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Change existing code to use CMPLX*() instead of cpack*() where possible. 

I am currently working on building openlibm against stock copies of
<math.h>, instead of the openlibm.h header. It seems that a C compliant
<math.h> header can be used as a drop-in replacement for openlibm.h,
with the exception that it lacks cpack*().

In FreeBSD SVN r275819 I patched up the math library by replacing
cpack*() by CMPLX*(). That way many functions become less tied to the
intrinsics of the math library. Make the same change to openlibm.
This commit is contained in:
Ed Schouten 2015-01-08 12:02:56 +01:00
parent 0b2a647742
commit 5d6cb09b96
20 changed files with 143 additions and 127 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
src/k_exp.c
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@ -103,6 +103,6 @@ __ldexp_cexp(double complex z, int expt)
half_expt = expt - half_expt;
INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0);
return (cpack(cos(y) * exp_x * scale1 * scale2,
return (CMPLX(cos(y) * exp_x * scale1 * scale2,
sin(y) * exp_x * scale1 * scale2));
}

2
src/k_expf.c
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@ -82,6 +82,6 @@ __ldexp_cexpf(float complex z, int expt)
half_expt = expt - half_expt;
SET_FLOAT_WORD(scale2, (0x7f + half_expt) << 23);
return (cpackf(cosf(y) * exp_x * scale1 * scale2,
return (CMPLXF(cosf(y) * exp_x * scale1 * scale2,
sinf(y) * exp_x * scale1 * scale2));
}

44
src/openlibm.h
View File

@ -204,7 +204,7 @@ typedef union {
#define IMAGPART(z) ((z).a[1])
/*
* Inline functions that can be used to construct complex values.
* Macros that can be used to construct complex values.
*
* The C99 standard intends x+I*y to be used for this, but x+I*y is
* currently unusable in general since gcc introduces many overflow,
@ -217,18 +217,20 @@ typedef union {
* and gcc 4.7 added a __builtin_complex feature to simplify implementation
* of CMPLX in libc, so we can take advantage of these features if they
* are available.
*
* If __builtin_complex is not available, resort to using inline
* functions instead. These can unfortunately not be used to construct
* compile-time constants.
*/
#if defined(CMPLXF) && defined(CMPLX) && defined(CMPLXL) /* C11 */
# define cpackf(x,y) CMPLXF(x,y)
# define cpack(x,y) CMPLX(x,y)
# define cpackl(x,y) CMPLXL(x,y)
#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 7)) && !defined(__INTEL_COMPILER)
# define cpackf(x,y) __builtin_complex ((float) (x), (float) (y))
# define cpack(x,y) __builtin_complex ((double) (x), (double) (y))
# define cpackl(x,y) __builtin_complex ((long double) (x), (long double) (y))
#else /* define our own cpack functions */
#define HAVE_BUILTIN_COMPLEX (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 7)) && !defined(__INTEL_COMPILER)
#ifndef CMPLXF
#if HAVE_BUILTIN_COMPLEX
# define CMPLXF(x,y) __builtin_complex ((float) (x), (float) (y))
#else
static __inline float complex
cpackf(float x, float y)
CMPLXF(float x, float y)
{
float_complex z;
@ -236,9 +238,15 @@ cpackf(float x, float y)
IMAGPART(z) = y;
return (z.f);
}
#endif
#endif
#ifndef CMPLX
#if HAVE_BUILTIN_COMPLEX
# define CMPLX(x,y) __builtin_complex ((double) (x), (double) (y))
#else
static __inline double complex
cpack(double x, double y)
CMPLX(double x, double y)
{
double_complex z;
@ -246,9 +254,15 @@ cpack(double x, double y)
IMAGPART(z) = y;
return (z.f);
}
#endif
#endif
#ifndef CMPLXL
#if HAVE_BUILTIN_COMPLEX
# define CMPLXL(x,y) __builtin_complex ((long double) (x), (long double) (y))
#else
static __inline long double complex
cpackl(long double x, long double y)
CMPLXL(long double x, long double y)
{
long_double_complex z;
@ -256,7 +270,9 @@ cpackl(long double x, long double y)
IMAGPART(z) = y;
return (z.f);
}
#endif /* define our own cpack functions */
#endif
#endif
//VBS
//#endif /* _COMPLEX_H */

