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* Fix i386 atanhl spurious underflows (bug 18049).Joseph Myers2015-05-191-0/+5
| | | | | | | | | | | | | | | | The i386 implementation of atanhl, for small arguments, does a calculation that involves computing twice the square of the argument, resulting in spurious underflows for some arguments. This patch fixes this by just returning the argument when its exponent is below -32, with underflow being forced as needed for subnormal arguments. Tested for x86 and x86_64. [BZ #18049] * sysdeps/i386/fpu/e_atanhl.S (__ieee754_atanhl): For exponents below -32, return the argument, with underflow if subnormal. * math/auto-libm-test-in: Add more tests of atanh. * math/auto-libm-test-out: Regenerated.
* Fix atanhl missing underflows (bug 16352).Joseph Myers2015-05-151-7/+6
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Similar to various other bugs in this area, some atanh implementations do not raise the underflow exception for subnormal arguments, when the result is tiny and inexact. This patch forces the exception in a similar way to previous fixes. (No change in this regard is needed for the i386 implementation; special handling to force underflows in these cases will only be needed there when the spurious underflows, bug 18049, get fixed.) Tested for x86_64, x86, powerpc and mips64. [BZ #16352] * sysdeps/i386/fpu/e_atanh.S (dbl_min): New object. (__ieee754_atanh): Force underflow exception for results with small absolute value. * sysdeps/i386/fpu/e_atanhf.S (flt_min): New object. (__ieee754_atanhf): Force underflow exception for results with small absolute value. * sysdeps/ieee754/dbl-64/e_atanh.c: Include <float.h>. (__ieee754_atanh): Force underflow exception for results with small absolute value. * sysdeps/ieee754/flt-32/e_atanhf.c: Include <float.h>. (__ieee754_atanhf): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-128/e_atanhl.c: Include <float.h>. (__ieee754_atanhl): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-128ibm/e_atanhl.c: Include <float.h>. (__ieee754_atanhl): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-96/e_atanhl.c: Include <float.h>. (__ieee754_atanhl): Force underflow exception for results with small absolute value. * math/auto-libm-test-in: Do not allow missing underflow exceptions from atanh. * math/auto-libm-test-out: Regenerated.
* Fix tanf spurious underflows (bug 18221).Joseph Myers2015-05-151-0/+2
| | | | | | | | | | | | | | | | The flt-32 implementation of tanf produces spurious underflow exceptions for some small arguments, through computing values on the order of x^5. This patch fixes this by adjusting the threshold for returning x (or, as applicable, +/- 1/x) to 2**-13 (the next term in the power series being x^3/3). Tested for x86_64 and x86. [BZ #18221] * sysdeps/ieee754/flt-32/k_tanf.c (__kernel_tanf): Use 2**-13 not 2**-28 as threshold for returning x or +/- 1/x. * math/auto-libm-test-in: Add more tests of tan. * math/auto-libm-test-out: Regenerated.
* Fix lgammaf spurious underflows (bug 18220).Joseph Myers2015-05-151-0/+1
| | | | | | | | | | | | | | | | | The flt-32 implementation of lgammaf produces spurious underflow exceptions for some large arguments, because of calculations involving x^-2 multiplied by small constants. This patch fixes this by adjusting the threshold for a simpler computation to 2**26 (the error in the simpler computation is on the order of 0.5 * log (x), for a result on the order of x * log (x)). Tested for x86_64 and x86. [BZ #18220] * sysdeps/ieee754/flt-32/e_lgammaf_r.c (__ieee754_lgammaf_r): Use 2**26 not 2**58 as threshold for returning x * (log (x) - 1). * math/auto-libm-test-in: Add another test of lgamma. * math/auto-libm-test-out: Regenerated.
* Fix erfcf spurious underflows (bug 18217).Joseph Myers2015-05-151-0/+2
| | | | | | | | | | | | | | | | | | The flt-32 implementation of erfcf produces spurious underflow exceptions for some arguments close to 0, because of calculations squaring the argument and then multiplying by small constants. This patch fixes this by adjusting the threshold for arguments for which the result is so close to 1 that 1 - x will give the right result from 2**-56 to 2**-26. (If 1 - x * 2/sqrt(pi) were used, the errors would be on the order of x^3 and a much larger threshold could be used.) Tested for x86_64 and x86. [BZ #18217] * sysdeps/ieee754/flt-32/s_erff.c (__erfcf): Use 2**-26 not 2**-56 as threshold for returning 1 - x. * math/auto-libm-test-in: Add more tests of erfc. * math/auto-libm-test-out: Regenerated.
