# This is a shell archive.  Remove anything before this line,
# then unpack it by saving it in a file and typing "sh file".
#
# Wrapped by (C) Jim Thomas <jimthomas@hpcll218> on Tue Nov  5 16:13:26 1996
#
# This archive contains:
#	math_complex_enhancements.ps	
#

LANG=""; export LANG
PATH=/bin:/usr/bin:$PATH; export PATH

echo x - math_complex_enhancements.ps
sed 's/^@//' >math_complex_enhancements.ps <<'@EOF'
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@.673 .067(3.  Enhancement:)J
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1.116 .112(  Provide a function for )J
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@.777 .078(fused multiply-add)J
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@.098 .01(:  )J
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@.661 .066( computes)J
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@.164(x\312*\312y\312+\312z)A
f0_12 sf
@.463 .046(  \(as if\) as one ternary operation.  IEC 559 implementations must deliver the)J
78 613 :M
-.022(result with just one IEC 559-style rounding.)A
78 637 :M
f1_12 sf
@.312(Rationale:)A
f0_12 sf
1.03 .103(  In many cases, clever use of fused multiply-add leads to much improved)J
48 637 :M
(5)S
54 637 :M
(0)S
78 649 :M
@.871 .087(code.  However, unexpected use of fused multiply-add by the compiler can undermine)J
78 661 :M
@.138 .014(carefully written code.  The )J
216 661 :M
f3_10 sf
@.044(FP_CONTRACT)A
f0_12 sf
@.139 .014( directive in the current floating-point spec can)J
78 673 :M
@.389 .039(be used to disallow use of fused multiply-add.  What's still needed is a way to guarantee)J
endp
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f0_12 sf
-.032(WG14/N619 X3J11/96-83)A
431 14 :M
-.095(10/15/96)A
42 722 :M
(4)S
404 722 :M
-.088(Enhancements)A
42 50 :M
1.551 .155(its use just in particular situations.  Many current machines provide hardware fused)J
42 62 :M
-.003(multiply-add instructions;  software implementation can be used for others.)A
42 86 :M
f1_12 sf
-.132(Edits:)A
73 86 :M
f0_12 sf
(  )S
f2_12 sf
-.002( Insert the following subclause in 7.x in the <math.h> section:)A
18 98 :M
f0_12 sf
(5)S
42 113 :M
f1_14 sf
-.002(7.x.y  Fused multiply-add)A
42 140 :M
f1_12 sf
-.025(7.x.y.1  The )A
f3_10 sf
-.031(fma)A
f1_12 sf
-.03( function)A
42 164 :M
-.097(Synopsis)A
12 164 :M
f0_12 sf
(1)S
18 164 :M
(0)S
78 188 :M
f3_10 sf
(#include <math.h>)S
78 199 :M
(double fma\(double x, double y, double z\);)S
42 222 :M
f1_12 sf
-.031(Description)A
12 222 :M
f0_12 sf
(1)S
18 222 :M
(5)S
60 246 :M
-.219(The )A
82 246 :M
f3_10 sf
-.052(fma)A
f0_12 sf
-.045( function computes )A
195 246 :M
f3_10 sf
-.025(x\312*\312y\312+\312z)A
f0_12 sf
-.02(, rounded as one ternary operation.)A
42 270 :M
f1_12 sf
-.053(Returns)A
12 282 :M
f0_12 sf
(2)S
18 282 :M
(0)S
60 294 :M
-.219(The )A
82 294 :M
f3_10 sf
-.035(fma)A
f0_12 sf
-.028( function returns the value of )A
