# Vector-scalar real arithmetic functions Perform element-wise operations on combinations of vectors of real values and scalar 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 ### Vector-scalar addition operations [`static func add(Float, U) -> [Float]`](/documentation/Accelerate/vDSP/add(_:_:)-53nh9) Returns the single-precision element-wise sum of a vector and a scalar value. [`static func add(Double, U) -> [Double]`](/documentation/Accelerate/vDSP/add(_:_:)-9mv1a) Returns the double-precision element-wise sum of a vector and a scalar value. [`static func add(Float, U, result: inout V)`](/documentation/Accelerate/vDSP/add(_:_:result:)-2w0o9) Calculates the single-precision element-wise sum of a vector and a scalar value. [`static func add(Double, U, result: inout V)`](/documentation/Accelerate/vDSP/add(_:_:result:)-2531u) Calculates the single-precision element-wise sum of a vector and a scalar value. [`extern void vDSP_vsaddi(const int *__A, vDSP_Stride __IA, const int *__B, int *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsaddi) Calculates the integer element-wise sum of a vector and a scalar value, using the specified stride. [`extern void vDSP_vsadd(const float *__A, vDSP_Stride __IA, const float *__B, float *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsadd) Calculates the single-precision element-wise sum of a vector and a scalar value, using the specified stride. [`extern void vDSP_vsaddD(const double *__A, vDSP_Stride __IA, const double *__B, double *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsaddD) Calculates the double-precision element-wise sum of a vector and a scalar value, using the specified stride. ### Vector-scalar multiplication operations [`static func multiply(Float, U) -> [Float]`](/documentation/Accelerate/vDSP/multiply(_:_:)-993yp) Returns the single-precision element-wise product of a vector and a scalar value. [`static func multiply(Double, U) -> [Double]`](/documentation/Accelerate/vDSP/multiply(_:_:)-9dxnc) Returns the double-precision element-wise product of a vector and a scalar value. [`static func multiply(Float, U, result: inout V)`](/documentation/Accelerate/vDSP/multiply(_:_:result:)-358cn) Calculates the single-precision element-wise product of a vector and a scalar value. [`static func multiply(Double, U, result: inout V)`](/documentation/Accelerate/vDSP/multiply(_:_:result:)-4xorc) Calculates the double-precision element-wise product of a vector and a scalar value. [`extern void vDSP_vsmul(const float *__A, vDSP_Stride __IA, const float *__B, float *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsmul) Calculates the single-precision element-wise product of a vector and a scalar value, using the specified stride. [`extern void vDSP_vsmulD(const double *__A, vDSP_Stride __IA, const double *__B, double *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsmulD) Calculates the double-precision element-wise product of a vector and a scalar value, using the specified stride. ### Vector-scalar division operations [`static func divide(U, Float) -> [Float]`](/documentation/Accelerate/vDSP/divide(_:_:)-1uqmz) Calculates the single-precision element-wise division of a vector and a scalar value. [`static func divide(U, Double) -> [Double]`](/documentation/Accelerate/vDSP/divide(_:_:)-9nb4j) Calculates the double-precision element-wise division of a vector and a scalar value. [`static func divide(U, Float, result: inout V)`](/documentation/Accelerate/vDSP/divide(_:_:result:)-5hwb2) Calculates the single-precision element-wise division of a vector and a scalar value. [`static func divide(U, Double, result: inout V)`](/documentation/Accelerate/vDSP/divide(_:_:result:)-44mff) Calculates the double-precision element-wise division of a vector and a scalar value. [`extern void vDSP_vsdivi(const int *__A, vDSP_Stride __IA, const int *__B, int *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsdivi) Calculates the integer element-wise division of a vector and a scalar value, using the specified stride. [`extern void vDSP_vsdiv(const float *__A, vDSP_Stride __IA, const float *__B, float *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsdiv) Calculates the single-precision element-wise division of a vector and a scalar value, using the specified stride. [`extern void vDSP_vsdivD(const double *__A, vDSP_Stride __IA, const double *__B, double *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsdivD) Calculates