s_cexp.c index abe178f..9e11d51 100644 --- a/lib/msun/src/s_cexp.c +++ b/lib/msun/src/s_cexp.c @@ -50,22 +50,22 @@ cexp(double complex z) /* cexp(x + I 0) = exp(x) + I 0 */ if ((hy | ly) == 0) - return (cpack(exp(x), y)); + return (CMPLX(exp(x), y)); EXTRACT_WORDS(hx, lx, x); /* cexp(0 + I y) = cos(y) + I sin(y) */ if (((hx & 0x7fffffff) | lx) == 0) - return (cpack(cos(y), sin(y))); + return (CMPLX(cos(y), sin(y))); if (hy >= 0x7ff00000) { if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) { /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ - return (cpack(y - y, y - y)); + return (CMPLX(y - y, y - y)); } else if (hx & 0x80000000) { /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ - return (cpack(0.0, 0.0)); + return (CMPLX(0.0, 0.0)); } else { /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ - return (cpack(x, y - y)); + return (CMPLX(x, y - y)); } } @@ -84,6 +84,6 @@ cexp(double complex z) * - x = NaN (spurious inexact exception from y) */ exp_x = exp(x); - return (cpack(exp_x * cos(y), exp_x * sin(y))); + return (CMPLX(exp_x * cos(y), exp_x * sin(y))); } } diff --git a/lib/msun/src/s_cexpf.c b/lib/msun/src/s_cexpf.c index 0e30d08..0138cd1 100644 --- a/lib/msun/src/s_cexpf.c +++ b/lib/msun/src/s_cexpf.c @@ -50,22 +50,22 @@ cexpf(float complex z) /* cexp(x + I 0) = exp(x) + I 0 */ if (hy == 0) - return (cpackf(expf(x), y)); + return (CMPLXF(expf(x), y)); GET_FLOAT_WORD(hx, x); /* cexp(0 + I y) = cos(y) + I sin(y) */ if ((hx & 0x7fffffff) == 0) - return (cpackf(cosf(y), sinf(y))); + return (CMPLXF(cosf(y), sinf(y))); if (hy >= 0x7f800000) { if ((hx & 0x7fffffff) != 0x7f800000) { /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ - return (cpackf(y - y, y - y)); + return (CMPLXF(y - y, y - y)); } else if (hx & 0x80000000) { /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ - return (cpackf(0.0, 0.0)); + return (CMPLXF(0.0, 0.0)); } else { /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ - return (cpackf(x, y - y)); + return (CMPLXF(x, y - y)); } } @@ -84,6 +84,6 @@ cexpf(float complex z) * - x = NaN (spurious inexact exception from y) */ exp_x = expf(x); - return (cpackf(exp_x * cosf(y), exp_x * sinf(y))); + return (CMPLXF(exp_x * cosf(y), exp_x * sinf(y))); } } diff --git a/lib/msun/src/s_conj.c b/lib/msun/src/s_conj.c index 5770c29..d0dd051 100644 --- a/lib/msun/src/s_conj.c +++ b/lib/msun/src/s_conj.c @@ -34,5 +34,5 @@ double complex conj(double complex z) { - return (cpack(creal(z), -cimag(z))); + return (CMPLX(creal(z), -cimag(z))); } diff --git a/lib/msun/src/s_conjf.c b/lib/msun/src/s_conjf.c index b090760..c4cf127 100644 --- a/lib/msun/src/s_conjf.c +++ b/lib/msun/src/s_conjf.c @@ -34,5 +34,5 @@ float complex conjf(float complex z) { - return (cpackf(crealf(z), -cimagf(z))); + return (CMPLXF(crealf(z), -cimagf(z))); } diff --git a/lib/msun/src/s_conjl.c b/lib/msun/src/s_conjl.c index 0e431ef..a4604b6 100644 --- a/lib/msun/src/s_conjl.c +++ b/lib/msun/src/s_conjl.c @@ -34,5 +34,5 @@ long double complex