# Vector-vector real arithmetic functions Perform element-wise operations on vectors of real values. ## Discussion The vDSP library provides a suite of general-purpose, high-performance arithmetic functions that are alternatives to `for` loops and `map` when you apply operations on collections of floating-point values. See for a summary of available operations. ## Topics ### Binary addition operations [`static func add(T, U) -> [Float]`](/documentation/Accelerate/vDSP/add(_:_:)-7swvf) Returns the single-precision element-wise sum of two vectors. [`static func add(T, U) -> [Double]`](/documentation/Accelerate/vDSP/add(_:_:)-2ftxc) Returns the double-precision element-wise sum of two vectors. [`static func add(T, U, result: inout V)`](/documentation/Accelerate/vDSP/add(_:_:result:)-3vzwi) Calculates the single-precision element-wise sum of two vectors. [`static func add(T, U, result: inout V)`](/documentation/Accelerate/vDSP/add(_:_:result:)-338hl) Calculates the double-precision element-wise sum of two vectors. [`extern void vDSP_vadd(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, float *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vadd) Calculates the single-precision element-wise sum of two vectors, using the specified stride. [`extern void vDSP_vaddD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, double *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vaddD) Calculates the double-precision element-wise sum of two vectors, using the specified stride. ### Binary subtraction operations [`static func subtract(U, T) -> [Float]`](/documentation/Accelerate/vDSP/subtract(_:_:)-9xmo8) Returns the single-precision element-wise subtraction of two vectors. [`static func subtract(U, T) -> [Double]`](/documentation/Accelerate/vDSP/subtract(_:_:)-8o5ai) Returns the double-precision element-wise subtraction of two vectors. [`static func subtract(U, T, result: inout V)`](/documentation/Accelerate/vDSP/subtract(_:_:result:)-2p3fa) Calculates the single-precision element-wise subtraction of two vectors. [`static func subtract(U, T, result: inout V)`](/documentation/Accelerate/vDSP/subtract(_:_:result:)-1ianx) Calculates the double-precision element-wise subtraction of two vectors. [`extern void vDSP_vsub(const float *__B, vDSP_Stride __IB, const float *__A, vDSP_Stride __IA, float *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsub) Calculates the single-precision element-wise subtraction of two vectors, using the specified stride. [`extern void vDSP_vsubD(const double *__B, vDSP_Stride __IB, const double *__A, vDSP_Stride __IA, double *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsubD) Calculates the double-precision element-wise subtraction of two vectors, using the specified stride. ### Binary multiplication operations [`static func multiply(T, U) -> [Float]`](/documentation/Accelerate/vDSP/multiply(_:_:)-9zgw) Returns the single-precision element-wise product of two vectors. [`static func multiply(T, U) -> [Double]`](/documentation/Accelerate/vDSP/multiply(_:_:)-1ckqt) Returns the double-precision element-wise product of two vectors. [`static func multiply(T, U, result: inout V)`](/documentation/Accelerate/vDSP/multiply(_:_:result:)-155f3) Calculates the single-precision element-wise product of two vectors. [`static func multiply(T, U, result: inout V)`](/documentation/Accelerate/vDSP/multiply(_:_:result:)-3ptjl) Calculates the double-precision element-wise product of two vectors. [`extern void vDSP_vmul(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, float *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vmul) Calculates the single-precision element-wise product of two vectors, using the specified stride. [`extern void vDSP_vmulD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, double *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vmulD) Calculates the double-precision element-wise product of two vectors, using the specified stride. ### Binary division operations [`static func divide(T, U) -> [Float]`](/documentation/Accelerate/vDSP/divide(_:_:)-6nfsi) Returns the single-precision element-wise division of two vectors. [`static func divide(T, U) -> [Double]`](/documentation/Accelerate/vDSP/divide(_:_:)-8swnm) Returns the double-precision element-wise division of two vectors. [`static func divide(T, U, result: inout V)`](/documentation/Accelerate/vDSP/divide(_:_:result:)-7ejy9) Calculates the single-precision element-wise division of two vectors. [`static func divide(T, U, result: inout V)`](/documentation/Accelerate/vDSP/divide(_:_:result:)-6gtmm) Calculates the double-precision element-wise division of two vectors. [`extern void vDSP_vdiv(const float *__B, vDSP_Stride __IB, const float *__A, vDSP_Stride __IA, float *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vdiv) Calculates the single-precision element-wise division of two vectors, using the specified stride. [`extern void vDSP_vdivD(const double *__B, vDSP_Stride __IB, const double *__A, vDSP_Stride __IA, double *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vdivD) Calculates the double-precision element-wise division of two vectors, using the specified stride. ### Binary addition and subtraction operations [`static func addSubtract(S, T, addResult: