diff --git a/candle-core/examples/llama/main.rs b/candle-core/examples/llama/main.rs
index eb681f4b..3fc893e3 100644
--- a/candle-core/examples/llama/main.rs
+++ b/candle-core/examples/llama/main.rs
@@ -487,6 +487,7 @@ fn main() -> Result<()> {
     let mut rng = thread_rng();
     let start_gen = std::time::Instant::now();
     for index in 0..args.sample_len {
+        let start_gen = std::time::Instant::now();
         let ctxt = &tokens[tokens.len().saturating_sub(CONTEXT_SIZE)..];
         let input = Tensor::new(ctxt, &device)?;
         let logits = llama.forward(&input, &freqs_cis)?;
@@ -496,6 +497,7 @@ fn main() -> Result<()> {
         let next_token = distr.sample(&mut rng) as u32;
         tokens.push(next_token);
         new_tokens.push(next_token);
+        println!("> {:?}", start_gen.elapsed());
         println!(
             "{} token: {} '{}'",
             index + 1,
diff --git a/candle-core/src/cuda_backend.rs b/candle-core/src/cuda_backend.rs
index 9d9a5f99..40b7e67f 100644
--- a/candle-core/src/cuda_backend.rs
+++ b/candle-core/src/cuda_backend.rs
@@ -1,7 +1,9 @@
-use crate::{CpuStorage, DType, Layout, Shape};
+use crate::{CpuStorage, DType, Layout, Shape, WithDType};
 use candle_kernels as kernels;
 use cudarc::cublas::{Gemm, GemmConfig, StridedBatchedConfig};
-use cudarc::driver::{CudaFunction, CudaSlice, DeviceSlice, LaunchAsync, LaunchConfig};
+use cudarc::driver::{
+    CudaFunction, CudaSlice, DeviceRepr, DeviceSlice, LaunchAsync, LaunchConfig, ValidAsZeroBits,
+};
 use half::{bf16, f16};
 use std::sync::Arc;
 
@@ -242,6 +244,260 @@ enum CudaStorageSlice {
     F32(CudaSlice<f32>),
     F64(CudaSlice<f64>),
 }
+type S = CudaStorageSlice;
+
+trait Map1 {
+    fn f<T: DeviceRepr + WithDType + ValidAsZeroBits>(
+        &self,
+        src: &CudaSlice<T>,
+        dev: &CudaDevice,
+        layout: &Layout,
+    ) -> Result<CudaSlice<T>>;
+
+    fn map(&self, s: &S, d: &CudaDevice, l: &Layout) -> Result<S> {
+        let out = match s {
+            S::U32(s) => S::U32(self.f(s, d, l)?),
+            S::BF16(s) => S::BF16(self.f(s, d, l)?),
+            S::F16(s) => S::F16(self.f(s, d, l)?),
+            S::F32(s) => S::F32(self.f(s, d, l)?),
+            S::F64(s) => S::F64(self.f(s, d, l)?),
+        };
+        Ok(out)
+    }
+}
+
+trait Map2 {
+    fn f<T: DeviceRepr + WithDType + ValidAsZeroBits>(
+        &self,
+        src1: &CudaSlice<T>,
+        layout1: &Layout,
+        src2: &CudaSlice<T>,
+        layout2: &Layout,
+        dev: &CudaDevice,
+    ) -> Result<CudaSlice<T>>;
+
+    fn map(&self, s1: &S, l1: &Layout, s2: &S, l2: &Layout, d: &CudaDevice) -> Result<S> {
+        let out = match (s1, s2) {
+            (S::U32(s1), S::U32(s2)) => S::U32(self.f(s1, l1, s2, l2, d)?),
+            (S::BF16(s1), S::BF16(s2)) => S::BF16(self.f(s1, l1, s2, l2, d)?),
+            (S::F16(s1), S::F16(s2)) => S::F16(self.f(s1, l1, s2, l2, d)?),
+            (S::F32(s1), S::F32(s2)) => S::F32(self.f(s1, l1, s2, l2, d)?),
+            (S::F64(s1), S::F64(s2)) => S::F64(self.f(s1, l1, s2, l2, d)?),
+            _ => return Err(CudaError::InternalError("dtype mismatch in binary op")),
+        };
+        Ok(out)
+    }
+}
+
+struct Clone;
+impl Map1 for Clone {
+    fn f<T: DeviceRepr>(
+        &self,
+        s: &CudaSlice<T>,
+        _: &CudaDevice,
+        _: &Layout,
+    ) -> Result<CudaSlice<T>> {
+        Ok(s.try_clone()?)