conjl(long double complex z) { - return (cpackl(creall(z), -cimagl(z))); + return (CMPLXL(creall(z), -cimagl(z))); } diff --git a/lib/msun/src/s_cproj.c b/lib/msun/src/s_cproj.c index 8e9404c..2f0db6e 100644 --- a/lib/msun/src/s_cproj.c +++ b/lib/msun/src/s_cproj.c @@ -39,7 +39,7 @@ cproj(double complex z) if (!isinf(creal(z)) && !isinf(cimag(z))) return (z); else - return (cpack(INFINITY, copysign(0.0, cimag(z)))); + return (CMPLX(INFINITY, copysign(0.0, cimag(z)))); } #if LDBL_MANT_DIG == 53 diff --git a/lib/msun/src/s_cprojf.c b/lib/msun/src/s_cprojf.c index 68ea77b..bd27bdc 100644 --- a/lib/msun/src/s_cprojf.c +++ b/lib/msun/src/s_cprojf.c @@ -39,5 +39,5 @@ cprojf(float complex z) if (!isinf(crealf(z)) && !isinf(cimagf(z))) return (z); else - return (cpackf(INFINITY, copysignf(0.0, cimagf(z)))); + return (CMPLXF(INFINITY, copysignf(0.0, cimagf(z)))); } diff --git a/lib/msun/src/s_cprojl.c b/lib/msun/src/s_cprojl.c index 07385bc..5cccc91 100644 --- a/lib/msun/src/s_cprojl.c +++ b/lib/msun/src/s_cprojl.c @@ -39,5 +39,5 @@ cprojl(long double complex z) if (!isinf(creall(z)) && !isinf(cimagl(z))) return (z); else - return (cpackl(INFINITY, copysignl(0.0, cimagl(z)))); + return (CMPLXL(INFINITY, copysignl(0.0, cimagl(z)))); } diff --git a/lib/msun/src/s_csinh.c b/lib/msun/src/s_csinh.c index c192f30..7af3634 100644 --- a/lib/msun/src/s_csinh.c +++ b/lib/msun/src/s_csinh.c @@ -32,6 +32,8 @@ * * Exceptional values are noted in the comments within the source code. * These values and the return value were taken from n1124.pdf. + * The sign of the result for some exceptional values is unspecified but + * must satisfy both sinh(conj(z)) == conj(sinh(z)) and sinh(-z) == -sinh(z). */ #include <sys/cdefs.h> @@ -62,48 +64,45 @@ csinh(double complex z) /* Handle the nearly-non-exceptional cases where x and y are finite. */ if (ix < 0x7ff00000 && iy < 0x7ff00000) { if ((iy | ly) == 0) - return (cpack(sinh(x), y)); - if (ix < 0x40360000) /* small x: normal case */ - return (cpack(sinh(x) * cos(y), cosh(x) * sin(y))); + return (CMPLX(sinh(x), y)); + if (ix < 0x40360000) /* |x| < 22: normal case */ + return (CMPLX(sinh(x) * cos(y), cosh(x) * sin(y))); /* |x| >= 22, so cosh(x) ~= exp(|x|) */ if (ix < 0x40862e42) { /* x < 710: exp(|x|) won't overflow */ h = exp(fabs(x)) * 0.5; - return (cpack(copysign(h, x) * cos(y), h * sin(y))); + return (CMPLX(copysign(h, x) * cos(y), h * sin(y))); } else if (ix < 0x4096bbaa) { /* x < 1455: scale to avoid overflow */ - z = __ldexp_cexp(cpack(fabs(x), y), -1); - return (cpack(creal(z) * copysign(1, x), cimag(z))); + z = __ldexp_cexp(CMPLX(fabs(x), y), -1); + return (CMPLX(creal(z) * copysign(1, x), cimag(z))); } else { /* x >= 1455: the result always overflows */ h = huge * x; - return (cpack(h * cos(y), h * h * sin(y))); + return (CMPLX(h * cos(y), h * h * sin(y))); } } /* - * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN. - * The sign of 0 in the result is unspecified. Choice = normally - * the same as dNaN. Raise the invalid