28
src/s_ccosh.c
View File

@ -62,23 +62,23 @@ ccosh(double complex z)
/* Handle the nearly-non-exceptional cases where x and y are finite. */
if (ix < 0x7ff00000 && iy < 0x7ff00000) {
if ((iy | ly) == 0)
return (cpack(cosh(x), x * y));
return (CMPLX(cosh(x), x * y));
if (ix < 0x40360000) /* small x: normal case */
return (cpack(cosh(x) * cos(y), sinh(x) * sin(y)));
return (CMPLX(cosh(x) * cos(y), sinh(x) * sin(y)));
/* |x| >= 22, so cosh(x) ~= exp(|x|) */
if (ix < 0x40862e42) {
/* x < 710: exp(|x|) won't overflow */
h = exp(fabs(x)) * 0.5;
return (cpack(h * cos(y), copysign(h, x) * sin(y)));
return (CMPLX(h * cos(y), copysign(h, x) * sin(y)));
} else if (ix < 0x4096bbaa) {
/* x < 1455: scale to avoid overflow */
z = __ldexp_cexp(cpack(fabs(x), y), -1);
return (cpack(creal(z), cimag(z) * copysign(1, x)));
z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
return (CMPLX(creal(z), cimag(z) * copysign(1, x)));
} else {
/* x >= 1455: the result always overflows */
h = huge * x;
return (cpack(h * h * cos(y), h * sin(y)));
return (CMPLX(h * h * cos(y), h * sin(y)));
}
}
@ -92,7 +92,7 @@ ccosh(double complex z)
* the same as d(NaN).
*/
if ((ix | lx) == 0 && iy >= 0x7ff00000)
return (cpack(y - y, copysign(0, x * (y - y))));
return (CMPLX(y - y, copysign(0, x * (y - y))));
/*
* cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
@ -102,8 +102,8 @@ ccosh(double complex z)
*/
if ((iy | ly) == 0 && ix >= 0x7ff00000) {
if (((hx & 0xfffff) | lx) == 0)
return (cpack(x * x, copysign(0, x) * y));
return (cpack(x * x, copysign(0, (x + x) * y)));
return (CMPLX(x * x, copysign(0, x) * y));
return (CMPLX(x * x, copysign(0, (x + x) * y)));
}
/*
@ -115,7 +115,7 @@ ccosh(double complex z)
* nonzero x. Choice = don't raise (except for signaling NaNs).
*/
if (ix < 0x7ff00000 && iy >= 0x7ff00000)
return (cpack(y - y, x * (y - y)));
return (CMPLX(y - y, x * (y - y)));
/*
* cosh(+-Inf + I NaN) = +Inf + I d(NaN).
@ -128,8 +128,8 @@ ccosh(double complex z)
*/
if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
if (iy >= 0x7ff00000)
return (cpack(x * x, x * (y - y)));
return (cpack((x * x) * cos(y), x * sin(y)));
return (CMPLX(x * x, x * (y - y)));
return (CMPLX((x * x) * cos(y), x * sin(y)));
}
/*
@ -143,7 +143,7 @@ ccosh(double complex z)
* Optionally raises the invalid floating-point exception for finite
* nonzero y. Choice = don't raise (except for signaling NaNs).
*/
return (cpack((x * x) * (y - y), (x + x) * (y - y)));
return (CMPLX((x * x) * (y - y), (x + x) * (y - y)));
}
DLLEXPORT double complex
@ -151,5 +151,5 @@ ccos(double complex z)
{
/* ccos(z) = ccosh(I * z) */
return (ccosh(cpack(-cimag(z), creal(z))));
return (ccosh(CMPLX(-cimag(z), creal(z))));
}