* Fix atanf spurious underflows (bug 18196).Joseph Myers2015-05-141-0/+1
| | | | | | | | | | | | | | | | The sysdeps/ieee754/flt-32 version of atanf produces spurious underflow exceptions for some large arguments, because of computations that compute x^-4. This patch fixes this by adjusting the threshold for large arguments (for which +/- pi/2 can just be returned, the correct result being roughly +/- pi/2 - 1/x) from 2^34 to 2^25. Tested for x86_64 and x86. [BZ #18196] * sysdeps/ieee754/flt-32/s_atanf.c (__atanf): Use 2^25 not 2^34 as threshold for large arguments. * math/auto-libm-test-in: Add another test of atan. * math/auto-libm-test-out: Regenerated.
* Fix log1p missing underflows (bug 16339).Joseph Myers2015-05-141-5/+4
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Similar to various other bugs in this area, some log1p implementations do not raise the underflow exception for subnormal arguments, when the result is tiny and inexact. This patch forces the exception in a similar way to previous fixes. (The ldbl-128ibm implementation doesn't currently need any change as it already generates this exception, albeit through code that would generate spurious exceptions in other cases; special code for this issue will only be needed there when fixing the spurious exceptions.) Tested for x86_64, x86, powerpc and mips64. [BZ #16339] * sysdeps/i386/fpu/s_log1p.S (dbl_min): New object. (__log1p): Force underflow exception for results with small absolute value. * sysdeps/i386/fpu/s_log1pf.S (flt_min): New object. (__log1pf): Force underflow exception for results with small absolute value. * sysdeps/ieee754/dbl-64/s_log1p.c: Include <float.h>. (__log1p): Force underflow exception for results with small absolute value. * sysdeps/ieee754/flt-32/s_log1pf.c: Include <float.h>. (__log1pf): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-128/s_log1pl.c: Include <float.h>. (__log1pl): Force underflow exception for results with small absolute value. * math/auto-libm-test-in: Do not allow missing underflow exceptions from log1p. * math/auto-libm-test-out: Regenerated.
* Add more tests of csqrt, lgamma, log10, sinh.Joseph Myers2015-05-081-0/+4
| | | | | | | | | | | | | This patch adds more randomly-generated tests of various libm functions that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of csqrt, lgamma, log10 and sinh. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of acosh, atanh, cos, csqrt, erfc, sin, sincos.Joseph Myers2015-05-061-0/+8
| | | | | | | | | | | | | This patch adds more randomly-generated tests of various libm functions that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of acosh, atanh, cos, csqrt, erfc, sin and sincos. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add further tests of libm functions.Joseph Myers2015-05-051-0/+23
| | | | | | | | | | | | | | | | | This patch adds more randomly-generated tests of various libm functions that are observed to increase ulps on x86_64. (This process must eventually converge, when my random test generation stops finding inputs that increase the listed ulps, except maybe for any cases uncovered where the errors exceed the maximum allowed 9ulp error and so indicate actual libm bugs needing fixing.) Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of acosh, atanh, clog, clog10, csqrt, erfc, exp2, expm1, log10, log2 and sinh. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of libm functions.Joseph Myers2015-05-021-0/+23
| | | | | | | | | | | | | | This patch adds more randomly-generated tests of various libm functions that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of atan, clog, clog10, cos, csqrt, erf, erfc, exp2, lgamma, log1p, sin, sincos, tanh and tgamma. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of tgamma.Joseph Myers2015-05-011-0/+4
| | | | | | | | | | | | This patch adds some randomly-generated tests of tgamma that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of tgamma. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of tanh.Joseph Myers2015-05-011-0/+10
| | | | | | | | | | | | This patch adds some randomly-generated tests of tanh that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of tanh. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of tan.Joseph Myers2015-05-011-0/+2
| | | | | | | | | | | | This patch adds some randomly-generated tests of tan that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of tan. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of cos, sin, sincos.Joseph Myers2015-05-011-0/+3
| | | | | | | | | | | | This patch adds some randomly-generated tests of cos, sin and sincos that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of cos, sin and sincos. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add another test of pow.Joseph Myers2015-05-011-0/+1
| | | | | | | | | | | This patch adds a randomly-generated test of pow that is observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add another test of pow. * math/auto-libm-test-out: Regenerated. * sysdeps/x86_64/fpu/libm-test-ulps: Update.