+    }
+}
+
+fn kernel_name<T: WithDType>(root: &str) -> String {
+    let dtype = T::DTYPE.as_str();
+    format!("{root}_{dtype}")
+}
+
+struct Affine(f64, f64);
+impl Map1 for Affine {
+    fn f<T: DeviceRepr + WithDType>(
+        &self,
+        src: &CudaSlice<T>,
+        dev: &CudaDevice,
+        layout: &Layout,
+    ) -> Result<CudaSlice<T>> {
+        let shape = layout.shape();
+        let dims = shape.dims();
+        let el = shape.elem_count();
+        let cfg = LaunchConfig::for_num_elems(el as u32);
+        let ds = dev.htod_copy([dims, layout.stride()].concat())?;
+        let src = &src.slice(layout.start_offset()..);
+        let func = dev.get_or_load_func(&kernel_name::<T>("affine"), kernels::AFFINE)?;
+        // SAFETY: Set later by running the kernel.
+        let out = unsafe { dev.alloc::<T>(el) }?;
+        let params = (
+            el,
+            dims.len(),
+            &ds,
+            src,
+            &out,
+            T::from_f64(self.0),
+            T::from_f64(self.1),
+        );
+        // SAFETY: ffi.
+        unsafe { func.launch(cfg, params) }?;
+        Ok(out)
+    }
+}
+
+struct Sum<'a>(&'a [usize]);
+impl<'a> Map1 for Sum<'a> {
+    fn f<T: DeviceRepr + WithDType + ValidAsZeroBits>(
+        &self,
+        src: &CudaSlice<T>,
+        dev: &CudaDevice,
+        layout: &Layout,
+    ) -> Result<CudaSlice<T>> {
+        let shape = layout.shape();
+        let src_dims = shape.dims();
+        let el = shape.elem_count();
+        let mut dst_el = el;
+        for &sum_dim in self.0.iter() {
+            dst_el /= src_dims[sum_dim];
+        }
+        let mut sum_dims = self.0.to_vec();
+        // Sort the sum_dims as they have to be processed from left to right when converting the
+        // indexes.
+        sum_dims.sort();
+        let sum_dims_l: Vec<usize> = sum_dims.iter().map(|&d| src_dims[d]).collect();
+        let sum_dims_s: Vec<usize> = sum_dims
+            .iter()
+            .map(|&d| src_dims[d + 1..].iter().product::<usize>())
+            .collect();
+        let cfg = LaunchConfig::for_num_elems(el as u32);
+        let ds = dev.htod_copy([src_dims, layout.stride(), &sum_dims_l, &sum_dims_s].concat())?;
+        let src = &src.slice(layout.start_offset()..);
+        let func = dev.get_or_load_func(&kernel_name::<T>("sum"), kernels::REDUCE)?;
+        let out = dev.alloc_zeros::<T>(dst_el)?;
+        let params = (el, src_dims.len(), sum_dims.len(), &ds, src, &out);
+        // SAFETY: ffi.
+        unsafe { func.launch(cfg, params) }?;
+        Ok(out)
+    }
+}
+
+impl<U: crate::op::UnaryOp> Map1 for U {
+    fn f<T: DeviceRepr + WithDType + ValidAsZeroBits>(
+        &self,
+        src: &CudaSlice<T>,
+        dev: &CudaDevice,
+        layout: &Layout,
+    ) -> Result<CudaSlice<T>> {
+        let shape = layout.shape();
+        let dims = shape.dims();
+        let el_count = shape.elem_count();
+        let cfg = LaunchConfig::for_num_elems(el_count as u32);
+        let ds = dev.htod_copy([dims, layout.stride()].concat())?;
+        let src = &src.slice(layout.start_offset()..);
+        let func = dev.get_or_load_func(&kernel_name::<T>(U::KERNEL), kernels::UNARY)?;
+        // SAFETY: Set later by running the kernel.