28
src/s_ccoshf.c
View File

@ -55,50 +55,50 @@ ccoshf(float complex z)
if (ix < 0x7f800000 && iy < 0x7f800000) {
if (iy == 0)
return (cpackf(coshf(x), x * y));
return (CMPLXF(coshf(x), x * y));
if (ix < 0x41100000) /* small x: normal case */
return (cpackf(coshf(x) * cosf(y), sinhf(x) * sinf(y)));
return (CMPLXF(coshf(x) * cosf(y), sinhf(x) * sinf(y)));
/* |x| >= 9, so cosh(x) ~= exp(|x|) */
if (ix < 0x42b17218) {
/* x < 88.7: expf(|x|) won't overflow */
h = expf(fabsf(x)) * 0.5f;
return (cpackf(h * cosf(y), copysignf(h, x) * sinf(y)));
return (CMPLXF(h * cosf(y), copysignf(h, x) * sinf(y)));
} else if (ix < 0x4340b1e7) {
/* x < 192.7: scale to avoid overflow */
z = __ldexp_cexpf(cpackf(fabsf(x), y), -1);
return (cpackf(crealf(z), cimagf(z) * copysignf(1, x)));
z = __ldexp_cexpf(CMPLXF(fabsf(x), y), -1);
return (CMPLXF(crealf(z), cimagf(z) * copysignf(1, x)));
} else {
/* x >= 192.7: the result always overflows */
h = huge * x;
return (cpackf(h * h * cosf(y), h * sinf(y)));
return (CMPLXF(h * h * cosf(y), h * sinf(y)));
}
}
if (ix == 0 && iy >= 0x7f800000)
return (cpackf(y - y, copysignf(0, x * (y - y))));
return (CMPLXF(y - y, copysignf(0, x * (y - y))));
if (iy == 0 && ix >= 0x7f800000) {
if ((hx & 0x7fffff) == 0)
return (cpackf(x * x, copysignf(0, x) * y));
return (cpackf(x * x, copysignf(0, (x + x) * y)));
return (CMPLXF(x * x, copysignf(0, x) * y));
return (CMPLXF(x * x, copysignf(0, (x + x) * y)));
}
if (ix < 0x7f800000 && iy >= 0x7f800000)
return (cpackf(y - y, x * (y - y)));
return (CMPLXF(y - y, x * (y - y)));
if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) {
if (iy >= 0x7f800000)
return (cpackf(x * x, x * (y - y)));
return (cpackf((x * x) * cosf(y), x * sinf(y)));
return (CMPLXF(x * x, x * (y - y)));
return (CMPLXF((x * x) * cosf(y), x * sinf(y)));
}
return (cpackf((x * x) * (y - y), (x + x) * (y - y)));
return (CMPLXF((x * x) * (y - y), (x + x) * (y - y)));
}
DLLEXPORT float complex
ccosf(float complex z)
{
return (ccoshf(cpackf(-cimagf(z), crealf(z))));
return (ccoshf(CMPLXF(-cimagf(z), crealf(z))));
}

12
src/s_cexp.c
View File

@ -50,22 +50,22 @@ cexp(double complex z)
/* cexp(x + I 0) = exp(x) + I 0 */
if ((hy | ly) == 0)
return (cpack(exp(x), y));
return (CMPLX(exp(x), y));
EXTRACT_WORDS(hx, lx, x);
/* cexp(0 + I y) = cos(y) + I sin(y) */
if (((hx & 0x7fffffff) | lx) == 0)
return (cpack(cos(y), sin(y)));
return (CMPLX(cos(y), sin(y)));
if (hy >= 0x7ff00000) {
if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
return (cpack(y - y, y - y));
return (CMPLX(y - y, y - y));
} else if (hx & 0x80000000) {
/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
return (cpack(0.0, 0.0));
return (CMPLX(0.0, 0.0));
} else {
/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
return (cpack(x, y - y));
return (CMPLX(x, y - y));
}
}
@ -84,6 +84,6 @@ cexp(double complex z)
* - x = NaN (spurious inexact exception from y)
*/
exp_x = exp(x);
return (cpack(exp_x * cos(y), exp_x * sin(y)));
return (CMPLX(exp_x * cos(y), exp_x * sin(y)));
}
}

12
src/s_cexpf.c
View File

@ -50,22 +50,22 @@ cexpf(float complex z)
/* cexp(x + I 0) = exp(x) + I 0 */
if (hy == 0)
return (cpackf(expf(x), y));
return (CMPLXF(expf(x), y));
GET_FLOAT_WORD(hx, x);
/* cexp(0 + I y) = cos(y) + I sin(y) */
if ((hx & 0x7fffffff) == 0)
return (cpackf(cosf(y), sinf(y)));
return (CMPLXF(cosf(y), sinf(y)));
if (hy >= 0x7f800000) {
if ((hx & 0x7fffffff) != 0x7f800000) {
/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
return (cpackf(y - y, y - y));
return (CMPLXF(y - y, y - y));
} else if (hx & 0x80000000) {
/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
return (cpackf(0.0, 0.0));
return (CMPLXF(0.0, 0.0));
} else {
/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
return (cpackf(x, y - y));
return (CMPLXF(x, y - y));
}
}
@ -84,6 +84,6 @@ cexpf(float complex z)
* - x = NaN (spurious inexact exception from y)
*/
exp_x = expf(x);
return (cpackf(exp_x * cosf(y), exp_x * sinf(y)));
return (CMPLXF(exp_x * cosf(y), exp_x * sinf(y)));
}
}