the double-precision element-wise division of a vector and a scalar value, using the specified stride. ### Scalar-vector division operations [`static func divide(Float, U) -> [Float]`](/documentation/Accelerate/vDSP/divide(_:_:)-70npt) Returns the single-precision element-wise division of a scalar value and a vector. [`static func divide(Double, U) -> [Double]`](/documentation/Accelerate/vDSP/divide(_:_:)-73m8v) Returns the double-precision element-wise division of a scalar value and a vector. [`static func divide(Float, U, result: inout V)`](/documentation/Accelerate/vDSP/divide(_:_:result:)-3emlk) Calculates the single-precision element-wise division of a scalar value and a vector. [`static func divide(Double, U, result: inout V)`](/documentation/Accelerate/vDSP/divide(_:_:result:)-18qa3) Calculates the double-precision element-wise division of a scalar value and a vector. [`extern void vDSP_svdiv(const float *__A, const float *__B, vDSP_Stride __IB, float *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_svdiv) Calculates the single-precision element-wise division of a scalar value and a vector, using the specified stride. [`extern void vDSP_svdivD(const double *__A, const double *__B, vDSP_Stride __IB, double *__C, vDSP_Stride __IC, vDSP_Length __N);`](/documentation/Accelerate/vDSP_svdivD) Calculates the double-precision element-wise division of a scalar value and a vector, using the specified stride. ### Vector-vector-scalar add-multiply operations [`static func multiply(addition: (a: T, b: U), Float) -> [Float]`](/documentation/Accelerate/vDSP/multiply(addition:_:)-4fnbx) Returns the single-precision element-wise product of the sum of two vectors and a scalar value. [`static func multiply(addition: (a: T, b: U), Double) -> [Double]`](/documentation/Accelerate/vDSP/multiply(addition:_:)-4c9in) Returns the double-precision element-wise product of the sum of two vectors and a scalar value. [`static func multiply(addition: (a: T, b: U), Float, result: inout V)`](/documentation/Accelerate/vDSP/multiply(addition:_:result:)-6x7xq) Calculates the single-precision element-wise product of the sum of two vectors and a scalar value. [`static func multiply(addition: (a: T, b: U), Double, result: inout V)`](/documentation/Accelerate/vDSP/multiply(addition:_:result:)-7dujy) Calculates the double-precision element-wise product of the sum of two vectors and a scalar value. [`extern void vDSP_vasm(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, const float *__C, float *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vasm) Calculates the single-precision element-wise product of the sum of two vectors and a scalar value, using the specified stride. [`extern void vDSP_vasmD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, const double *__C, double *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vasmD) Calculates the double-precision element-wise product of the sum of two vectors and a scalar value, using the specified stride. ### Vector-vector-scalar subtract-multiply operations [`static func multiply(subtraction: (a: T, b: U), Float) -> [Float]`](/documentation/Accelerate/vDSP/multiply(subtraction:_:)-106pt) Returns the single-precision element-wise product of the difference of two vectors and a scalar value. [`static func multiply(subtraction: (a: T, b: U), Double) -> [Double]`](/documentation/Accelerate/vDSP/multiply(subtraction:_:)-3gxn3) Returns the double-precision element-wise product of the difference of two vectors and a scalar value. [`static func multiply(subtraction: (a: T, b: U), Float, result: inout V)`](/documentation/Accelerate/vDSP/multiply(subtraction:_:result:)-5l106) Calculates the single-precision element-wise product of the difference of two vectors and a scalar value. [`static func multiply(subtraction: (a: T, b: U), Double, result: inout V)`](/documentation/Accelerate/vDSP/multiply(subtraction:_:result:)-lhn7) Calculates the double-precision element-wise product of the difference of two vectors and a scalar value. [`extern void vDSP_vsbsm(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, const float *__C, float *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsbsm) Calculates the single-precision element-wise product of the difference of two vectors and a scalar value, using the specified stride. [`extern void vDSP_vsbsmD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, const