Lines Matching refs:is
5 | setoxd does the same except the input value is a denormalized
20 | The returned result is within 0.85 ulps in 64 significant bit, i.e.
21 | within 0.5001 ulp to 53 bits if the result is subsequently rounded
22 | to double precision. The result is provably monotonic in double
28 | first one is measured when the function is invoked the first time
30 | second one is measured when the function is reinvoked at the same
34 | argument X whose magnitude is less than 16380 log2, which
35 | is the usual situation. For the less common arguments,
66 | compact representation of |X| is used. This format is a
73 | is also in the compact form. Thus taking the branch
74 | to Step 2 guarantees |X| < 16380 log(2). There is no harm
75 | to have a small number of cases where |X| is less than,
76 | but close to, 16380 log(2) and the branch to Step 9 is
86 | Notes: The calculation in 2.2 is really performed by
96 | Another effect of using a single-precision "constant" is
97 | that the calculated value Z is
108 | b) N*L1 is exact because N is no longer than 22 bits and
109 | L1 is no longer than 24 bits.
110 | c) The calculation X+N*L1 is also exact due to cancellation.
111 | Thus, R is practically X+N(L1+L2) to full 64 bits.
112 | d) It is important to estimate how large can |R| be after
130 | made as "short" as possible: A1 (which is 1/2), A4 and A5
134 | Note that 0.0062 is slightly bigger than 0.57 log2/64.
135 | c) To fully utilize the pipeline, p is separated into
144 | Notes: 2^(J/64) is stored as T and t where T+t approximates
145 | 2^(J/64) to roughly 85 bits; T is in extended precision
146 | and t is in single precision. Note also that T is rounded
148 | reason for such a special form is that T-1, T-2, and T-8
164 | When that is the case, AdjScale = 2^(M1) where M1 is
166 | Possible exception in 6.4 is overflow or underflow.
167 | The inexact exception is not generated in 6.4. Although
170 | flag is worth in practical uses.
177 | raised by 7.3. That is the only exception raised by 7.3.
180 | the FMOVEM may not seem relevant since X is normalized,
227 | However, it is conceivable |X| can be small very often
228 | because EXPM1 is intended to evaluate exp(X)-1 accurately
229 | when |X| is small. For further details on the comparisons,
250 | made as "short" as possible: A1 (which is 1/2), A5 and A6
255 | c) To fully utilize the pipeline, p is separated into
264 | Notes: 2^(J/64) is stored as T and t where T+t approximates
265 | 2^(J/64) to roughly 85 bits; T is in extended precision
266 | and t is in single precision. Note also that T is rounded
268 | reason for such a special form is that T-1, T-2, and T-8
270 | in Step 6 below. The total relative error in p is no
295 | Notes: The idea is to return "X - tiny" under the user
304 | made as "short" as possible: B1 (which is 1/2), B9 to B12
306 | B2 is double extended.
310 | Note that 0.251 is slightly bigger than 1/4.
311 | c) To fully preserve accuracy, the polynomial is computed
314 | d) To fully utilize the pipeline, Q is separated into
450 |--entry point for EXP(X), X is denormalized
462 |--entry point for EXP(X), here X is finite, non-zero, and not NaN's
480 |--This is the normal branch: 2^(-65) <= |X| < 16380 log2.
492 andil #0x3F,%d0 | ...D0 is J = N mod 64
496 asrl #6,%d0 | ...D0 is M
502 |--fp1,fp2 saved on the stack. fp0 is N, fp1 is X,
503 |--a0 points to 2^(J/64), D0 is biased expo. of 2^(M)
508 faddx %fp2,%fp0 | ...fp0 is R, reduced arg.