2
src/s_conj.c
View File

@ -35,5 +35,5 @@ DLLEXPORT double complex
conj(double complex z)
{
return (cpack(creal(z), -cimag(z)));
return (CMPLX(creal(z), -cimag(z)));
}

2
src/s_conjf.c
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@ -35,5 +35,5 @@ DLLEXPORT float complex
conjf(float complex z)
{
return (cpackf(crealf(z), -cimagf(z)));
return (CMPLXF(crealf(z), -cimagf(z)));
}

2
src/s_conjl.c
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@ -35,5 +35,5 @@ DLLEXPORT long double complex
conjl(long double complex z)
{
return (cpackl(creall(z), -cimagl(z)));
return (CMPLXL(creall(z), -cimagl(z)));
}

2
src/s_cproj.c
View File

@ -39,7 +39,7 @@ cproj(double complex z)
if (!isinf(creal(z)) && !isinf(cimag(z)))
return (z);
else
return (cpack(INFINITY, copysign(0.0, cimag(z))));
return (CMPLX(INFINITY, copysign(0.0, cimag(z))));
}
#if LDBL_MANT_DIG == 53

2
src/s_cprojf.c
View File

@ -39,5 +39,5 @@ cprojf(float complex z)
if (!isinf(crealf(z)) && !isinf(cimagf(z)))
return (z);
else
return (cpackf(INFINITY, copysignf(0.0, cimagf(z))));
return (CMPLXF(INFINITY, copysignf(0.0, cimagf(z))));
}

2
src/s_cprojl.c
View File

@ -39,5 +39,5 @@ cprojl(long double complex z)
if (!isinf(creall(z)) && !isinf(cimagl(z)))
return (z);
else
return (cpackl(INFINITY, copysignl(0.0, cimagl(z))));
return (CMPLXL(INFINITY, copysignl(0.0, cimagl(z))));
}

30
src/s_csinh.c
View File

@ -62,23 +62,23 @@ csinh(double complex z)
/* Handle the nearly-non-exceptional cases where x and y are finite. */
if (ix < 0x7ff00000 && iy < 0x7ff00000) {
if ((iy | ly) == 0)
return (cpack(sinh(x), y));
return (CMPLX(sinh(x), y));
if (ix < 0x40360000) /* small x: normal case */
return (cpack(sinh(x) * cos(y), cosh(x) * sin(y)));
return (CMPLX(sinh(x) * cos(y), cosh(x) * sin(y)));
/* |x| >= 22, so cosh(x) ~= exp(|x|) */
if (ix < 0x40862e42) {
/* x < 710: exp(|x|) won't overflow */
h = exp(fabs(x)) * 0.5;
return (cpack(copysign(h, x) * cos(y), h * sin(y)));
return (CMPLX(copysign(h, x) * cos(y), h * sin(y)));
} else if (ix < 0x4096bbaa) {
/* x < 1455: scale to avoid overflow */
z = __ldexp_cexp(cpack(fabs(x), y), -1);
return (cpack(creal(z) * copysign(1, x), cimag(z)));
z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
return (CMPLX(creal(z) * copysign(1, x), cimag(z)));
} else {
/* x >= 1455: the result always overflows */
h = huge * x;
return (cpack(h * cos(y), h * h * sin(y)));
return (CMPLX(h * cos(y), h * h * sin(y)));
}
}
@ -92,7 +92,7 @@ csinh(double complex z)
* the same as d(NaN).
*/
if ((ix | lx) == 0 && iy >= 0x7ff00000)
return (cpack(copysign(0, x * (y - y)), y - y));
return (CMPLX(copysign(0, x * (y - y)), y - y));
/*
* sinh(+-Inf +- I 0) = +-Inf + I +-0.
@ -101,8 +101,8 @@ csinh(double complex z)
*/
if ((iy | ly) == 0 && ix >= 0x7ff00000) {
if (((hx & 0xfffff) | lx) == 0)
return (cpack(x, y));
return (cpack(x, copysign(0, y)));
return (CMPLX(x, y));
return (CMPLX(x, copysign(0, y)));
}
/*
@ -114,7 +114,7 @@ csinh(double complex z)
* nonzero x. Choice = don't raise (except for signaling NaNs).
*/
if (ix < 0x7ff00000 && iy >= 0x7ff00000)
return (cpack(y - y, x * (y - y)));
return (CMPLX(y - y, x * (y - y)));
/*
* sinh(+-Inf + I NaN) = +-Inf + I d(NaN).
@ -129,8 +129,8 @@ csinh(double complex z)
*/
if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
if (iy >= 0x7ff00000)
return (cpack(x * x, x * (y - y)));
return (cpack(x * cos(y), INFINITY * sin(y)));
return (CMPLX(x * x, x * (y - y)));
return (CMPLX(x * cos(y), INFINITY * sin(y)));
}
/*
@ -144,7 +144,7 @@ csinh(double complex z)
* Optionally raises the invalid floating-point exception for finite
* nonzero y. Choice = don't raise (except for signaling NaNs).
*/
return (cpack((x * x) * (y - y), (x + x) * (y - y)));
return (CMPLX((x * x) * (y - y), (x + x) * (y - y)));
}
DLLEXPORT double complex
@ -152,6 +152,6 @@ csin(double complex z)
{
/* csin(z) = -I * csinh(I * z) */
z = csinh(cpack(-cimag(z), creal(z)));
return (cpack(cimag(z), -creal(z)));
z = csinh(CMPLX(-cimag(z), creal(z)));
return (CMPLX(cimag(z), -creal(z)));
}