floating-point exception. + * sinh(+-0 +- I Inf) = +-0 + I dNaN. + * The sign of 0 in the result is unspecified. Choice = same sign + * as the argument. Raise the invalid floating-point exception. * - * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN). - * The sign of 0 in the result is unspecified. Choice = normally - * the same as d(NaN). + * sinh(+-0 +- I NaN) = +-0 + I d(NaN). + * The sign of 0 in the result is unspecified. Choice = same sign + * as the argument. */ - if ((ix | lx) == 0 && iy >= 0x7ff00000) - return (cpack(copysign(0, x * (y - y)), y - y)); + if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */ + return (CMPLX(x, y - y)); /* * sinh(+-Inf +- I 0) = +-Inf + I +-0. * * sinh(NaN +- I 0) = d(NaN) + I +-0. */ - if ((iy | ly) == 0 && ix >= 0x7ff00000) { - if (((hx & 0xfffff) | lx) == 0) - return (cpack(x, y)); - return (cpack(x, copysign(0, y))); - } + if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */ + return (CMPLX(x + x, y)); /* * sinh(x +- I Inf) = dNaN + I dNaN. @@ -113,45 +112,45 @@ csinh(double complex z) * Optionally raises the invalid floating-point exception for finite * nonzero x. Choice = don't raise (except for signaling NaNs). */ - if (ix < 0x7ff00000 && iy >= 0x7ff00000) - return (cpack(y - y, x * (y - y))); + if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */ + return (CMPLX(y - y, y - y)); /* * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). - * The sign of Inf in the result is unspecified. Choice = normally - * the same as d(NaN). + * The sign of Inf in the result is unspecified. Choice = same sign + * as the argument. * - * sinh(+-Inf +- I Inf) = +Inf + I dNaN. - * The sign of Inf in the result is unspecified. Choice = always +. - * Raise the invalid floating-point exception. + * sinh(+-Inf +- I Inf) = +-Inf + I dNaN. + * The sign of Inf in the result is unspecified. Choice = same sign + * as the argument. Raise the invalid floating-point exception. * * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) */ - if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { + if (ix == 0x7ff00000 && lx == 0) { if (iy >= 0x7ff00000) - return (cpack(x * x, x * (y - y))); - return (cpack(x * cos(y), INFINITY * sin(y))); + return (CMPLX(x, y - y)); + return (CMPLX(x * cos(y), INFINITY * sin(y))); } /* - * sinh(NaN + I NaN) = d(NaN) + I d(NaN). + * sinh(NaN1 + I NaN2) = d(NaN1, NaN2) + I d(NaN1, NaN2). * - * sinh(NaN +- I Inf) = d(NaN) + I d(NaN). + * sinh(NaN +- I Inf) = d(NaN, dNaN) + I d(NaN, dNaN). * Optionally raises the invalid floating-point exception. * Choice = raise. * - * sinh(NaN + I y) = d(NaN) + I d(NaN). + * sinh(NaN + I y) = d(NaN) + I d(NaN). * Optionally raises the invalid floating-point exception for finite * nonzero y. Choice = don't raise (except for signaling NaNs). */ - return (cpack((x * x) * (y - y), (x + x) * (y - y))); + return (CMPLX((x + x) * (y - y), (x * x) * (y - y))); } double complex csin(double complex z) { - /* csin(z) = -I * csinh(I * z) */ - z = csinh(cpack(-cimag(z), creal(z))); - return (cpack(cimag(z), -creal(z))); + /* csin(z) = -I * csinh(I * z) = I * conj(csinh(I * conj(z))). */ + z = csinh(CMPLX(cimag(z), creal(z))); + return (CMPLX(cimag(z), creal(z))); } diff --git a/lib/msun/src/s_csinhf.c b/lib/msun/src/s_csinhf.c index c523125..c9d9d3c 100644 --- a/lib/msun/src/s_csinhf.c +++ b/lib/msun/src/s_csinhf.c @@ -25,7 +25,7 @@ */ /* - * Hyperbolic sine of a complex argument z. See s_csinh.c for details. + * Float version of csinh(). See s_csinh.c for details. */ #include <sys/cdefs.h> @@ -55,51 +55,48 @@ csinhf(float complex z) if (ix < 0x7f800000 && iy < 0x7f800000) { if (iy == 0) - return (cpackf(sinhf(x), y)); - if (ix < 0x41100000) /* small x: normal case */ - return (cpackf(sinhf(x) * cosf(y), coshf(x) * sinf(y))); + return (CMPLXF(sinhf(x), y)); + if (ix < 0x41100000) /* |x| < 9: normal case */ + return (CMPLXF(sinhf(x) * cosf(y), coshf(x) * sinf(y))); /* |x| >= 9, so cosh(x) ~= exp(|x|) */ if (ix < 0x42b17218) { /* x < 88.7: expf(|x|) won't overflow */ - h = expf(fabsf(x)) * 0.5f; - return (cpackf(copysignf(h, x) * cosf(y), h * sinf(y))); + h = expf(fabsf(x)) * 0.5F; + return (CMPLXF(copysignf(h, x) * cosf(y), h * sinf(y))); } else if (ix < 0x4340b1e7) { /* x < 192.7: scale to avoid overflow */ - z = __ldexp_cexpf(cpackf(fabsf(x), y), -1); - return (cpackf(crealf(z) * copysignf(1, x), cimagf(z))); + z = __ldexp_cexpf(CMPLXF(fabsf(x), y), -1); + return (CMPLXF(crealf(z) * copysignf(1, x), cimagf(z))); } else { /* x >= 192.7: the result always overflows */ h = huge * x; - return (cpackf(h * cosf(y), h * h * sinf(y))); + return (CMPLXF(h * cosf(y), h * h * sinf(y))); } } - if (ix == 0 && iy >= 0x7f800000) - return (cpackf(copysignf(0, x * (y - y)), y - y)); + if (ix == 0) /* && iy >= 0x7f800000 */ + return (CMPLXF(x, y - y)); - if (iy == 0 && ix >= 0x7f800000) { - if ((hx & 0x7fffff) == 0) - return (cpackf(x, y)); - return (cpackf(x, copysignf(0, y))); - } + if (iy == 0) /* && ix >= 0x7f800000 */ + return (CMPLXF(x + x, y)); - if (ix < 0x7f800000 && iy >= 0x7f800000) - return (cpackf(y - y, x * (y - y))); + if (ix < 0x7f800000) /* && iy >= 0x7f800000 */ + return (CMPLXF(y - y, y - y)); - if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) { + if (ix == 0x7f800000) { if (iy >= 0x7f800000) - return (cpackf(x * x, x * (y - y))); - return (cpackf(x * cosf(y), INFINITY * sinf(y))); + return (CMPLXF(x, y - y)); + return (CMPLXF(x * cosf(y), INFINITY * sinf(y))); } - return (cpackf((x * x) * (y - y), (x + x) * (y - y))); + return (CMPLXF((x + x) * (y - y), (x * x) * (y - y))); } float complex csinf(float complex z) { - z = csinhf(cpackf(-cimagf(z), crealf(z))); - return (cpackf(cimagf(z), -crealf(z))); + z = csinhf(CMPLXF(cimagf(z), crealf(z))); + return (CMPLXF(cimagf(z), crealf(z))); } diff --git a/lib/msun/src/s_csqrt.c b/lib/msun/src/s_csqrt.c index 18a7ae3..75e12d8 100644 --- a/lib/msun/src/s_csqrt.c +++ b/lib/msun/src/s_csqrt.c @@ -58,12 +58,12 @@ csqrt(double complex z) /* Handle special