531 movew %d0,SCALE(%a6) | ...SCALE is 2^(M) in extended
545 fmovex (%a1)+,%fp1 | ...fp1 is lead. pt. of 2^(J/64)
546 faddx %fp2,%fp0 | ...fp0 is EXP(R) - 1
572 fmovemx (%a0),%fp0-%fp0 | ...in case X is denormalized
592 andil #0x3F,%d0 | ...D0 is J = N mod 64
596 asrl #6,%d0 | ...D0 is K
598 asrl #1,%d0 | ...D0 is M1
599 subl %d0,L_SCR1(%a6) | ...a1 is M
605 movel L_SCR1(%a6),%d0 | ...D0 is M
620 |--entry point for EXPM1(X), here X is denormalized
627 |--entry point for EXPM1(X), here X is finite, non-zero, non-NaN
647 |--This is the case: 1/4 <= |X| <= 70 log2.
659 andil #0x3F,%d0 | ...D0 is J = N mod 64
663 asrl #6,%d0 | ...D0 is M
668 |--fp1,fp2 saved on the stack. fp0 is N, fp1 is X,
674 faddx %fp2,%fp0 | ...fp0 is R, reduced arg.
676 addiw #0x3FFF,%d0 | ...D0 is biased expo. of 2^M
696 movew %d0,SC(%a6) | ...SC is 2^(M) in extended
702 movel L_SCR1(%a6),%d0 | ...D0 is M
703 negw %d0 | ...D0 is -M
711 movew %d0,ONEBYSC(%a6) | ...OnebySc is -2^(-M)
737 fmoves 12(%a1),%fp1 | ...fp1 is t
738 faddx ONEBYSC(%a6),%fp1 | ...fp1 is t+OnebySc
754 fmovex (%a1)+,%fp1 | ...fp1 is T
755 fadds (%a1),%fp0 | ...fp0 is p+t
756 faddx ONEBYSC(%a6),%fp1 | ...fp1 is T+OnebySc
776 movel #0x80010000,SC(%a6) | ...SC is -2^(-16382)
800 fmovex (%a0),%fp0 | ...fp0 is X
801 fmulx %fp0,%fp0 | ...fp0 is S := X*X
803 fmoves #0x2F30CAA8,%fp1 | ...fp1 is B12
804 fmulx %fp0,%fp1 | ...fp1 is S*B12
805 fmoves #0x310F8290,%fp2 | ...fp2 is B11
806 fadds #0x32D73220,%fp1 | ...fp1 is B10+S*B12
808 fmulx %fp0,%fp2 | ...fp2 is S*B11
809 fmulx %fp0,%fp1 | ...fp1 is S*(B10 + ...
811 fadds #0x3493F281,%fp2 | ...fp2 is B9+S*...
812 faddd EM1B8,%fp1 | ...fp1 is B8+S*...
814 fmulx %fp0,%fp2 | ...fp2 is S*(B9+...
815 fmulx %fp0,%fp1 | ...fp1 is S*(B8+...
817 faddd EM1B7,%fp2 | ...fp2 is B7+S*...
818 faddd EM1B6,%fp1 | ...fp1 is B6+S*...
820 fmulx %fp0,%fp2 | ...fp2 is S*(B7+...
821 fmulx %fp0,%fp1 | ...fp1 is S*(B6+...
823 faddd EM1B5,%fp2 | ...fp2 is B5+S*...
824 faddd EM1B4,%fp1 | ...fp1 is B4+S*...
826 fmulx %fp0,%fp2 | ...fp2 is S*(B5+...
827 fmulx %fp0,%fp1 | ...fp1 is S*(B4+...
829 faddd EM1B3,%fp2 | ...fp2 is B3+S*...
830 faddx EM1B2,%fp1 | ...fp1 is B2+S*...
832 fmulx %fp0,%fp2 | ...fp2 is S*(B3+...
833 fmulx %fp0,%fp1 | ...fp1 is S*(B2+...
835 fmulx %fp0,%fp2 | ...fp2 is S*S*(B3+...)
836 fmulx (%a0),%fp1 | ...fp1 is X*S*(B2...
838 fmuls #0x3F000000,%fp0 | ...fp0 is S*B1
839 faddx %fp2,%fp1 | ...fp1 is Q
844 faddx %fp1,%fp0 | ...fp0 is S*B1+Q
858 fmoves #0xBF800000,%fp0 | ...fp0 is -1