double *__C, double *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsbsmD) Calculates the double-precision element-wise product of the difference of two vectors and a scalar value, using the specified stride. ### Vector-scalar-vector multiply-subtract operations [`static func subtract(multiplication: (a: U, b: Float), T) -> [Float]`](/documentation/Accelerate/vDSP/subtract(multiplication:_:)-3zm6l) Calculates the single-precision element-wise difference of the product of a vector and a scalar value, and a vector. [`static func subtract(multiplication: (a: U, b: Double), T) -> [Double]`](/documentation/Accelerate/vDSP/subtract(multiplication:_:)-2hhme) Calculates the double-precision element-wise difference of the product of a vector and a scalar value, and a vector. [`static func subtract(multiplication: (a: U, b: Float), T, result: inout V)`](/documentation/Accelerate/vDSP/subtract(multiplication:_:result:)-86gx3) Calculates the single-precision element-wise difference of the product of a vector and a scalar value, and a vector. [`static func subtract(multiplication: (a: U, b: Double), T, result: inout V)`](/documentation/Accelerate/vDSP/subtract(multiplication:_:result:)-9p12h) Calculates the double-precision element-wise difference of the product of a vector and a scalar value, and a vector. [`extern void vDSP_vsmsb(const float *__A, vDSP_Stride __IA, const float *__B, const float *__C, vDSP_Stride __IC, float *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsmsb) Calculates the single-precision element-wise difference of the product of a vector and a scalar value, and a vector, using the specified stride. [`extern void vDSP_vsmsbD(const double *__A, vDSP_Stride __IA, const double *__B, const double *__C, vDSP_Stride __IC, double *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsmsbD) Calculates the double-precision element-wise difference of the product of a vector and a scalar value, and a vector, using the specified stride. ### Vector-vector-scalar multiply-add operations [`static func add(multiplication: (a: T, b: U), Float) -> [Float]`](/documentation/Accelerate/vDSP/add(multiplication:_:)-36vhq) Returns the single-precision element-wise sum of the product of two vectors, and a scalar value. [`static func add(multiplication: (a: T, b: U), Double) -> [Double]`](/documentation/Accelerate/vDSP/add(multiplication:_:)-9dxlr) Returns the double-precision element-wise sum of the product of two vectors, and a scalar value. [`static func add(multiplication: (a: T, b: U), Float, result: inout V)`](/documentation/Accelerate/vDSP/add(multiplication:_:result:)-8dau) Calculates the single-precision element-wise sum of the product of two vectors, and a scalar value. [`static func add(multiplication: (a: T, b: U), Double, result: inout V)`](/documentation/Accelerate/vDSP/add(multiplication:_:result:)-2wpvw) Calculates the double-precision element-wise sum of the product of two vectors, and a scalar value. [`extern void vDSP_vmsa(const float *__A, vDSP_Stride __IA, const float *__B, vDSP_Stride __IB, const float *__C, float *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vmsa) Calculates the single-precision element-wise sum of the product of two vectors, and a scalar value, using the specified stride. [`extern void vDSP_vmsaD(const double *__A, vDSP_Stride __IA, const double *__B, vDSP_Stride __IB, const double *__C, double *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vmsaD) Calculates the double-precision element-wise sum of the product of two vectors, and a scalar value, using the specified stride. ### Vector-scalar-vector multiply-add operations [`static func add(multiplication: (a: T, b: Float), U) -> [Float]`](/documentation/Accelerate/vDSP/add(multiplication:_:)-7aut1) Returns the single-precision element-wise addition of the product of a vector and a scalar value, and a vector. [`static func add(multiplication: (a: T, b: Double), U) -> [Double]`](/documentation/Accelerate/vDSP/add(multiplication:_:)-1bsuq) Returns the double-precision element-wise addition of the product of a vector and a scalar value, and a vector. [`static func add(multiplication: (a: T, b: Float), U, result: inout V)`](/documentation/Accelerate/vDSP/add(multiplication:_:result:)-6n4jf) Calculates the single-precision element-wise addition of the product of a vector and a scalar value, and a vector. [`static func add(multiplication: (a: T, b: Double), U, result: inout V)`](/documentation/Accelerate/vDSP/add(multiplication:_:result:)-2i5om) Calculates the double-precision element-wise addition of the product of a vector and a scalar value, and a vector. [`extern void vDSP_vsma(const float *__A, vDSP_Stride __IA, const float *__B, const float *__C, vDSP_Stride __IC, float *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsma) Calculates the single-precision element-wise addition of the product of a vector and a scalar value, and a vector, using the specified stride. [`extern void vDSP_vsmaD(const double *__A, vDSP_Stride __IA, const double *__B, const double *__C, vDSP_Stride __IC, double *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsmaD) Calculates the double-precision element-wise addition of the product of a vector and a scalar value, and a vector, using the specified stride. ### Vector-scalar-scalar multiply-add operations [`static func add(multiplication: (a: U, b: Float), Float) -> [Float]`](/documentation/Accelerate/vDSP/add(multiplication:_:)-3tw93) Returns the single-precision element-wise addition of the product of a vector and a scalar value, and a vector. [`static func add(multiplication: (a: U, b: Double), Double) -> [Double]`](/documentation/Accelerate/vDSP/add(multiplication:_:)-4e3tj) Returns the double-precision element-wise addition of the product of a vector and a scalar value, and a vector. [`static func add(multiplication: (a: U, b: Float), Float, result: inout V)`](/documentation/Accelerate/vDSP/add(multiplication:_:result:)-1rob9) Calculates the single-precision element-wise addition of the product of a vector and a scalar value, and a scalar. [`static func add(multiplication: (a: U, b: Double), Double, result: inout V)`](/documentation/Accelerate/vDSP/add(multiplication:_:result:)-8ixx9) Calculates the double-precision element-wise addition of the product of a vector and a scalar value, and a scalar. [`extern void vDSP_vsmsa(const float *__A, vDSP_Stride __IA, const float *__B, const float *__C, float *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsmsa) Calculates the single-precision element-wise addition of the product of a vector and a scalar value, and a scalar value, using the specified stride. [`extern void vDSP_vsmsaD(const double *__A, vDSP_Stride __IA, const double *__B, const double *__C, double *__D, vDSP_Stride __ID, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsmsaD) Calculates the double-precision element-wise addition of the product of a vector and a scalar value, and a scalar value, using the specified stride. ### Vector-scalar-vector-scalar multiply-multiply-add operations [`static func add(multiplication: (a: T, b: Float), multiplication: (c: U, d: Float)) -> [Float]`](/documentation/Accelerate/vDSP/add(multiplication:multiplication:)-8rjh8) Returns the single-precision element-wise addition of two vector-scalar products. [`static func add(multiplication: (a: T, b: Double), multiplication: (c: U, d: Double)) -> [Double]`](/documentation/Accelerate/vDSP/add(multiplication:multiplication:)-563ub) Returns the double-precision element-wise addition of two vector-scalar products. [`static func add(multiplication: (a: T, b: Float), multiplication: (c: U, d: Float), result: inout V)`](/documentation/Accelerate/vDSP/add(multiplication:multiplication:result:)-663mk) Calculates the single-precision element-wise addition of two vector-scalar products. [`static func add(multiplication: (a: T, b: Double), multiplication: (c: U, d: Double), result: inout V)`](/documentation/Accelerate/vDSP/add(multiplication:multiplication:result:)-9xe8k) Calculates the double-precision element-wise addition of two vector-scalar products. [`extern void vDSP_vsmsma(const float *__A, vDSP_Stride __IA, const float *__B, const float *__C, vDSP_Stride __IC, const float *__D, float *__E, vDSP_Stride __IE, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsmsma) Calculates the single-precision element-wise addition of two vector-scalar products, using the specified stride. [`extern void vDSP_vsmsmaD(const double *__A, vDSP_Stride __IA, const double *__B, const double *__C, vDSP_Stride __IC, const double *__D, double *__E, vDSP_Stride __IE, vDSP_Length __N);`](/documentation/Accelerate/vDSP_vsmsmaD) Calculates the double-precision element-wise addition of two vector-scalar products, 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)