Chromium Code Reviews
chromiumcodereview-hr@appspot.gserviceaccount.com (chromiumcodereview-hr) | Please choose your nickname with Settings | Help | Chromium Project | Gerrit Changes | Sign out
(326)

Issues Search
    My Issues | Starred     Open | Closed | All

Unified Diff: fusl/src/math/jn.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
Use n/p to move between diff chunks; N/P to move between comments. Draft comments are only viewable by you.
Jump to:
View side-by-side diff with in-line comments
Download patch
« fusl/arch/aarch64/atomic_arch.h ('K') | « fusl/src/math/j1f.c ('k') | fusl/src/math/jnf.c » ('j') | no next file with comments »
Expand Comments ('e') | Collapse Comments ('c') | Show Comments Hide Comments ('s')
Index: fusl/src/math/jn.c
diff --git a/fusl/src/math/jn.c b/fusl/src/math/jn.c
index 4878a54fedaebf474d1c3ee5c3993ea28e22998a..a0dcbafcbf8fbc1da96d1a417e3a414e481b5fd8 100644
--- a/fusl/src/math/jn.c
+++ b/fusl/src/math/jn.c
@@ -36,245 +36,259 @@
#include "libm.h"
-static const double invsqrtpi = 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */
+static const double invsqrtpi =
+ 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */
-double jn(int n, double x)
-{
- uint32_t ix, lx;
- int nm1, i, sign;
- double a, b, temp;
+double jn(int n, double x) {
+ uint32_t ix, lx;
+ int nm1, i, sign;
+ double a, b, temp;
- EXTRACT_WORDS(ix, lx, x);
- sign = ix>>31;
- ix &= 0x7fffffff;
+ EXTRACT_WORDS(ix, lx, x);
+ sign = ix >> 31;
+ ix &= 0x7fffffff;
- if ((ix | (lx|-lx)>>31) > 0x7ff00000) /* nan */
- return x;
+ if ((ix | (lx | -lx) >> 31) > 0x7ff00000) /* nan */
+ return x;
- /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
- * Thus, J(-n,x) = J(n,-x)
- */
- /* nm1 = |n|-1 is used instead of |n| to handle n==INT_MIN */
- if (n == 0)
- return j0(x);
- if (n < 0) {
- nm1 = -(n+1);
- x = -x;
- sign ^= 1;
- } else
- nm1 = n-1;
- if (nm1 == 0)
- return j1(x);
+ /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
+ * Thus, J(-n,x) = J(n,-x)
+ */
+ /* nm1 = |n|-1 is used instead of |n| to handle n==INT_MIN */
+ if (n == 0)
+ return j0(x);
+ if (n < 0) {
+ nm1 = -(n + 1);
+ x = -x;
+ sign ^= 1;
+ } else
+ nm1 = n - 1;
+ if (nm1 == 0)
+ return j1(x);
- sign &= n; /* even n: 0, odd n: signbit(x) */
- x = fabs(x);
- if ((ix|lx) == 0 || ix == 0x7ff00000) /* if x is 0 or inf */
- b = 0.0;
- else if (nm1 < x) {
- /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
- if (ix >= 0x52d00000) { /* x > 2**302 */
- /* (x >> n**2)
- * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Let s=sin(x), c=cos(x),
- * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
- *
- * n sin(xn)*sqt2 cos(xn)*sqt2
- * ----------------------------------
- * 0 s-c c+s
- * 1 -s-c -c+s
- * 2 -s+c -c-s
- * 3 s+c c-s
- */
- switch(nm1&3) {
- case 0: temp = -cos(x)+sin(x); break;
- case 1: temp = -cos(x)-sin(x); break;
- case 2: temp = cos(x)-sin(x); break;
- default:
- case 3: temp = cos(x)+sin(x); break;
- }
- b = invsqrtpi*temp/sqrt(x);
- } else {
- a = j0(x);
- b = j1(x);
- for (i=0; i<nm1; ) {
- i++;
- temp = b;
- b = b*(2.0*i/x) - a; /* avoid underflow */
- a = temp;
- }
- }
- } else {
- if (ix < 0x3e100000) { /* x < 2**-29 */
- /* x is tiny, return the first Taylor expansion of J(n,x)
- * J(n,x) = 1/n!*(x/2)^n - ...
