Index: head/lib/msun/src/s_csqrt.c =================================================================== --- head/lib/msun/src/s_csqrt.c (revision 336399) +++ head/lib/msun/src/s_csqrt.c (revision 336400) @@ -1,114 +1,124 @@ /*- * SPDX-License-Identifier: BSD-2-Clause-FreeBSD * * Copyright (c) 2007 David Schultz * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ #include __FBSDID("$FreeBSD$"); #include #include #include #include "math_private.h" /* * gcc doesn't implement complex multiplication or division correctly, * so we need to handle infinities specially. We turn on this pragma to * notify conforming c99 compilers that the fast-but-incorrect code that * gcc generates is acceptable, since the special cases have already been * handled. */ #pragma STDC CX_LIMITED_RANGE ON /* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */ #define THRESH 0x1.a827999fcef32p+1022 double complex csqrt(double complex z) { double complex result; - double a, b; - double t; - int scale; + double a, b, rx, ry, scale, t; a = creal(z); b = cimag(z); /* Handle special cases. */ if (z == 0) return (CMPLX(0, b)); if (isinf(b)) return (CMPLX(INFINITY, b)); if (isnan(a)) { t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ return (CMPLX(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */ } if (isinf(a)) { /* * csqrt(inf + NaN i) = inf + NaN i * csqrt(inf + y i) = inf + 0 i * csqrt(-inf + NaN i) = NaN +- inf i * csqrt(-inf + y i) = 0 + inf i */ if (signbit(a)) return (CMPLX(fabs(b - b), copysign(a, b))); else return (CMPLX(a, copysign(b - b, b))); } if (isnan(b)) { t = (a - a) / (a - a); /* raise invalid */ return (CMPLX(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */ } /* Scale to avoid overflow. */ if (fabs(a) >= THRESH || fabs(b) >= THRESH) { - a *= 0.25; - b *= 0.25; - scale = 1; + /* + * Don't scale a or b if this might give (spurious) + * underflow. Then the unscaled value is an equivalent + * infinitesmal (or 0). + */ + if (fabs(a) >= 0x1p-1020) + a *= 0.25; + if (fabs(b) >= 0x1p-1020) + b *= 0.25; + scale = 2; } else { - scale = 0; + scale = 1; } + /* Scale to reduce inaccuracies when both components are denormal. */ + if (fabs(a) < 0x1p-1022 && fabs(b) < 0x1p-1022) { + a *= 0x1p54; + b *= 0x1p54; + scale = 0x1p-27; + } + /* Algorithm 312, CACM vol 10, Oct 1967. */ if (a >= 0) { t = sqrt((a + hypot(a, b)) * 0.5); - result = CMPLX(t, b / (2 * t)); + rx = t; + ry = b / (2 * t); } else { t = sqrt((-a + hypot(a, b)) * 0.5); - result = CMPLX(fabs(b) / (2 * t), copysign(t, b)); + rx = fabs(b) / (2 * t); + ry = copysign(t, b); } - /* Rescale. */ - if (scale) - return (result * 2); - else - return (result); + return (CMPLX(rx * scale, ry * scale)); } #if LDBL_MANT_DIG == 53 __weak_reference(csqrt, csqrtl); #endif Index: head/lib/msun/src/s_csqrtl.c =================================================================== --- head/lib/msun/src/s_csqrtl.c (revision 336399) +++ head/lib/msun/src/s_csqrtl.c (revision 336400) @@ -1,118 +1,128 @@ /*- * SPDX-License-Identifier: BSD-2-Clause-FreeBSD * * Copyright (c) 2007-2008 David Schultz * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ #include __FBSDID("$FreeBSD$"); #include #include #include #include "math_private.h" /* * gcc doesn't implement complex multiplication or division correctly, * so we need to handle infinities specially. We turn on this pragma to * notify conforming c99 compilers that the fast-but-incorrect code that * gcc generates is acceptable, since the special cases have already been * handled. */ #pragma STDC CX_LIMITED_RANGE ON /* * We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). * Rather than determining the fully precise value at which we might * overflow, just use a threshold of approximately LDBL_MAX / 4. */ #if LDBL_MAX_EXP != 0x4000 #error "Unsupported long double format" #else #define THRESH 0x1p16382L #endif long double complex csqrtl(long double complex z) { long double complex result; - long double a, b; - long double t; - int scale; + long double a, b, rx, ry, scale, t; a = creall(z); b = cimagl(z); /* Handle special cases. */ if (z == 0) return (CMPLXL(0, b)); if (isinf(b)) return (CMPLXL(INFINITY, b)); if (isnan(a)) { t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ return (CMPLXL(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */ } if (isinf(a)) { /* * csqrt(inf + NaN i) = inf + NaN i * csqrt(inf + y i) = inf + 0 i * csqrt(-inf + NaN i) = NaN +- inf i * csqrt(-inf + y i) = 0 + inf i */ if (signbit(a)) return (CMPLXL(fabsl(b - b), copysignl(a, b))); else return (CMPLXL(a, copysignl(b - b, b))); } if (isnan(b)) { t = (a - a) / (a - a); /* raise invalid */ return (CMPLXL(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */ } /* Scale to avoid overflow. */ if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { - a *= 0.25; - b *= 0.25; - scale = 1; + /* + * Don't scale a or b if this might give (spurious) + * underflow. Then the unscaled value is an equivalent + * infinitesmal (or 0). + */ + if (fabsl(a) >= 0x1p-16380L) + a *= 0.25; + if (fabsl(b) >= 0x1p-16380L) + b *= 0.25; + scale = 2; } else { - scale = 0; + scale = 1; } + /* Scale to reduce inaccuracies when both components are denormal. */ + if (fabsl(a) < 0x1p-16382L && fabsl(b) < 0x1p-16382L) { + a *= 0x1p64; + b *= 0x1p64; + scale = 0x1p-32; + } + /* Algorithm 312, CACM vol 10, Oct 1967. */ if (a >= 0) { t = sqrtl((a + hypotl(a, b)) * 0.5); - result = CMPLXL(t, b / (2 * t)); + rx = t; + ry = b / (2 * t); } else { t = sqrtl((-a + hypotl(a, b)) * 0.5); - result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b)); + rx = fabsl(b) / (2 * t); + ry = copysignl(t, b); } - /* Rescale. */ - if (scale) - return (result * 2); - else - return (result); + return (CMPLXL(rx * scale, ry * scale)); }