* Add more tests of lgamma.Joseph Myers2015-05-011-0/+8
| | | | | | | | | | | | This patch adds some randomly-generated tests of lgamma that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of lgamma. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of log, log10, log1p, log2.Joseph Myers2015-05-011-0/+23
| | | | | | | | | | | | | This patch adds some randomly-generated tests of log, log10, log1p and log2 that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of log, log10, log2 and log1p. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of exp, exp10, exp2, expm1.Joseph Myers2015-05-011-0/+15
| | | | | | | | | | | | | This patch adds some randomly-generated tests of exp, exp10, exp2 and expm1 that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of exp, exp10, exp2 and expm1. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of erf, erfc.Joseph Myers2015-05-011-0/+14
| | | | | | | | | | | | This patch adds some randomly-generated tests of erf and erfc that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of erf and erfc. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of csqrt.Joseph Myers2015-04-301-0/+14
| | | | | | | | | | | | This patch adds some randomly-generated tests of csqrt that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of csqrt. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add further tests of cosh and sinh.Joseph Myers2015-04-301-0/+5
| | | | | | | | | | | | This patch adds some further randomly-generated tests of cosh and sinh that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of cosh and sinh. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of clog and clog10.Joseph Myers2015-04-091-0/+16
| | | | | | | | | | | | This patch adds some randomly-generated tests of clog and clog10 that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of clog and clog10. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of atanh.Joseph Myers2015-04-081-0/+2
| | | | | | | | | | | | This patch adds some randomly-generated tests of atanh that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of atanh. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of atan.Joseph Myers2015-04-081-0/+3
| | | | | | | | | | | | This patch adds some randomly-generated tests of atan that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of atan. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of cbrt.Joseph Myers2015-04-081-0/+4
| | | | | | | | | | | This patch adds some randomly-generated tests of cbrt that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of cbrt. * math/auto-libm-test-out: Regenerated. * sysdeps/x86_64/fpu/libm-test-ulps: Update.
* Add more tests of cabs.Joseph Myers2015-04-081-0/+6
| | | | | | | | | | | | This patch adds some randomly-generated tests of cabs that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of cabs. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Fix dbl-64 atan2 in non-default rounding modes (bug 18210, bug 18211).Joseph Myers2015-04-081-0/+34
| | | | | | | | | | | | | | | | | | | | | | The dbl-64 implementation of atan2 does computations that expect to run in round-to-nearest mode, and in other modes the errors can accumulate to more than the maximum accepted 9ulp. This patch makes it use FE_TONEAREST internally, similar to other functions with such issues. Tests that previously produced large errors are added for atan2 and the closely related carg, clog and clog10 functions. Tested for x86_64 and x86 and ulps updated accordingly. [BZ #18210] [BZ #18211] * sysdeps/ieee754/dbl-64/e_atan2.c: Include <fenv.h>. (__ieee754_atan2): Set FE_TONEAREST mode for internal computations. * math/auto-libm-test-in: Add more tests of atan2, carg, clog and clog10. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Fix dbl-64 atan in non-default rounding modes (bug 18197).Joseph Myers2015-04-081-0/+2
| | | | | | | | | | | | | | | The dbl-64 implementation of atan does computations that expect to run in round-to-nearest mode, and in other modes the errors can accumulate to more than the maximum accepted 9ulp. This patch makes it use FE_TONEAREST internally, similar to other functions with such issues. Tested for x86_64 and x86; no ulps updates needed. [BZ #18197] * sysdeps/ieee754/dbl-64/s_atan.c: Include <fenv.h>. (atan): Set FE_TONEAREST mode for internal computations. * math/auto-libm-test-in: Add more tests of atan. * math/auto-libm-test-out: Regenerated.
