a ›¬d|>¡}t dd¡}||}ttt|ƒt|ƒ|tƒƒ|kslJ‚ttt|ƒt|ƒ|tƒƒ|ksJ‚qqdS)zR Test that inexact integer powers are rounded in the right direction. iÒ)ré5éÈé2ééédN) ÚrandomÚseedÚrangeÚrandintZto_intZmpf_powÚfrom_intÚ round_downÚround_up)ÚprecÚiÚaÚbÚabr r r Útest_pow_integer_directions   "r cCsîdd„}dD]Ô\}}|t_tdƒtdƒ| d}tdƒtdƒ| d}| }| }|t_t}||d|ƒdkszJ‚||d|ƒdksŽJ‚||d|ƒdks¢J‚||d|ƒdks¶J‚||d|ƒdksÊJ‚||d|ƒdksÞJ‚||d|ƒdksòJ‚||d|ƒdksJ‚||d |ƒdksJ‚||d |ƒdks4J‚||d |ƒdksJJ‚||d |ƒdks`J‚||d |ƒdksvJ‚||d |ƒdksŒJ‚||d |ƒdks¢J‚||d |ƒdks¸J‚t}||d|ƒdksÒJ‚||d|ƒdksèJ‚||d|ƒdksþJ‚||d|ƒdksJ‚||d|ƒdks*J‚||d|ƒdks@J‚||d|ƒdksVJ‚||d|ƒdkslJ‚||d |ƒdks‚J‚||d |ƒdks˜J‚||d |ƒdks®J‚||d |ƒdksÄJ‚||d |ƒdksÚJ‚||d |ƒdksðJ‚||d |ƒdksJ‚||d |ƒdksJ‚t}||d|ƒdks6J‚||d|ƒdksLJ‚||d|ƒdksbJ‚||d|ƒdksxJ‚||d|ƒdksŽJ‚||d|ƒdks¤J‚||d|ƒdksºJ‚||d|ƒdksÐJ‚||d |ƒdksæJ‚||d |ƒdksüJ‚||d |ƒdksJ‚||d |ƒdks(J‚||d |ƒdks>J‚||d |ƒdksTJ‚||d |ƒdksjJ‚||d |ƒdks€J‚t}||d|ƒdksšJ‚||d|ƒdks°J‚||d|ƒdksÆJ‚||d|ƒdksÜJ‚||d|ƒdksòJ‚||d|ƒdksJ‚||d|ƒdksJ‚||d|ƒdks4J‚||d |ƒdksJJ‚||d |ƒdks`J‚||d |ƒdksvJ‚||d |ƒdksŒJ‚||d |ƒdks¢J‚||d |ƒdks¸J‚||d |ƒdksÎJ‚||d |ƒdks J‚q d t_d S) aµ Stress test directed rounding for powers with integer exponents. Basically, we look at the following cases: >>> 1.0001 ** -5 # doctest: +SKIP 0.99950014996500702 >>> 0.9999 ** -5 # doctest: +SKIP 1.000500150035007 >>> (-1.0001) ** -5 # doctest: +SKIP -0.99950014996500702 >>> (-0.9999) ** -5 # doctest: +SKIP -1.000500150035007 >>> 1.0001 ** -6 # doctest: +SKIP 0.99940020994401269 >>> 0.9999 ** -6 # doctest: +SKIP 1.0006002100560125 >>> (-1.0001) ** -6 # doctest: +SKIP 0.99940020994401269 >>> (-0.9999) ** -6 # doctest: +SKIP 1.0006002100560125 etc. We run the tests with values a very small epsilon away from 1: small enough that the result is indistinguishable from 1 when rounded to nearest at the output precision. We check that the result is not erroneously rounded to 1 in cases where the rounding should be done strictly away from 1. cSstt|j|tj|ƒƒS)N)Zmake_mpfZ mpf_pow_intZ_mpf_rr)ÚxÚnÚrr r r ÚpowrCsz'test_pow_epsilon_rounding..powr))ré)iˆi¸ rrééÿÿÿÿééûÿÿÿiúÿÿÿrN)rrr rrZ round_ceilingZ round_floorr )r$ZinprecZoutprecZpos10001Zpos09999Zneg10001Zneg09999r#r r r Útest_pow_epsilon_rounding#sš r*)ZmpmathZ mpmath.libmprr r r*r r r r Ús