+        let out = unsafe { dev.alloc::<T>(el_count) }?;
+        let params = (el_count, dims.len(), &ds, src, &out);
+        // SAFETY: ffi.
+        unsafe { func.launch(cfg, params) }?;
+        Ok(out)
+    }
+}
+
+struct Embedding<'a>(&'a CudaStorage, &'a Layout);
+impl<'a> Map1 for Embedding<'a> {
+    fn f<T: DeviceRepr + WithDType + ValidAsZeroBits>(
+        &self,
+        rhs: &CudaSlice<T>,
+        dev: &CudaDevice,
+        rhs_l: &Layout,
+    ) -> Result<CudaSlice<T>> {
+        let ids_l = &self.1;
+        let ids = match &self.0.slice {
+            CudaStorageSlice::U32(slice) => slice.slice(ids_l.start_offset()..),
+            _ => Err(CudaError::UnexpectedDType {
+                msg: "embedding ids should be u32",
+                expected: DType::U32,
+                got: self.0.dtype(),
+            })?,
+        };
+        let ids = &ids;
+        let shape = ids_l.shape();
+        let (v_size, h_size) = rhs_l
+            .shape()
+            .r2()
+            .map_err(|e| CudaError::WrappedError(Box::new(e)))?;
+        let dims = shape.dims();
+        let el = shape.elem_count();
+        let cfg = LaunchConfig::for_num_elems(el as u32);
+        let ds = dev.htod_copy([dims, ids_l.stride()].concat())?;
+        let rhs = &rhs.slice(rhs_l.start_offset()..);
+        let func = dev.get_or_load_func(&kernel_name::<T>("emb"), kernels::EMBEDDINGS)?;
+        // SAFETY: Set later by running the kernel.
+        let out = unsafe { dev.alloc::<T>(el * h_size) }?;
+        let params = (el, dims.len(), &ds, ids, rhs, &out, h_size, v_size);
+        // SAFETY: ffi.
+        unsafe { func.launch(cfg, params) }?;
+        Ok(out)
+    }
+}
+
+struct WhereCond<'a>(&'a CudaStorage, &'a Layout);
+impl<'a> Map2 for WhereCond<'a> {
+    fn f<T: DeviceRepr + WithDType + ValidAsZeroBits>(
+        &self,
+        t: &CudaSlice<T>,
+        layout_t: &Layout,
+        f: &CudaSlice<T>,
+        layout_f: &Layout,
+        dev: &CudaDevice,
+    ) -> Result<CudaSlice<T>> {
+        let ids_l = &self.1;
+        let ids = match &self.0.slice {
+            CudaStorageSlice::U32(slice) => slice.slice(ids_l.start_offset()..),
+            _ => Err(CudaError::UnexpectedDType {
+                msg: "where conditions should be u32",
+                expected: DType::U32,
+                got: self.0.dtype(),
+            })?,
+        };
+        let ids = &ids;
+        let shape = ids_l.shape();
+        let dims = shape.dims();
+        let el = shape.elem_count();
+        let cfg = LaunchConfig::for_num_elems(el as u32);
+        let ds =
+            dev.htod_copy([dims, ids_l.stride(), layout_t.stride(), layout_f.stride()].concat())?;
+        let t = &t.slice(layout_t.start_offset()..);
+        let f = &f.slice(layout_f.start_offset()..);
+        let func = dev.get_or_load_func(&kernel_name::<T>("where"), kernels::TERNARY)?;
+        // SAFETY: Set later by running the kernel.