inout U, subtractResult: inout V)`](/documentation/Accelerate/vDSP/addSubtract(_:_:addResult:subtractResult:)-6qxwa) Calculates the single-precision element-wise sum and subtraction of two vectors. [`static func addSubtract(S, T, addResult: inout U, subtractResult: inout V)`](/documentation/Accelerate/vDSP/addSubtract(_:_:addResult:subtractResult:)-avzd) Calculates the double-precision element-wise sum and subtraction of two vectors. [`void vDSP_vaddsub(const float *__I0, vDSP_Stride __I0S, const float *__I1, vDSP_Stride __I1S, float *__O0, vDSP_Stride __O0S, float *__O1, vDSP_Stride __O1S, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vaddsub) Calculates the single-precision element-wise sum and subtraction of two vectors, using the specified stride. [`void vDSP_vaddsubD(const double *__I0, vDSP_Stride __I0S, const double *__I1, vDSP_Stride __I1S, double *__O0, vDSP_Stride __O0S, double *__O1, vDSP_Stride __O1S, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vaddsubD) Calculates the double-precision element-wise sum and subtraction of two vectors, using the specified stride. ### Ternary add-multiply operations [`static func multiply(addition: (a: S, b: T), U) -> [Float]`](/documentation/Accelerate/vDSP/multiply(addition:_:)-7t59) Returns the single-precision element-wise product of a vector and the sum of two vectors. [`static func multiply(addition: (a: S, b: T), U) -> [Double]`](/documentation/Accelerate/vDSP/multiply(addition:_:)-1wt61) Returns the double-precision element-wise product of a vector and the sum of two vectors. [`static func multiply(addition: (a: S, b: T), U, result: inout V)`](/documentation/Accelerate/vDSP/multiply(addition:_:result:)-3jqts) Calculates the single-precision element-wise product of a vector and the sum of two vectors. [`static func multiply(addition: (a: S, b: T), U, result: inout V)`](/documentation/Accelerate/vDSP/multiply(addition:_:result:)-5sqwo) Calculates the double-precision element-wise product of a vector and the sum of two vectors. [`extern void vDSP_vam(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, const float *__C, vDSP_Stride __IC, float *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vam) Calculates the single-precision element-wise product of a vector and the sum of two vectors, using the specified stride. [`extern void vDSP_vamD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, const double *__C, vDSP_Stride __IC, double *__D, vDSP_Stride __IDD, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vamD) Calculates the double-precision element-wise product of a vector and the sum of two vectors, using the specified stride. ### Ternary multiply-add operations [`static func add(multiplication: (a: S, b: T), U) -> [Float]`](/documentation/Accelerate/vDSP/add(multiplication:_:)-9bgb2) Returns the single-precision element-wise sum of a vector and the product of two vectors. [`static func add(multiplication: (a: S, b: T), U) -> [Double]`](/documentation/Accelerate/vDSP/add(multiplication:_:)-4667v) Returns the double-precision element-wise sum of a vector and the product of two vectors. [`static func add(multiplication: (a: S, b: T), U, result: inout V)`](/documentation/Accelerate/vDSP/add(multiplication:_:result:)-1srn8) Calculates the single-precision element-wise sum of a vector and the product of two vectors. [`static func add(multiplication: (a: S, b: T), U, result: inout V)`](/documentation/Accelerate/vDSP/add(multiplication:_:result:)-48vyq) Calculates the double-precision element-wise sum of a vector and the product of two vectors. [`extern void vDSP_vma(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, const float *__C, vDSP_Stride __IC, float *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vma) Calculates the single-precision element-wise sum of a vector and the product of two vectors, using the specified stride. [`extern void vDSP_vmaD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, const double *__C, vDSP_Stride __IC, double *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vmaD) Calculates the double-precision element-wise sum of a vector and the product of two vectors, using the specified stride. ### Ternary multiply-subtract operations [`static func subtract(multiplication: (a: T, b: U), S) -> [Float]`](/documentation/Accelerate/vDSP/subtract(multiplication:_:)-6u3sp) Returns the single-precision element-wise difference of a vector and the product of two vectors. [`static func subtract(multiplication: (a: T, b: U), S) -> [Double]`](/documentation/Accelerate/vDSP/subtract(multiplication:_:)-9gphg) Returns the double-precision element-wise difference of a vector and the product of two vectors. [`static func subtract(multiplication: (a: T, b: U), S, result: inout V)`](/documentation/Accelerate/vDSP/subtract(multiplication:_:result:)-6b91s) Calculates the single-precision element-wise difference of a vector and the product of two vectors. [`static func subtract(multiplication: (a: T, b: U), S, result: inout V)`](/documentation/Accelerate/vDSP/subtract(multiplication:_:result:)-3f2bw) Calculates the double-precision element-wise difference of a vector and the product of two vectors. [`extern void vDSP_vmsb(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, const