242 294 :M
f3_10 sf
-.025(x\312*\312y\312+\312z)A
f0_12 sf
-.02(, rounded as one ternary operation.)A
42 321 :M
f2_12 sf
-.016(Insert the following subclause in X.9 of the IEC 559 annex:)A
42 351 :M
f1_14 sf
-.007(X.9.y  Fused multiply-add)A
12 351 :M
f0_12 sf
(2)S
18 351 :M
(5)S
42 378 :M
f1_12 sf
-.055(X.9.y.1  The )A
107 378 :M
f3_10 sf
-.062(fma)A
f1_12 sf
-.059( function)A
60 402 :M
f3_10 sf
@.415(fma\(x,y,z\))A
f0_12 sf
1.2 .12( computes )J
f3_10 sf
@.415(x\312*\312y\312+\312z)A
f0_12 sf
1.225 .123(, correctly rounded \(IEC 559 style\) once.  The)J
42 414 :M
@.087 .009(function treats infinities, NaNs, signed zeros, and subnormals in a manner consistent with)J
12 414 :M
(3)S
18 414 :M
(0)S
42 426 :M
-.005(the basic arithmetic operations covered by IEC 559.)A
45 438 :M
(    )S
42 450 :M
f2_12 sf
@.88 .088(Include fma in the list of <math.h> \(but not <complex.h>\) functions that have a type-)J
42 462 :M
-.049(generic macro.)A
12 474 :M
f0_12 sf
(3)S
18 474 :M
(5)S
42 498 :M
f1_12 sf
@.588 .059(4.  Enhancement:  )J
142 498 :M
f0_12 sf
@.513 .051(Change the corresponding real type for the imaginary unit from the)J
42 510 :M
-.01(narrowest floating type for expression evaluation to the )A
311 510 :M
f3_10 sf
-.069(float)A
f0_12 sf
-.061( type.)A
42 534 :M
f1_12 sf
@.287 .029(Rationale:  )J
f0_12 sf
@.322 .032(This change facilitates portable use of expressions involving )J
401 534 :M
f3_10 sf
@.086(I)A
f0_12 sf
@.294 .029( as arguments)J
12 534 :M
(4)S
18 534 :M
(0)S
42 546 :M
(to )S
f3_10 sf
-.02(printf)A
f0_12 sf
-.016(, without regard to the expression evaluation method.  For example,)A
78 570 :M
f3_10 sf
(double y;)S
78 581 :M
(...)S
78 592 :M
(printf\("%e", I*y\);)S
12 592 :M
f0_12 sf
(4)S
18 592 :M
(5)S
42 615 :M
2.178 .218(would be erroneous with the current spec if the implementation uses long double)J
42 627 :M
-.014(expression evaluation.)A
endp
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78 14 :M
f0_12 sf
-.075(Draft 10/15/96)A
382 14 :M
-.032(WG14/N619 X3J11/96-83)A
78 722 :M
-.088(Enhancements)A
504 722 :M
(5)S
78 50 :M
f1_12 sf
-.132(Edits:)A
109 50 :M
f0_12 sf
@.062 .006(  )J
f2_12 sf
@.431 .043(In 7.x in the complex arithmetic spec, replace)J
340 50 :M
f0_12 sf
@.258 .026( "... whose corresponding real type)J
78 64 :M
1.794 .179(is the narrowest real floating type used for expression evaluation)J
417 61 :M
f0_9 sf
(1)S
421 64 :M
f0_12 sf
@.56 .056(" )J
f2_12 sf
@.587(with)A
453 64 :M
f0_12 sf
1.816 .182( "... whose)J
78 76 :M
-.034(corresponding real type is )A
f3_10 sf
-.043(float)A
f0_12 sf
(")S
240 76 :M
f2_12 sf
-.013(, removing the footnote.)A
54 100 :M
f0_12 sf
(5)S
78 112 :M
f1_12 sf
@.294 .029(5.   Enhancement:)J
173 112 :M
f0_12 sf
@.194 .019(  Change )J
f3_10 sf
@.099(imaginary)A
f0_12 sf
@.243 .024( from a keyword to a macro and reserve it in the)J
78 124 :M
-.008(manner of other library macros.)A
78 148 :M
