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!< (not less than) operator !<= (not less than or equal) operator !<> (not less or greater than) operator !<>= (unordered) operator != (not equal) operator !> (not greater than) operator !>= (not greater than or equal) operator * (multiply) operator [1] + (plus) operator [1] / (divide) operator [1] [2] 680x0-based Macintosh computers numerics environment [1] porting from [1] 8087 coprocessor < (less than) operator assembler [1] [2] defined <= (less than or equal to) operator <> (less or greater than) operator <>= (ordered) operator == (equal to) operator assembler [1] [2] defined > (greater than) operator assembler [1] [2] defined >= (greater than or equal to) operator

absolute value assembler compiler accessing the environment assembler instructions [1] C functions C functions, prerequisite [1] accuracy decimal to binary conversions [1] of basic arithmetic operations acos function acosh function addition [1] assembler invalid exception, generating address mode AINT annuity function ANSI X3J11.1 [1] antilog functions. See exponential functions APDA arc cosine arc cosine, hyperbolic arc sine arc sine, hyperbolic arc tangent [1] [2] arc tangent, hyperbolic argument reduction [1] [2] arithmetic assembler instructions arithmetic operations [1] addition [1] assembler automatic type conversions [1] division [1] multiplication [1] remainder round-to-integer [1] square root [1] subtraction [1] arithmetic, IEEE standard [1] [2] asin function asinh function assembler [1] conversions [1] data formats [1] environmental access [1] operations supported [1] atan function atan2 function atanh function atomic operations auxiliary functions [1] assembler [1] exponent field, return nan function nextafter functions scaling sign manipulation

base 2 exponential BASIC beq assembler instruction bge assembler instruction bgt assembler instruction bias of exponents [1] binary logarithm binary to decimal conversions [1] C functions double-double format [1] strings [1] structures [1] [2] ble assembler instruction blt assembler instruction bne assembler instruction bng assembler instruction bnl assembler instruction bnu assembler instruction branch assembler instructions [1] bta assembler instruction bun assembler instruction

C language compilers, FPCE recommendations for [1] conformance to IEEE 754 [1] constants, floating-point [1] [2] conversions [1] data types, new [1] double type. See double format environmental controls [1] expression evaluation [1] float type. See single format function calls, conversions during [1] long double type. See double-double format transcendental functions [1] CDC computers ceil function classcomp SANE function classdouble SANE function classes of floating-point numbers [1] assembler [1] compiler [1] classextended SANE function classfloat SANE function common logarithm comp data type (porting) [1] comparison functions comparison operations. See comparisons comparison operators [1] comparisons [1] assembler (branch instructions) assembler instructions C functions invalid exception, generating involving Infinities [1] involving NaNs [1] compatibility across architectures [1] compiler optimizations and evaluation of floating-point constant expressions [1] and floating-point environment [1] and widest-need evaluation [1] complementary error function compound function computer approximation of real numbers [1] Condition Register [1] [2] constants, floating-point evaluation [1] hexadecimal contraction operators [1] controlling the environment assembler instructions [1] C functions [1] conversions [1] accuracy of decimal to binary [1] assembler [1] between decimal formats [1] [2] between floating-point formats [1] [2] [3] binary to decimal [1] [2] C functions [1] ceil function decimal to binary [1] C functions double-double format [1] double-double to decimal [1] during expression evaluation [1] floating-point to integer [1] [2] [3] [4] floor function inexact exception integer to floating-point [1] [2] [3] invalid exception [1] [2] nearbyint function overflow exception rint function [1] rinttol function round function roundtol function SANE [1] trunc function underflow exception copysign function invalid exception SANE cos function cosh function cosine cosine, hyperbolic CR. See Condition Register Cray computers current rounding direction [1] nearbyint function rint function [1] rinttol function