* Add more tests of acosh, asinh and atanh.Joseph Myers2015-03-251-0/+20
| | | | | | | | | | | | | This patch adds some randomly-generated tests of acosh, asinh and atanh that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of acosh, asinh and atanh. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add another test of asin.Joseph Myers2015-03-251-0/+1
| | | | | | | | | | | | This patch adds a randomly-generated test of asin that is observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add another test of asin. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of asin.Joseph Myers2015-03-251-0/+4
| | | | | | | | | | | | This patch adds some randomly-generated tests of asin that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of asin. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of acos.Joseph Myers2015-03-251-0/+6
| | | | | | | | | | | | This patch adds some randomly-generated tests of acos that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of acos. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of expm1.Joseph Myers2015-03-251-0/+4
| | | | | | | | | | | | This patch adds some randomly-generated tests of expm1 that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of expm1. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of cosh, sinh.Joseph Myers2015-03-241-0/+11
| | | | | | | | | | | | This patch adds some randomly-generated tests of cosh and sinh that are observed to increase ulps on x86_64. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of cosh and sinh. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add more tests of log2.Joseph Myers2015-03-241-0/+6
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | In testing for x86_64 on an AMD processor, I observed libm test failures of the form: testing long double (without inline functions) Failure: Test: log2_downward (0x2.b7e151628aed4p+0) Result: is: 1.44269504088896356633e+00 0xb.8aa3b295c17f67600000p-3 should be: 1.44269504088896356622e+00 0xb.8aa3b295c17f67500000p-3 difference: 1.08420217248550443400e-19 0x8.00000000000000000000p-66 ulp : 1.0000 max.ulp : 0.0000 Maximal error of `log2_downward' is : 1 ulp accepted: 0 ulp These issues arise because the maximum ulps when regenerating on one processor are not the same as on another processor, so regeneration on several processors may be needed when updating libm-test-ulps to avoid failures for some users testing glibc - but such regeneration on multiple processors is inconvenient. Causes can be: on x86 and, for x86_64, for long double, variation in results of x87 instructions for transcendental operations between processors; on x86, variation in compiler excess precision between compiler versions and configurations; on any processor where the compiler may contract expressions using fused multiply-add, variation in what contraction occurs. Although it's hard to be sure libm-test-ulps covers all ulps that may be seen in any configuration for the given architecture, in practice it helps simply to add wider test coverage to make it more likely that, when testing on one processor, the ulps seen are the biggest that can be seen for that function on that processor, and hopefully they are also the biggest that can be seen for that function in other configurations for that architecture. Thus, this patch adds some tests of log2 that increase the ulps I see on x86_64 on an Intel processor, so that hopefully future from-scratch regenerations on that processor will produce ulps big enough not to have errors from testing on AMD processors. These tests were found by randomly generating inputs and seeing what produced ulps larger than those currently in libm-test-ulps. Of course such increases also improve the accuracy of the empirical table of known ulps generated from libm-test-ulps files that goes in the manual. Tested for x86_64 and x86 and ulps updated accordingly. * math/auto-libm-test-in: Add more tests of log2. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Add test for bug 18104.Joseph Myers2015-03-101-0/+1
| | | | | | [BZ #18104] * math/auto-libm-test-in: Add another test of pow. * math/auto-libm-test-out: Regenerated.
* Fix ldbl-96, ldbl-128ibm atanhl inaccuracy (bug 18046, bug 18047).Joseph Myers2015-02-271-0/+31
| | | | | | | | | | | | | | | | | | | | | | | | | The threshold in ldbl-96 atanhl for when to return the argument, 0x1p-28, is a bit too big, and that in ldbl-128ibm atanhl is much too big (the relevant condition being x^3/3 being < 0.5ulp of x), resulting in errors a bit above the limits of those considered acceptable in glibc in the ldbl-96 case, and in large errors in the ldbl-128ibm case. This patch changes those implementations to use more appropriate thresholds and adds tests around the thresholds for various formats. Tested for x86_64, x86 and powerpc. x86_64 and x86 ulps updated accordingly. [BZ #18046] [BZ #18047] * sysdeps/ieee754/ldbl-128ibm/e_atanhl.c (__ieee754_atanhl): Use 0x1p-56L as threshold for just returning the argument. * sysdeps/ieee754/ldbl-96/e_atanhl.c (__ieee754_atanhl): Use 0x1p-32L as threshold for just returning the argument. * math/auto-libm-test-in: Add more tests of atanh. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulp: Likewise.
