Math Functions Specifications and Recommendations
"Explore the detailed specifications and recommendations of math functions in IEC 60559 and C11 standards, covering exponential, logarithmic, trigonometric, and special cases. Discover the diverse range of mathematical functions and their implementations."
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TS 18661 Part 4 Supplementary Functions WG 14 N1797 2014-04-07
Math functions IEC 60559:2011 specifies and recommends these math functions: exp exp2 exp10 expm1 exp2m1 exp10m1 log log2 log10 logp1=log1p log2p1 log10p1 [ 1, + ] hypot(x, y) rSqrt = 1/ x compound(x, n) = (1 + x)n [ , + ] [ , + ] [0, + ] [ , + ] [ , + ] [0, + ] [ 1, + ] Z
Math functions (2) rootn(x, n) = x1/n pown(x, n) = xn pow(x, y) = xy powr(x, y) = xy sin cos tan sinPi(x) = sin( x) and cosPi(x) = cos( x) tanPi(x) = tan( x) [ , + ] Z [ , + ] Z [ , + ] [ , + ] [0, + ] [ , + ] ( , + ) ( , + ) [ , + ]
Math functions (3) atan2Pi(y, x) asin acos atan atan2(y, x) sinh cosh tanh asinh acosh atanh [ , + ] [ , + ] [ 1, +1] [ , + ] [ , + ] [ , + ] [ , + ] [ , + ] [+1, + ] [ 1, +1]
Math function binding Some IEC 60559 math functions already in C11 TS adds the rest, in Library 7.12 Mathematics and Annex F Also, for completeness tanpi [ , + ] asinpi acospi [ 1, +1] TS does not require IEC 60559-specified correct rounding Names with cr prefixes reserved for correctly rounded verisons, e.g., crsin for correctly rounded sin function
Math function binding (2) Added tgmath macros for new functions Reserved names for complex versions of new functions, for binary floating types
Math function names Added logp1 equivalent to log1p For consistency with log2p1 and log10p1 And to avoid the confusing log21p and log101p Used compoundn for compound(x, n) Because of existing compound(x, y) extensions Fits with scalbn(x, n) and others Otherwise used IEC 60559 names, without camelCase (IEC 60559 does not require using its names)
Math function special cases IEC 60559 and C11 Annex F treat special cases the same New functions follow same principles TS follows C11 style for specifying math errors in 7.12
Sum reductions IEC 60559:2011 specifies and recommends sum reduction operations on vectors p and q of length n: sum(p, n) dot(p, q, n) sumSquare(p, n) sumAbs(p, n) i=1,npi i=1,npi qi i=1,npi2 i=1,n|pi|
Scaled products IEC 60559 specifies and recommends scaled product reduction operations: compute without over/underflow pr = scaled product and sf = scale factor such that result product = pr radixsf scaledProd(p, n) scaledProdSum(p, q, n) scaledProdDiff(p, q, n) i=1,npi i=1,n(pi+ qi) i=1,n(pi qi)
Reduction function names IEC 60559 sum dot sumSquare sumAbs scaledProd scaledProdSum scaledProdDiff TS 16881-4 reduc_sum reduc_sumprod reduc_sumsq reduc_sumabs scaled_prod scaled_prodsum scaled_proddiff
Reduction function interfaces double reduc_sum ( size_t n, const double p[static n] ); double scaled_prod ( size_t n, const double p[static n], intmax_t * restrict sfptr ); Arrays indexed 0 to n - 1
IEC 60559 reductions Result values not fully specified like other IEC 60559 operations Implementation can (re)order operations and use extra range and precision, for speed and accuracy Must avoid over/underflow, except if final result of sum reduction deserves over/underflow
Reduction special cases Follows general principles for special cases, e.g., reduc_sum(n, p) returns a NaN if any member of array p is a NaN. reduc_sum(n, p) returns a NaN and raises the invalid floating-point exception if any two members of array p are infinities with different signs. Otherwise, reduc_sum(n, p) returns if the members of p include one or more infinities (with the same sign).
Reduction special cases (2) For scaled product: scaled_prod(n, p, sfptr) returns a NaN if any member of array p is a NaN. scaled_prod(n, p, sfptr) returns a NaN and raises the invalid floating-point exception if any two members of array p are a zero and an infinity. Otherwise, scaled_prod(n, p, sfptr) returns an infinity if any member of array p is an infinity. Otherwise, scaled_prod(n, p, sfptr) returns a zero if any member of array p is a zero. Otherwise, scaled_prod(n, p, sfptr) returns a NaN and raises the invalid floating-point exception if the scale factor is outside the range of the intmax_t type.
