"TMS320C55x DSP Library DSPLIB Programmer's Reference"

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Appendix BACalculating the Reciprocal of a Q15 NumberThe most optimal method for calculating the inverse of a fractional number(Y=1/X) is to normalize the number first. This limits the range of the numberas follows:0.5 Xnorm 1–1 Xnorm –0.5 (1)The resulting equation becomesY 1(Xnorm *2 n )orY 2nXnormwhere n = 1, 2, 3, …, 14, 15Letting Ye 2 n :Ye 2 n (3)Substituting (3) into equation (2):Y Ye *1(4)XnormLetting Ym 1Xnorm :Ym 1(5)XnormSubstituting (5) into equation (4):Y Ye * Ym (6)For the given range of Xnorm, the range of Ym is:1 Ym 2–2 Ym –1 (7)To calculate the value of Ym, various options are possible:a) Taylor Series Expansionb) 2nd,3rd,4th,.. Order Polynomial (Line Of Best Fit)c) Successive Approximation(2)B-1
Calculating the Reciprocal of a Q15 NumberThe method chosen in this example is (c). Successive approximation yieldsthe most optimum code versus speed versus accuracy option. The methodoutlined below yields an accuracy of 15 bits.Assume Ym(new) exact value of1Xnorm :Ym(new) 1XnormorYm(new)*X 1(c1)(c2)Assume Ym(old) estimate of value 1 X :Ym(old)*Xnorm 1 DyxorDxy Ym(old)*Xnorm 1where Dyx = error in calculationAssume that Ym(new) and Ym(old) are related as follows:Ym(new) Ym(old) Dywhere Dy = difference in valuesSubstituting (c2) and (c4) into (c3):Ym(old)*Xnorm Ym(new)*Xnorm Dxy(Ym(new) Dy)*Xnorm Ym(new)*Xnorm DxyYm(new)*Xnorm Dy * Xnorm Ym(new)*Xnorm DxyDy * Xnorm DxyDy Dxy *1XnormAssume that 1/Xnorm is approximately equal to Ym(old):Dy Dxy * Ym(old) (approx)Substituting (c6) into (c4):Ym(new) Ym(old) Dxy * Ym(old)Substituting for Dxy from (c3) into (c7):Ym(new) Ym(old) (Ym(old)*Xnorm 1) * Ym(old)Ym(new) Ym(old) Ym(old) 2 * Xnorm Ym(old)Ym(new) 2*Ym(old) Ym(old) 2 * Xnorm(c3)(c4)(c5)(c6)(c7)(c8)B-2
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TMS320C55x DSP LibraryProgrammer’
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PrefaceRead This FirstAbout This Ma
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Contentsatan16 . . . . . . . . . .
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DSP Routines1.1 DSP RoutinesThe TI
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DSPLIB Content / How to Install DSP
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Chapter 3Using DSPLIBThis chapter d
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Calling a DSPLIB Function from C3.2
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Calling a DSPLIB Function from Asse
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How DSPLIB Deals with Overflow and
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Chapter 4Function DescriptionsThis
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DSPLIB Functions4.2 DSPLIB Function
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DSPLIB FunctionsTable 4-2. Summary
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acorracorrFunctionArgumentsAutocorr
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addCycles †Code size(in bytes)Aub
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atan16Description This function cal
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expbexpFunctionBlock Exponent Imple
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cfftBenchmarks(preliminary)Cycles
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cfirCFFT - NOSCALEFFT Size Cycles
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cfirImplementation Notes The first
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cifftcifftFunctionInverse Complex F
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convolCIFFT - NOSCALEFFT Size Cycle
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convol1Figure 4-6. h Array in Memor
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convol2Figure 4-8. r Array in Memor
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convol2Figure 4-10. x Array in Memo
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dlmsImplementation NotesSpecial deb
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expnImplementation NotesDelayed ver
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firr[nx]Pointer to output vector of
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fir2Figure 4-14. x Array in Memoryo
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fir2Special Requirementsnh must be
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firdecr[nx/D]dbuffer[nh+1]nxnhDofla
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firinterpIoflagInterpolation factor
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firlatpbuffer [nh]nxnhoflagDelay bu
Page 67 and 68: firsnh2oflagHalf the number of coef
Page 69 and 70: fltoq15Figure 4-21. r Array in Memo
Page 71 and 72: hilb16dbuffer[nh + 2] Pointer to de
Page 73 and 74: iir32Figure 4-23. x Array in Memory
Page 75 and 76: iir32In the case of multiple-buffer
Page 77 and 78: iircas4nxoflagNumber of elements of
Page 79 and 80: iircas51This function retains the a
Page 81 and 82: iirlatBenchmarks(preliminary)Cycles
Page 83 and 84: ldiv16ldiv16Function32-bit by 16-bi
Page 85 and 86: log_10Special Requirements noneImpl
Page 87 and 88: lognThe coefficients Bi used in the
Page 89 and 90: maxidxmaxidxFunctionIndex of the Ma
Page 91 and 92: maxvecDescription Returns the maxim
Page 93 and 94: minvecminvalFunctionMinimum Value o
Page 95 and 96: mmulDescriptionAlgorithmThis functi
Page 97 and 98: negr[nx]Pointer to output data vect
Page 99 and 100: powernxoflagNumber of elements of i
Page 101 and 102: and16AlgorithmNot applicableOverflo
Page 103 and 104: and16initBenchmarksCycles Core: 13
Page 105 and 106: fftThe initial estimate can be obta
Page 107 and 108: ifftrifftFunctionInverse Real FFT (
Page 109 and 110: sqrt_16DescriptionComputes the sine
Page 111 and 112: subr[nx]nxscaleoflagPointer to outp
Page 113 and 114: What DSPLIB Benchmarks are Provided
Page 115 and 116: DSPLIB Software Updates6.1 DSPLIB S
Page 117: Q3.12 Format / Q.15 Format / Q.31 F
Page 121 and 122: IndexIndex16-bit reciprocal functio
Page 123: Indexmmul 4-74mtrans 4-76mul32 4-76
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