f1_12 sf
@.459(Rationale:)A
f0_12 sf
1.87 .187(  This allows implementing the complex arithmetic \(informative\) annex)J
78 160 :M
-.009(without breaking C conformance.)A
48 160 :M
(1)S
54 160 :M
(0)S
78 184 :M
f1_12 sf
-.132(Edits:)A
109 184 :M
f0_12 sf
(  )S
f2_12 sf
-.033(Remove section Y.2.)A
78 208 :M
-.013(At the beginning of \(old\) Y.3 add the paragraph:)A
48 220 :M
f0_12 sf
(1)S
54 220 :M
(5)S
96 232 :M
@.312 .031(Inclusion of the header )J
f3_10 sf
@.106(<complex.h>)A
f0_12 sf
@.344 .034( enables designations for imaginary types.  The)J
78 244 :M
-.011(header defines the macro)A
114 268 :M
f3_10 sf
(imaginary)S
48 279 :M
f0_12 sf
(2)S
54 279 :M
(0)S
78 291 :M
f2_12 sf
-.019(At the beginning of \(old\) Y.6 add:)A
96 315 :M
f0_12 sf
-.063(The header )A
153 315 :M
f3_10 sf
-.011(<complex.h>)A
f0_12 sf
-.009( defines the macro)A
114 339 :M
f3_10 sf
(imaginary)S
48 339 :M
f0_12 sf
(2)S
54 339 :M
(5)S
114 361 :M
f0_10 sf
@.978 .098([The implementation might define )J
262 361 :M
f3_9 sf
@.251(imaginary)A
f0_10 sf
@.694 .069( to be a keyword in the implementation's)J
114 372 :M
-.069(namespace.])A
48 395 :M
f0_12 sf
(3)S
54 395 :M
(0)S
78 407 :M
f1_12 sf
@.238 .024(6.  Enhancement:  )J
176 407 :M
f0_12 sf
@.069 .007(Replace the current )J
f3_10 sf
@.146 .015(scalb\(double, long\))J
388 407 :M
f0_12 sf
@.183 .018( function with the pair of)J
78 419 :M
@.338 .034(functions )J
f3_10 sf
@.586 .059(scalbn\(double, long\))J
249 419 :M
f0_12 sf
@.363 .036( and )J
f3_10 sf
1.581 .158(scalb\(double, double\))J
f0_12 sf
@.571 .057(, and provide the )J
492 419 :M
f3_10 sf
(int)S
78 431 :M
f0_12 sf
-.123(function )A
121 431 :M
f3_10 sf
-.024(ilogb)A
f0_12 sf
-.018( in addition to the current )A
276 431 :M
f3_10 sf
-.072(double)A
f0_12 sf
-.061( function )A
358 431 :M
f3_10 sf
(logb)S
f0_12 sf
(.)S
78 455 :M
f1_12 sf
2.157 .216(Rationale:  )J
143 455 :M
f3_10 sf
1.01 .101(scalb\(double, double\))J
273 455 :M
f0_12 sf
1.322 .132( and )J
f3_10 sf
@.85(ilogb)A
f0_12 sf
2.208 .221( are in XPG4 V2 and are widely)J
48 455 :M
(3)S
54 455 :M
(5)S
78 467 :M
1.401 .14(implemented.  Some applications are better served by a floating second argument to)J
78 479 :M
@.972 .097(scalb[n], others by an integral one, and similarly regarding the return type for [i]logb.)J
78 491 :M
@.832 .083(The transition problems for early C9X implementors and users is mitigated by the fact)J
78 503 :M
1.641 .164(that calls to scalb\(double, long\) would still work when silently replaced by calls to)J
78 515 :M
-.046(scalb\(double, double\).)A
48 515 :M
(4)S
54 515 :M
(0)S
78 539 :M
f1_12 sf
-.132(Edits:)A
109 539 :M
f0_12 sf
@.476 .048(  )J
117 539 :M
f2_12 sf
@.256 .026(Change the name of the current scalb function to:  )J
f3_10 sf
@.095(scalbn)A
f2_12 sf
@.412 .041(. Throughout, replace)J
78 551 :M
-.01(references to the old )A
f9_10 sf
-.013(scalb)A
f2_12 sf
-.01( function with ones to )A
