Index: head/lib/msun/src/s_csqrt.c =================================================================== --- head/lib/msun/src/s_csqrt.c (revision 336411) +++ head/lib/msun/src/s_csqrt.c (revision 336412) @@ -1,124 +1,115 @@ /*- * 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)). */ +/* For avoiding 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, 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) { /* * 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 = 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); rx = t; ry = b / (2 * t); } else { t = sqrt((-a + hypot(a, b)) * 0.5); rx = fabs(b) / (2 * t); ry = copysign(t, b); } return (CMPLX(rx * scale, ry * scale)); } #if LDBL_MANT_DIG == 53 __weak_reference(csqrt, csqrtl); #endif Index: head/lib/msun/src/s_csqrtf.c =================================================================== --- head/lib/msun/src/s_csqrtf.c (revision 336411) +++ head/lib/msun/src/s_csqrtf.c (revision 336412) @@ -1,90 +1,84 @@ /*- * 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 "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 - float complex csqrtf(float complex z) { - float a = crealf(z), b = cimagf(z); double t; + float a, b; + a = creal(z); + b = cimag(z); + /* Handle special cases. */ if (z == 0) return (CMPLXF(0, b)); if (isinf(b)) return (CMPLXF(INFINITY, b)); if (isnan(a)) { t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ return (CMPLXF(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */ } if (isinf(a)) { /* * csqrtf(inf + NaN i) = inf + NaN i * csqrtf(inf + y i) = inf + 0 i * csqrtf(-inf + NaN i) = NaN +- inf i * csqrtf(-inf + y i) = 0 + inf i */ if (signbit(a)) return (CMPLXF(fabsf(b - b), copysignf(a, b))); else return (CMPLXF(a, copysignf(b - b, b))); } if (isnan(b)) { t = (a - a) / (a - a); /* raise invalid */ return (CMPLXF(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */ } /* * We compute t in double precision to avoid overflow and to * provide correct rounding in nearly all cases. * This is Algorithm 312, CACM vol 10, Oct 1967. */ if (a >= 0) { t = sqrt((a + hypot(a, b)) * 0.5); - return (CMPLXF(t, b / (2.0 * t))); + return (CMPLXF(t, b / (2 * t))); } else { t = sqrt((-a + hypot(a, b)) * 0.5); - return (CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b))); + return (CMPLXF(fabsf(b) / (2 * t), copysignf(t, b))); } } Index: head/lib/msun/src/s_csqrtl.c =================================================================== --- head/lib/msun/src/s_csqrtl.c (revision 336411) +++ head/lib/msun/src/s_csqrtl.c (revision 336412) @@ -1,128 +1,121 @@ /*- * 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. + * THRESH is now calculated portably (up to 113-bit precision). However, + * the denormal threshold is hard-coded for a 15-bit exponent with the usual + * bias. s_logl.c and e_hypotl have less hard-coding but end up requiring + * the same for the exponent and more for the mantissa. */ -#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 + +/* For avoiding overflow for components >= LDBL_MAX / (1 + sqrt(2)). */ +#define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L) long double complex csqrtl(long double complex z) { long double complex result; 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) { /* * 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 = 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); rx = t; ry = b / (2 * t); } else { t = sqrtl((-a + hypotl(a, b)) * 0.5); rx = fabsl(b) / (2 * t); ry = copysignl(t, b); } return (CMPLXL(rx * scale, ry * scale)); }