GitHub - jacob-navia/qlib: A version of the cephes mathematical library for ARM and x86

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A version of the cephes mathematical library for ARM and x86

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Name		Name	Last commit message	Last commit date
Latest commit History 37 Commits
aarch64		aarch64
arm64		arm64
cephes		cephes
doc		doc
libmq/libmq.xcodeproj/project.xcworkspace		libmq/libmq.xcodeproj/project.xcworkspace
statslib		statslib
x86_64/mac		x86_64/mac
.gitignore		.gitignore
COPYRIGHT		COPYRIGHT
Makefile		Makefile
README		README
cmplx.c		cmplx.c
const.c		const.c
drand.c		drand.c
f128.c		f128.c
floor.c		floor.c
gamma.c		gamma.c
igam.c		igam.c
igami.c		igami.c
incbet.c		incbet.c
incbi.c		incbi.c
log.c		log.c
mconf.h		mconf.h
mpfr_time.c		mpfr_time.c
mtherr.c		mtherr.c
ndtri.c		ndtri.c
polevl.c		polevl.c
pow.c		pow.c
powi.c		powi.c
protos.h		protos.h
qacosh.c		qacosh.c
qagm.c		qagm.c
qairy.c		qairy.c
qasin.c		qasin.c
qasinh.c		qasinh.c
qatanh.c		qatanh.c
qatn.c		qatn.c
qbeta.c		qbeta.c
qcalc.c		qcalc.c
qcalc.h		qcalc.h
qcatalan.c		qcatalan.c
qcbrt.c		qcbrt.c
qccalc.c		qccalc.c
qcerf.c		qcerf.c
qcgamma.c		qcgamma.c
qchyp1f1.c		qchyp1f1.c
qcmplx.c		qcmplx.c
qcomplexLog.c		qcomplexLog.c
qconst.c		qconst.c
qcos.c		qcos.c
qcosh.c		qcosh.c
qcpolylog.c		qcpolylog.c
qdawsn.c		qdawsn.c
qei.c		qei.c
qellie.c		qellie.c
qellik.c		qellik.c
qellpe.c		qellpe.c
qellpj.c		qellpj.c
qellpk.c		qellpk.c
qerf.c		qerf.c
qerfc.c		qerfc.c
qeuclid.c		qeuclid.c
qexp.c		qexp.c
qexp10.c		qexp10.c
qexp2.c		qexp2.c
qexpm1.c		qexpm1.c
qexpn.c		qexpn.c
qfac.c		qfac.c
qfloor.c		qfloor.c
qfltbi.c		qfltbi.c
qflti.c		qflti.c
qfresf.c		qfresf.c
qfrexp.c		qfrexp.c
qgamma.c		qgamma.c
qgammacoef.c		qgammacoef.c
qgammacof.h		qgammacof.h
qhead.h		qhead.h
qhy2f1.c		qhy2f1.c
qhyperg.c		qhyperg.c
qhypot.c		qhypot.c
qigam.c		qigam.c
qigami.c		qigami.c
qin.c		qin.c
qincb.c		qincb.c
qincbi.c		qincbi.c
qine.c		qine.c
qinv_fact.c		qinv_fact.c
qinv_fact.h		qinv_fact.h
qjn.c		qjn.c
qjypn.c		qjypn.c
qjyqn.c		qjyqn.c
qk0.c		qk0.c
qkn.c		qkn.c
qkne.c		qkne.c
qkolmogorov.c		qkolmogorov.c
qlog.c		qlog.c
qlog1.c		qlog1.c
qlog10.c		qlog10.c
qmtst.aarch64		qmtst.aarch64
qmtst.arm64		qmtst.arm64

Repository files navigation

A: DIRECTORY LAYOUT
   ----------------
1: The four operations are written in arm64 assembler (directory aarch64), or
   in x86 assembly (directory x86_64).
   The subdirectories here are:
   aarch64: asm code for arm64 / Linux
   arm64:   asm code for Macintosh M1 CPU
   cephes:  The original sources I started from.
   x86_64:  asm code for PCs
   doc:     TEX documentation for everything
   
2: The "bsr64" function is essential, and not optional as the assembly 
   functions. Sources for this function are in x86_64 or aarch64.
3: The statistics library is in the "statslib" directory.
4: The Makefile comes configured for either ARM64 or X86 linux. It is untested
   under windows. It defaults to using the asm accelerators
B: OTHER
   -----
5: TO ELIMINATE ASM ACCELERATORS (say, in a new machine):
   1: Change the variable "ASM" in the makefile to the empty string.
   2: #define NOASM in qfltbi.c around line 4.
   3: Recompile. You will still need the bsr64 function. Write that in C.
C: OUTPUT
   ------
6: The programs that are built are:
   libmq.a (qfloat library)
   qcalc   (interactive calculator)
   qmtst   (Test of math functions)
   qtime   (times the performance of the four operations)
   qparanoi Tests the floating point. Note that there is a flaw in division.
           It should be the only flaw.
7: Results of the qmtst run
Consistency test of math functions with asm accelerators: Tue Mar  6 13:57:29 2018
Max and rms errors for 10000 random arguments.
A = absolute error criterion (but relative if >1):
Otherwise, estimate is of relative error
x =   sqrt( square(x) ):  max = 1.945E-0135   rms = 3.567E-0136
x =   atan(    tan(x) ):  max = 5.451E-0135   rms = 1.193E-0135
x =   cbrt(   cube(x) ):  max = 1.906E-0135   rms = 4.315E-0137
x =    sin(   asin(x) ):  max = 1.091E-0134   rms = 2.953E-0135
x =    log(    exp(x) ):  max = 3.113E-0134   rms = 1.068E-0135
x =   log2(   exp2(x) ):  max = 1.977E-0134 A rms = 1.145E-0135 A
x =  log10(  exp10(x) ):  max = 8.342E-0134   rms = 1.766E-0135
x =  acosh(   cosh(x) ):  max = 2.746E-0135   rms = 7.772E-0136
x = pow( pow(x,a),1/a ):  max = 2.678E-0133   rms = 6.301E-0135
x =   tanh(  atanh(x) ):  max = 2.513E-0134   rms = 2.364E-0135
x =  asinh(   sinh(x) ):  max = 2.745E-0135   rms = 7.853E-0136
x =    cos(   acos(x) ):  max = 1.101E-0134 A rms = 1.777E-0135 A
Absolute error and only 2000 trials:
x =  ndtri(   ndtr(x) ):  max = 8.038E-0114   rms = 2.819E-0115
Legendre  ellpk,  ellpe:  max = 2.47E-0132   rms = 9.623E-0134
lgam(x) = log(gamma(x)):  max = 6.191E-0135 A rms = 1.035E-0135 A


D: Modifications to the software as distributed
1: Added functions:
   Catalan(n) --> nth catalan number
   remquo (see C standard)
2: All constants have been verified and rounded to 448 bits using the PARI 
   calculator or Mathematica
   sqrt will use floating point to start the newton iteration. (faster)
   Many functions rewritten (itoq, qtoe, qtanh etc)

For any questions write to:

jacob@jacob.remcomp.fr

ENJOY!