f9_10 sf
-.013(scalbn)A
f2_12 sf
(.)S
78 575 :M
-.002(Insert the following subclause in 7.x.6 of the <math.h> section:)A
48 575 :M
f0_12 sf
(4)S
54 575 :M
(5)S
78 662 :M
(                                                )S
78 659.48 -.48 .48 222.48 659 .48 78 659 @a
78 673 :M
f0_9 sf
(1)S
82 676 :M
f0_10 sf
-.089(  If )A
f3_9 sf
-.169(FLT_EVAL_METHOD)A
f0_10 sf
-.114( equals 0, 1, or 2, then )A
f3_9 sf
-.169(_Imaginary_I)A
f0_10 sf
-.127( has the corresponding real type )A
452 676 :M
f3_9 sf
-.456(float)A
f0_10 sf
(,)S
78 687 :M
f3_9 sf
-.256(double)A
f0_10 sf
-.158(, or)A
f3_9 sf
-.256( )A
f3_10 sf
-.284(l)A
f3_9 sf
-.256(ong\312double)A
f0_10 sf
-.189(, respectively.)A
endp
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42 14 :M
f0_12 sf
-.032(WG14/N619 X3J11/96-83)A
431 14 :M
-.095(10/15/96)A
42 722 :M
(6)S
404 722 :M
-.088(Enhancements)A
42 50 :M
f1_12 sf
-.023(7.x.6.y  The )A
f3_10 sf
-.028(scalb)A
f1_12 sf
-.027( function)A
42 74 :M
-.097(Synopsis)A
78 98 :M
f3_10 sf
(#include <math.h>)S
18 98 :M
f0_12 sf
(5)S
78 109 :M
f3_10 sf
(double scalb\(double x, double y\);)S
42 132 :M
f1_12 sf
-.031(Description)A
60 159 :M
f0_12 sf
2.572 .257(The )J
86 159 :M
f3_10 sf
@.482(scalb)A
f0_12 sf
1.588 .159( function computes )J
222 159 :M
f3_10 sf
@.691(x\312*\312FLT_RADIX)A
0 -3 rm
@.691(y)A
0 3 rm
f0_12 sf
1.788 .179(, for integral values )J
f3_10 sf
@.691(y)A
f0_12 sf
@.657 .066(.  If )J
453 159 :M
f3_10 sf
1.059(y)A
f0_12 sf
1.618 .162( is)J
12 159 :M
(1)S
18 159 :M
(0)S
42 171 :M
-.002(nonintegral, the result is implementation-defined.  A range error may occur.)A
42 195 :M
f1_12 sf
-.053(Returns)A
60 222 :M
f0_12 sf
-.219(The )A
82 222 :M
f3_10 sf
-.033(scalb)A
f0_12 sf
-.026( function returns the value of )A
254 222 :M
f3_10 sf
-.008(x\312*\312FLT_RADIX)A
0 -3 rm
(y)S
0 3 rm
f0_12 sf
-.006(, for integral values )A
f3_10 sf
(y)S
f0_12 sf
(.)S
12 222 :M
(1)S
18 222 :M
(5)S
42 258 :M
f2_12 sf
-.025(Insert the following subclause in X.9.3:)A
42 285 :M
f1_12 sf
-.055(X.9.y.1  The )A
107 285 :M
f3_10 sf
-.052(scalb)A
f1_12 sf
-.049( function)A
12 285 :M
f0_12 sf
(2)S
18 285 :M
(0)S
42 309 :M
(\245)S
60 309 :M
f3_10 sf
-.023(scalb\(-x, y\))A
f0_12 sf
-.018( and )A
f3_10 sf
-.023(-scalb\(x, y\))A
f0_12 sf
-.019( are equivalent.)A
42 321 :M
(\245)S
60 321 :M
f3_10 sf
-.024(scalb\(x, y\))A
f0_12 sf
-.02( returns a NaN if )A
210 321 :M
f3_10 sf
(y)S
f0_12 sf
-.04( is nonintegral.)A
42 333 :M
(\245)S
60 333 :M
f3_10 sf
(scalb\(x, )S
cF f5_10 sf
(\261)S
sf
(0\))S
f0_12 sf
( returns )S
f3_10 sf
(x)S
f0_12 sf
(.)S
42 345 :M
(\245)S
60 345 :M
f3_10 sf
-.009(scalb\(+0, +INFINITY\))A
f0_12 sf
-.007( returns a NaN and raises the invalid exception.)A
12 345 :M
(2)S
18 345 :M
(5)S
42 357 :M
(\245)S
60 357 :M
f3_10 sf
-.022(scalb\(+0, y\))A
f0_12 sf
-.017( returns +0, for integral )A
247 357 :M
f3_10 sf
-.245(y)A
f0_12 sf
-.261( < )A
266 357 :M
f3_10 sf
