Date: Mon, 15 Jun 2015 20:16:53 +0000 (UTC) From: Tijl Coosemans <tijl@FreeBSD.org> To: src-committers@freebsd.org, svn-src-all@freebsd.org, svn-src-head@freebsd.org Subject: svn commit: r284426 - head/lib/msun/src Message-ID: <201506152016.t5FKGrvW047856@svn.freebsd.org>
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Author: tijl Date: Mon Jun 15 20:16:53 2015 New Revision: 284426 URL: https://svnweb.freebsd.org/changeset/base/284426 Log: Fix some exceptional cases where the sign of the result is unspecified but must still satisfy csinh(conj(z)) == conj(csinh(z)) and csinh(-z) == -csinh(z). This allows eliminating two negations from csin(z). In collaboration with: bde Modified: head/lib/msun/src/s_csinh.c head/lib/msun/src/s_csinhf.c Modified: head/lib/msun/src/s_csinh.c ============================================================================== --- head/lib/msun/src/s_csinh.c Mon Jun 15 20:12:15 2015 (r284425) +++ head/lib/msun/src/s_csinh.c Mon Jun 15 20:16:53 2015 (r284426) @@ -32,6 +32,8 @@ * * Exceptional values are noted in the comments within the source code. * These values and the return value were taken from n1124.pdf. + * The sign of the result for some exceptional values is unspecified but + * must satisfy both sinh(conj(z)) == conj(sinh(z)) and sinh(-z) == -sinh(z). */ #include <sys/cdefs.h> @@ -63,7 +65,7 @@ csinh(double complex z) if (ix < 0x7ff00000 && iy < 0x7ff00000) { if ((iy | ly) == 0) return (CMPLX(sinh(x), y)); - if (ix < 0x40360000) /* small x: normal case */ + if (ix < 0x40360000) /* |x| < 22: normal case */ return (CMPLX(sinh(x) * cos(y), cosh(x) * sin(y))); /* |x| >= 22, so cosh(x) ~= exp(|x|) */ @@ -83,27 +85,24 @@ csinh(double complex z) } /* - * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN. - * The sign of 0 in the result is unspecified. Choice = normally - * the same as dNaN. Raise the invalid floating-point exception. - * - * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN). - * The sign of 0 in the result is unspecified. Choice = normally - * the same as d(NaN). + * sinh(+-0 +- I Inf) = +-0 + I dNaN. + * The sign of 0 in the result is unspecified. Choice = same sign + * as the argument. Raise the invalid floating-point exception. + * + * sinh(+-0 +- I NaN) = +-0 + I d(NaN). + * The sign of 0 in the result is unspecified. Choice = same sign + * as the argument. */ - if ((ix | lx) == 0 && iy >= 0x7ff00000) - return (CMPLX(copysign(0, x * (y - y)), y - y)); + if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */ + return (CMPLX(x, y - y)); /* * sinh(+-Inf +- I 0) = +-Inf + I +-0. * * sinh(NaN +- I 0) = d(NaN) + I +-0. */ - if ((iy | ly) == 0 && ix >= 0x7ff00000) { - if (((hx & 0xfffff) | lx) == 0) - return (CMPLX(x, y)); - return (CMPLX(x, copysign(0, y))); - } + if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */ + return (CMPLX(x + x, y)); /* * sinh(x +- I Inf) = dNaN + I dNaN. @@ -113,45 +112,45 @@ csinh(double complex z) * Optionally raises the invalid floating-point exception for finite * nonzero x. Choice = don't raise (except for signaling NaNs). */ - if (ix < 0x7ff00000 && iy >= 0x7ff00000) - return (CMPLX(y - y, x * (y - y))); + if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */ + return (CMPLX(y - y, y - y)); /* * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). - * The sign of Inf in the result is unspecified. Choice = normally - * the same as d(NaN). + * The sign of Inf in the result is unspecified. Choice = same sign + * as the argument. * - * sinh(+-Inf +- I Inf) = +Inf + I dNaN. - * The sign of