* Fix ldbl-128/ldbl-128ibm acosl inaccuracy (bug 18038, bug 18039).Joseph Myers2015-02-261-0/+31
| | | | | | | | | | | | | | | | | | | | | The ldbl-128 and ldbl-128ibm implementations of acosl have similar bugs, using a threshold of 0x1p-57L to determine when they just return pi/2. Since the result pi/2 - asinl (x) is roughly pi/2 - x for small x, the relevant cut-off is actually x being < 0.5ulp of 1. This patch fixes the implementations to use that cut-off and adds tests of small acos arguments. Tested for powerpc and mips64. Also tested for x86_64 and x86; no ulps updates needed. [BZ #18038] [BZ #18039] * sysdeps/ieee754/ldbl-128/e_acosl.c (__ieee754_acosl): Only return pi/2 for arguments below 0x1p-113L. * sysdeps/ieee754/ldbl-128ibm/e_acosl.c (__ieee754_acosl): Only return pi/2 for arguments below 0x1p-106L. * math/auto-libm-test-in: Add more tests of acos. * math/auto-libm-test-out: Regenerated.
* Fix asin missing underflows (bug 16351).Joseph Myers2015-02-261-5/+4
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Similar to various other bugs in this area, some asin implementations do not raise the underflow exception for subnormal arguments, when the result is tiny and inexact. This patch forces the exception in a similar way to previous fixes. Tested for x86_64, x86, powerpc and mips64. [BZ #16351] * sysdeps/i386/fpu/e_asin.S (dbl_min): New object. (MO): New macro. (__ieee754_asin): Force underflow exception for results with small absolute value. * sysdeps/i386/fpu/e_asinf.S (flt_min): New object. (MO): New macro. (__ieee754_asinf): Force underflow exception for results with small absolute value. * sysdeps/ieee754/dbl-64/e_asin.c: Include <float.h> and <math.h>. (__ieee754_asin): Force underflow exception for results with small absolute value. * sysdeps/ieee754/flt-32/e_asinf.c: Include <float.h>. (__ieee754_asinf): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-128/e_asinl.c: Include <float.h>. (__ieee754_asinl): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-128ibm/e_asinl.c: Include <float.h>. (__ieee754_asinl): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-96/e_asinl.c: Include <float.h>. (__ieee754_asinl): Force underflow exception for results with small absolute value. * sysdeps/x86_64/fpu/multiarch/e_asin.c [HAVE_FMA4_SUPPORT]: Include <math.h>. * math/auto-libm-test-in: Do not mark underflow exceptions as possibly missing for bug 16351. * math/auto-libm-test-out: Regenerated.
