[337] | 1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_csqrt.c */
|
---|
| 2 | /*-
|
---|
| 3 | * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
|
---|
| 4 | * All rights reserved.
|
---|
| 5 | *
|
---|
| 6 | * Redistribution and use in source and binary forms, with or without
|
---|
| 7 | * modification, are permitted provided that the following conditions
|
---|
| 8 | * are met:
|
---|
| 9 | * 1. Redistributions of source code must retain the above copyright
|
---|
| 10 | * notice, this list of conditions and the following disclaimer.
|
---|
| 11 | * 2. Redistributions in binary form must reproduce the above copyright
|
---|
| 12 | * notice, this list of conditions and the following disclaimer in the
|
---|
| 13 | * documentation and/or other materials provided with the distribution.
|
---|
| 14 | *
|
---|
| 15 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
---|
| 16 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
---|
| 17 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
---|
| 18 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
---|
| 19 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
---|
| 20 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
---|
| 21 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
---|
| 22 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
---|
| 23 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
---|
| 24 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
---|
| 25 | * SUCH DAMAGE.
|
---|
| 26 | */
|
---|
| 27 |
|
---|
| 28 | #include "libm.h"
|
---|
| 29 |
|
---|
| 30 | /*
|
---|
| 31 | * gcc doesn't implement complex multiplication or division correctly,
|
---|
| 32 | * so we need to handle infinities specially. We turn on this pragma to
|
---|
| 33 | * notify conforming c99 compilers that the fast-but-incorrect code that
|
---|
| 34 | * gcc generates is acceptable, since the special cases have already been
|
---|
| 35 | * handled.
|
---|
| 36 | */
|
---|
| 37 | #pragma STDC CX_LIMITED_RANGE ON
|
---|
| 38 |
|
---|
| 39 | /* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */
|
---|
| 40 | #define THRESH 0x1.a827999fcef32p+1022
|
---|
| 41 |
|
---|
| 42 | double complex csqrt(double complex z)
|
---|
| 43 | {
|
---|
| 44 | double complex result;
|
---|
| 45 | double a, b;
|
---|
| 46 | double t;
|
---|
| 47 | int scale;
|
---|
| 48 |
|
---|
| 49 | a = creal(z);
|
---|
| 50 | b = cimag(z);
|
---|
| 51 |
|
---|
| 52 | /* Handle special cases. */
|
---|
| 53 | if (z == 0)
|
---|
| 54 | return CMPLX(0, b);
|
---|
| 55 | if (isinf(b))
|
---|
| 56 | return CMPLX(INFINITY, b);
|
---|
| 57 | if (isnan(a)) {
|
---|
| 58 | t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
|
---|
| 59 | return CMPLX(a, t); /* return NaN + NaN i */
|
---|
| 60 | }
|
---|
| 61 | if (isinf(a)) {
|
---|
| 62 | /*
|
---|
| 63 | * csqrt(inf + NaN i) = inf + NaN i
|
---|
| 64 | * csqrt(inf + y i) = inf + 0 i
|
---|
| 65 | * csqrt(-inf + NaN i) = NaN +- inf i
|
---|
| 66 | * csqrt(-inf + y i) = 0 + inf i
|
---|
| 67 | */
|
---|
| 68 | if (signbit(a))
|
---|
| 69 | return CMPLX(fabs(b - b), copysign(a, b));
|
---|
| 70 | else
|
---|
| 71 | return CMPLX(a, copysign(b - b, b));
|
---|
| 72 | }
|
---|
| 73 | /*
|
---|
| 74 | * The remaining special case (b is NaN) is handled just fine by
|
---|
| 75 | * the normal code path below.
|
---|
| 76 | */
|
---|
| 77 |
|
---|
| 78 | /* Scale to avoid overflow. */
|
---|
| 79 | if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
|
---|
| 80 | a *= 0.25;
|
---|
| 81 | b *= 0.25;
|
---|
| 82 | scale = 1;
|
---|
| 83 | } else {
|
---|
| 84 | scale = 0;
|
---|
| 85 | }
|
---|
| 86 |
|
---|
| 87 | /* Algorithm 312, CACM vol 10, Oct 1967. */
|
---|
| 88 | if (a >= 0) {
|
---|
| 89 | t = sqrt((a + hypot(a, b)) * 0.5);
|
---|
| 90 | result = CMPLX(t, b / (2 * t));
|
---|
| 91 | } else {
|
---|
| 92 | t = sqrt((-a + hypot(a, b)) * 0.5);
|
---|
| 93 | result = CMPLX(fabs(b) / (2 * t), copysign(t, b));
|
---|
| 94 | }
|
---|
| 95 |
|
---|
| 96 | /* Rescale. */
|
---|
| 97 | if (scale)
|
---|
| 98 | result *= 2;
|
---|
| 99 | return result;
|
---|
| 100 | }
|
---|