% 'Annot.NUMBER34': class PDFDictionary 5 0 obj The double-precision binary floating-point exponent is encoded using an offset-binary representation, with the zero offset being 1023; also known as exponent bias in the IEEE 754 standard. /Rect [ 154.9029 % 'Annot.NUMBER21': class LinkAnnotation /Type /Annot >> 49 0 obj /Rect [ 218.6453 /Rect [ 218.6453 0 ] % 'Annot.NUMBER30': class PDFDictionary % 'Annot.NUMBER42': class PDFDictionary 0 Between 252=4,503,599,627,370,496 and 253=9,007,199,254,740,992 the representable numbers are exactly the integers. /Type /Annot >> 252.6473 /URI (http://en.wikipedia.org/w/index.php?title=Computer_numbering_format) >> 682.9469 ] % 'Annot.NUMBER11': class PDFDictionary The format is written with the significand having an implicit integer bit of value 1 (except for special data, see the exponent encoding below). 745.9469 ] % 'Annot.NUMBER1': class PDFDictionary 357.7736 ] 526.7852 By default, 1/3 rounds down, instead of up like single precision, because of the odd number of bits in the significand. /URI (http://en.wikipedia.org/w/index.php?title=Offset_binary) >> /URI (http://en.wikipedia.org/w/index.php?title=Denormal_number) >> 0 ] /XObject << /FormXob.9b2767a2ee1f7b38f4e43e7aa600e77e 49 0 R >> >> 289.6373 endobj << /A << /S /URI 52 0 obj /Type /Action 48 0 obj Floating point is used to represent fractional values, or when a wider range is needed than is provided by fixed point (of the same bit width), even if at the cost of precision. << /A << /S /URI % 'Annot.NUMBER31': class PDFDictionary /Length 2337 % 'Annot.NUMBER12': class PDFDictionary 586.7852 ] 50 0 R ] stream Before the widespread adoption of IEEE 754-1985, the representation and properties of floating-point data types depended on the computer manufacturer and computer model, and upon decisions made by programming-language implementers. 700.9469 730.9469 /URI (http://en.wikipedia.org/w/index.php?title=Decimal64_floating-point_format) >> /ProcSet [ /PDF /FormXob.c955ad7b5979d31f7c755ec85d6d814c 36 0 R Gb"/igQ'33#Xn:a+5L+7kT>ha9CVU)>e2fZS_kRVV,jY^l>&E'Ob2jF(JuPq>m7@X9mgPFZMNiN6Wp`SgGcbM/5q^QD[17ec/lkAVnE$0G4iGL^Fj^3M2E-o.:`.WA'*#f@NL)Z$mEZDG]Q9WtN=2BD?8Rb]j>m@S"JB9?>FM^A7GM]86kdKDIr&:mP?]i\%0^e))XW%1;B34F[r;MA2LSS>LB=`-&8b6:+K#HJp8LhueZ$CQ1UmF.,45FL,Nofrro-UafG_JHYo'@'1[#Tt'X=GX#ek^EHmPsdT?i8aeEL!KdcG,"LTf4#p]t#DObrJiogO\SE;D(9i7&t#-Y88s;gIHjcpg![=tWW$rpUBUlt;r)D_#jW@c(K8`d\NL_&c@*e\ZiLnoL2bVNDS#+ZMRYXRP>D7I"6;6r%VQIpUqR=SkOt;]f28\5H=Oq9RBW3nq6ejjfdr=#5FUP7r-n4/7gH\>KKAC:f[h+tMfbIVSJfM6he[)0l`:25pj,T^ng'ep3PSA,WD4i/"^cK]#r"XrcrPbfg^c3NUM$A\6dL^_T(D)o`bh@o3Pc3s,C]c?%;J?32U/I,s"JbYU`Z#]K5')S-MNGb2Kf"guq-48XpM/ZmSBD^&L!ihlO;O[k[27!c6/h]*)]Hi]W9Mi9&_F%Rkm(BD9AR/V(:*^D.S50bM/F[Ht3`JBGD2.X;Z8.V78.j@^.O_^i+&j(*;K0-Vp/\R-FSHX-UrqXA0^GX;N4D:1(6@#a>bS[&B;@H'Go9bQ8L1);lGm4-C=PNs10i8VB2([24kZi#LMF@TS-3G0fl!UN;6`Y$96LAg>?KX=XNVq&;?Ur]c\)9UW!5VYN#d^&.A"4QD7X&X*Y14/`:]k1[]6h5d3A05fa.q%@;Rg+16[N4I6HuJkLjuY6S)Dr:i(aRNak*bh0GmXj0;(bQQ2S!bk)ehLuA?P?aite! /Type /Annot >> 586.7852 /Rect [ 218.6453 % 'FormXob.b7ef22158eced5ffef628bb550a8d6e0': class PDFImageXObject Converter to 64 Bit Double Precision IEEE 754 Binary Floating Point Standard System: Converting Base 10 Decimal Numbers. /Subtype /Link /ColorSpace /DeviceRGB /Subtype /Link 33 0 obj << /A << /S /URI << /A << /S /URI 54 0 obj 598.7852 /ColorSpace /DeviceRGB 45 0 obj /Rect [ 491.6292 667.9469 ] /Width 740 >> 240.1463 0 stream % 'Annot.NUMBER22': class PDFDictionary 562.7852 44 0 R /Type /Action /Border [ 0 Using double-precision floating-point variables and mathematical functions (e.g., sin, cos, atan2, log, exp and sqrt) are slower than working with their single precision counterparts. /Height 50 /Type /Annot >> /Type /Annot >> 764.9469 ] However, on 32-bit x86 with extended precision by default, some compilers may not conform to the C standard and/or the arithmetic may suffer from double rounding.