- */
- if (nm1 > 32) /* underflow */
- b = 0.0;
- else {
- temp = x*0.5;
- b = temp;
- a = 1.0;
- for (i=2; i<=nm1+1; i++) {
- a *= (double)i; /* a = n! */
- b *= temp; /* b = (x/2)^n */
- }
- b = b/a;
- }
- } else {
- /* use backward recurrence */
- /* x x^2 x^2
- * J(n,x)/J(n-1,x) = ---- ------ ------ .....
- * 2n - 2(n+1) - 2(n+2)
- *
- * 1 1 1
- * (for large x) = ---- ------ ------ .....
- * 2n 2(n+1) 2(n+2)
- * -- - ------ - ------ -
- * x x x
- *
- * Let w = 2n/x and h=2/x, then the above quotient
- * is equal to the continued fraction:
- * 1
- * = -----------------------
- * 1
- * w - -----------------
- * 1
- * w+h - ---------
- * w+2h - ...
- *
- * To determine how many terms needed, let
- * Q(0) = w, Q(1) = w(w+h) - 1,
- * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
- * When Q(k) > 1e4 good for single
- * When Q(k) > 1e9 good for double
- * When Q(k) > 1e17 good for quadruple
- */
- /* determine k */
- double t,q0,q1,w,h,z,tmp,nf;
- int k;
+ sign &= n; /* even n: 0, odd n: signbit(x) */
+ x = fabs(x);
+ if ((ix | lx) == 0 || ix == 0x7ff00000) /* if x is 0 or inf */
+ b = 0.0;
+ else if (nm1 < x) {
+ /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+ if (ix >= 0x52d00000) { /* x > 2**302 */
+ /* (x >> n**2)
+ * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Let s=sin(x), c=cos(x),
+ * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+ *
+ * n sin(xn)*sqt2 cos(xn)*sqt2
+ * ----------------------------------
+ * 0 s-c c+s
+ * 1 -s-c -c+s
+ * 2 -s+c -c-s
+ * 3 s+c c-s
+ */
+ switch (nm1 & 3) {
+ case 0:
+ temp = -cos(x) + sin(x);
+ break;
+ case 1:
+ temp = -cos(x) - sin(x);
+ break;
+ case 2:
+ temp = cos(x) - sin(x);
+ break;
+ default:
+ case 3:
+ temp = cos(x) + sin(x);
+ break;
+ }
+ b = invsqrtpi * temp / sqrt(x);
+ } else {
+ a = j0(x);
+ b = j1(x);
+ for (i = 0; i < nm1;) {
+ i++;
+ temp = b;
+ b = b * (2.0 * i / x) - a; /* avoid underflow */
+ a = temp;
+ }
+ }
+ } else {
+ if (ix < 0x3e100000) { /* x < 2**-29 */
+ /* x is tiny, return the first Taylor expansion of J(n,x)
+ * J(n,x) = 1/n!*(x/2)^n - ...
+ */
+ if (nm1 > 32) /* underflow */
+ b = 0.0;
+ else {
+ temp = x * 0.5;
+ b = temp;
+ a = 1.0;
+ for (i = 2; i <= nm1 + 1; i++) {
+ a *= (double)i; /* a = n! */
+ b *= temp; /* b = (x/2)^n */
+ }
+ b = b / a;
+ }
+ } else {
+ /* use backward recurrence */
+ /* x x^2 x^2
+ * J(n,x)/J(n-1,x) = ---- ------ ------ .....
+ * 2n - 2(n+1) - 2(n+2)
+ *
+ * 1 1 1
+ * (for large x) = ---- ------ ------ .....
