From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: by sourceware.org (Postfix, from userid 2155) id E2DA3385E014; Thu, 26 Mar 2020 11:26:34 +0000 (GMT) DKIM-Filter: OpenDKIM Filter v2.11.0 sourceware.org E2DA3385E014 Content-Type: text/plain; charset="us-ascii" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit From: Corinna Vinschen To: newlib-cvs@sourceware.org Subject: [newlib-cygwin] Fix spurious underflow exceptions for Bessel functions for double(from glibc bug 14155) X-Act-Checkin: newlib-cygwin X-Git-Author: Joseph S. Myers X-Git-Refname: refs/heads/master X-Git-Oldrev: 009c7a0553b6d59f0d5ed79210069a9c7c336184 X-Git-Newrev: 5e24839658f6576b68b26c977897b9ad3fc3c23f Message-Id: <20200326112634.E2DA3385E014@sourceware.org> Date: Thu, 26 Mar 2020 11:26:34 +0000 (GMT) X-BeenThere: newlib-cvs@sourceware.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Newlib GIT logs List-Unsubscribe: , List-Archive: List-Help: List-Subscribe: , X-List-Received-Date: Thu, 26 Mar 2020 11:26:35 -0000 https://sourceware.org/git/gitweb.cgi?p=newlib-cygwin.git;h=5e24839658f6576b68b26c977897b9ad3fc3c23f commit 5e24839658f6576b68b26c977897b9ad3fc3c23f Author: Joseph S. Myers Date: Wed Mar 25 11:18:44 2020 -0700 Fix spurious underflow exceptions for Bessel functions for double(from glibc bug 14155) This fix comes from glibc, from files which originated from the same place as the newlib files. Those files in glibc carry the same license as the newlib files. Bug 14155 is spurious underflow exceptions from Bessel functions for large arguments. (The correct results for large x are roughly constant * sin or cos (x + constant) / sqrt (x), so no underflow exceptions should occur based on the final result.) There are various places underflows may occur in the intermediate calculations that cause the failures listed in that bug. This patch fixes problems for the double version where underflows occur in calculating the intermediate functions P and Q (in particular, x**-12 gets computed while calculating Q). Appropriate approximations are used for P and Q for arguments at least 0x1p28 and above to avoid the underflows. For sufficiently large x - 0x1p129 and above - the code already has a cut-off to avoid calculating P and Q at all, which means the approximations -0.125 / x and 0.375 / x can't themselves cause underflows calculating Q. This cut-off is heuristically reasonable for the point beyond which Q can be neglected (based on expecting around 0x1p-64 to be the least absolute value of sin or cos for large arguments representable in double). The float versions use a cut-off 0x1p17, which is less heuristically justifiable but should still only affect values near zeroes of the Bessel functions where these implementations are intrinsically inaccurate anyway (bugs 14469-14472), and should serve to avoid underflows (the float underflow for jn in bug 14155 probably comes from the recurrence to compute jn). ldbl-96 uses 0x1p129, which may not really be enough heuristically (0x1p143 or so might be safer - 143 = 64 + 79, number of mantissa bits plus total number of significant bits in representation) but again should avoid underflows and only affect values where the code is substantially inaccurate anyway. ldbl-128 and ldbl-128ibm share a completely different implementation with no such cut-off, which I propose to fix separately. Signed-off-by: Keith Packard Diff: --- newlib/libm/math/e_j0.c | 6 ++++-- newlib/libm/math/e_j1.c | 6 ++++-- newlib/libm/math/ef_j0.c | 6 +++--- newlib/libm/math/ef_j1.c | 4 ++-- 4 files changed, 13 insertions(+), 9 deletions(-) diff --git a/newlib/libm/math/e_j0.c b/newlib/libm/math/e_j0.c index 13773cbf9..d3af9d32c 100644 --- a/newlib/libm/math/e_j0.c +++ b/newlib/libm/math/e_j0.c @@ -338,7 +338,8 @@ static double pS2[5] = { __int32_t ix; GET_HIGH_WORD(ix,x); ix &= 0x7fffffff; - if(ix>=0x40200000) {p = pR8; q= pS8;} + if (ix>=0x41b00000) {return one;} + else if(ix>=0x40200000){p = pR8; q= pS8;} else if(ix>=0x40122E8B){p = pR5; q= pS5;} else if(ix>=0x4006DB6D){p = pR3; q= pS3;} else {p = pR2; q= pS2;} @@ -474,7 +475,8 @@ static double qS2[6] = { __int32_t ix; GET_HIGH_WORD(ix,x); ix &= 0x7fffffff; - if(ix>=0x40200000) {p = qR8; q= qS8;} + if (ix>=0x41b00000) {return -.125/x;} + else if(ix>=0x40200000){p = qR8; q= qS8;} else if(ix>=0x40122E8B){p = qR5; q= qS5;} else if(ix>=0x4006DB6D){p = qR3; q= qS3;} else {p = qR2; q= qS2;} diff --git a/newlib/libm/math/e_j1.c b/newlib/libm/math/e_j1.c index 098eb569e..72855e3fa 100644 --- a/newlib/libm/math/e_j1.c +++ b/newlib/libm/math/e_j1.c @@ -336,7 +336,8 @@ static double ps2[5] = { __int32_t ix; GET_HIGH_WORD(ix,x); ix &= 0x7fffffff; - if(ix>=0x40200000) {p = pr8; q= ps8;} + if (ix>=0x41b00000) {return one;} + else if(ix>=0x40200000){p = pr8; q= ps8;} else if(ix>=0x40122E8B){p = pr5; q= ps5;} else if(ix>=0x4006DB6D){p = pr3; q= ps3;} else {p = pr2; q= ps2;} @@ -473,7 +474,8 @@ static double qs2[6] = { __int32_t ix; GET_HIGH_WORD(ix,x); ix &= 0x7fffffff; - if(ix>=0x40200000) {p = qr8; q= qs8;} + if (ix>=0x41b00000) {return .375/x;} + else if(ix>=0x40200000){p = qr8; q= qs8;} else if(ix>=0x40122E8B){p = qr5; q= qs5;} else if(ix>=0x4006DB6D){p = qr3; q= qs3;} else {p = qr2; q= qs2;} diff --git a/newlib/libm/math/ef_j0.c b/newlib/libm/math/ef_j0.c index 866cfcf96..854801f1d 100644 --- a/newlib/libm/math/ef_j0.c +++ b/newlib/libm/math/ef_j0.c @@ -74,7 +74,7 @@ static float zero = 0.0; * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) */ - if(ix>0x80000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(x); + if(ix>0x5c000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(x); else { u = pzerof(x); v = qzerof(x); z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(x); @@ -156,14 +156,14 @@ v04 = 4.4111031494e-10; /* 0x2ff280c2 */ if ((s*c)0x80000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x); + if(ix>0x5c000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x); else { u = pzerof(x); v = qzerof(x); z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x); } return z; } - if(ix<=0x32000000) { /* x < 2**-27 */ + if(ix<=0x39800000) { /* x < 2**-27 */ return(u00 + tpi*__ieee754_logf(x)); } z = x*x; diff --git a/newlib/libm/math/ef_j1.c b/newlib/libm/math/ef_j1.c index 01bd24cf1..f4c9c9dd3 100644 --- a/newlib/libm/math/ef_j1.c +++ b/newlib/libm/math/ef_j1.c @@ -75,7 +75,7 @@ static float zero = 0.0; * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) */ - if(ix>0x80000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(y); + if(ix>0x5c000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(y); else { u = ponef(y); v = qonef(y); z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(y); @@ -153,7 +153,7 @@ static float V0[5] = { * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) * to compute the worse one. */ - if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x); + if(ix>0x5c000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x); else { u = ponef(x); v = qonef(x); z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x);