(+INFINITY)S
f0_12 sf
(.)S
42 369 :M
(\245)S
60 369 :M
f3_10 sf
-.02(scalb\(+INFINITY, y\))A
f0_12 sf
-.015( returns )A
f3_10 sf
-.02(+INFINITY)A
f0_12 sf
-.015(, for integral )A
330 369 :M
f3_10 sf
-.245(y)A
f0_12 sf
-.261( > )A
349 369 :M
f3_10 sf
(-INFINITY)S
f0_12 sf
(.)S
42 381 :M
(\245)S
60 381 :M
f3_10 sf
-.014(scalb\(x, -INFINITY\))A
f0_12 sf
-.011( returns +0, for finite positive-signed )A
354 381 :M
f3_10 sf
(x)S
f0_12 sf
(.)S
42 393 :M
(\245)S
60 393 :M
f3_10 sf
-.028(scalb\(x, +INFINITY\))A
f0_12 sf
-.02( returns )A
f3_10 sf
-.028(+INFINITY)A
f0_12 sf
-.021(, for positive )A
331 393 :M
f3_10 sf
(x)S
f0_12 sf
(.)S
42 405 :M
(\245)S
60 405 :M
f3_10 sf
-.006(scalb\(+INFINITY, -INFINITY\))A
f0_12 sf
-.006( returns a NaN.)A
12 405 :M
(3)S
18 405 :M
(0)S
42 417 :M
(\245)S
60 417 :M
f3_10 sf
-.024(scalb\(x, y\))A
f0_12 sf
-.019( returns a NaN, if )A
213 417 :M
f3_10 sf
-.27(x)A
f0_12 sf
-.24( or )A
235 417 :M
f3_10 sf
-.109(y)A
f0_12 sf
-.097( is a NaN.)A
42 441 :M
f2_12 sf
@.504 .05(Include scalb in the list of <math.h> \(but not <complex.h>\) functions that have a type-)J
42 453 :M
-.049(generic macro.)A
12 465 :M
f0_12 sf
(3)S
18 465 :M
(5)S
42 477 :M
f2_12 sf
-.025(Insert the following subclause in 7.x.6:)A
42 501 :M
f1_12 sf
-.023(7.x.6.y  The )A
f3_10 sf
-.028(ilogb)A
f1_12 sf
-.027( function)A
42 525 :M
-.097(Synopsis)A
12 525 :M
f0_12 sf
(4)S
18 525 :M
(0)S
78 549 :M
f3_10 sf
(#include <math.h>)S
78 560 :M
(int ilogb\(long double x\);)S
42 583 :M
f1_12 sf
-.031(Description)A
12 583 :M
f0_12 sf
(4)S
18 583 :M
(5)S
60 607 :M
@.208 .021(The )J
f3_10 sf
@.081(ilogb)A
f0_12 sf
@.232 .023( function extracts the exponent of )J
f3_10 sf
@.081(x)A
f0_12 sf
@.152 .015( as a signed )J
345 607 :M
f3_10 sf
@.081(int)A
f0_12 sf
@.198 .02( value.  It is equivalent)J
42 619 :M
@.467 .047(to )J
f3_10 sf
@.295(\(int\)logb\(x\))A
f0_12 sf
@.763 .076(, for finite nonzero )J
229 619 :M
f3_10 sf
@.411(x)A
f0_12 sf
1.159 .116(, computes the value )J
345 619 :M
f3_10 sf
@.438(INT_MIN)A
f0_12 sf
@.405 .041( if )J
f3_10 sf
@.438(x)A
f0_12 sf
1.008 .101( is zero, and)J
42 631 :M
-.035(computes the value )A
138 631 :M
f3_10 sf
-.024(INT_MAX)A
f0_12 sf
-.014( if )A
f3_10 sf
(x)S
f0_12 sf
-.019( is infinite or NaN.)A
12 643 :M
(5)S
18 643 :M
(0)S
78 655 :M
f0_10 sf
@.294([)A
f3_9 sf
@.477(ilogb)A
f0_10 sf
1.142 .114(\(NaN\) = )J
f3_9 sf
@.477(INT_MAX)A
f0_10 sf
1.554 .155( matches the fdlibm implementation, not XPG4 V2, which)J
78 666 :M
-.183(specifies )A
f3_9 sf
-.263(INT_MIN)A
f0_10 sf
-.19(;  )A
158 666 :M
f3_9 sf
-.081(INT_MAX)A
f0_10 sf
-.062( is more natural in some implementations.])A
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f0_12 sf
-.075(Draft 10/15/96)A
382 14 :M
-.032(WG14/N619 X3J11/96-83)A
78 722 :M
-.088(Enhancements)A
504 722 :M
(7)S
78 50 :M
f1_12 sf
-.053(Returns)A
96 74 :M
f0_12 sf
-.219(The )A
118 74 :M
f3_10 sf
-.029(ilogb)A
f0_12 sf