+        let out = unsafe { dev.alloc::<T>(el) }?;
+        let params = (el, dims.len(), &ds, ids, t, f, &out);
+        // SAFETY: ffi
+        unsafe { func.launch(cfg, params) }?;
+        Ok(out)
+    }
+}
+
+impl<U: crate::op::BinaryOp> Map2 for U {
+    fn f<T: DeviceRepr + WithDType + ValidAsZeroBits>(
+        &self,
+        lhs: &CudaSlice<T>,
+        lhs_l: &Layout,
+        rhs: &CudaSlice<T>,
+        rhs_l: &Layout,
+        dev: &CudaDevice,
+    ) -> Result<CudaSlice<T>> {
+        let shape = lhs_l.shape();
+        let dims = shape.dims();
+        let elem_count = shape.elem_count();
+        let cfg = LaunchConfig::for_num_elems(elem_count as u32);
+        let dims_and_strides = dev.htod_copy([dims, lhs_l.stride(), rhs_l.stride()].concat())?;
+        let lhs = &lhs.slice(lhs_l.start_offset()..);
+        let rhs = &rhs.slice(rhs_l.start_offset()..);
+        let func = dev.get_or_load_func(&kernel_name::<T>(U::KERNEL), kernels::BINARY)?;
+        // SAFETY: Set later by running the kernel.
+        let out = unsafe { dev.alloc::<T>(elem_count) }?;
+        let params = (elem_count, dims.len(), &dims_and_strides, lhs, rhs, &out);
+        // SAFETY: ffi
+        unsafe { func.launch(cfg, params) }?;
+        Ok(out)
+    }
+}
 
 fn slice_src_and_dst<'a, T>(
     src: &'a CudaSlice<T>,
@@ -332,14 +588,8 @@ fn gemm_config<T>(
 }
 
 impl CudaStorage {
-    pub fn try_clone(&self) -> Result<Self> {
-        let slice = match &self.slice {
-            CudaStorageSlice::U32(slice) => CudaStorageSlice::U32(slice.try_clone()?),
-            CudaStorageSlice::BF16(slice) => CudaStorageSlice::BF16(slice.try_clone()?),
-            CudaStorageSlice::F16(slice) => CudaStorageSlice::F16(slice.try_clone()?),
-            CudaStorageSlice::F32(slice) => CudaStorageSlice::F32(slice.try_clone()?),
-            CudaStorageSlice::F64(slice) => CudaStorageSlice::F64(slice.try_clone()?),
-        };
+    pub fn try_clone(&self, layout: &Layout) -> Result<Self> {
+        let slice = Clone.map(&self.slice, self.device(), layout)?;
         let device = self.device.clone();
         Ok(Self { slice, device })
     }
@@ -420,152 +670,14 @@ impl CudaStorage {
     }
 
     pub(crate) fn affine(&self, layout: &Layout, mul: f64, add: f64) -> Result<Self> {
-        let shape = layout.shape();
-        let dims = shape.dims();
-        let el_count = shape.elem_count();
-        let cfg = LaunchConfig::for_num_elems(el_count as u32);
-        let dev = self.device();
-        let ds = dev.htod_copy([dims, layout.stride()].concat())?;
-        let slice = match &self.slice {
-            CudaStorageSlice::U32(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func("affine_u32", kernels::AFFINE)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<u32>(el_count) }?;
-                let params = (el_count, dims.len(), &ds, arg, &out, mul as u32, add as u32);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::U32(out)
-            }
-            CudaStorageSlice::BF16(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func("affine_bf16", kernels::AFFINE)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<bf16>(el_count) }?;
-                let params = (
-                    el_count,
-                    dims.len(),
-                    &ds,
-                    arg,
-                    &out,
-                    bf16::from_f64(mul),
-                    bf16::from_f64(add),
-                );
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::BF16(out)
-            }
-            CudaStorageSlice::F16(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func("affine_f16", kernels::AFFINE)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f16>(el_count) }?;
-                let params = (
-                    el_count,
-                    dims.len(),
-                    &ds,
-                    arg,
-                    &out,
-                    f16::from_f64(mul),
-                    f16::from_f64(add),
-                );
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F16(out)
-            }
-            CudaStorageSlice::F32(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func("affine_f32", kernels::AFFINE)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f32>(el_count) }?;
-                let params = (el_count, dims.len(), &ds, arg, &out, mul as f32, add as f32);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F32(out)
-            }
-            CudaStorageSlice::F64(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func("affine_f64", kernels::AFFINE)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f64>(el_count) }?;
-                let params = (el_count, dims.len(), &ds, arg, &out, mul, add);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F64(out)
-            }
-        };
-        let device = dev.clone();
+        let device = self.device().clone();
+        let slice = Affine(mul, add).map(&self.slice, &device, layout)?;
         Ok(Self { slice, device })
     }
 
     pub(crate) fn sum(&self, layout: &Layout, sum_dims: &[usize]) -> Result<Self> {
-        let shape = layout.shape();
-        let src_dims = shape.dims();
-        let el = shape.elem_count();
-        let mut dst_el = el;
-        for &sum_dim in sum_dims.iter() {
-            dst_el /= src_dims[sum_dim];
-        }
-        let mut sum_dims = sum_dims.to_vec();
-        // Sort the sum_dims as they have to be processed from left to right when converting the
-        // indexes.
