Date: Fri, 21 Oct 2011 06:29:32 +0000 (UTC) From: David Schultz <das@FreeBSD.org> To: src-committers@freebsd.org, svn-src-all@freebsd.org, svn-src-head@freebsd.org Subject: svn commit: r226599 - head/lib/msun/src Message-ID: <201110210629.p9L6TWQb009912@svn.freebsd.org>
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Author: das Date: Fri Oct 21 06:29:32 2011 New Revision: 226599 URL: http://svn.freebsd.org/changeset/base/226599 Log: Improved handling of large x in ccosh{,f}(): - Handle cases where exp(x) would overflow, but ccosh(x) ~= exp(x) / 2 shouldn't. - Use the ccosh(x) ~= exp(x) / 2 approximation to simplify the calculation when x is large. Similarly for csinh(). Also fixed the return value of csinh(-Inf +- 0i). Modified: head/lib/msun/src/s_ccosh.c head/lib/msun/src/s_ccoshf.c head/lib/msun/src/s_csinh.c head/lib/msun/src/s_csinhf.c Modified: head/lib/msun/src/s_ccosh.c ============================================================================== --- head/lib/msun/src/s_ccosh.c Fri Oct 21 06:28:47 2011 (r226598) +++ head/lib/msun/src/s_ccosh.c Fri Oct 21 06:29:32 2011 (r226599) @@ -42,10 +42,12 @@ __FBSDID("$FreeBSD$"); #include "math_private.h" +static const double huge = 0x1p1023; + double complex ccosh(double complex z) { - double x, y; + double x, y, h; int32_t hx, hy, ix, iy, lx, ly; x = creal(z); @@ -61,8 +63,23 @@ ccosh(double complex z) if (ix < 0x7ff00000 && iy < 0x7ff00000) { if ((iy | ly) == 0) return (cpack(cosh(x), x * y)); - /* XXX We don't handle |x| > DBL_MAX ln(2) yet. */ - return (cpack(cosh(x) * cos(y), sinh(x) * sin(y))); + if (ix < 0x40360000) /* small x: normal case */ + return (cpack(cosh(x) * cos(y), sinh(x) * sin(y))); + + /* |x| >= 22, so cosh(x) ~= exp(|x|) */ + if (ix < 0x40862e42) { + /* x < 710: exp(|x|) won't overflow */ + h = exp(fabs(x)) * 0.5; + return (cpack(h * cos(y), copysign(h, x) * sin(y))); + } else if (ix < 0x4096bbaa) { + /* x < 1455: scale to avoid overflow */ + z = __ldexp_cexp(cpack(fabs(x), y), -1); + return (cpack(creal(z), cimag(z) * copysign(1, x))); + } else { + /* x >= 1455: the result always overflows */ + h = huge * x; + return (cpack(h * h * cos(y), h * sin(y))); + } } /* Modified: head/lib/msun/src/s_ccoshf.c ============================================================================== --- head/lib/msun/src/s_ccoshf.c Fri Oct 21 06:28:47 2011 (r226598) +++ head/lib/msun/src/s_ccoshf.c Fri Oct 21 06:29:32 2011 (r226599) @@ -36,10 +36,12 @@ __FBSDID("$FreeBSD$"); #include "math_private.h" +static const float huge = 0x1p127; + float complex ccoshf(float complex z) { - float x, y; + float x, y, h; int32_t hx, hy, ix, iy; x = crealf(z); @@ -54,8 +56,23 @@ ccoshf(float complex z) if (ix < 0x7f800000 && iy < 0x7f800000) { if (iy == 0) return (cpackf(coshf(x), x * y)); - /* XXX We don't handle |x| > FLT_MAX ln(2) yet. */ - return (cpackf(coshf(x) * cosf(y), sinhf(x) * sinf(y))); + if (ix < 0x41100000) /* small x: normal case */ + return (cpackf(coshf(x) * cosf(y), sinhf(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; + return (cpackf(h * cosf(y), copysignf(h, x) * sinf(y))); + } else if (ix < 0x4340b1e7) { + /* x < 192.7: scale to avoid overflow */ + z = __ldexp_cexpf(cpackf(fabsf(x), y), -1); + return (cpackf(crealf(z), cimagf(z) * copysignf(1, x))); + } else { + /* x >= 192.7: the result always overflows */ + h = huge * x; + return (cpackf(h * h * cosf(y), h * sinf(y))); + } } if (ix == 0 && iy >= 0x7f800000) Modified: head/lib/msun/src/s_csinh.c ============================================================================== --- head/lib/msun/src/s_csinh.c Fri Oct 21 06:28:47 2011 (r226598) +++ head/lib/msun/src/s_csinh.c Fri Oct 21 06:29:32 2011 (r226599) @@ -42,10 +42,12 @@ __FBSDID("$FreeBSD$"); #include "math_private.h" +static const double huge = 0x1p1023; + double complex csinh(double complex z) { - double x, y; + double x, y, h; int32_t hx, hy, ix, iy, lx, ly; x = creal(z); @@ -61,8 +63,23 @@ csinh(double complex z) if (ix < 0x7ff00000 && iy < 0x7ff00000) { if ((iy | ly) == 0) return (cpack(sinh(x), y)); - /* XXX We don't handle |x| > DBL_MAX ln(2) yet. */ - return (cpack(sinh(x) * cos(y), cosh(x) * sin(y))); + if (ix < 0x40360000) /* small x: normal case */ + return (cpack(sinh(x) * cos(y), cosh(x) * sin(y))); + + /* |x| >= 22, so cosh(x) ~= exp(|x|) */ + if (ix < 0x40862e42) { + /* x < 710: exp(|x|) won't overflow */ + h = exp(fabs(x)) * 0.5; + return (cpack(copysign(h, x) * cos(y), h * sin(y))); + } else if (ix < 0x4096bbaa) { + /* x < 1455: scale to avoid overflow */ + z = __ldexp_cexp(cpack(fabs(x), y), -1); + return (cpack(creal(z) * copysign(1, x), cimag(z))); + } else { + /* x >= 1455: the result always overflows */ + h = huge * x; + return (cpack(h * cos(y), h * h * sin(y))); + } } /* @@ -78,13 +95,13 @@ csinh(double complex z) return (cpack(copysign(0, x * (y - y)), y - y)); /* - * sinh(+-Inf +- I 0) = +-Inf + I (+-)(+-)0. + * 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 (cpack(x, copysign(0, x) * y)); + return (cpack(x, y)); return (cpack(x, copysign(0, y))); } Modified: head/lib/msun/src/s_csinhf.c ============================================================================== --- head/lib/msun/src/s_csinhf.c Fri Oct 21 06:28:47 2011 (r226598) +++ head/lib/msun/src/s_csinhf.c Fri Oct 21 06:29:32 2011 (r226599) @@ -36,10 +36,12 @@ __FBSDID("$FreeBSD$"); #include "math_private.h" +static const float huge = 0x1p127; + float complex csinhf(float complex z) { - float x, y; + float x, y, h; int32_t hx, hy, ix, iy; x = crealf(z); @@ -54,8 +56,23 @@ csinhf(float complex z) if (ix < 0x7f800000 && iy < 0x7f800000) { if (iy == 0) return (cpackf(sinhf(x), y)); - /* XXX We don't handle |x| > FLT_MAX ln(2) yet. */ - return (cpackf(sinhf(x) * cosf(y), coshf(x) * sinf(y))); + if (ix < 0x41100000) /* small x: normal case */ + return (cpackf(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; + return (cpackf(copysignf(h, x) * cosf(y), h * sinf(y))); + } else if (ix < 0x4340b1e7) { + /* x < 192.7: scale to avoid overflow */ + z = __ldexp_cexpf(cpackf(fabsf(x), y), -1); + return (cpackf(crealf(z) * copysignf(1, x), cimagf(z))); + } else { + /* x >= 192.7: the result always overflows */ + h = huge * x; + return (cpackf(h * cosf(y), h * h * sinf(y))); + } } if (ix == 0 && iy >= 0x7f800000) @@ -63,7 +80,7 @@ csinhf(float complex z) if (iy == 0 && ix >= 0x7f800000) { if ((hx & 0x7fffff) == 0) - return (cpackf(x, copysignf(0, x) * y)); + return (cpackf(x, y)); return (cpackf(x, copysignf(0, y))); }
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