30
src/s_csinhf.c
View File

@ -55,51 +55,51 @@ csinhf(float complex z)
if (ix < 0x7f800000 && iy < 0x7f800000) {
if (iy == 0)
return (cpackf(sinhf(x), y));
return (CMPLXF(sinhf(x), y));
if (ix < 0x41100000) /* small x: normal case */
return (cpackf(sinhf(x) * cosf(y), coshf(x) * sinf(y)));
return (CMPLXF(sinhf(x) * cosf(y), coshf(x) * sinf(y)));
/* |x| >= 9, so cosh(x) ~= exp(|x|) */
if (ix < 0x42b17218) {
/* x < 88.7: expf(|x|) won't overflow */
h = expf(fabsf(x)) * 0.5f;
return (cpackf(copysignf(h, x) * cosf(y), h * sinf(y)));
return (CMPLXF(copysignf(h, x) * cosf(y), h * sinf(y)));
} else if (ix < 0x4340b1e7) {
/* x < 192.7: scale to avoid overflow */
z = __ldexp_cexpf(cpackf(fabsf(x), y), -1);
return (cpackf(crealf(z) * copysignf(1, x), cimagf(z)));
z = __ldexp_cexpf(CMPLXF(fabsf(x), y), -1);
return (CMPLXF(crealf(z) * copysignf(1, x), cimagf(z)));
} else {
/* x >= 192.7: the result always overflows */
h = huge * x;
return (cpackf(h * cosf(y), h * h * sinf(y)));
return (CMPLXF(h * cosf(y), h * h * sinf(y)));
}
}
if (ix == 0 && iy >= 0x7f800000)
return (cpackf(copysignf(0, x * (y - y)), y - y));
return (CMPLXF(copysignf(0, x * (y - y)), y - y));
if (iy == 0 && ix >= 0x7f800000) {
if ((hx & 0x7fffff) == 0)
return (cpackf(x, y));
return (cpackf(x, copysignf(0, y)));
return (CMPLXF(x, y));
return (CMPLXF(x, copysignf(0, y)));
}
if (ix < 0x7f800000 && iy >= 0x7f800000)
return (cpackf(y - y, x * (y - y)));
return (CMPLXF(y - y, x * (y - y)));
if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) {
if (iy >= 0x7f800000)
return (cpackf(x * x, x * (y - y)));
return (cpackf(x * cosf(y), INFINITY * sinf(y)));
return (CMPLXF(x * x, x * (y - y)));
return (CMPLXF(x * cosf(y), INFINITY * sinf(y)));
}
return (cpackf((x * x) * (y - y), (x + x) * (y - y)));
return (CMPLXF((x * x) * (y - y), (x + x) * (y - y)));
}
DLLEXPORT float complex
csinf(float complex z)
{
z = csinhf(cpackf(-cimagf(z), crealf(z)));
return (cpackf(cimagf(z), -crealf(z)));
z = csinhf(CMPLXF(-cimagf(z), crealf(z)));
return (CMPLXF(cimagf(z), -crealf(z)));
}