* Fix ldbl-128ibm asinhl inaccuracy (bug 18020).Joseph Myers2015-02-251-0/+61
| | | | | | | | | | | | | | | | | | | The ldbl-128ibm implementation of asinhl uses cut-offs of 0x1p28 and 0x1p-29 to determine when to use simpler formulas that avoid possible overflow / underflow. Both those cut-offs are inappropriate for this format, resulting in large errors. This patch changes the code to use more appropriate cut-offs of 0x1p56 and 0x1p-56, adding tests around the cut-offs for various floating-point formats. Tested for powerpc. Also tested for x86_64 and x86 and updated ulps. [BZ #18020] * sysdeps/ieee754/ldbl-128ibm/s_asinhl.c (__asinhl): Use 2**56 and 2**-56 not 2**28 and 2**-29 as thresholds for simpler formulas. * math/auto-libm-test-in: Add more tests of asinh. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Fix ldbl-128ibm acoshl inaccuracy (bug 18019).Joseph Myers2015-02-251-0/+31
| | | | | | | | | | | | | | | | | | The ldbl-128ibm implementation of acoshl uses a cut-off of 0x1p28 to determine when to use log(x) + log(2) as a formula. That cut-off is too small for this format, resulting in large errors. This patch changes it to a more appropriate cut-off of 0x1p56, adding tests around the cut-offs for various floating-point formats. Tested for powerpc. Also tested for x86_64 and x86 and updated ulps. [BZ #18019] * sysdeps/ieee754/ldbl-128ibm/e_acoshl.c (__ieee754_acoshl): Use 2**56 not 2**28 as threshold for log (2x) formula. * math/auto-libm-test-in: Add more tests of acosh. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
* Fix atan / atan2 missing underflows (bug 15319).Joseph Myers2015-02-181-15/+21
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | This patch fixes bug 15319, missing underflows from atan / atan2 when the result of atan is very close to its small argument (or that of atan2 is very close to the ratio of its arguments, which may be an exact division). The usual approach of doing an underflowing computation if the computed result is subnormal is followed. For 32-bit x86, there are extra complications: the inline __ieee754_atan2 in bits/mathinline.h needs to be disabled for float and double because other libm functions using it generally rely on getting proper underflow exceptions from it, while the out-of-line functions have to remove excess range and precision from the underflowing result so as to return an exact 0 in the case where errno should be set for underflow to 0. (The failures I saw without that are similar to those Carlos reported for other functions, where I haven't seen a response to <https://sourceware.org/ml/libc-alpha/2015-01/msg00485.html> confirming if my diagnosis is correct. Arguably all libm functions with float and double returns should remove excess range and precision, but that's a separate matter.) The x86_64 long double case reported in a comment in bug 15319 is not a bug (it's an argument of LDBL_MIN, and x86_64 is an after-rounding architecture so the correct IEEE result is not to raise underflow in the given rounding mode, in addition to treating the result as an exact LDBL_MIN being within the newly clarified documentation of accuracy goals). I'm presuming that the fpatan instruction can be trusted to raise appropriate exceptions when the (long double) result underflows (after rounding) and so no changes are needed for x86 / x86_64 long double functions here; empirically this is the case for the cases covered in the testsuite, on my system. Tested for x86_64, x86, powerpc and mips64. Only 32-bit x86 needs ulps updates (for the changes to inlines meaning some functions no longer get excess precision from their __ieee754_atan2* calls). [BZ #15319] * sysdeps/i386/fpu/e_atan2.S (dbl_min): New object. (MO): New macro. (__ieee754_atan2): For results with small absolute value, force underflow exception and remove excess range and precision from return value. * sysdeps/i386/fpu/e_atan2f.S (flt_min): New object. (MO): New macro. (__ieee754_atan2f): For results with small absolute value, force underflow exception and remove excess range and precision from return value. * sysdeps/i386/fpu/s_atan.S (dbl_min): New object. (MO): New macro. (__atan): For results with small absolute value, force underflow exception and remove excess range and precision from return value. * sysdeps/i386/fpu/s_atanf.S (flt_min): New object. (MO): New macro. (__atanf): For results with small absolute value, force underflow exception and remove excess range and precision from return value. * sysdeps/ieee754/dbl-64/e_atan2.c: Include <float.h> and <math.h>. (__ieee754_atan2): Force underflow exception for results with small absolute value. * sysdeps/ieee754/dbl-64/s_atan.c: Include <float.h> and <math_private.h>. (atan): Force underflow exception for results with small absolute value. * sysdeps/ieee754/flt-32/s_atanf.c: Include <float.h>. (__atanf): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-128/s_atanl.c: Include <float.h> and <math.h>. (__atanl): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-128ibm/s_atanl.c: Include <float.h>. (__atanl): Force underflow exception for results with small absolute value. * sysdeps/x86/fpu/bits/mathinline.h [!__SSE2_MATH__ && !__x86_64__ && __LIBC_INTERNAL_MATH_INLINES] (__ieee754_atan2): Only define inline for long double. * sysdeps/x86_64/fpu/multiarch/e_atan2.c [HAVE_FMA4_SUPPORT || HAVE_AVX_SUPPORT]: Include <math.h>. * math/auto-libm-test-in: Do not mark underflow exceptions as possibly missing for bug 15319. Add more tests of atan2. * math/auto-libm-test-out: Regenerated. * math/libm-test.inc (casin_test_data): Do not mark underflow exceptions as possibly missing for bug 15319. (casinh_test_data): Likewise. * sysdeps/i386/fpu/libm-test-ulps: Update.