data formats [1] assembler [1] choosing [1] classes of numbers [1] assembler [1] compiler [1] compiler [1] converting between [1] [2] [3] diagrams [1] diagrams, symbols used in double format [1] double-double format [1] expression evaluation format [1] minimum evaluation format [1] [2] precision of [1] range of [1] SANE [1] [2] semantic type single format [1] widening for efficiency [1] [2] dec2f function dec2l function dec2num function dec2numl function dec2s function dec2str function decform structure definition [1] digits field [1] [2] style field [1] decimal data, reading and writing [1] decimal formatting structure [1] [2] decimal fractions [1] decimal output fixed-style [1] floating-style decimal strings [1] decimal structure [1] [2] definition [1] exp field [1] [2] sgn field [1] [2] sig field [1] [2] decimal to binary conversions [1] C functions double-double format [1] strings [1] structures [1] [2] decimal to decimal conversions [1] [2] DECIMAL_DIG constant default environment [1] default rounding direction [1] denormalized numbers density of double-double format SANE [1] DENORMALNUM SANE constant density of denormalized numbers density of single-precision numbers difference operation assembler defined [1] difference, positive function DIVBYZERO SANE constant divide-by-zero exception assembler defined [1] division [1] assembler by zero invalid exception, generating double format [1] as minimum evaluation format [1] [2] compiler [1] [2] converting from double-double format [1] converting from single format assembler [1] defined [1] converting to double-double format [1] converting to single format assembler [1] defined [1] diagram diagram, symbols used in precision range representation of values double type. See double format double-double format [1] as minimum evaluation format [1] compared to extended format [1] compiler [1] [2] converting from double format [1] converting from single format [1] converting to decimal [1] converting to double format [1] converting to single format [1] diagram diagram, symbols used in interpretation of values [1] precision [1] [2] range DOUBLE_SIZE macro double_t typedef [1] for compatibility [1] in transcendental function declarations downward rounding defined [1] floor function DOWNWARD SANE constant

elementary functions. See transcendental functions environment [1] accessing assembler instructions [1] C functions C functions prerequisite [1] assembler [1] C functions, types [1] default [1] ignoring restoring assembler [1] compiler [1] [2] SANE [1] saving assembler [1] compiler [1] [2] setting (compiler) use environment SANE type environmental access switch defined [1] purpose, note on environmental controls [1] assembler instructions [1] C functions [1] SANE [1] erf function erfc function error functions evaluation format [1] minimum [1] [2] widest need [1] evaluation rules exception handling [1] exception SANE type exceptional events [1] exceptions [1] assembler instructions C functions clearing assembler [1] compiler [1] [2] descriptions of [1] divide-by-zero [1] enabling and disabling (assembler) [1] in Condition Register inexact [1] invalid [1] overflow [1] preserving assembler [1] compiler [1] [2] raising assembler [1] compiler restoring (compiler) saving assembler [1] compiler [1] [2] setting assembler [1] compiler [1] [2] testing assembler compiler underflow [1] exp function exp1 SANE function exp2 function expm1 function exponent defined determining value of [1] [2] exponential functions base 2 exponential natural exponential natural exponential \xC7 1 expression evaluation format [1] expression evaluation methods [1] compared [1] compiler [1] examples [1] floating-point constants [1] minimum evaluation format only [1] [2] SANE [1] widest-need evaluation [1] [2] extended data type [1] compared to double-double format [1] in definitions of float_t and double_t [1] in transcendental function declarations