14
src/s_csqrt.c
View File

@ -60,12 +60,12 @@ csqrt(double complex z)
/* Handle special cases. */
if (z == 0)
return (cpack(0, b));
return (CMPLX(0, b));
if (isinf(b))
return (cpack(INFINITY, b));
return (CMPLX(INFINITY, b));
if (isnan(a)) {
t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
return (cpack(a, t)); /* return NaN + NaN i */
return (CMPLX(a, t)); /* return NaN + NaN i */
}
if (isinf(a)) {
/*
@ -75,9 +75,9 @@ csqrt(double complex z)
* csqrt(-inf + y i) = 0 + inf i
*/
if (signbit(a))
return (cpack(fabs(b - b), copysign(a, b)));
return (CMPLX(fabs(b - b), copysign(a, b)));
else
return (cpack(a, copysign(b - b, b)));
return (CMPLX(a, copysign(b - b, b)));
}
/*
* The remaining special case (b is NaN) is handled just fine by
@ -96,10 +96,10 @@ csqrt(double complex z)
/* Algorithm 312, CACM vol 10, Oct 1967. */
if (a >= 0) {
t = sqrt((a + hypot(a, b)) * 0.5);
result = cpack(t, b / (2 * t));
result = CMPLX(t, b / (2 * t));
} else {
t = sqrt((-a + hypot(a, b)) * 0.5);
result = cpack(fabs(b) / (2 * t), copysign(t, b));
result = CMPLX(fabs(b) / (2 * t), copysign(t, b));
}
/* Rescale. */

14
src/s_csqrtf.c
View File

@ -51,12 +51,12 @@ csqrtf(float complex z)
/* Handle special cases. */
if (z == 0)
return (cpackf(0, b));
return (CMPLXF(0, b));
if (isinf(b))
return (cpackf(INFINITY, b));
return (CMPLXF(INFINITY, b));
if (isnan(a)) {
t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
return (cpackf(a, t)); /* return NaN + NaN i */
return (CMPLXF(a, t)); /* return NaN + NaN i */
}
if (isinf(a)) {
/*
@ -66,9 +66,9 @@ csqrtf(float complex z)
* csqrtf(-inf + y i) = 0 + inf i
*/
if (signbit(a))
return (cpackf(fabsf(b - b), copysignf(a, b)));
return (CMPLXF(fabsf(b - b), copysignf(a, b)));
else
return (cpackf(a, copysignf(b - b, b)));
return (CMPLXF(a, copysignf(b - b, b)));
}
/*
* The remaining special case (b is NaN) is handled just fine by
@ -82,9 +82,9 @@ csqrtf(float complex z)
*/
if (a >= 0) {
t = sqrt((a + hypot(a, b)) * 0.5);
return (cpackf(t, b / (2.0 * t)));
return (CMPLXF(t, b / (2.0 * t)));
} else {
t = sqrt((-a + hypot(a, b)) * 0.5);
return (cpackf(fabsf(b) / (2.0 * t), copysignf(t, b)));
return (CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b)));
}
}