* Fix exp2 spurious underflows (bug 16560).Joseph Myers2015-02-121-0/+18
| | | | | | | | | | | | | | | | | | | | | | This patch fixes the remaining part of bug 16560, spurious underflows from exp2 of arguments close to 0 (when the result is close to 1, so should not underflow), by just using 1+x instead of a more complicated calculation when the argument is sufficiently small. Tested for x86_64, x86 and mips64. [BZ #16560] * math/e_exp2l.c [LDBL_MANT_DIG == 106] (LDBL_EPSILON): Undefine and redefine. (__ieee754_exp2l): Do not multiply small fractional parts by M_LN2l. * sysdeps/i386/fpu/e_exp2l.S (__ieee754_exp2l): Just add 1 to small argument. * sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Likewise. * sysdeps/ieee754/flt-32/e_exp2f.c (__ieee754_exp2f): Likewise. * sysdeps/x86_64/fpu/e_exp2l.S (__ieee754_exp2l): Likewise. * math/auto-libm-test-in: Add more tests of exp2. * math/auto-libm-test-out: Regenerated.
* soft-fp: Fix _FP_FMA when product is zero and third argument is finite (bug ↵Joseph Myers2015-02-061-0/+10
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | 17932). soft-fp's _FP_FMA fails to set the result's exponent for cases where the result of the multiplication is 0, yielding incorrect (arbitrary, depending on uninitialized values) results for those cases. This affects libm for architectures using soft-fp to implement fma. This patch adds the exponent setting and tests for this case. Tested for ARM soft-float (which uses soft-fp fma), x86_64 and x86 (to verify not introducing new libm test failures there). (This bug showed up in testing my patch to move the Linux kernel to current soft-fp. math/Makefile has "override CFLAGS += -Wno-uninitialized" which would have stopped compiler warnings from showing up this problem, although I wouldn't be surprised if removing that shows spurious warnings from this code, if the compiler fails to follow that various cases where the exponent is uninitialized don't need it initialized because the class is set to a value meaning the uninitialized exponent isn't used.) [BZ #17932] * soft-fp/op-common.h (_FP_FMA): Set exponent of result in case where multiplication results in zero and third argument is finite and nonzero. * math/auto-libm-test-in: Add more tests of fma. * math/auto-libm-test-out: Regenerated.
* Update copyright dates with scripts/update-copyrights.Joseph Myers2015-01-021-1/+1
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* Fix exp10 spurious underflows (bug 16560).Joseph Myers2014-06-251-0/+18
| | | | | | | | | | | | | | | | | | | | | | | | | This patch fixes spurious underflows from exp10 for arguments near 0 (part of bug 16560; that bug also includes spurious underflows from exp2, which are not fixed by this patch). The problem is underflows in the internal computation converting the exp10 argument to arguments for exp (with extra precision), and the fix is simply to return 1 early for arguments near enough to 0 (just as arguments with large enough magnitude have their own overflow / underflow logic at the start of the function). Tested x86_64 and x86 and ulps updated accordingly; also tested for powerpc32 and mips64 to validate the ldbl-128ibm and ldbl-128 changes. [BZ #16560] * sysdeps/ieee754/dbl-64/e_exp10.c (__ieee754_exp10): Return 1 for arguments close to 0. * sysdeps/ieee754/ldbl-128/e_exp10l.c (__ieee754_exp10l): Likewise. * sysdeps/ieee754/ldbl-128ibm/e_exp10l.c (__ieee754_exp10l): Likewise. * math/auto-libm-test-in: Add more tests of exp10. * math/auto-libm-test-out: Regenerated. * sysdeps/x86_64/fpu/libm-test-ulps: Update.
