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-rw-r--r--lib/libm/lgammal.c115
1 files changed, 33 insertions, 82 deletions
diff --git a/lib/libm/lgammal.c b/lib/libm/lgammal.c
index 6c137e20..4bb58d09 100644
--- a/lib/libm/lgammal.c
+++ b/lib/libm/lgammal.c
@@ -104,17 +104,12 @@ static const long double
/* lgam(1+x) = 0.5 x + x a(x)/b(x)
-0.268402099609375 <= x <= 0
peak relative error 6.6e-22 */
- a0 = -6.343246574721079391729402781192128239938E2L,
- a1 = 1.856560238672465796768677717168371401378E3L,
- a2 = 2.404733102163746263689288466865843408429E3L,
- a3 = 8.804188795790383497379532868917517596322E2L,
- a4 = 1.135361354097447729740103745999661157426E2L,
- a5 = 3.766956539107615557608581581190400021285E0L,
+ a0 = -6.343246574721079391729402781192128239938E2L, a1 = 1.856560238672465796768677717168371401378E3L,
+ a2 = 2.404733102163746263689288466865843408429E3L, a3 = 8.804188795790383497379532868917517596322E2L,
+ a4 = 1.135361354097447729740103745999661157426E2L, a5 = 3.766956539107615557608581581190400021285E0L,
- b0 = 8.214973713960928795704317259806842490498E3L,
- b1 = 1.026343508841367384879065363925870888012E4L,
- b2 = 4.553337477045763320522762343132210919277E3L,
- b3 = 8.506975785032585797446253359230031874803E2L,
+ b0 = 8.214973713960928795704317259806842490498E3L, b1 = 1.026343508841367384879065363925870888012E4L,
+ b2 = 4.553337477045763320522762343132210919277E3L, b3 = 8.506975785032585797446253359230031874803E2L,
b4 = 6.042447899703295436820744186992189445813E1L,
/* b5 = 1.000000000000000000000000000000000000000E0 */
@@ -130,58 +125,40 @@ static const long double
-0.230003726999612341262659542325721328468 <= x
<= 0.2699962730003876587373404576742786715318
peak relative error 2.1e-21 */
- g0 = 3.645529916721223331888305293534095553827E-18L,
- g1 = 5.126654642791082497002594216163574795690E3L,
- g2 = 8.828603575854624811911631336122070070327E3L,
- g3 = 5.464186426932117031234820886525701595203E3L,
- g4 = 1.455427403530884193180776558102868592293E3L,
- g5 = 1.541735456969245924860307497029155838446E2L,
+ g0 = 3.645529916721223331888305293534095553827E-18L, g1 = 5.126654642791082497002594216163574795690E3L,
+ g2 = 8.828603575854624811911631336122070070327E3L, g3 = 5.464186426932117031234820886525701595203E3L,
+ g4 = 1.455427403530884193180776558102868592293E3L, g5 = 1.541735456969245924860307497029155838446E2L,
g6 = 4.335498275274822298341872707453445815118E0L,
- h0 = 1.059584930106085509696730443974495979641E4L,
- h1 = 2.147921653490043010629481226937850618860E4L,
- h2 = 1.643014770044524804175197151958100656728E4L,
- h3 = 5.869021995186925517228323497501767586078E3L,
- h4 = 9.764244777714344488787381271643502742293E2L,
- h5 = 6.442485441570592541741092969581997002349E1L,
+ h0 = 1.059584930106085509696730443974495979641E4L, h1 = 2.147921653490043010629481226937850618860E4L,
+ h2 = 1.643014770044524804175197151958100656728E4L, h3 = 5.869021995186925517228323497501767586078E3L,
+ h4 = 9.764244777714344488787381271643502742293E2L, h5 = 6.442485441570592541741092969581997002349E1L,
/* h6 = 1.000000000000000000000000000000000000000E0 */
/* lgam (x+1) = -0.5 x + x u(x)/v(x)
-0.100006103515625 <= x <= 0.231639862060546875
peak relative error 1.3e-21 */
- u0 = -8.886217500092090678492242071879342025627E1L,
- u1 = 6.840109978129177639438792958320783599310E2L,
- u2 = 2.042626104514127267855588786511809932433E3L,
- u3 = 1.911723903442667422201651063009856064275E3L,
- u4 = 7.447065275665887457628865263491667767695E2L,
- u5 = 1.132256494121790736268471016493103952637E2L,
+ u0 = -8.886217500092090678492242071879342025627E1L, u1 = 6.840109978129177639438792958320783599310E2L,
+ u2 = 2.042626104514127267855588786511809932433E3L, u3 = 1.911723903442667422201651063009856064275E3L,
+ u4 = 7.447065275665887457628865263491667767695E2L, u5 = 1.132256494121790736268471016493103952637E2L,
u6 = 4.484398885516614191003094714505960972894E0L,
- v0 = 1.150830924194461522996462401210374632929E3L,
- v1 = 3.399692260848747447377972081399737098610E3L,
- v2 = 3.786631705644460255229513563657226008015E3L,
- v3 = 1.966450123004478374557778781564114347876E3L,
- v4 = 4.741359068914069299837355438370682773122E2L,
- v5 = 4.508989649747184050907206782117647852364E1L,
+ v0 = 1.150830924194461522996462401210374632929E3L, v1 = 3.399692260848747447377972081399737098610E3L,