+ * 2n 2(n+1) 2(n+2)
+ * -- - ------ - ------ -
+ * x x x
+ *
+ * Let w = 2n/x and h=2/x, then the above quotient
+ * is equal to the continued fraction:
+ * 1
+ * = -----------------------
+ * 1
+ * w - -----------------
+ * 1
+ * w+h - ---------
+ * w+2h - ...
+ *
+ * To determine how many terms needed, let
+ * Q(0) = w, Q(1) = w(w+h) - 1,
+ * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+ * When Q(k) > 1e4 good for single
+ * When Q(k) > 1e9 good for double
+ * When Q(k) > 1e17 good for quadruple
+ */
+ /* determine k */
+ double t, q0, q1, w, h, z, tmp, nf;
+ int k;
- nf = nm1 + 1.0;
- w = 2*nf/x;
- h = 2/x;
- z = w+h;
- q0 = w;
- q1 = w*z - 1.0;
- k = 1;
- while (q1 < 1.0e9) {
- k += 1;
- z += h;
- tmp = z*q1 - q0;
- q0 = q1;
- q1 = tmp;
- }
- for (t=0.0, i=k; i>=0; i--)
- t = 1/(2*(i+nf)/x - t);
- a = t;
- b = 1.0;
- /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
- * Hence, if n*(log(2n/x)) > ...
- * single 8.8722839355e+01
- * double 7.09782712893383973096e+02
- * long double 1.1356523406294143949491931077970765006170e+04
- * then recurrent value may overflow and the result is
- * likely underflow to zero
- */
- tmp = nf*log(fabs(w));
- if (tmp < 7.09782712893383973096e+02) {
- for (i=nm1; i>0; i--) {
- temp = b;
- b = b*(2.0*i)/x - a;
- a = temp;
- }
- } else {
- for (i=nm1; i>0; i--) {
- temp = b;
- b = b*(2.0*i)/x - a;
- a = temp;
- /* scale b to avoid spurious overflow */
- if (b > 0x1p500) {
- a /= b;
- t /= b;
- b = 1.0;
- }
- }
- }
- z = j0(x);
- w = j1(x);
- if (fabs(z) >= fabs(w))
- b = t*z/b;
- else
- b = t*w/a;
- }
- }
- return sign ? -b : b;
+ nf = nm1 + 1.0;
+ w = 2 * nf / x;
+ h = 2 / x;
+ z = w + h;
+ q0 = w;
+ q1 = w * z - 1.0;
+ k = 1;
+ while (q1 < 1.0e9) {
+ k += 1;
+ z += h;
+ tmp = z * q1 - q0;
+ q0 = q1;
+ q1 = tmp;
+ }
+ for (t = 0.0, i = k; i >= 0; i--)
+ t = 1 / (2 * (i + nf) / x - t);
+ a = t;
+ b = 1.0;
+ /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+ * Hence, if n*(log(2n/x)) > ...
+ * single 8.8722839355e+01
+ * double 7.09782712893383973096e+02
+ * long double 1.1356523406294143949491931077970765006170e+04
+ * then recurrent value may overflow and the result is
+ * likely underflow to zero
+ */
+ tmp = nf * log(fabs(w));
+ if (tmp < 7.09782712893383973096e+02) {
+ for (i = nm1; i > 0; i--) {
+ temp = b;
+ b = b * (2.0 * i) / x - a;
+ a = temp;
+ }
+ } else {
+ for (i = nm1; i > 0; i--) {
+ temp = b;
+ b = b * (2.0 * i) / x - a;
+ a = temp;
+ /* scale b to avoid spurious overflow */
+ if (b > 0x1p500) {
+ a /= b;
+ t /= b;
+ b = 1.0;
+ }
+ }
+ }
+ z = j0(x);
+ w = j1(x);
+ if (fabs(z) >= fabs(w))
+ b = t * z / b;
+ else
+ b = t * w / a;
+ }
+ }
+ return sign ? -b : b;
}
+double yn(int n, double x) {
+ uint32_t ix, lx, ib;