-        sum_dims.sort();
-        let sum_dims_l: Vec<usize> = sum_dims.iter().map(|&d| src_dims[d]).collect();
-        let sum_dims_s: Vec<usize> = sum_dims
-            .iter()
-            .map(|&d| src_dims[d + 1..].iter().product::<usize>())
-            .collect();
-        let cfg = LaunchConfig::for_num_elems(el as u32);
-        let dev = self.device();
-        let ds = dev.htod_copy([src_dims, layout.stride(), &sum_dims_l, &sum_dims_s].concat())?;
-        let slice = match &self.slice {
-            CudaStorageSlice::U32(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func("sum_u32", kernels::REDUCE)?;
-                let out = dev.alloc_zeros::<u32>(dst_el)?;
-                let params = (el, src_dims.len(), sum_dims.len(), &ds, arg, &out);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::U32(out)
-            }
-            CudaStorageSlice::BF16(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func("sum_bf16", kernels::REDUCE)?;
-                let out = dev.alloc_zeros::<bf16>(dst_el)?;
-                let params = (el, src_dims.len(), sum_dims.len(), &ds, arg, &out);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::BF16(out)
-            }
-            CudaStorageSlice::F16(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func("sum_f16", kernels::REDUCE)?;
-                let out = dev.alloc_zeros::<f16>(dst_el)?;
-                let params = (el, src_dims.len(), sum_dims.len(), &ds, arg, &out);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F16(out)
-            }
-            CudaStorageSlice::F32(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func("sum_f32", kernels::REDUCE)?;
-                let out = dev.alloc_zeros::<f32>(dst_el)?;
-                let params = (el, src_dims.len(), sum_dims.len(), &ds, arg, &out);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F32(out)
-            }
-            CudaStorageSlice::F64(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func("sum_f64", kernels::REDUCE)?;
-                let out = dev.alloc_zeros::<f64>(dst_el)?;
-                let params = (el, src_dims.len(), sum_dims.len(), &ds, arg, &out);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F64(out)
-            }
-        };
-        let device = dev.clone();
+        let device = self.device().clone();
+        let slice = Sum(sum_dims).map(&self.slice, &device, layout)?;
         Ok(Self { slice, device })
     }
 
@@ -576,58 +688,8 @@ impl CudaStorage {
     }
 
     pub(crate) fn unary_impl<U: crate::op::UnaryOp>(&self, layout: &Layout) -> Result<Self> {
-        let shape = layout.shape();
-        let dims = shape.dims();
-        let el_count = shape.elem_count();
-        let cfg = LaunchConfig::for_num_elems(el_count as u32);
-        let dev = &self.device;
-        let ds = dev.htod_copy([dims, layout.stride()].concat())?;
-        let slice = match &self.slice {
-            CudaStorageSlice::U32(_arg) => {
-                todo!("No unary kernels for u32");
-            }
-            CudaStorageSlice::BF16(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func(U::KERNEL_BF16, kernels::UNARY)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<bf16>(el_count) }?;
-                let params = (el_count, dims.len(), &ds, arg, &out);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::BF16(out)
-            }
-            CudaStorageSlice::F16(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func(U::KERNEL_F16, kernels::UNARY)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f16>(el_count) }?;
-                let params = (el_count, dims.len(), &ds, arg, &out);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F16(out)
-            }
-            CudaStorageSlice::F32(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func(U::KERNEL_F32, kernels::UNARY)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f32>(el_count) }?;
-                let params = (el_count, dims.len(), &ds, arg, &out);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F32(out)
-            }