Inf in the result is unspecified. Choice = always +. - * Raise the invalid floating-point exception. + * sinh(+-Inf +- I Inf) = +-Inf + I dNaN. + * The sign of Inf in the result is unspecified. Choice = same sign + * as the argument. Raise the invalid floating-point exception. * * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) */ - if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { + if (ix == 0x7ff00000 && lx == 0) { if (iy >= 0x7ff00000) - return (CMPLX(x * x, x * (y - y))); + return (CMPLX(x, y - y)); return (CMPLX(x * cos(y), INFINITY * sin(y))); } /* - * sinh(NaN + I NaN) = d(NaN) + I d(NaN). + * sinh(NaN1 + I NaN2) = d(NaN1, NaN2) + I d(NaN1, NaN2). * - * sinh(NaN +- I Inf) = d(NaN) + I d(NaN). + * sinh(NaN +- I Inf) = d(NaN, dNaN) + I d(NaN, dNaN). * Optionally raises the invalid floating-point exception. * Choice = raise. * - * sinh(NaN + I y) = d(NaN) + I d(NaN). + * sinh(NaN + I y) = d(NaN) + I d(NaN). * Optionally raises the invalid floating-point exception for finite * nonzero y. Choice = don't raise (except for signaling NaNs). */ - return (CMPLX((x * x) * (y - y), (x + x) * (y - y))); + return (CMPLX((x + x) * (y - y), (x * x) * (y - y))); } double complex csin(double complex z) { - /* csin(z) = -I * csinh(I * z) */ - z = csinh(CMPLX(-cimag(z), creal(z))); - return (CMPLX(cimag(z), -creal(z))); + /* csin(z) = -I * csinh(I * z) = I * conj(csinh(I * conj(z))). */ + z = csinh(CMPLX(cimag(z), creal(z))); + return (CMPLX(cimag(z), creal(z))); } Modified: head/lib/msun/src/s_csinhf.c ============================================================================== --- head/lib/msun/src/s_csinhf.c Mon Jun 15 20:12:15 2015 (r284425) +++ head/lib/msun/src/s_csinhf.c Mon Jun 15 20:16:53 2015 (r284426) @@ -25,7 +25,7 @@ */ /* - * Hyperbolic sine of a complex argument z. See s_csinh.c for details. + * Float version of csinh(). See s_csinh.c for details. */ #include <sys/cdefs.h> @@ -56,13 +56,13 @@ csinhf(float complex z) if (ix < 0x7f800000 && iy < 0x7f800000) { if (iy == 0) return (CMPLXF(sinhf(x), y)); - if (ix < 0x41100000) /* small x: normal case */ + if (ix < 0x41100000) /* |x| < 9: normal case */ 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; + h = expf(fabsf(x)) * 0.5F; return (CMPLXF(copysignf(h, x) * cosf(y), h * sinf(y))); } else if (ix < 0x4340b1e7) { /* x < 192.7: scale to avoid overflow */ @@ -75,31 +75,28 @@ csinhf(float complex z) } } - if (ix == 0 && iy >= 0x7f800000) - return (CMPLXF(copysignf(0, x * (y - y)), y - y)); + if (ix == 0) /* && iy >= 0x7f800000 */ + return (CMPLXF(x, y - y)); - if (iy == 0 && ix >= 0x7f800000) { - if ((hx & 0x7fffff) == 0) - return (CMPLXF(x, y)); - return (CMPLXF(x, copysignf(0, y))); - } + if (iy == 0) /* && ix >= 0x7f800000 */ + return (CMPLXF(x + x, y)); - if (ix < 0x7f800000 && iy >= 0x7f800000) - return (CMPLXF(y - y, x * (y - y))); + if (ix < 0x7f800000) /* && iy >= 0x7f800000 */ + return (CMPLXF(y - y, y - y)); - if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) { + if (ix == 0x7f800000) { if (iy >= 0x7f800000) - return (CMPLXF(x * x, x * (y - y))); + return (CMPLXF(x, y - y)); return (CMPLXF(x * cosf(y), INFINITY * sinf(y))); } - return (CMPLXF((x * x) * (y - y), (x + x) * (y - y))); + return (CMPLXF((x + x) * (y - y), (x * x) * (y - y))); } float complex csinf(float complex z) { - z = csinhf(CMPLXF(-cimagf(z), crealf(z))); - return (CMPLXF(cimagf(z), -crealf(z))); + z = csinhf(CMPLXF(cimagf(z), crealf(z))); + return (CMPLXF(cimagf(z), crealf(z))); }
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