39 #define isinf(x)	(fabs(x) == INFINITY)  argument
41 #define isnan(x)	((x) != (x))  argument
44 #define signbit(x)	(__builtin_signbit(x))  argument
155 do_hard_work(double x, double y, double *rx, int *B_is_usable, double *B,  in do_hard_work()  argument
161 	R = hypot(x, y + 1);		/* |z+I| */  in do_hard_work()
162 	S = hypot(x, y - 1);		/* |z-I| */  in do_hard_work()
179 		if (y == 1 && x < DBL_EPSILON * DBL_EPSILON / 128) {  in do_hard_work()
184 			*rx = sqrt(x);  in do_hard_work()
185 		} else if (x >= DBL_EPSILON * fabs(y - 1)) {  in do_hard_work()
190 			Am1 = f(x, 1 + y, R) + f(x, 1 - y, S);  in do_hard_work()
197 			*rx = x / sqrt((1 - y) * (1 + y));  in do_hard_work()
232 		if (y == 1 && x < DBL_EPSILON / 128) {  in do_hard_work()
237 			*sqrt_A2my2 = sqrt(x) * sqrt((A + y) / 2);  in do_hard_work()
238 		} else if (x >= DBL_EPSILON * fabs(y - 1)) {  in do_hard_work()
245 			Amy = f(x, y + 1, R) + f(x, y - 1, S);  in do_hard_work()
255 			*sqrt_A2my2 = x * (4 / DBL_EPSILON / DBL_EPSILON) * y /  in do_hard_work()
279 	double x, y, ax, ay, rx, ry, B, sqrt_A2my2, new_y;  in casinh()  local
283 	x = creal(z);  in casinh()
285 	ax = fabs(x);  in casinh()
288 	if (isnan(x) || isnan(y)) {  in casinh()
290 		if (isinf(x))  in casinh()
291 			return (CMPLX(x, y + y));  in casinh()
294 			return (CMPLX(y, x + x));  in casinh()
297 			return (CMPLX(x + x, y));  in casinh()
303 		return (CMPLX(nan_mix(x, y), nan_mix(x, y)));  in casinh()
308 		if (signbit(x) == 0)  in casinh()
312 		return (CMPLX(copysign(creal(w), x), copysign(cimag(w), y)));  in casinh()
316 	if (x == 0 && y == 0)  in casinh()
330 	return (CMPLX(copysign(rx, x), copysign(ry, y)));  in casinh()
360 	double x, y, ax, ay, rx, ry, B, sqrt_A2mx2, new_x;  in cacos()  local
365 	x = creal(z);  in cacos()
367 	sx = signbit(x);  in cacos()
369 	ax = fabs(x);  in cacos()
372 	if (isnan(x) || isnan(y)) {  in cacos()
374 		if (isinf(x))  in cacos()
378 			return (CMPLX(x + x, -y));  in cacos()
380 		if (x == 0)  in cacos()
387 		return (CMPLX(nan_mix(x, y), nan_mix(x, y)));  in cacos()
401 	if (x == 1 && y == 0)  in cacos()
408 		return (CMPLX(pio2_hi - (x - pio2_lo), -y));  in cacos()
459 	double x, y;  in clog_for_large_values()  local
462 	x = creal(z);  in clog_for_large_values()
464 	ax = fabs(x);  in clog_for_large_values()
485 		return (CMPLX(log(hypot(x / m_e, y / m_e)) + 1, atan2(y, x)));  in clog_for_large_values()
492 		return (CMPLX(log(hypot(x, y)), atan2(y, x)));  in clog_for_large_values()
494 	return (CMPLX(log(ax * ax + ay * ay) / 2, atan2(y, x)));  in clog_for_large_values()
511 sum_squares(double x, double y)  in sum_squares()  argument
516 		return (x * x);  in sum_squares()
518 	return (x * x + y * y);  in sum_squares()
531 real_part_reciprocal(double x, double y)  in real_part_reciprocal()  argument
541 	GET_HIGH_WORD(hx, x);  in real_part_reciprocal()
548 	if (ix - iy >= CUTOFF << 20 || isinf(x))  in real_part_reciprocal()
549 		return (1 / x);		/* +-Inf -> +-0 is special */  in real_part_reciprocal()
551 		return (x / y / y);	/* should avoid double div, but hard */  in real_part_reciprocal()
553 		return (x / (x * x + y * y));  in real_part_reciprocal()
556 	x *= scale;  in real_part_reciprocal()
558 	return (x / (x * x + y * y) * scale);  in real_part_reciprocal()
576 	double x, y, ax, ay, rx, ry;  in catanh()  local
578 	x = creal(z);  in catanh()
580 	ax = fabs(x);  in catanh()
585 		return (CMPLX(atanh(x), y));  in catanh()
588 	if (x == 0)  in catanh()
589 		return (CMPLX(x, atan(y)));  in catanh()
591 	if (isnan(x) || isnan(y)) {  in catanh()
593 		if (isinf(x))  in catanh()
594 			return (CMPLX(copysign(0, x), y + y));  in catanh()
597 			return (CMPLX(copysign(0, x),  in catanh()
604 		return (CMPLX(nan_mix(x, y), nan_mix(x, y)));  in catanh()
608 		return (CMPLX(real_part_reciprocal(x, y),  in catanh()
633 	return (CMPLX(copysign(rx, x), copysign(ry, y)));  in catanh()