-            CudaStorageSlice::F64(arg) => {
-                let arg = &arg.slice(layout.start_offset()..);
-                let func = dev.get_or_load_func(U::KERNEL_F64, kernels::UNARY)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f64>(el_count) }?;
-                let params = (el_count, dims.len(), &ds, arg, &out);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F64(out)
-            }
-        };
-        let device = dev.clone();
+        let device = self.device().clone();
+        let slice = U::V.map(&self.slice, &device, layout)?;
         Ok(Self { slice, device })
     }
 
@@ -637,72 +699,8 @@ impl CudaStorage {
         lhs_l: &Layout,
         rhs_l: &Layout,
     ) -> Result<Self> {
-        let shape = lhs_l.shape();
-        let dims = shape.dims();
-        let elem_count = shape.elem_count();
-        let cfg = LaunchConfig::for_num_elems(elem_count as u32);
-        let dev = self.device();
-        let dims_and_strides = dev.htod_copy([dims, lhs_l.stride(), rhs_l.stride()].concat())?;
-        let slice = match (&self.slice, &rhs.slice) {
-            (CudaStorageSlice::BF16(lhs), CudaStorageSlice::BF16(rhs)) => {
-                let lhs = &lhs.slice(lhs_l.start_offset()..);
-                let rhs = &rhs.slice(rhs_l.start_offset()..);
-                let func = dev.get_or_load_func(B::KERNEL_BF16, kernels::BINARY)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<bf16>(elem_count) }?;
-                let params = (elem_count, dims.len(), &dims_and_strides, lhs, rhs, &out);
-                // SAFETY: ffi
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::BF16(out)
-            }
-            (CudaStorageSlice::F16(lhs), CudaStorageSlice::F16(rhs)) => {
-                let lhs = &lhs.slice(lhs_l.start_offset()..);
-                let rhs = &rhs.slice(rhs_l.start_offset()..);
-                let func = dev.get_or_load_func(B::KERNEL_F16, kernels::BINARY)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f16>(elem_count) }?;
-                let params = (elem_count, dims.len(), &dims_and_strides, lhs, rhs, &out);
-                // SAFETY: ffi
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F16(out)
-            }
-            (CudaStorageSlice::F32(lhs), CudaStorageSlice::F32(rhs)) => {
-                let lhs = &lhs.slice(lhs_l.start_offset()..);
-                let rhs = &rhs.slice(rhs_l.start_offset()..);
-                let func = dev.get_or_load_func(B::KERNEL_F32, kernels::BINARY)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f32>(elem_count) }?;
-                let params = (elem_count, dims.len(), &dims_and_strides, lhs, rhs, &out);
-                // SAFETY: ffi
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F32(out)
-            }
-            (CudaStorageSlice::F64(lhs), CudaStorageSlice::F64(rhs)) => {
-                let lhs = &lhs.slice(lhs_l.start_offset()..);
-                let rhs = &rhs.slice(rhs_l.start_offset()..);
-                // SAFETY: Set later by running the kernel.
-                let func = dev.get_or_load_func(B::KERNEL_F64, kernels::BINARY)?;
-                let out = unsafe { dev.alloc::<f64>(elem_count) }?;
-                let params = (elem_count, dims.len(), &dims_and_strides, lhs, rhs, &out);
-                // SAFETY: ffi
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F64(out)
-            }
-            (CudaStorageSlice::U32(lhs), CudaStorageSlice::U32(rhs)) => {
-                let lhs = &lhs.slice(lhs_l.start_offset()..);
-                let rhs = &rhs.slice(rhs_l.start_offset()..);
-                // SAFETY: Set later by running the kernel.
-                let func = dev.get_or_load_func(B::KERNEL_U32, kernels::BINARY)?;
-                let out = unsafe { dev.alloc::<u32>(elem_count) }?;
-                let params = (elem_count, dims.len(), &dims_and_strides, lhs, rhs, &out);
-                // SAFETY: ffi
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::U32(out)
-            }
-            // The dtypes should have been checked at this point so this is an internal error.
