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Unified Diff: fusl/src/math/tgamma.c

Issue 1714623002: [fusl] clang-format fusl (Closed) Base URL: git@github.com:domokit/mojo.git@master
Patch Set: headers too Created 4 years, 10 months ago
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Index: fusl/src/math/tgamma.c
diff --git a/fusl/src/math/tgamma.c b/fusl/src/math/tgamma.c
index 28f6e0f8327a9368c0c39bc2db4b25033cb24895..feb0616ec674db8028211c684652d0b5ae9b99f6 100644
--- a/fusl/src/math/tgamma.c
+++ b/fusl/src/math/tgamma.c
@@ -27,147 +27,166 @@ most ideas and constants are from boost and python
static const double pi = 3.141592653589793238462643383279502884;
/* sin(pi x) with x > 0x1p-100, if sin(pi*x)==0 the sign is arbitrary */
-static double sinpi(double x)
-{
- int n;
-
- /* argument reduction: x = |x| mod 2 */
- /* spurious inexact when x is odd int */
- x = x * 0.5;
- x = 2 * (x - floor(x));
-
- /* reduce x into [-.25,.25] */
- n = 4 * x;
- n = (n+1)/2;
- x -= n * 0.5;
-
- x *= pi;
- switch (n) {
- default: /* case 4 */
- case 0:
- return __sin(x, 0, 0);
- case 1:
- return __cos(x, 0);
- case 2:
- return __sin(-x, 0, 0);
- case 3:
- return -__cos(x, 0);
- }
+static double sinpi(double x) {
+ int n;
+
+ /* argument reduction: x = |x| mod 2 */
+ /* spurious inexact when x is odd int */
+ x = x * 0.5;
+ x = 2 * (x - floor(x));
+
+ /* reduce x into [-.25,.25] */
+ n = 4 * x;
+ n = (n + 1) / 2;
+ x -= n * 0.5;
+
+ x *= pi;
+ switch (n) {
+ default: /* case 4 */
+ case 0:
+ return __sin(x, 0, 0);
+ case 1:
+ return __cos(x, 0);
+ case 2:
+ return __sin(-x, 0, 0);
+ case 3:
+ return -__cos(x, 0);
+ }
}
#define N 12
-//static const double g = 6.024680040776729583740234375;
+// static const double g = 6.024680040776729583740234375;
static const double gmhalf = 5.524680040776729583740234375;
-static const double Snum[N+1] = {
- 23531376880.410759688572007674451636754734846804940,
- 42919803642.649098768957899047001988850926355848959,
- 35711959237.355668049440185451547166705960488635843,
- 17921034426.037209699919755754458931112671403265390,
- 6039542586.3520280050642916443072979210699388420708,
- 1439720407.3117216736632230727949123939715485786772,
- 248874557.86205415651146038641322942321632125127801,
- 31426415.585400194380614231628318205362874684987640,
- 2876370.6289353724412254090516208496135991145378768,
- 186056.26539522349504029498971604569928220784236328,
- 8071.6720023658162106380029022722506138218516325024,
- 210.82427775157934587250973392071336271166969580291,
- 2.5066282746310002701649081771338373386264310793408,
+static const double Snum[N + 1] = {
+ 23531376880.410759688572007674451636754734846804940,
+ 42919803642.649098768957899047001988850926355848959,
+ 35711959237.355668049440185451547166705960488635843,
+ 17921034426.037209699919755754458931112671403265390,
+ 6039542586.3520280050642916443072979210699388420708,
+ 1439720407.3117216736632230727949123939715485786772,
+ 248874557.86205415651146038641322942321632125127801,
+ 31426415.585400194380614231628318205362874684987640,
+ 2876370.6289353724412254090516208496135991145378768,
+ 186056.26539522349504029498971604569928220784236328,
+ 8071.6720023658162106380029022722506138218516325024,
+ 210.82427775157934587250973392071336271166969580291,
+ 2.5066282746310002701649081771338373386264310793408,
};
-static const double Sden[N+1] = {
- 0, 39916800, 120543840, 150917976, 105258076, 45995730, 13339535,
- 2637558, 357423, 32670, 1925, 66, 1,
+static const double Sden[N + 1] = {
+ 0, 39916800, 120543840, 150917976, 105258076, 45995730, 13339535,
+ 2637558, 357423, 32670, 1925, 66, 1,
};
/* n! for small integer n */
static const double fact[] = {
- 1, 1, 2, 6, 24, 120, 720, 5040.0, 40320.0, 362880.0, 3628800.0, 39916800.0,
- 479001600.0, 6227020800.0, 87178291200.0, 1307674368000.0, 20922789888000.0,
- 355687428096000.0, 6402373705728000.0, 121645100408832000.0,
- 2432902008176640000.0, 51090942171709440000.0, 1124000727777607680000.0,
