Lines Matching +full:- +full:q
3 * Natural logarithm for 128-bit long double precision.
24 * On the interval [-1/128, +1/128] the logarithm of 1+x is approximated by
25 * log(1+x) = x - 0.5 x^2 + x^3 P(x) .
33 * IEEE 0.875, 1.125 100000 1.2e-34 4.1e-35
34 * IEEE 0.125, 8 100000 1.2e-34 4.1e-35
39 * This program uses integer operations on bit fields of floating-point
45 /* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov>
61 #include "quadmath-imp.h"
63 /* log(1+x) = x - .5 x^2 + x^3 l(x)
64 -.0078125 <= x <= +.0078125
65 peak relative error 1.2e-37 */
67 l3 = 3.333333333333333333333333333333336096926E-1Q,
68 l4 = -2.499999999999999999999999999486853077002E-1Q,
69 l5 = 1.999999999999999999999999998515277861905E-1Q,
70 l6 = -1.666666666666666666666798448356171665678E-1Q,
71 l7 = 1.428571428571428571428808945895490721564E-1Q,
72 l8 = -1.249999999999999987884655626377588149000E-1Q,
73 l9 = 1.111111111111111093947834982832456459186E-1Q,
74 l10 = -1.000000000000532974938900317952530453248E-1Q,
75 l11 = 9.090909090915566247008015301349979892689E-2Q,
76 l12 = -8.333333211818065121250921925397567745734E-2Q,
77 l13 = 7.692307559897661630807048686258659316091E-2Q,
78 l14 = -7.144242754190814657241902218399056829264E-2Q,
79 l15 = 6.668057591071739754844678883223432347481E-2Q;
81 /* Lookup table of ln(t) - (t-1)
85 -5.5345593589352099112142921677820359632418E-2Q,
86 -5.2108257402767124761784665198737642086148E-2Q,
87 -4.8991686870576856279407775480686721935120E-2Q,
88 -4.5993270766361228596215288742353061431071E-2Q,
89 -4.3110481649613269682442058976885699556950E-2Q,
90 -4.0340872319076331310838085093194799765520E-2Q,
91 -3.7682072451780927439219005993827431503510E-2Q,
92 -3.5131785416234343803903228503274262719586E-2Q,
93 -3.2687785249045246292687241862699949178831E-2Q,
94 -3.0347913785027239068190798397055267411813E-2Q,
95 -2.8110077931525797884641940838507561326298E-2Q,
96 -2.5972247078357715036426583294246819637618E-2Q,
97 -2.3932450635346084858612873953407168217307E-2Q,
98 -2.1988775689981395152022535153795155900240E-2Q,
99 -2.0139364778244501615441044267387667496733E-2Q,
100 -1.8382413762093794819267536615342902718324E-2Q,
101 -1.6716169807550022358923589720001638093023E-2Q,
102 -1.5138929457710992616226033183958974965355E-2Q,
103 -1.3649036795397472900424896523305726435029E-2Q,
104 -1.2244881690473465543308397998034325468152E-2Q,
105 -1.0924898127200937840689817557742469105693E-2Q,
106 -9.6875626072830301572839422532631079809328E-3Q,
107 -8.5313926245226231463436209313499745894157E-3Q,
108 -7.4549452072765973384933565912143044991706E-3Q,
109 -6.4568155251217050991200599386801665681310E-3Q,
110 -5.5356355563671005131126851708522185605193E-3Q,
111 -4.6900728132525199028885749289712348829878E-3Q,
112 -3.9188291218610470766469347968659624282519E-3Q,
113 -3.2206394539524058873423550293617843896540E-3Q,
114 -2.5942708080877805657374888909297113032132E-3Q,
115 -2.0385211375711716729239156839929281289086E-3Q,
116 -1.5522183228760777967376942769773768850872E-3Q,
117 -1.1342191863606077520036253234446621373191E-3Q,
118 -7.8340854719967065861624024730268350459991E-4Q,
119 -4.9869831458030115699628274852562992756174E-4Q,
120 -2.7902661731604211834685052867305795169688E-4Q,
121 -1.2335696813916860754951146082826952093496E-4Q,
122 -3.0677461025892873184042490943581654591817E-5Q,
125 -3.0359557945051052537099938863236321874198E-5Q,