-            _ => return Err(CudaError::InternalError("dtype mismatch in binary op")),
-        };
-        let device = dev.clone();
+        let device = self.device().clone();
+        let slice = B::V.map(&self.slice, lhs_l, &rhs.slice, rhs_l, &device)?;
         Ok(Self { slice, device })
     }
 
@@ -740,163 +738,18 @@ impl CudaStorage {
         &self,
         layout: &Layout,
         t: &Self,
-        layout_t: &Layout,
+        t_l: &Layout,
         f: &Self,
-        layout_f: &Layout,
+        f_l: &Layout,
     ) -> Result<Self> {
-        let ids = match &self.slice {
-            CudaStorageSlice::U32(slice) => slice.slice(layout.start_offset()..),
-            _ => Err(CudaError::UnexpectedDType {
-                msg: "where conditions should be u32",
-                expected: DType::U32,
-                got: self.dtype(),
-            })?,
-        };
-        let ids = &ids;
-        let shape = layout.shape();
-        let dims = shape.dims();
-        let el = shape.elem_count();
-        let cfg = LaunchConfig::for_num_elems(el as u32);
-        let dev = self.device();
-        let ds =
-            dev.htod_copy([dims, layout.stride(), layout_t.stride(), layout_f.stride()].concat())?;
-        let slice = match (&t.slice, &f.slice) {
-            (CudaStorageSlice::BF16(t), CudaStorageSlice::BF16(f)) => {
-                let t = &t.slice(layout_t.start_offset()..);
-                let f = &f.slice(layout_f.start_offset()..);
-                let func = dev.get_or_load_func("where_bf16", kernels::TERNARY)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<bf16>(el) }?;
-                let params = (el, dims.len(), &ds, ids, t, f, &out);
-                // SAFETY: ffi
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::BF16(out)
-            }
-            (CudaStorageSlice::F16(t), CudaStorageSlice::F16(f)) => {
-                let t = &t.slice(layout_t.start_offset()..);
-                let f = &f.slice(layout_f.start_offset()..);
-                let func = dev.get_or_load_func("where_f16", kernels::TERNARY)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f16>(el) }?;
-                let params = (el, dims.len(), &ds, ids, t, f, &out);
-                // SAFETY: ffi
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F16(out)
-            }
-            (CudaStorageSlice::F32(t), CudaStorageSlice::F32(f)) => {
-                let t = &t.slice(layout_t.start_offset()..);
-                let f = &f.slice(layout_f.start_offset()..);
-                let func = dev.get_or_load_func("where_f32", kernels::TERNARY)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f32>(el) }?;
-                let params = (el, dims.len(), &ds, ids, t, f, &out);
-                // SAFETY: ffi
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F32(out)
-            }
-            (CudaStorageSlice::F64(t), CudaStorageSlice::F64(f)) => {
-                let t = &t.slice(layout_t.start_offset()..);
-                let f = &f.slice(layout_f.start_offset()..);
-                // SAFETY: Set later by running the kernel.
-                let func = dev.get_or_load_func("where_f64", kernels::TERNARY)?;
-                let out = unsafe { dev.alloc::<f64>(el) }?;
-                let params = (el, dims.len(), &ds, ids, t, f, &out);
-                // SAFETY: ffi
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F64(out)
-            }
-            (CudaStorageSlice::U32(t), CudaStorageSlice::U32(f)) => {
-                let t = &t.slice(layout_t.start_offset()..);
-                let f = &f.slice(layout_f.start_offset()..);
-                // SAFETY: Set later by running the kernel.
-                let func = dev.get_or_load_func("where_u32", kernels::TERNARY)?;
-                let out = unsafe { dev.alloc::<u32>(el) }?;
-                let params = (el, dims.len(), &ds, ids, t, f, &out);
-                // SAFETY: ffi
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::U32(out)
-            }
-            // The dtypes should have been checked at this point so this is an internal error.