fabs assembler instruction fabs function [1] [2] fadd assembler instruction fcmpo assembler instruction fcmpu assembler instruction fctiw assembler instruction [1] fctiwz assembler instruction [1] fdim function fdiv assembler instruction feclearexcept function fegetenv function definition fegetexcept function definition with fesetexcept function fegetround function definition with fesetround function feholdexcept function fenv.h file [1] [2] fenv_access pragma option [1] fenv_t type [1] feraiseexcept function fesetenv function fesetexcept function fesetround function fetestexcept function feupdateenv function definition with feholdexcept function [1] fexcept_t type [1] FE_ALL_EXCEPT constant [1] FE_DFL_ENV constant [1] FE_DIVBYZERO constant FE_DOWNWARD constant FE_INEXACT constant FE_INVALID constant FE_OVERFLOW constant FE_TONEAREST constant FE_TOWARDZERO constant FE_UNDERFLOW constant FE_UPWARD constant financial functions float type. See single format floating-point constants evaluation [1] hexadecimal floating-point data formats. See data formats floating-point environment. See environment floating-point exceptions. See exceptions floating-point expressions, evaluating [1] [2] floating-point numbers classes of [1] assembler [1] compiler [1] converting to integer [1] integers, converting to [1] assembler [1] compiler truncating [1] splitting floating-point registers [1] floating-point result flags [1] Floating-Point Status and Control Register (FPSCR). See FPSCR floating-point values, interpreting [1] floating-point variables, initialization [1] float_t typedef [1] [2] floor function flush-to-zero systems fmadd assembler instruction fmax function fmin function fmod function fmr assembler instruction fmsub assembler instruction fmul assembler instruction fnabs assembler instruction fneg assembler instruction fnmadd assembler instruction fnmsub assembler instruction format conventions for this book [1] formats. See data formats formatters, numeric formatting output fixed-style decimal [1] floating-style decimal Fortran fp.h file functions [1] [2] porting to FPCE technical report [1] compiler, recommendations for [1] conversions [1] data types environmental access [1] expression evaluation [1] transcendental functions [1] fpclassify macro FPSCR exception bits format [1] manipulation [1] result flags [1] rounding direction fp_contract pragma [1] fp_wide_function_parameters pragma fp_wide_function_returns pragma fp_wide_variables pragma [1] fraction field defined determining value of frexp function frsp assembler instruction fsub assembler instruction functions [1] auxiliary [1] comparison error exponential financial gamma hyperbolic logarithmic sign manipulation trigonometric

IBM Q format IEEE arithmetic advantages [1] operations [1] IEEE data formats [1] . See also single format, double format IEEE standard advantages [1] arithmetic operations [1] auxiliary functions [1] C language [1] comparisons [1] conversions required [1] data formats [1] exceptions [1] rounding direction modes [1] [2] . See also rounding direction rounding precision modes [1] IEEE Standard 754. See IEEE standard IEEE Standard 854 logb function nearbyint function IEEE standard arithmetic. See IEEE arithmetic IEEEDEFAULTENV SANE constant inexact exception [1] assembler conversions INEXACT SANE constant INFINITE SANE constant Infinities [1] as alternative to stopping [1] [2] comparisons [1] converting to decimal [1] converting to floating-point converting to integer converting to string double-double format negative positive SANE [1] INFINITY constant initialization of floating-point variables [1] instant rounding INT integer types integers, converting [1] assembler compiler rounding [1] truncating [1] interpreting floating-point values [1] interval arithmetic invalid exception [1] assembler conversions signaling NaN, result of [1] invalid operation flag INVALID SANE constant invalid-operation exception. See invalid exception inverse operations ipower SANE function isfinite macro isnan macro isnormal macro

MathLib [1] conversions [1] data types, new [1] environmental controls [1] expression evaluation extensions [1] porting to transcendental functions [1] maximum function MC68881 coprocessor mcrfs assembler instruction [1] minimum evaluation format [1] compared to widest-need evaluation [1] compiler recommendations [1] examples [1] minimum function mixed formats modf function modulo function [1] move assembler instructions mtfsfi assembler instruction multiplication [1] assembler invalid exception, generating multiply-add assembler instructions enabling and disabling [1] format

NAN constant nan function PowerPC Numerics SANE NaNs [1] as alternative to stopping [1] [2] comparisons [1] converting to decimal [1] converting to floating-point [1] converting to integer converting to string creating double-double format porting programs quiet [1] [2] SANE [1] signaling [1] [2] [3] natural exponential natural exponential minus 1 natural logarithm [1] [2] NCEG [1] nearbyint function negative Infinity. See Infinities negative zero. See zero nextafter functions PowerPC Numerics SANE normalized numbers [1] compared to denormalized numbers [1] double-double format NORMALNUM SANE constant not unordered comparison Not-a-Number. See NaNs num2dec function definition numbers, classes of [1] assembler [1] compiler [1] numclass SANE type Numerical C Extensions Group [1]

operations [1] arithmetic assembler defined [1] assembler [1] comparison assembler [1] [2] defined [1] compiler [1] conversion assembler [1] compiler [1] SANE [1] subject to arithmetic conversions [1] optimizations and evaluation of floating-point constant expressions [1] and floating-point environment [1] and widest-need evaluation [1] ordered comparison assembler defined output fixed-style decimal [1] floating-style decimal overflow [1] assembler conversions OVERFLOW SANE constant