126 -1.2081346403474584914595395755316412213151E-4Q,
127 -2.7044071846562177120083903771008342059094E-4Q,
128 -4.7834133324631162897179240322783590830326E-4Q,
129 -7.4363569786340080624467487620270965403695E-4Q,
130 -1.0654639687057968333207323853366578860679E-3Q,
131 -1.4429854811877171341298062134712230604279E-3Q,
132 -1.8753781835651574193938679595797367137975E-3Q,
133 -2.3618380914922506054347222273705859653658E-3Q,
134 -2.9015787624124743013946600163375853631299E-3Q,
135 -3.4938307889254087318399313316921940859043E-3Q,
136 -4.1378413103128673800485306215154712148146E-3Q,
137 -4.8328735414488877044289435125365629849599E-3Q,
138 -5.5782063183564351739381962360253116934243E-3Q,
139 -6.3731336597098858051938306767880719015261E-3Q,
140 -7.2169643436165454612058905294782949315193E-3Q,
141 -8.1090214990427641365934846191367315083867E-3Q,
142 -9.0486422112807274112838713105168375482480E-3Q,
143 -1.0035177140880864314674126398350812606841E-2Q,
144 -1.1067990155502102718064936259435676477423E-2Q,
145 -1.2146457974158024928196575103115488672416E-2Q,
146 -1.3269969823361415906628825374158424754308E-2Q,
147 -1.4437927104692837124388550722759686270765E-2Q,
148 -1.5649743073340777659901053944852735064621E-2Q,
149 -1.6904842527181702880599758489058031645317E-2Q,
150 -1.8202661505988007336096407340750378994209E-2Q,
151 -1.9542647000370545390701192438691126552961E-2Q,
152 -2.0924256670080119637427928803038530924742E-2Q,
153 -2.2346958571309108496179613803760727786257E-2Q,
154 -2.3810230892650362330447187267648486279460E-2Q,
155 -2.5313561699385640380910474255652501521033E-2Q,
156 -2.6856448685790244233704909690165496625399E-2Q,
157 -2.8438398935154170008519274953860128449036E-2Q,
158 -3.0058928687233090922411781058956589863039E-2Q,
159 -3.1717563112854831855692484086486099896614E-2Q,
160 -3.3413836095418743219397234253475252001090E-2Q,
161 -3.5147290019036555862676702093393332533702E-2Q,
162 -3.6917475563073933027920505457688955423688E-2Q,
163 -3.8723951502862058660874073462456610731178E-2Q,
164 -4.0566284516358241168330505467000838017425E-2Q,
165 -4.2444048996543693813649967076598766917965E-2Q,
166 -4.4356826869355401653098777649745233339196E-2Q,
167 -4.6304207416957323121106944474331029996141E-2Q,
168 -4.8285787106164123613318093945035804818364E-2Q,
169 -5.0301169421838218987124461766244507342648E-2Q,
170 -5.2349964705088137924875459464622098310997E-2Q,
171 -5.4431789996103111613753440311680967840214E-2Q,
172 -5.6546268881465384189752786409400404404794E-2Q,
173 -5.8693031345788023909329239565012647817664E-2Q,
174 -6.0871713627532018185577188079210189048340E-2Q,
175 -6.3081958078862169742820420185833800925568E-2Q,
176 -6.5323413029406789694910800219643791556918E-2Q,
177 -6.7595732653791419081537811574227049288168E-2Q
182 ln2a = 6.93145751953125e-1Q,
183 ln2b = 1.4286068203094172321214581765680755001344E-6Q;
198 /* log(0) = -infinity. */ in logq()
201 return -0.5Q / ZERO; in logq()
206 return (x - x) / ZERO; in logq()
221 k = (m - 0xff00) >> 9; in logq()
229 e -= 1; in logq()
234 k = (m - 0xfe00) >> 10; in logq()
241 if ((x <= 1.0078125Q) && (x >= 0.9921875Q)) in logq()
245 z = x - 1; in logq()
254 Express log(u/t) = log(1+z), where z = u/t - 1 = (u-t)/t. in logq()
256 z = (u.value - t.value) / t.value; in logq()
273 y -= 0.5 * w; in logq()
276 y += logtbl[k-26]; /* log(t) - (t-1) */ in logq()
277 y += (t.value - 1); in logq()