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- Change comments to be more consistent with s_ccosh.c and s_csinh.c.

Browse Source 
- Fix a case where NaNs were not mixed correctly and signalling NaNs were
  not converted to quiet NaNs.
- Eliminate two negations from ctan(z).

In collaboration with:	bde
This commit is contained in:
Tijl Coosemans 2015-06-15 20:40:44 +00:00
parent f0f050e0f9
commit 68b433d790
2 changed files with 21 additions and 20 deletions
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35
lib/msun/src/s_ctanh.c
View File

@ -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
@ -102,24 +102,25 @@ ctanh(double complex z)
*/
if (ix >= 0x7ff00000) {
if ((ix & 0xfffff) | lx) /* x is NaN */
return (CMPLX(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 (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 (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 (CMPLX(copysign(1, x),
4 * sin(y) * cos(y) * exp_mx * exp_mx));
@ -138,7 +139,7 @@ double complex
ctan(double complex z)
{
/* ctan(z) = -I * ctanh(I * z) */
z = ctanh(CMPLX(-cimag(z), creal(z)));
return (CMPLX(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)));
}

6
lib/msun/src/s_ctanhf.c
View File

@ -60,7 +60,7 @@ ctanhf(float complex z)
if (!isfinite(y))
return (CMPLXF(y - y, y - y));
if (ix >= 0x41300000) { /* x >= 11 */
if (ix >= 0x41300000) { /* |x| >= 11 */
float exp_mx = expf(-fabsf(x));
return (CMPLXF(copysignf(1, x),
4 * sinf(y) * cosf(y) * exp_mx * exp_mx));
@ -78,7 +78,7 @@ float complex
ctanf(float complex z)
{
z = ctanhf(CMPLXF(-cimagf(z), crealf(z)));
return (CMPLXF(cimagf(z), -crealf(z)));
z = ctanhf(CMPLXF(cimagf(z), crealf(z)));
return (CMPLXF(cimagf(z), crealf(z)));
}