cases. */ if (z == 0) - return (cpack(0, b)); + return (CMPLX(0, b)); if (isinf(b)) - return (cpack(INFINITY, b)); + return (CMPLX(INFINITY, b)); if (isnan(a)) { t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ - return (cpack(a, t)); /* return NaN + NaN i */ + return (CMPLX(a, t)); /* return NaN + NaN i */ } if (isinf(a)) { /* @@ -73,9 +73,9 @@ csqrt(double complex z) * csqrt(-inf + y i) = 0 + inf i */ if (signbit(a)) - return (cpack(fabs(b - b), copysign(a, b))); + return (CMPLX(fabs(b - b), copysign(a, b))); else - return (cpack(a, copysign(b - b, b))); + return (CMPLX(a, copysign(b - b, b))); } /* * The remaining special case (b is NaN) is handled just fine by @@ -94,10 +94,10 @@ csqrt(double complex z) /* Algorithm 312, CACM vol 10, Oct 1967. */ if (a >= 0) { t = sqrt((a + hypot(a, b)) * 0.5); - result = cpack(t, b / (2 * t)); + result = CMPLX(t, b / (2 * t)); } else { t = sqrt((-a + hypot(a, b)) * 0.5); - result = cpack(fabs(b) / (2 * t), copysign(t, b)); + result = CMPLX(fabs(b) / (2 * t), copysign(t, b)); } /* Rescale. */ diff --git a/lib/msun/src/s_csqrtf.c b/lib/msun/src/s_csqrtf.c index da7fe18..7ee513f 100644 --- a/lib/msun/src/s_csqrtf.c +++ b/lib/msun/src/s_csqrtf.c @@ -49,12 +49,12 @@ csqrtf(float complex z) /* Handle special cases. */ if (z == 0) - return (cpackf(0, b)); + return (CMPLXF(0, b)); if (isinf(b)) - return (cpackf(INFINITY, b)); + return (CMPLXF(INFINITY, b)); if (isnan(a)) { t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ - return (cpackf(a, t)); /* return NaN + NaN i */ + return (CMPLXF(a, t)); /* return NaN + NaN i */ } if (isinf(a)) { /* @@ -64,9 +64,9 @@ csqrtf(float complex z) * csqrtf(-inf + y i) = 0 + inf i */ if (signbit(a)) - return (cpackf(fabsf(b - b), copysignf(a, b))); + return (CMPLXF(fabsf(b - b), copysignf(a, b))); else - return (cpackf(a, copysignf(b - b, b))); + return (CMPLXF(a, copysignf(b - b, b))); } /* * The remaining special case (b is NaN) is handled just fine by @@ -80,9 +80,9 @@ csqrtf(float complex z) */ if (a >= 0) { t = sqrt((a + hypot(a, b)) * 0.5); - return (cpackf(t, b / (2.0 * t))); + return (CMPLXF(t, b / (2.0 * t))); } else { t = sqrt((-a + hypot(a, b)) * 0.5); - return (cpackf(fabsf(b) / (2.0 * t), copysignf(t, b))); + return (CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b))); } } diff --git a/lib/msun/src/s_csqrtl.c b/lib/msun/src/s_csqrtl.c index dd18e1e..ea2ef27 100644 --- a/lib/msun/src/s_csqrtl.c +++ b/lib/msun/src/s_csqrtl.c @@ -58,12 +58,12 @@ csqrtl(long double complex z) /* Handle special cases. */ if (z == 0) - return (cpackl(0, b)); + return (CMPLXL(0, b)); if (isinf(b)) - return (cpackl(INFINITY, b)); + return (CMPLXL(INFINITY, b)); if (isnan(a)) { t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ - return (cpackl(a, t)); /* return NaN + NaN i */ + return (CMPLXL(a, t)); /* return NaN + NaN i */ } if (isinf(a)) { /* @@ -73,9 +73,9 @@ csqrtl(long double complex z) * csqrt(-inf + y i) = 0 + inf i */ if (signbit(a)) - return (cpackl(fabsl(b - b), copysignl(a, b))); + return (CMPLXL(fabsl(b - b), copysignl(a, b))); else - return (cpackl(a, copysignl(b - b, b))); + return (CMPLXL(a, copysignl(b - b, b))); } /* * The remaining special case (b is NaN) is handled just fine by @@ -94,10 +94,10 @@ csqrtl(long double complex z) /* Algorithm 312, CACM vol 10, Oct 1967. */ if (a >= 0) { t = sqrtl((a + hypotl(a, b)) * 0.5); - result = cpackl(t, b / (2 * t)); + result = CMPLXL(t, b / (2 * t)); } else { t = sqrtl((-a + hypotl(a, b)) * 0.5); - result = cpackl(fabsl(b) / (2 * t), copysignl(t, b)); + result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b)); } /* Rescale. */ diff --git a/lib/msun/src/s_ctanh.c b/lib/msun/src/s_ctanh.c index d427e28..f5b9bdd 100644 --- a/lib/msun/src/s_ctanh.c +++ b/lib/msun/src/s_ctanh.c @@ -25,7 +25,7 @@ */ /* - * Hyperbolic tangent of a complex argument z = x + i y. + * Hyperbolic tangent of a complex argument z = x + I y. * * The algorithm is from: * @@ -44,15 +44,15 @@ * * tanh(z) = sinh(z) / cosh(z) * - * sinh(x) cos(y) + i cosh(x) sin(y) + * sinh(x) cos(y) + I cosh(x) sin(y) * = --------------------------------- - * cosh(x) cos(y) + i sinh(x) sin(y) + * cosh(x) cos(y) + I sinh(x) sin(y) * - * cosh(x) sinh(x) / cos^2(y) + i tan(y) + * cosh(x) sinh(x) / cos^2(y) + I tan(y) * = ------------------------------------- * 1 + sinh^2(x) / cos^2(y) * - * beta rho s + i t + * beta rho s + I t * = ---------------- * 1 + beta s^2 * @@ -85,16 +85,16 @@ ctanh(double complex z) ix = hx & 0x7fffffff; /* - * ctanh(NaN + i 0) = NaN + i 0 + * ctanh(NaN +- I 0) = d(NaN) +- I 0 * - * ctanh(NaN + i y) = NaN + i NaN for y != 0 + * ctanh(NaN + I y) = d(NaN,y) + I d(NaN,y) for y != 0 * * The imaginary part has the sign of x*sin(2*y), but there's no * special effort to get this right. * - * ctanh(+-Inf +- i Inf) = +-1 +- 0 + * ctanh(+-Inf +- I Inf) = +-1 +- I 0 * - * ctanh(+-Inf + i y) = +-1 + 0 sin(2y) for y finite + * ctanh(+-Inf + I y) = +-1 + I 0 sin(2y) for y finite * * The imaginary part of the sign is unspecified. This special * case is only needed to avoid a spurious invalid exception when @@ -102,26 +102,27 @@ ctanh(double complex z) */ if (ix >= 0x7ff00000) { if ((ix & 0xfffff) | lx) /* x is NaN */ - return (cpack(x, (y == 0 ? y : x * y))); + return (CMPLX((x + 0) * (y + 0), + y == 0 ? y : (x + 0) * (y + 0))); SET_HIGH_WORD(x, hx - 0x40000000); /* x = copysign(1, x) */ - return (cpack(x, copysign(0, isinf(y) ? y : sin(y) * cos(y)))); + return (CMPLX(x, copysign(0, isinf(y) ? y : sin(y) * cos(y)))); } /* - * ctanh(x + i NAN) = NaN + i NaN - * ctanh(x +- i Inf) = NaN + i NaN + * ctanh(x + I NaN) = d(NaN) + I d(NaN) + * ctanh(x +- I Inf) = dNaN + I dNaN */ if (!isfinite(y)) - return (cpack(y - y, y - y)); + return (CMPLX(y - y, y - y)); /* - * ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the + * ctanh(+-huge +- I y) ~= +-1 +- I 2sin(2y)/exp(2x), using the * approximation sinh^2(huge) ~= exp(2*huge) / 4. * We use a modified formula to avoid spurious overflow. */ - if (ix >= 