This web page examines advanced mathematics instructions in assembly language. Specific examples of instructions from various processors are used to illustrate the general nature of assembly language.
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EMOD Extended Multiply and Integerize; DEC VAX; performs accurate range reduction of math function arguments, the floating point multiplier extension operand (second operand) is concatenated with the floating point multiplier (first operand) to gain eight additional low order fraction bits, the multiplicand operand (third operand) is multiplied by the extended multiplier operand, after multiplication the integer portion (fourth operand) is extracted and a 32 bit (EMODF) or 64 bit (EMODD) floating point number is formed from the fractional part of the product by truncating extra bits, the multiplication is such that the result is equivalent to the exact product truncated (before normalization) to a fraction field of 32 bits in floating or 64 bits in double (fifth operand); clears or sets flags
TBLS Table Lookup and Interpolate (Signed, Rounded); Motorola 68300; signed lookup and interpolation of independent variable X from a compressed linear data table or between two register-based table entries of linear representations of dependent variable Y as a function of X; ENTRY(n) + {(ENTRY(n+1) - ENTRY(n)) * Dx[7:0]} / 256 into Dx; table version: data register low word contains the independent variable X, 8-bit integer part and 8-bit fractional part with assumed radix point located between bits 7 and 8, source effective address points to beginning of table in memory, integer part scaled to data size (byte, word, or longword) and used as offset from beginning of table, selected table entry (a linear representation of dependent variable Y) is subtracted from the next consecutive table entry, then multiplied by the interpolation fraction, then divided by 256, then added to the first table entry, and then stored in the data register; register version: data register low byte contains the independent variable X 8-bit fractional part with assumed radix point located between bits 7 and 8, two data registers contain the byte, word, or longword table entries (a linear representation of dependent variable Y), first data register-based table entry is subtracted from the second data register-based table entry, then multiplied by the interpolation fraction, then divided by 256, then added to the first table entry, and then stored in the destination (X) data register, the register interpolation mode may be used with several table lookup and interpolations to model multidimentional functions; rounding is selected by the ‘R’ instruction field, for a rounding adjustment of -1, 0, or +1; sets or clears flags
TBLSN Table Lookup and Interpolate (Signed, Not Rounded); Motorola 68300; signed lookup and interpolation of independent variable X from a compressed linear data table or between two register-based table entries of linear representations of dependent variable Y as a function of X; ENTRY(n) * 256 + (ENTRY(n+1) - ENTRY(n)) * Dx[7:0] into Dx; table version: data register low word contains the independent variable X, 8-bit integer part and 8-bit fractional part with assumed radix point located between bits 7 and 8, source effective address points to beginning of table in memory, integer part scaled to data size (byte, word, or longword) and used as offset from beginning of table, selected table entry (a linear representation of dependent variable Y) multiplied by 256, then added to the value determined by (selected table entry subtracted from the next consecutive table entry, then multiplied by the interpolation fraction), and then stored in the data register; register version: data register low byte contains the independent variable X 8-bit fractional part with assumed radix point located between bits 7 and 8, two data registers contain the byte, word, or longword table entries (a linear representation of dependent variable Y), first data register-based table entry is multiplied by 256, then added to the value determined by (first data register-based table entry subtracted from the second data register-based table entry, then multiplied by the interpolation fraction), and then stored in the destination (X) data register, the register interpolation mode may be used with several table lookup and interpolations to model multidimentional functions; sets or clears flags
TBLU Table Lookup and Interpolate (Unsigned, Rounded); Motorola 68300; unsigned lookup and interpolation of independent variable X from a compressed linear data table or between two register-based table entries of linear representations of dependent variable Y as a function of X; ENTRY(n) + {(ENTRY(n+1) - ENTRY(n)) * Dx[7:0]} / 256 into Dx; table version: data register low word contains the independent variable X, 8-bit integer part and 8-bit fractional part with assumed radix point located between bits 7 and 8, source effective address points to beginning of table in memory, integer part scaled to data size (byte, word, or longword) and used as offset from beginning of table, selected table entry (a linear representation of dependent variable Y) is subtracted from the next consecutive table entry, then multiplied by the interpolation fraction, then divided by 256, then added to the first table entry, and then stored in the data register; register version: data register low byte contains the independent variable X 8-bit fractional part with assumed radix point located between bits 7 and 8, two data registers contain the byte, word, or longword table entries (a linear representation of dependent variable Y), first data register-based table entry is subtracted from the second data register-based table entry, then multiplied by the interpolation fraction, then divided by 256, then added to the first table entry, and then stored in the destination (X) data register, the register interpolation mode may be used with several table lookup and interpolations to model multidimentional functions; rounding is selected by the ‘R’ instruction field, for a rounding adjustment of 0 or +1; sets or clears flags
TBLUN Table Lookup and Interpolate (Unsigned, Not Rounded); Motorola 68300; unsigned lookup and interpolation of independent variable X from a compressed linear data table or between two register-based table entries of linear representations of dependent variable Y as a function of X; ENTRY(n) * 256 + (ENTRY(n+1) - ENTRY(n)) * Dx[7:0] into Dx; table version: data register low word contains the independent variable X, 8-bit integer part and 8-bit fractional part with assumed radix point located between bits 7 and 8, source effective address points to beginning of table in memory, integer part scaled to data size (byte, word, or longword) and used as offset from beginning of table, selected table entry (a linear representation of dependent variable Y) multiplied by 256, then added to the value determined by (selected table entry subtracted from the next consecutive table entry, then multiplied by the interpolation fraction), and then stored in the data register; register version: data register low byte contains the independent variable X 8-bit fractional part with assumed radix point located between bits 7 and 8, two data registers contain the byte, word, or longword table entries (a linear representation of dependent variable Y), first data register-based table entry is multiplied by 256, then added to the value determined by (first data register-based table entry subtracted from the second data register-based table entry, then multiplied by the interpolation fraction), and then stored in the destination (X) data register, the register interpolation mode may be used with several table lookup and interpolations to model multidimentional functions; sets or clears flags
POLY Polynomial Evaluation; DEC VAX; performs fast calculation of math functions, for degree times (second operand) evaluate a function using Horner’s method, where d=degree (second operand), x=argument (first operand), and result = C[0] + x*(C[1] + x*(C[2] + … x*C[d])), float result stored in D0 register, double float result stored in D0:D1 register pair, the table address operand (third operand) points to a table of polynomial coefficients ordered from highest order term of the polynomial through lower order coefficients stored at increasing addresses, the data type of the coefficients must be the same as the data type of the argument operand (first operand), the unsigned word degree operand (second operand) specifies the highest numbered coefficient to participate in the evaluation (POLYF polynomial evaluation floating, POLYD polynomial evaluation double float); D0 through D4 registers modified by POLYF, D0 through D5 registers modified by POLYD; sets or clears flags
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