float *__C, vDSP_Stride __IC, float *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vmsb) Calculates the single-precision element-wise difference of a vector and the product of two vectors, using the specified stride. [`extern void vDSP_vmsbD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, const double *__C, vDSP_Stride __IC, double *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vmsbD) Calculates the double-precision element-wise difference of a vector and the product of two vectors, using the specified stride. ### Ternary subtract-multiply operations [`static func multiply(subtraction: (a: S, b: T), U) -> [Float]`](/documentation/Accelerate/vDSP/multiply(subtraction:_:)-6y7g6) Returns the single-precision element-wise product of a vector and the differences of two vectors. [`static func multiply(subtraction: (a: S, b: T), U) -> [Double]`](/documentation/Accelerate/vDSP/multiply(subtraction:_:)-8a8sr) Returns the double-precision element-wise product of a vector and the differences of two vectors. [`static func multiply(subtraction: (a: S, b: T), U, result: inout V)`](/documentation/Accelerate/vDSP/multiply(subtraction:_:result:)-36flg) Calculates the single-precision element-wise product of a vector and the differences of two vectors. [`static func multiply(subtraction: (a: S, b: T), U, result: inout V)`](/documentation/Accelerate/vDSP/multiply(subtraction:_:result:)-ziw4) Calculates the double-precision element-wise product of a vector and the differences of two vectors. [`extern void vDSP_vsbm(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, const float *__C, vDSP_Stride __IC, float *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsbm) Calculates the single-precision element-wise product of a vector and the differences of two vectors, using the specified stride. [`extern void vDSP_vsbmD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, const double *__C, vDSP_Stride __IC, double *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsbmD) Calculates the double-precision element-wise product of a vector and the differences of two vectors, using the specified stride. ### Quaternary multiply-multiply-add operations [`extern void vDSP_vmma(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, const float *__C, vDSP_Stride __IC, const float *__D, vDSP_Stride __ID, float *__E, vDSP_Stride __IE, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vmma) Calculates the single-precision element-wise sum of the products of two pairs of vectors, using the specified stride. [`extern void vDSP_vmmaD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, const double *__C, vDSP_Stride __IC, const double *__D, vDSP_Stride __ID, double *__E, vDSP_Stride __IE, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vmmaD) Calculates the double-precision element-wise sum of the products of two pairs of vectors, using the specified stride. ### Quaternary multiply-multiply-subtract operations [`static func subtract(multiplication: (a: T, b: U), multiplication: (c: R, d: S)) -> [Float]`](/documentation/Accelerate/vDSP/subtract(multiplication:multiplication:)-1ghyu) Returns the single-precision element-wise difference of the products of two pairs of vectors. [`static func subtract(multiplication: (a: T, b: U), multiplication: (c: R, d: S)) -> [Double]`](/documentation/Accelerate/vDSP/subtract(multiplication:multiplication:)-22a4b) Returns the double-precision element-wise difference of the products of two pairs of vectors. [`static func subtract(multiplication: (a: T, b: U), multiplication: (c: R, d: S), result: inout V)`](/documentation/Accelerate/vDSP/subtract(multiplication:multiplication:result:)-8ofjj) Calculates the single-precision element-wise difference of the products of two pairs of vectors. [`static func subtract(multiplication: (a: T, b: U), multiplication: (c: R, d: S), result: inout V)`](/documentation/Accelerate/vDSP/subtract(multiplication:multiplication:result:)-48y6i) Calculates the double-precision element-wise difference of the products of two pairs of vectors. [`extern void vDSP_vmmsb(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, const float *__C, vDSP_Stride __IC, const float *__D, vDSP_Stride __ID, float *__E, vDSP_Stride __IE, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vmmsb) Calculates the single-precision element-wise difference of the products of two pairs of vectors, using the specified stride. [`extern void vDSP_vmmsbD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, const double *__C, vDSP_Stride __IC, const double *__D, vDSP_Stride __ID, double *__E, vDSP_Stride __IE, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vmmsbD) Calculates the double-precision element-wise difference of the products of two pairs of vectors, using the specified stride. ### Quaternary add-add-multiply operations [`static func multiply(addition: (a: S, b: T), addition: (c: U, d: U)) -> [Float]`](/documentation/Accelerate/vDSP/multiply(addition:addition:)-1voy8) Returns the single-precision element-wise product of the sums of two pairs of vectors. [`static func multiply(addition: (a: S, b: T), addition: (c: U, d: U)) -> [Double]`](/documentation/Accelerate/vDSP/multiply(addition:addition:)-7rs) Returns the