-.024( function returns the exponent of )A
308 74 :M
f3_10 sf
-.06(x)A
f0_12 sf
-.049( as a signed )A
373 74 :M
f3_10 sf
-.118(int)A
f0_12 sf
-.105( value.)A
54 98 :M
(5)S
78 110 :M
f1_12 sf
@.925 .092(7.  Enhancement:  )J
f0_12 sf
1.021 .102(Add )J
205 110 :M
f3_10 sf
@.289(x\312/\312x)A
f0_12 sf
@.4 .04( --> )J
f3_10 sf
@.289(1.0)A
f0_12 sf
@.772 .077( to the list of invalid optimizations, in the new)J
78 122 :M
-.019(example added as part of the floating-point spec.)A
78 146 :M
f1_12 sf
4.047 .405(Rationale:  )J
f0_12 sf
4.27 .427(Some compilers do this optimization, which is invalid \(for all)J
78 158 :M
-.024(implementations\) if )A
f3_10 sf
(x)S
f0_12 sf
-.024( can be zero, infinite, or NaN.)A
48 158 :M
(1)S
54 158 :M
(0)S
78 182 :M
f1_12 sf
-.132(Edits:)A
109 182 :M
f0_12 sf
(  )S
f2_12 sf
-.014(To the new example in 5.1.2.3, add the line)A
114 206 :M
f3_10 sf
(y = x / x;)S
204 206 :M
(/* not equivalent to y = 1.0; */)S
48 217 :M
f0_12 sf
(1)S
54 217 :M
(5)S
78 241 :M
f1_12 sf
@.958 .096(8.  Enhancement:)J
172 241 :M
f0_12 sf
@.65 .065(  Provide the )J
f3_10 sf
@.329(cis)A
f0_12 sf
1.294 .129( function, defined by cis\(x\)\312=\312cos\(x\)\312+\312i*sin\(x\), to)J
78 253 :M
f3_10 sf
(<complex.h>)S
f0_12 sf
(.)S
78 277 :M
f1_12 sf
@.453(Rationale:)A
f0_12 sf
1.74 .174(  Although the obvious implementation is correct \(which would suggest)J
48 277 :M
(2)S
54 277 :M
(0)S
78 289 :M
1.468 .147(leaving it for the user to implement\), having a library function might promote more)J
78 301 :M
-.012(efficient implementation.)A
78 325 :M
f1_12 sf
-.132(Edits:)A
109 325 :M
f0_12 sf
(  )S
f2_12 sf
-.011(Add to 7.x.2 in <complex.h> the subclause:)A
48 337 :M
f0_12 sf
(2)S
54 337 :M
(5)S
78 349 :M
f1_12 sf
-.039(7.x.2.y   The cis function)A
78 373 :M
-.097(Synopsis)A
114 397 :M
f3_10 sf
(#include <complex.h>)S
48 397 :M
f0_12 sf
(3)S
54 397 :M
(0)S
114 408 :M
f3_10 sf
(double complex cis\(double x\);)S
78 431 :M
f1_12 sf
-.031(Description)A
96 455 :M
f0_12 sf
-.219(The )A
118 455 :M
f3_10 sf
-.052(cis)A
f0_12 sf
-.045( function computes )A
231 455 :M
f3_10 sf
(cos\(x\)\312+\312I*sin\(x\))S
f0_12 sf
(.)S
48 455 :M
(3)S
54 455 :M
(5)S
78 479 :M
f1_12 sf
-.053(Returns)A
96 503 :M
f0_12 sf
-.219(The )A
118 503 :M
f3_10 sf
-.035(cis)A
f0_12 sf
-.028( function returns the value of )A
278 503 :M
f3_10 sf
(cos\(x\)\312+\312I*sin\(x\))S
f0_12 sf
(.)S
48 515 :M
(4)S
54 515 :M
(0)S
78 527 :M
f2_12 sf
-.001(Add cis to the list of type-generic macros for <complex.h> functions.)A
78 566 :M
f1_12 sf
@.101 .01(9.  Enhancement:)J
169 566 :M
f0_12 sf
@.116 .012(  Provide the math functions: cube root \()J
f3_10 sf
@.043(cbrt)A
f0_12 sf
@.133 .013(\), Bessel functions of the)J
78 578 :M
@.113 .011(first kind \()J
130 578 :M
f3_10 sf
(j0)S
f0_12 sf
(, )S
f3_10 sf
(j1)S
f0_12 sf
(, )S
167 578 :M
f3_10 sf
@.07(jn)A
f0_12 sf
@.198 .02(\), Bessel functions of the second kind \()J
