4.4BSD/usr/share/man/cat3/hypot.0

HYPOT(3)                    BSD Programmer's Manual                   HYPOT(3)

NNAAMMEE
     hhyyppoott, ccaabbss - euclidean distance and complex absolute value functions

SSYYNNOOPPSSIISS
     ##iinncclluuddee <<mmaatthh..hh>>

     _d_o_u_b_l_e
     hhyyppoott(_d_o_u_b_l_e _x, _d_o_u_b_l_e _y);

     ssttrruucctt {{ddoouubbllee xx,, yy;;}} zz;;

     _d_o_u_b_l_e
     ccaabbss(_z);

DDEESSCCRRIIPPTTIIOONN
     The hhyyppoott() and ccaabbss() functions computes the sqrt(x*x+y*y) in such a way
     that underflow will not happen, and overflow occurs only if the final re-
     sult deserves it.

     hhyyppoott(_i_n_f_i_n_i_t_y, _v) = hhyyppoott(_v, _i_n_f_i_n_i_t_y) = +infinity for all _v, including
     _N_a_N.

EERRRROORR ((dduuee ttoo RRoouunnddooffff,, eettcc..))
     Below 0.97 _u_l_p_s. Consequently hhyyppoott(_5_._0, _1_2_._0) = 13.0 exactly; in gener-
     al, hypot and cabs return an integer whenever an integer might be expect-
     ed.

     The same cannot be said for the shorter and faster version of hypot and
     cabs that is provided in the comments in cabs.c; its error can exceed 1.2
     _u_l_p_s.

NNOOTTEESS
     As might be expected, hhyyppoott(_v, _N_a_N) and hhyyppoott(_N_a_N, _v) are _N_a_N for all
     _f_i_n_i_t_e _v; with "reserved operand" in place of "_N_a_N", the same is true on
     a VAX. But programmers on machines other than a VAX (if has no infinity)
     might be surprised at first to discover that hhyyppoott(_+_-_i_n_f_i_n_i_t_y, _N_a_N) =
     +infinity.  This is intentional; it happens because hhyyppoott(_i_n_f_i_n_i_t_y, _v) =
     +infinity for _a_l_l _v, finite or infinite.  Hence hhyyppoott(_i_n_f_i_n_i_t_y, _v) is in-
     dependent of _v. Unlike the reserved operand fault on a VAX, the IEEE _N_a_N
     is designed to disappear when it turns out to be irrelevant, as it does
     in hhyyppoott(_i_n_f_i_n_i_t_y, _N_a_N).

SSEEEE AALLSSOO
     math(3),  sqrt(3)

HHIISSTTOORRYY
     Both a hhyyppoott() function and a ccaabbss() function appeared in Version 7 AT&T
     UNIX.

4th Berkeley Distribution        June 4, 1993                                1