0x40360000) { /* x >= 22 */ + if (ix >= 0x40360000) { /* |x| >= 22 */ double exp_mx = exp(-fabs(x)); - return (cpack(copysign(1, x), + return (CMPLX(copysign(1, x), 4 * sin(y) * cos(y) * exp_mx * exp_mx)); } @@ -131,14 +132,14 @@ ctanh(double complex z) s = sinh(x); rho = sqrt(1 + s * s); /* = cosh(x) */ denom = 1 + beta * s * s; - return (cpack((beta * rho * s) / denom, t / denom)); + return (CMPLX((beta * rho * s) / denom, t / denom)); } double complex ctan(double complex z) { - /* ctan(z) = -I * ctanh(I * z) */ - z = ctanh(cpack(-cimag(z), creal(z))); - return (cpack(cimag(z), -creal(z))); + /* ctan(z) = -I * ctanh(I * z) = I * conj(ctanh(I * conj(z))) */ + z = ctanh(CMPLX(cimag(z), creal(z))); + return (CMPLX(cimag(z), creal(z))); } diff --git a/lib/msun/src/s_ctanhf.c b/lib/msun/src/s_ctanhf.c index 4be28d8..520bf77 100644 --- a/lib/msun/src/s_ctanhf.c +++ b/lib/msun/src/s_ctanhf.c @@ -51,18 +51,19 @@ ctanhf(float complex z) if (ix >= 0x7f800000) { if (ix & 0x7fffff) - return (cpackf(x, (y == 0 ? y : x * y))); + return (CMPLXF((x + 0) * (y + 0), + y == 0 ? y : (x + 0) * (y + 0))); SET_FLOAT_WORD(x, hx - 0x40000000); - return (cpackf(x, + return (CMPLXF(x, copysignf(0, isinf(y) ? y : sinf(y) * cosf(y)))); } if (!isfinite(y)) - return (cpackf(y - y, y - y)); + return (CMPLXF(y - y, y - y)); - if (ix >= 0x41300000) { /* x >= 11 */ + if (ix >= 0x41300000) { /* |x| >= 11 */ float exp_mx = expf(-fabsf(x)); - return (cpackf(copysignf(1, x), + return (CMPLXF(copysignf(1, x), 4 * sinf(y) * cosf(y) * exp_mx * exp_mx)); } @@ -71,14 +72,14 @@ ctanhf(float complex z) s = sinhf(x); rho = sqrtf(1 + s * s); denom = 1 + beta * s * s; - return (cpackf((beta * rho * s) / denom, t / denom)); + return (CMPLXF((beta * rho * s) / denom, t / denom)); } float complex ctanf(float complex z) { - z = ctanhf(cpackf(-cimagf(z), crealf(z))); - return (cpackf(cimagf(z), -crealf(z))); + z = ctanhf(CMPLXF(cimagf(z), crealf(z))); + return (CMPLXF(cimagf(z), crealf(z))); } diff --git a/lib/msun/src/s_scalbln.c b/lib/msun/src/s_scalbln.c index 2aa6900..5e4e42e 100644 --- a/lib/msun/src/s_scalbln.c +++ b/lib/msun/src/s_scalbln.c @@ -27,32 +27,28 @@ #include <sys/cdefs.h> __FBSDID("$FreeBSD$"); -#include <limits.h> #include <math.h> +#define NMAX 65536 +#define NMIN -65536 + double -scalbln (double x, long n) +scalbln(double x, long n) { - int in; - in = (n > INT_MAX) ? INT_MAX : (n < INT_MIN) ? INT_MIN : n; - return (scalbn(x, in)); + return (scalbn(x, (n > NMAX) ? NMAX : (n < NMIN) ? NMIN : (int)n)); } float -scalblnf (float x, long n) +scalblnf(float x, long n) { - int in; - in = (n > INT_MAX) ? INT_MAX : (n < INT_MIN) ? INT_MIN : n; - return (scalbnf(x, in)); + return (scalbnf(x, (n > NMAX) ? NMAX : (n < NMIN) ? NMIN : (int)n)); } long double -scalblnl (long double x, long n) +scalblnl(long double x, long n) { - int in; - in = (n > INT_MAX) ? INT_MAX : (n < INT_MIN) ? INT_MIN : n; - return (scalbnl(x, in)); + return (scalbnl(x, (n > NMAX) ? NMAX : (n < NMIN) ? NMIN : (int)n)); } |