14
src/s_csqrtl.c
View File

@ -59,12 +59,12 @@ csqrtl(long double complex z)
/* Handle special cases. */
if (z == 0)
return (cpackl(0, b));
return (CMPLXL(0, b));
if (isinf(b))
return (cpackl(INFINITY, b));
return (CMPLXL(INFINITY, b));
if (isnan(a)) {
t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
return (cpackl(a, t)); /* return NaN + NaN i */
return (CMPLXL(a, t)); /* return NaN + NaN i */
}
if (isinf(a)) {
/*
@ -74,9 +74,9 @@ csqrtl(long double complex z)
* csqrt(-inf + y i) = 0 + inf i
*/
if (signbit(a))
return (cpackl(fabsl(b - b), copysignl(a, b)));
return (CMPLXL(fabsl(b - b), copysignl(a, b)));
else
return (cpackl(a, copysignl(b - b, b)));
return (CMPLXL(a, copysignl(b - b, b)));
}
/*
* The remaining special case (b is NaN) is handled just fine by
@ -95,10 +95,10 @@ csqrtl(long double complex z)
/* Algorithm 312, CACM vol 10, Oct 1967. */
if (a >= 0) {
t = sqrtl((a + hypotl(a, b)) * 0.5);
result = cpackl(t, b / (2 * t));
result = CMPLXL(t, b / (2 * t));
} else {
t = sqrtl((-a + hypotl(a, b)) * 0.5);
result = cpackl(fabsl(b) / (2 * t), copysignl(t, b));
result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b));
}
/* Rescale. */

14
src/s_ctanh.c
View File

@ -102,9 +102,9 @@ ctanh(double complex z)
*/
if (ix >= 0x7ff00000) {
if ((ix & 0xfffff) | lx) /* x is NaN */
return (cpack(x, (y == 0 ? y : x * y)));
return (CMPLX(x, (y == 0 ? y : x * y)));
SET_HIGH_WORD(x, hx - 0x40000000); /* x = copysign(1, x) */
return (cpack(x, copysign(0, isinf(y) ? y : sin(y) * cos(y))));
return (CMPLX(x, copysign(0, isinf(y) ? y : sin(y) * cos(y))));
}
/*
@ -112,7 +112,7 @@ ctanh(double complex z)
* ctanh(x +- i Inf) = NaN + i NaN
*/
if (!isfinite(y))
return (cpack(y - y, y - y));
return (CMPLX(y - y, y - y));
/*
* ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the
@ -121,7 +121,7 @@ ctanh(double complex z)
*/
if (ix >= 0x40360000) { /* x >= 22 */
double exp_mx = exp(-fabs(x));
return (cpack(copysign(1, x),
return (CMPLX(copysign(1, x),
4 * sin(y) * cos(y) * exp_mx * exp_mx));
}
@ -131,7 +131,7 @@ ctanh(double complex z)
s = sinh(x);
rho = sqrt(1 + s * s); /* = cosh(x) */
denom = 1 + beta * s * s;
return (cpack((beta * rho * s) / denom, t / denom));
return (CMPLX((beta * rho * s) / denom, t / denom));
}
DLLEXPORT double complex
@ -139,6 +139,6 @@ ctan(double complex z)
{
/* ctan(z) = -I * ctanh(I * z) */
z = ctanh(cpack(-cimag(z), creal(z)));
return (cpack(cimag(z), -creal(z)));
z = ctanh(CMPLX(-cimag(z), creal(z)));
return (CMPLX(cimag(z), -creal(z)));
}

14
src/s_ctanhf.c
View File

@ -51,18 +51,18 @@ ctanhf(float complex z)
if (ix >= 0x7f800000) {
if (ix & 0x7fffff)
return (cpackf(x, (y == 0 ? y : x * y)));
return (CMPLXF(x, (y == 0 ? y : x * y)));
SET_FLOAT_WORD(x, hx - 0x40000000);
return (cpackf(x,
return (CMPLXF(x,
copysignf(0, isinf(y) ? y : sinf(y) * cosf(y))));
}
if (!isfinite(y))
return (cpackf(y - y, y - y));
return (CMPLXF(y - y, y - y));
if (ix >= 0x41300000) { /* x >= 11 */
float exp_mx = expf(-fabsf(x));
return (cpackf(copysignf(1, x),
return (CMPLXF(copysignf(1, x),
4 * sinf(y) * cosf(y) * exp_mx * exp_mx));
}
@ -71,14 +71,14 @@ ctanhf(float complex z)
s = sinhf(x);
rho = sqrtf(1 + s * s);
denom = 1 + beta * s * s;
return (cpackf((beta * rho * s) / denom, t / denom));
return (CMPLXF((beta * rho * s) / denom, t / denom));
}
DLLEXPORT float complex
ctanf(float complex z)
{
z = ctanhf(cpackf(-cimagf(z), crealf(z)));
return (cpackf(cimagf(z), -crealf(z)));
z = ctanhf(CMPLXF(-cimagf(z), crealf(z)));
return (CMPLXF(cimagf(z), -crealf(z)));
}