+ int nm1, sign, i;
+ double a, b, temp;
-double yn(int n, double x)
-{
- uint32_t ix, lx, ib;
- int nm1, sign, i;
- double a, b, temp;
+ EXTRACT_WORDS(ix, lx, x);
+ sign = ix >> 31;
+ ix &= 0x7fffffff;
- EXTRACT_WORDS(ix, lx, x);
- sign = ix>>31;
- ix &= 0x7fffffff;
+ if ((ix | (lx | -lx) >> 31) > 0x7ff00000) /* nan */
+ return x;
+ if (sign && (ix | lx) != 0) /* x < 0 */
+ return 0 / 0.0;
+ if (ix == 0x7ff00000)
+ return 0.0;
- if ((ix | (lx|-lx)>>31) > 0x7ff00000) /* nan */
- return x;
- if (sign && (ix|lx)!=0) /* x < 0 */
- return 0/0.0;
- if (ix == 0x7ff00000)
- return 0.0;
+ if (n == 0)
+ return y0(x);
+ if (n < 0) {
+ nm1 = -(n + 1);
+ sign = n & 1;
+ } else {
+ nm1 = n - 1;
+ sign = 0;
+ }
+ if (nm1 == 0)
+ return sign ? -y1(x) : y1(x);
- if (n == 0)
- return y0(x);
- if (n < 0) {
- nm1 = -(n+1);
- sign = n&1;
- } else {
- nm1 = n-1;
- sign = 0;
- }
- if (nm1 == 0)
- return sign ? -y1(x) : y1(x);
-
- if (ix >= 0x52d00000) { /* x > 2**302 */
- /* (x >> n**2)
- * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Let s=sin(x), c=cos(x),
- * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
- *
- * n sin(xn)*sqt2 cos(xn)*sqt2
- * ----------------------------------
- * 0 s-c c+s
- * 1 -s-c -c+s
- * 2 -s+c -c-s
- * 3 s+c c-s
- */
- switch(nm1&3) {
- case 0: temp = -sin(x)-cos(x); break;
- case 1: temp = -sin(x)+cos(x); break;
- case 2: temp = sin(x)+cos(x); break;
- default:
- case 3: temp = sin(x)-cos(x); break;
- }
- b = invsqrtpi*temp/sqrt(x);
- } else {
- a = y0(x);
- b = y1(x);
- /* quit if b is -inf */
- GET_HIGH_WORD(ib, b);
- for (i=0; i<nm1 && ib!=0xfff00000; ){
- i++;
- temp = b;
- b = (2.0*i/x)*b - a;
- GET_HIGH_WORD(ib, b);
- a = temp;
- }
- }
- return sign ? -b : b;
+ if (ix >= 0x52d00000) { /* x > 2**302 */
+ /* (x >> n**2)
+ * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Let s=sin(x), c=cos(x),
+ * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+ *
+ * n sin(xn)*sqt2 cos(xn)*sqt2
+ * ----------------------------------
+ * 0 s-c c+s
+ * 1 -s-c -c+s
+ * 2 -s+c -c-s
+ * 3 s+c c-s
+ */
+ switch (nm1 & 3) {
+ case 0:
+ temp = -sin(x) - cos(x);
+ break;
+ case 1:
+ temp = -sin(x) + cos(x);
+ break;
+ case 2:
+ temp = sin(x) + cos(x);
+ break;
+ default:
+ case 3:
+ temp = sin(x) - cos(x);
+ break;
+ }
+ b = invsqrtpi * temp / sqrt(x);
+ } else {
+ a = y0(x);
+ b = y1(x);
+ /* quit if b is -inf */
+ GET_HIGH_WORD(ib, b);
+ for (i = 0; i < nm1 && ib != 0xfff00000;) {
+ i++;
+ temp = b;
+ b = (2.0 * i / x) * b - a;
+ GET_HIGH_WORD(ib, b);
+ a = temp;
+ }
+ }
+ return sign ? -b : b;
}
« fusl/arch/aarch64/atomic_arch.h ('K') | « fusl/src/math/j1f.c ('k') | fusl/src/math/jnf.c » ('j') | no next file with comments »

Powered by Google App Engine
This is Rietveld 408576698