f3_10 sf
@.07(y0)A
f0_12 sf
@.058 .006(, )J
f3_10 sf
@.07(y1)A
f0_12 sf
@.063 .006(, )J
406 578 :M
f3_10 sf
@.042(yn)A
f0_12 sf
@.129 .013(\), and reentrant log)J
48 578 :M
(4)S
54 578 :M
(5)S
78 590 :M
-.08(gamma \()A
f3_10 sf
-.08(lgamma_r)A
f0_12 sf
-.093(\).)A
78 614 :M
f1_12 sf
-.018(Rationale:)A
f0_12 sf
-.017(  These are specified in XPG4 V2 and are widely implemented.)A
78 638 :M
f1_12 sf
-.132(Edits:)A
109 638 :M
f0_12 sf
1.429 .143(  )J
119 638 :M
f2_12 sf
1.206 .121(Add specification for the functions to the )J
f9_10 sf
@.412(<math.h>)A
f2_12 sf
@.982 .098( spec and to the IEC 559)J
48 638 :M
f0_12 sf
(5)S
54 638 :M
(0)S
78 650 :M
f2_12 sf
-.004(annex, and add the names to the list of type-generic macros.)A
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42 14 :M
f0_12 sf
-.032(WG14/N619 X3J11/96-83)A
431 14 :M
-.095(10/15/96)A
42 722 :M
(8)S
404 722 :M
-.088(Enhancements)A
42 50 :M
f1_12 sf
3.709 .371(10.  Enhancement:)J
152 50 :M
f0_12 sf
3.536 .354(  Provide foundational financial/growth functions: \(1+r\)^n)J
42 62 :M
(\()S
46 62 :M
f3_10 sf
-.033(compound)A
f0_12 sf
-.024(\) and \(1\312-\312\(1\312+\312r\)^\(-n\)\)\312/\312r \()A
220 62 :M
f3_10 sf
-.12(annuity)A
f0_12 sf
-.14(\).)A
42 86 :M
2.548 .255(Rationale:  These functions are key to implementation of several other financial)J
42 98 :M
@.499 .05(functions.  Straight forward implementation loses needed accuracy for some arguments.)J
18 98 :M
(5)S
42 110 :M
-.013(Shipping prior art has been around for years.)A
42 134 :M
f1_12 sf
-.132(Edits:)A
73 134 :M
f0_12 sf
1.429 .143(  )J
83 134 :M
f2_12 sf
1.206 .121(Add specification for the functions to the )J
f9_10 sf
@.412(<math.h>)A
f2_12 sf
@.982 .098( spec and to the IEC 559)J
42 146 :M
-.004(annex, and add the names to the list of type-generic macros.)A
12 158 :M
f0_12 sf
(1)S
18 158 :M
(0)S
42 182 :M
f1_12 sf
-.058(Other ideas:)A
42 206 :M
f0_12 sf
-.009(Use an encoding of the standardization date for the value of )A
332 206 :M
f3_10 sf
-.013(__STD_IEC_559__)A
f0_12 sf
-.01(.  \(Fred?\))A
12 218 :M
(1)S
18 218 :M
(5)S
42 230 :M
-.007(Use new alternate form of pragmas for translation directives.  \(Fred?\))A
42 254 :M
-.002(Remove use of trailing semicolons with the translation directive macros.  \(Douglas?\))A
42 278 :M
2.125 .213(Add the requirement that some form of error/exception reporting be implemented.)J
12 278 :M
(2)S
18 278 :M
(0)S
42 290 :M
-.05(\(Fred?\))A
42 314 :M
-.018(Provide the XPG4 V2 double-precision math constants.)A
42 338 :M
-.072(Provide a )A
91 338 :M
f3_10 sf
-.019(significand)A
f0_12 sf
-.015( function to compute scalb\(x, \(long\) logb\(x\)\).)A
12 338 :M
(2)S
18 338 :M
(5)S
42 362 :M
-.082(Clarify that )A
100 362 :M
f3_10 sf
(-z)S
f0_12 sf
-.011( negates real and imaginary parts.  \(rationale?\))A
12 398 :M
(3)S
18 398 :M
(0)S
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exit 0