* Fix x86/x86_64 expm1l spurious underflow exceptions (bug 16539).Joseph Myers2014-06-241-0/+2
| | | | | | | | | | | | | | | | | | | | | | | | | This patch fixes bug 16539, spurious underflow exceptions from x86 / x86-64 expm1l. The problem is that the computation of a base-2 exponent with extra precision involves spurious underflows for arguments that are small but not subnormal, so a check is added to just return the argument in those cases. (If the argument *is* subnormal, underflowing is correct and the existing code will always underflow, so it suffices to keep using the existing code in that case; some expm1 implementations have a bug (bug 16353) with missing underflow exceptions, but I don't think there's such a bug in this particular version.) Tested x86_64 and x86; no ulps updates needed. (auto-libm-test-out diffs omitted below.) [BZ #16539] * sysdeps/i386/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Just return the argument for normal arguments with exponent below -64. * sysdeps/x86_64/fpu/e_expl.S (IEEE754_EXPL) [USE_AS_EXPM1L]: Likewise. * math/auto-libm-test-in: Add another test of expm1. * math/auto-libm-test-out: Regenerated.
* Fix ldbl-128 erfl spurious underflows (bug 16287).Joseph Myers2014-06-241-0/+10
| | | | | | | | | | | | | | | | | | | | This patch fixes bug 16287, spurious underflows from ldbl-128 erfl arising from it calling erfcl for arguments with absolute value at least 1.0, although for large positive arguments erfcl correctly underflows but erfl shouldn't. The fix is simply to avoid calling erfcl, and just return 1, for arguments above a cut-off large enough that erfl correctly rounds to-nearest as 1 but not so large that erfcl underflows. Tested mips64. Also tested x86_64 and x86 to confirm the new tests (taken from the tests of erfc) don't cause any problems there; no ulps updates needed. [BZ #16287] * sysdeps/ieee754/ldbl-128/s_erfl.c (__erfl): Return 1 without calling __erfcl for arguments at least 16. * math/auto-libm-test-in: Add more tests of erf. * math/auto-libm-test-out: Regenerated.
* Fix cosh spurious underflows from expm1 (bug 16354), inaccurate results near ↵Joseph Myers2014-06-231-5/+8
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 (bug 17061). This patch fixes bug 16354, spurious underflows from cosh when a tiny argument is passed to expm1 and expm1 correctly underflows although the final result of cosh should be 1. As noted in that bug, some cases are latent because of expm1 implementations not raising underflow (bug 16353), but all the implementations are fixed similarly. They already contained checks for tiny arguments, but the checks were too late to avoid underflow from expm1 (although they would avoid underflow from subsequent squaring of the result of expm1); they are moved before the expm1 calls. The thresholds used for considering arguments tiny are not particularly consistent in how they relate to the precision of the floating-point format in question. They are, however, all sufficient to ensure that the round-to-nearest result of cosh is indeed 1 below the threshold (although sometimes they are smaller than necessary). But the previous logic did not return 1, but the previously computed 1 + expm1(abs(x)) value. And the thresholds in the ldbl-128 and ldbl-128ibm code (0x1p-71L - I suspect 0x3f8b was intended in the code instead of 0x3fb8 - and (roughly) 0x1p-55L) are not sufficient for that value to be 1. So by moving the test for tiny arguments, and consequently returning 1 directly now the expm1 value hasn't been computed by that point, this patch also fixes bug 17061, the (large number of ulps) inaccuracy for small arguments in those implementations. Tests for that bug are duly added. Tested x86_64 and x86 and ulps updated accordingly. Also tested for mips64 and powerpc32 to validate the ldbl-128 and ldbl-128ibm changes. [BZ #16354] [BZ #17061] * sysdeps/ieee754/dbl-64/e_cosh.c (__ieee754_cosh): Check for small arguments before calling __expm1. * sysdeps/ieee754/flt-32/e_coshf.c (__ieee754_coshf): Check for small arguments before calling __expm1f. * sysdeps/ieee754/ldbl-128/e_coshl.c (__ieee754_coshl): Check for small arguments before calling __expm1l. * sysdeps/ieee754/ldbl-128ibm/e_coshl.c (__ieee754_coshl): Likewise. * sysdeps/ieee754/ldbl-96/e_coshl.c (__ieee754_coshl): Likewise. * math/auto-libm-test-in: Add more cosh tests. Do not allow spurious underflow for some cosh tests. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update.
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