[5]. 17 0 R stream << /Contents 86 0 R 48 0 R /Resources << /Font 1 0 R /URI (http://en.wikipedia.org/w/index.php?title=IEEE_floating-point_standard) >> This is a decimal to binary floating-point converter. /Border [ 0 0 /Border [ 0 All bit patterns are valid encoding. 0 ] /URI (http://en.wikipedia.org/w/index.php?title=Half_precision_floating-point_format) >> 37 0 obj /URI (http://en.wikipedia.org/w/index.php?title=16-bit) >> 34 0 R �ү�+� 700.9469 endobj 353.6273 endobj /Subtype /Image 682.9469 /Rotate 0 0 14 0 R /Type /Action 270.1523 % Page dictionary endobj /Type /Action 586.7852 ] �ү�+� 0 ] /Text /Subtype /Link /URI (http://en.wikipedia.org/w/index.php?title=Computing) >> /Type /Action 595.2756 /Subtype /Link << /A << /S /URI 0 0 endobj /Border [ 0 21 0 R 586.7852 /Height 107 Double-precision floating-point format (sometimes called FP64 or float64) is a computer number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. /URI (http://en.wikipedia.org/w/index.php?title=Sign_bit) >> 263.1413 47 0 obj 20 0 obj % 'Annot.NUMBER15': class PDFDictionary /Subtype /Link /Length 2519 0 /Border [ 0 159.9629 % 'Page4': class PDFPage I would like to know how fortran 95 (f95) would convert a double precision (DP) with an exponent larger than can be held in a single precision (SP) exponent. Thus a modifier strictfp was introduced to enforce strict IEEE 754 computations. /Rect [ 244.8983 % 'Annot.NUMBER29': class PDFDictionary 0 ] /Type /Annot >> With the 52 bits of the fraction (F) significand appearing in the memory format, the total precision is therefore 53 bits (approximately 16 decimal digits, 53 log10(2) ≈ 15.955). /Rect [ 312.0729 /Type /Annot >> /Border [ 0 "$_uBd!E>?I~>endstream 11 0 obj 3 0 obj [2,a["DZaoK,'YT*9fDN.14Mbjjb@1)P]c^Nu`Yq&dM]5/5L!qr(q2/d&1YNCt'@i*,rb$+bUCn#U+j463n`f&E;UiqlY3G~>endstream 29 0 R /Width 1200 >> 27 0 R 36 0 obj 30 0 obj 15 0 R % 'Annot.NUMBER2': class PDFDictionary 31 0 obj % 'Annot.NUMBER14': class PDFDictionary 622.7852 ] << /A << /S /URI /Parent 83 0 R 514.7852 /Border [ 0 /Subtype /Link /Type /Annot >> 290.7446 << /Annots [ 2 0 R % 'Annot.NUMBER40': class PDFDictionary 667.9469 ] << /A << /S /URI /URI (http://en.wikipedia.org/w/index.php?title=Single_precision) >> % Font Helvetica 255.8783 0 ] !%Nc\6it> /ImageI ] >> /Subtype /Image 787.6635 /URI (http://en.wikipedia.org/w/index.php?title=Arbitrary-precision_arithmetic) >> endobj /MediaBox [ 0 /Subtype /Image 586.7852 /Rect [ 74.92556 << /A << /S /URI 538.7852 ] endobj �ү�+� % 'Annot.NUMBER17': class PDFDictionary /Trans << >> /Border [ 0 0 ] %���� ReportLab Generated PDF document http://www.reportlab.com {\displaystyle e} 19 0 R /Type /Annot >> 6 0 obj 0 �ү�+� /Type /Action /Width 753 >> << /A << /S /URI /F5+0 70 0 R 0 Single Precision: Single Precision is a format proposed by IEEE for representation of floating-point number. 0 ] Double precision is not required by the standards (except by the optional annex F of C99, covering IEEE 754 arithmetic), but on most systems, the double type corresponds to double precision. 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