Pascal PDP-11C pi constant pi SANE function porting programs from non-Macintosh computers [1] from SANE [1] positive difference function positive Infinity. See Infinities positive zero. See zero pow function PowerPC Numerics SANE power function PowerPC floating-point architecture [1] conversions [1] data formats [1] environmental access [1] operations supported [1] PowerPC Numerics advantages [1] conversions supported [1] data formats [1] environmental controls [1] expression evaluation [1] functions supported [1] operations supported [1] SANE, compared to [1] [2] SANE, porting from [1] pragmas fenv_access [1] fp_contract [1] fp_wide_function_parameters [1] fp_wide_function_returns [1] fp_wide_variables [1] precision of data formats [1] of expression evaluation [1] procentry SANE function procexit SANE function

random number generator [1] randomx function [1] range of data formats [1] real numbers computer approximation [1] order of recommendations, FPCE for compilers [1] registers Condition Register [1] [2] floating-point [1] FPSCR [1] [2] special-purpose [1] relation function relational operators [1] remainder function defined invalid exception, generating remquo function result flags [1] result, tiny [1] rint function [1] rinttol function round function round to integer operation [1] rounddir SANE type rounding defined instant rounding direction [1] assembler compiler control current [1] [2] [3] default [1] downward [1] saving (compiler) setting assembler compiler to nearest [1] toward zero [1] upward [1] rounding downward defined [1] floor function rounding modes. See rounding direction rounding precision modes [1] rounding to integer [1] rounding to nearest value [1] rounding toward zero defined [1] trunc function rounding upward ceil function defined [1] roundoff error with denormalized numbers [1] roundtol function

SANE compared to PowerPC Numerics [1] [2] conversions [1] data formats [1] denormalized numbers [1] environment [1] expression evaluation [1] Infinities [1] NaNs [1] operations [1] porting programs from [1] transcendental functions [1] sane.h file scalb function PowerPC Numerics SANE scaling functions ldexp function scalb function scanners semantic type setenvironment SANE function setexception SANE function setround SANE function sign bit sign manipulation functions copysign fabs function sign of zero [1] SIGN(A) SIGN(A,B) signaling NaNs [1] comparisons invalid exception signbit macro significand signnum SANE function sin function sine sine, hyperbolic single format [1] as minimum evaluation format [1] [2] compiler [1] [2] converting from double format assembler [1] defined [1] converting from double-double format [1] converting to double format assembler [1] defined [1] converting to double-double format [1] diagram diagram, symbols used in precision range representation of values single-precision numbers, density of sinh function small values and error analysis representing SNAN SANE constant special-purpose registers [1] sqrt function [1] square root operation defined [1] invalid exception, generating Standard Apple Numerics Environment (SANE). See SANE stfd assembler instruction stfdu assembler instruction stfdux assembler instruction stfdx assembler instruction stfs assembler instruction [1] [2] stfsu assembler instruction [1] [2] stfsux assembler instruction [1] [2] stfsx assembler instruction [1] [2] stopping program store assembler instructions [1] as conversion operations [1] formats [1] str2dec function string conversions [1] subtraction operation assembler defined [1] symbols in format diagrams

tagp parameter [1] tan function tangent tangent, hyperbolic tanh function testexception SANE function tiny result [1] to-nearest rounding [1] TONEAREST SANE constant toward +

rounding. See upward rounding toward \xC7

rounding. See downward rounding toward-zero rounding defined [1] trunc function TOWARDZERO SANE constant transcendental functions [1] assembler [1] defined [1] [2] SANE [1] transported code trigonometric functions trigonometric functions, hyperbolic Trunc function trunc function truncating floating-point to integer [1] [2] types. See data formats

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Legacy Document

Index

[']

A

B

C

D

E

F

G

H

I,J,K

L

M

N

O

P

Q

R

S

T

U

V

W,X,Y

Z