+ v2 = 3.786631705644460255229513563657226008015E3L, v3 = 1.966450123004478374557778781564114347876E3L,
+ v4 = 4.741359068914069299837355438370682773122E2L, v5 = 4.508989649747184050907206782117647852364E1L,
/* v6 = 1.000000000000000000000000000000000000000E0 */
/* lgam (x+2) = .5 x + x s(x)/r(x)
0 <= x <= 1
peak relative error 7.2e-22 */
- s0 = 1.454726263410661942989109455292824853344E6L,
- s1 = -3.901428390086348447890408306153378922752E6L,
- s2 = -6.573568698209374121847873064292963089438E6L,
- s3 = -3.319055881485044417245964508099095984643E6L,
- s4 = -7.094891568758439227560184618114707107977E5L,
- s5 = -6.263426646464505837422314539808112478303E4L,
+ s0 = 1.454726263410661942989109455292824853344E6L, s1 = -3.901428390086348447890408306153378922752E6L,
+ s2 = -6.573568698209374121847873064292963089438E6L, s3 = -3.319055881485044417245964508099095984643E6L,
+ s4 = -7.094891568758439227560184618114707107977E5L, s5 = -6.263426646464505837422314539808112478303E4L,
s6 = -1.684926520999477529949915657519454051529E3L,
- r0 = -1.883978160734303518163008696712983134698E7L,
- r1 = -2.815206082812062064902202753264922306830E7L,
- r2 = -1.600245495251915899081846093343626358398E7L,
- r3 = -4.310526301881305003489257052083370058799E6L,
- r4 = -5.563807682263923279438235987186184968542E5L,
- r5 = -3.027734654434169996032905158145259713083E4L,
+ r0 = -1.883978160734303518163008696712983134698E7L, r1 = -2.815206082812062064902202753264922306830E7L,
+ r2 = -1.600245495251915899081846093343626358398E7L, r3 = -4.310526301881305003489257052083370058799E6L,
+ r4 = -5.563807682263923279438235987186184968542E5L, r5 = -3.027734654434169996032905158145259713083E4L,
r6 = -4.501995652861105629217250715790764371267E2L,
/* r6 = 1.000000000000000000000000000000000000000E0 */
@@ -189,9 +166,8 @@ static const long double
x >= 8
Peak relative error 1.51e-21
w0 = LS2PI - 0.5 */
- w0 = 4.189385332046727417803e-1L, w1 = 8.333333333333331447505E-2L,
- w2 = -2.777777777750349603440E-3L, w3 = 7.936507795855070755671E-4L,
- w4 = -5.952345851765688514613E-4L, w5 = 8.412723297322498080632E-4L,
+ w0 = 4.189385332046727417803e-1L, w1 = 8.333333333333331447505E-2L, w2 = -2.777777777750349603440E-3L,
+ w3 = 7.936507795855070755671E-4L, w4 = -5.952345851765688514613E-4L, w5 = 8.412723297322498080632E-4L,
w6 = -1.880801938119376907179E-3L, w7 = 4.885026142432270781165E-3L;
/* sin(pi*x) assuming x > 2^-1000, if sin(pi*x)==0 the sign is arbitrary */
@@ -289,48 +265,27 @@ long double __lgammal_r(long double x, int *sg)
}
switch (i) {
case 0:
- p1 = a0 +
- y * (a1 + y * (a2 + y * (a3 + y * (a4 + y * a5))));
+ p1 = a0 + y * (a1 + y * (a2 + y * (a3 + y * (a4 + y * a5))));
p2 = b0 + y * (b1 + y * (b2 + y * (b3 + y * (b4 + y))));
r += 0.5 * y + y * p1 / p2;
break;
case 1:
- p1 = g0 +
- y * (g1 +
- y * (g2 +
- y * (g3 + y * (g4 + y * (g5 + y * g6)))));
- p2 = h0 +
- y * (h1 +
- y * (h2 +
- y * (h3 + y * (h4 + y * (h5 + y)))));
+ p1 = g0 + y * (g1 + y * (g2 + y * (g3 + y * (g4 + y * (g5 + y * g6)))));
+ p2 = h0 + y * (h1 + y * (h2 + y * (h3 + y * (h4 + y * (h5 + y)))));
p = tt + y * p1 / p2;
r += (tf + p);
break;
case 2:
- p1 = y *
- (u0 +
- y * (u1 +
- y * (u2 +
- y * (u3 +
- y * (u4 + y * (u5 + y * u6))))));
- p2 = v0 +
- y * (v1 +
- y * (v2 +
- y * (v3 + y * (v4 + y * (v5 + y)))));
+ p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * (u5 + y * u6))))));
+ p2 = v0 + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * (v5 + y)))));
r += (-0.5 * y + p1 / p2);
}
} else if (ix < 0x40028000) { /* 8.0 */
/* x < 8.0 */
i = (int)x;
y = x - (double)i;
- p = y *
- (s0 +
- y * (s1 +
- y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6))))));
- q = r0 +
- y * (r1 +
- y * (r2 +
- y * (r3 + y * (r4 + y * (r5 + y * (r6 + y))))));
+ p = y * (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6))))));
+ q = r0 + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * (r6 + y))))));
r = 0.5 * y + p / q;
z = 1.0;
/* lgamma(1+s) = log(s) + lgamma(s) */
@@ -353,11 +308,7 @@ long double __lgammal_r(long double x, int *sg)
t = logl(x);
z = 1.0 / x;
y = z * z;
- w = w0 +
- z * (w1 +
- y * (w2 +
- y * (w3 +
- y * (w4 + y * (w5 + y * (w6 + y * w7))))));
+ w = w0 + z * (w1 + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * (w6 + y * w7))))));
r = (x - 0.5) * (t - 1.0) + w;
} else /* 2**66 <= x <= inf */
r = x * (logl(x) - 1.0);
generated by cgit v1.2.3 (git 2.39.1) at 2026-04-05 14:27:13 +0000