+ 1,
+ 1,
+ 2,
+ 6,
+ 24,
+ 120,
+ 720,
+ 5040.0,
+ 40320.0,
+ 362880.0,
+ 3628800.0,
+ 39916800.0,
+ 479001600.0,
+ 6227020800.0,
+ 87178291200.0,
+ 1307674368000.0,
+ 20922789888000.0,
+ 355687428096000.0,
+ 6402373705728000.0,
+ 121645100408832000.0,
+ 2432902008176640000.0,
+ 51090942171709440000.0,
+ 1124000727777607680000.0,
};
/* S(x) rational function for positive x */
-static double S(double x)
-{
- double_t num = 0, den = 0;
- int i;
-
- /* to avoid overflow handle large x differently */
- if (x < 8)
- for (i = N; i >= 0; i--) {
- num = num * x + Snum[i];
- den = den * x + Sden[i];
- }
- else
- for (i = 0; i <= N; i++) {
- num = num / x + Snum[i];
- den = den / x + Sden[i];
- }
- return num/den;
+static double S(double x) {
+ double_t num = 0, den = 0;
+ int i;
+
+ /* to avoid overflow handle large x differently */
+ if (x < 8)
+ for (i = N; i >= 0; i--) {
+ num = num * x + Snum[i];
+ den = den * x + Sden[i];
+ }
+ else
+ for (i = 0; i <= N; i++) {
+ num = num / x + Snum[i];
+ den = den / x + Sden[i];
+ }
+ return num / den;
}
-double tgamma(double x)
-{
- union {double f; uint64_t i;} u = {x};
- double absx, y;
- double_t dy, z, r;
- uint32_t ix = u.i>>32 & 0x7fffffff;
- int sign = u.i>>63;
-
- /* special cases */
- if (ix >= 0x7ff00000)
- /* tgamma(nan)=nan, tgamma(inf)=inf, tgamma(-inf)=nan with invalid */
- return x + INFINITY;
- if (ix < (0x3ff-54)<<20)
- /* |x| < 2^-54: tgamma(x) ~ 1/x, +-0 raises div-by-zero */
- return 1/x;
-
- /* integer arguments */
- /* raise inexact when non-integer */
- if (x == floor(x)) {
- if (sign)
- return 0/0.0;
- if (x <= sizeof fact/sizeof *fact)
- return fact[(int)x - 1];
- }
-
- /* x >= 172: tgamma(x)=inf with overflow */
- /* x =< -184: tgamma(x)=+-0 with underflow */
- if (ix >= 0x40670000) { /* |x| >= 184 */
- if (sign) {
- FORCE_EVAL((float)(0x1p-126/x));
- if (floor(x) * 0.5 == floor(x * 0.5))
- return 0;
- return -0.0;
- }
- x *= 0x1p1023;
- return x;
- }
-
- absx = sign ? -x : x;
-
- /* handle the error of x + g - 0.5 */
- y = absx + gmhalf;
- if (absx > gmhalf) {
- dy = y - absx;
- dy -= gmhalf;
- } else {
- dy = y - gmhalf;
- dy -= absx;
- }
-
- z = absx - 0.5;
- r = S(absx) * exp(-y);
- if (x < 0) {
- /* reflection formula for negative x */
- /* sinpi(absx) is not 0, integers are already handled */
- r = -pi / (sinpi(absx) * absx * r);
- dy = -dy;
- z = -z;
- }
- r += dy * (gmhalf+0.5) * r / y;
- z = pow(y, 0.5*z);
- y = r * z * z;
- return y;
+double tgamma(double x) {
+ union {
+ double f;
+ uint64_t i;
+ } u = {x};
+ double absx, y;
+ double_t dy, z, r;
+ uint32_t ix = u.i >> 32 & 0x7fffffff;
+ int sign = u.i >> 63;
+
+ /* special cases */
+ if (ix >= 0x7ff00000)
+ /* tgamma(nan)=nan, tgamma(inf)=inf, tgamma(-inf)=nan with invalid */
+ return x + INFINITY;
+ if (ix < (0x3ff - 54) << 20)
+ /* |x| < 2^-54: tgamma(x) ~ 1/x, +-0 raises div-by-zero */
+ return 1 / x;
+
+ /* integer arguments */
+ /* raise inexact when non-integer */
+ if (x == floor(x)) {
+ if (sign)
+ return 0 / 0.0;
+ if (x <= sizeof fact / sizeof *fact)
+ return fact[(int)x - 1];
+ }
+
+ /* x >= 172: tgamma(x)=inf with overflow */
+ /* x =< -184: tgamma(x)=+-0 with underflow */
+ if (ix >= 0x40670000) { /* |x| >= 184 */
+ if (sign) {
+ FORCE_EVAL((float)(0x1p-126 / x));
+ if (floor(x) * 0.5 == floor(x * 0.5))
+ return 0;
+ return -0.0;
+ }
+ x *= 0x1p1023;
+ return x;
+ }
+
+ absx = sign ? -x : x;
+
+ /* handle the error of x + g - 0.5 */
+ y = absx + gmhalf;
+ if (absx > gmhalf) {
+ dy = y - absx;
+ dy -= gmhalf;
+ } else {
+ dy = y - gmhalf;
+ dy -= absx;
+ }
+
+ z = absx - 0.5;
+ r = S(absx) * exp(-y);
+ if (x < 0) {
+ /* reflection formula for negative x */
+ /* sinpi(absx) is not 0, integers are already handled */
+ r = -pi / (sinpi(absx) * absx * r);
+ dy = -dy;
+ z = -z;
+ }
+ r += dy * (gmhalf + 0.5) * r / y;
+ z = pow(y, 0.5 * z);
+ y = r * z * z;
+ return y;
}
#if 0

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