double-precision element-wise product of the sums of two pairs of vectors. [`static func multiply(addition: (a: S, b: T), addition: (c: U, d: U), result: inout V)`](/documentation/Accelerate/vDSP/multiply(addition:addition:result:)-7p21q) Calculates the single-precision element-wise product of the sums of two pairs of vectors. [`static func multiply(addition: (a: S, b: T), addition: (c: U, d: U), result: inout V)`](/documentation/Accelerate/vDSP/multiply(addition:addition:result:)-89hgk) Calculates the double-precision element-wise product of the sums of two pairs of vectors. [`extern void vDSP_vaam(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, const float *__C, vDSP_Stride __IC, const float *__D, vDSP_Stride __ID, float *__E, vDSP_Stride __IE, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vaam) Calculates the single-precision element-wise product of the sums of two pairs of vectors, using the specified stride. [`extern void vDSP_vaamD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, const double *__C, vDSP_Stride __IC, const double *__D, vDSP_Stride __ID, double *__E, vDSP_Stride __IE, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vaamD) Calculates the double-precision element-wise product of the sums of two pairs of vectors, using the specified stride. ### Quaternary subtract-subtract-multiply operations [`static func multiply(subtraction: (a: R, b: S), subtraction: (c: T, d: U)) -> [Float]`](/documentation/Accelerate/vDSP/multiply(subtraction:subtraction:)-1rnom) Returns the single-precision element-wise product of the differences of two pairs of vectors. [`static func multiply(subtraction: (a: R, b: S), subtraction: (c: T, d: U)) -> [Double]`](/documentation/Accelerate/vDSP/multiply(subtraction:subtraction:)-5pv8p) Returns the double-precision element-wise product of the differences of two pairs of vectors. [`static func multiply(subtraction: (a: R, b: S), subtraction: (c: T, d: U), result: inout V)`](/documentation/Accelerate/vDSP/multiply(subtraction:subtraction:result:)-rubk) Calculates the single-precision element-wise product of the differences of two pairs of vectors. [`static func multiply(subtraction: (a: R, b: S), subtraction: (c: T, d: U), result: inout V)`](/documentation/Accelerate/vDSP/multiply(subtraction:subtraction:result:)-4jjy5) Calculates the double-precision element-wise product of the differences of two pairs of vectors. [`extern void vDSP_vsbsbm(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, const float *__C, vDSP_Stride __IC, const float *__D, vDSP_Stride __ID, float *__E, vDSP_Stride __IE, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsbsbm) Calculates the single-precision element-wise product of the differences of two pairs of vectors, using the specified stride. [`extern void vDSP_vsbsbmD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, const double *__C, vDSP_Stride __IC, const double *__D, vDSP_Stride __ID, double *__E, vDSP_Stride __IE, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsbsbmD) Calculates the double-precision element-wise product of the differences of two pairs of vectors, using the specified stride. ### Quaternary add-subtract-multiply operations [`static func multiply(addition: (a: R, b: S), subtraction: (c: T, d: U)) -> [Float]`](/documentation/Accelerate/vDSP/multiply(addition:subtraction:)-6h89l) Returns the single-precision element-wise product of the sum of two vectors and the difference of two vectors. [`static func multiply(addition: (a: R, b: S), subtraction: (c: T, d: U)) -> [Double]`](/documentation/Accelerate/vDSP/multiply(addition:subtraction:)-7qfik) Returns the double-precision element-wise product of the sum of two vectors and the difference of two vectors. [`static func multiply(addition: (a: R, b: S), subtraction: (c: T, d: U), result: inout V)`](/documentation/Accelerate/vDSP/multiply(addition:subtraction:result:)-j688) Calculates the double-precision element-wise product of the sum of two vectors and the difference of two vectors. [`static func multiply(addition: (a: R, b: S), subtraction: (c: T, d: U), result: inout V)`](/documentation/Accelerate/vDSP/multiply(addition:subtraction:result:)-2rldl) Calculates the double-precision element-wise product of the sum of two vectors and the difference of two vectors. [`extern void vDSP_vasbm(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, const float *__C, vDSP_Stride __IC, const float *__D, vDSP_Stride __ID, float *__E, vDSP_Stride __IE, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vasbm) Calculates the double-precision element-wise product of the sum of two vectors and the difference of two vectors, using the specified stride. [`extern void vDSP_vasbmD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, const double *__C, vDSP_Stride __IC, const double *__D, vDSP_Stride __ID, double *__E, vDSP_Stride __IE, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vasbmD) Calculates the double-precision element-wise product of the sum of two vectors and the difference of two vectors, using the specified stride. --- Copyright © 2026 Apple Inc. All rights reserved. | [Terms of Use](https://www.apple.com/legal/internet-services/terms/site.html) | [Privacy Policy](https://www.apple.com/privacy/privacy-policy)