Fix some exceptional cases where the sign of the result is unspecified
but must still satisfy ccosh(conj(z)) == conj(ccosh(z)) and ccosh(-z) == ccosh(z). In collaboration with: bde
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svn2git
2020-12-20 02:59:44 +00:00
svn path=/head/; revision=284423
@ -32,6 +32,8 @@
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*
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* Exceptional values are noted in the comments within the source code.
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* These values and the return value were taken from n1124.pdf.
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* The sign of the result for some exceptional values is unspecified but
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* must satisfy both cosh(conj(z)) == conj(cosh(z)) and cosh(-z) == cosh(z).
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*/
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#include <sys/cdefs.h>
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@ -63,7 +65,7 @@ ccosh(double complex z)
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if (ix < 0x7ff00000 && iy < 0x7ff00000) {
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if ((iy | ly) == 0)
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return (CMPLX(cosh(x), x * y));
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if (ix < 0x40360000) /* small x: normal case */
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if (ix < 0x40360000) /* |x| < 22: normal case */
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return (CMPLX(cosh(x) * cos(y), sinh(x) * sin(y)));
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/* |x| >= 22, so cosh(x) ~= exp(|x|) */
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@ -83,28 +85,27 @@ ccosh(double complex z)
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}
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/*
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* cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0.
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* The sign of 0 in the result is unspecified. Choice = normally
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* the same as dNaN. Raise the invalid floating-point exception.
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* cosh(+-0 +- I Inf) = dNaN + I (+-)(+-)0.
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* The sign of 0 in the result is unspecified. Choice = product
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* of the signs of the argument. Raise the invalid floating-point
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* exception.
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*
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* cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0.
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* The sign of 0 in the result is unspecified. Choice = normally
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* the same as d(NaN).
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* cosh(+-0 +- I NaN) = d(NaN) + I (+-)(+-)0.
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* The sign of 0 in the result is unspecified. Choice = product
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* of the signs of the argument.
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*/
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if ((ix | lx) == 0 && iy >= 0x7ff00000)
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return (CMPLX(y - y, copysign(0, x * (y - y))));
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if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */
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return (CMPLX(y - y, x * copysign(0, y)));
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/*
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* cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
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*
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* cosh(NaN +- I 0) = d(NaN) + I sign(d(NaN, +-0))0.
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* The sign of 0 in the result is unspecified.
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* cosh(NaN +- I 0) = d(NaN) + I (+-)(+-)0.
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* The sign of 0 in the result is unspecified. Choice = product
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* of the signs of the argument.
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*/
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if ((iy | ly) == 0 && ix >= 0x7ff00000) {
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if (((hx & 0xfffff) | lx) == 0)
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return (CMPLX(x * x, copysign(0, x) * y));
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return (CMPLX(x * x, copysign(0, (x + x) * y)));
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}
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if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */
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return (CMPLX(x * x, copysign(0, x) * y));
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/*
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* cosh(x +- I Inf) = dNaN + I dNaN.
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@ -114,7 +115,7 @@ ccosh(double complex z)
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* Optionally raises the invalid floating-point exception for finite
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* nonzero x. Choice = don't raise (except for signaling NaNs).
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*/
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if (ix < 0x7ff00000 && iy >= 0x7ff00000)
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if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */
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return (CMPLX(y - y, x * (y - y)));
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/*
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@ -126,10 +127,10 @@ ccosh(double complex z)
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*
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* cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y)
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*/
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if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
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if (ix == 0x7ff00000 && lx == 0) {
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if (iy >= 0x7ff00000)
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return (CMPLX(x * x, x * (y - y)));
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return (CMPLX((x * x) * cos(y), x * sin(y)));
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return (CMPLX(INFINITY, x * (y - y)));
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return (CMPLX(INFINITY * cos(y), x * sin(y)));
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}
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/*
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@ -25,7 +25,7 @@
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*/
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/*
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* Hyperbolic cosine of a complex argument. See s_ccosh.c for details.
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* Float version of ccosh(). See s_ccosh.c for details.
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*/
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#include <sys/cdefs.h>
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@ -56,13 +56,13 @@ ccoshf(float complex z)
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if (ix < 0x7f800000 && iy < 0x7f800000) {
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if (iy == 0)
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return (CMPLXF(coshf(x), x * y));
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if (ix < 0x41100000) /* small x: normal case */
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if (ix < 0x41100000) /* |x| < 9: normal case */
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return (CMPLXF(coshf(x) * cosf(y), sinhf(x) * sinf(y)));
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/* |x| >= 9, so cosh(x) ~= exp(|x|) */
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if (ix < 0x42b17218) {
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/* x < 88.7: expf(|x|) won't overflow */
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h = expf(fabsf(x)) * 0.5f;
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h = expf(fabsf(x)) * 0.5F;
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return (CMPLXF(h * cosf(y), copysignf(h, x) * sinf(y)));
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} else if (ix < 0x4340b1e7) {
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/* x < 192.7: scale to avoid overflow */
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@ -75,22 +75,19 @@ ccoshf(float complex z)
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}
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}
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if (ix == 0 && iy >= 0x7f800000)
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return (CMPLXF(y - y, copysignf(0, x * (y - y))));
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if (ix == 0) /* && iy >= 0x7f800000 */
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return (CMPLXF(y - y, x * copysignf(0, y)));
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if (iy == 0 && ix >= 0x7f800000) {
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if ((hx & 0x7fffff) == 0)
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return (CMPLXF(x * x, copysignf(0, x) * y));
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return (CMPLXF(x * x, copysignf(0, (x + x) * y)));
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}
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if (iy == 0) /* && ix >= 0x7f800000 */
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return (CMPLXF(x * x, copysignf(0, x) * y));
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if (ix < 0x7f800000 && iy >= 0x7f800000)
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if (ix < 0x7f800000) /* && iy >= 0x7f800000 */
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return (CMPLXF(y - y, x * (y - y)));
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if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) {
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if (ix == 0x7f800000) {
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if (iy >= 0x7f800000)
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return (CMPLXF(x * x, x * (y - y)));
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return (CMPLXF((x * x) * cosf(y), x * sinf(y)));
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return (CMPLXF(INFINITY, x * (y - y)));
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return (CMPLXF(INFINITY * cosf(y), x * sinf(y)));
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}
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return (CMPLXF((x * x) * (y - y), (x + x) * (y - y)));
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