-            _ => Err(CudaError::InternalError("dtype mismatch in binary op"))?,
-        };
-        let device = dev.clone();
+        let device = self.device().clone();
+        let slice = WhereCond(self, layout).map(&t.slice, t_l, &f.slice, f_l, &device)?;
         Ok(Self { slice, device })
     }
 
     pub(crate) fn embedding(&self, layout: &Layout, rhs: &Self, rhs_l: &Layout) -> Result<Self> {
-        let ids = match &self.slice {
-            CudaStorageSlice::U32(slice) => slice.slice(layout.start_offset()..),
-            _ => Err(CudaError::UnexpectedDType {
-                msg: "embedding ids should be u32",
-                expected: DType::U32,
-                got: self.dtype(),
-            })?,
-        };
-        let ids = &ids;
-        let shape = layout.shape();
-        let (v_size, h_size) = rhs_l
-            .shape()
-            .r2()
-            .map_err(|e| CudaError::WrappedError(Box::new(e)))?;
-        let dims = shape.dims();
-        let el = shape.elem_count();
-        let cfg = LaunchConfig::for_num_elems(el as u32);
-        let dev = self.device();
-        let ds = dev.htod_copy([dims, layout.stride()].concat())?;
-        let slice = match &rhs.slice {
-            // The kernels below assume that rhs is contiguous.
-            CudaStorageSlice::U32(arg) => {
-                let arg = &arg.slice(rhs_l.start_offset()..);
-                let func = dev.get_or_load_func("emb_u32", kernels::EMBEDDINGS)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<u32>(el * h_size) }?;
-                let params = (el, dims.len(), &ds, ids, arg, &out, h_size, v_size);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::U32(out)
-            }
-            CudaStorageSlice::BF16(arg) => {
-                let arg = &arg.slice(rhs_l.start_offset()..);
-                let func = dev.get_or_load_func("emb_bf16", kernels::EMBEDDINGS)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<bf16>(el * h_size) }?;
-                let params = (el, dims.len(), &ds, ids, arg, &out, h_size, v_size);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::BF16(out)
-            }
-            CudaStorageSlice::F16(arg) => {
-                let arg = &arg.slice(rhs_l.start_offset()..);
-                let func = dev.get_or_load_func("emb_f16", kernels::EMBEDDINGS)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f16>(el * h_size) }?;
-                let params = (el, dims.len(), &ds, ids, arg, &out, h_size, v_size);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F16(out)
-            }
-            CudaStorageSlice::F32(arg) => {
-                let arg = &arg.slice(rhs_l.start_offset()..);
-                let func = dev.get_or_load_func("emb_f32", kernels::EMBEDDINGS)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f32>(el * h_size) }?;
-                let params = (el, dims.len(), &ds, ids, arg, &out, h_size, v_size);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F32(out)
-            }
-            CudaStorageSlice::F64(arg) => {
-                let arg = &arg.slice(rhs_l.start_offset()..);
-                let func = dev.get_or_load_func("emb_f64", kernels::EMBEDDINGS)?;
-                // SAFETY: Set later by running the kernel.
-                let out = unsafe { dev.alloc::<f64>(el * h_size) }?;
-                let params = (el, dims.len(), &ds, ids, arg, &out, h_size, v_size);
-                // SAFETY: ffi.
-                unsafe { func.launch(cfg, params) }?;
-                CudaStorageSlice::F64(out)
-            }
-        };
-        let device = dev.clone();
+        let device = self.device().clone();
+        let slice = Embedding(self, layout).map(&rhs.slice, &device, rhs_l)?;
         Ok(Self { slice, device })
     }
 
diff --git a/candle-core/src/dummy_cuda_backend.rs b/candle-core/src/dummy_cuda_backend.rs
index 8193b1af..b025eeab 100644
--- a/candle-core/src/dummy_cuda_backend.rs
+++ b/candle-core/src/dummy_cuda_backend.rs
@@ -44,7 +44,7 @@ impl CudaDevice {
 pub struct CudaStorage;
 
 impl CudaStorage {
-    pub fn try_clone(&self) -> Result<Self> {
+    pub fn try_clone(&self, _: &Layout) -> Result<Self> {
         Err(Error::NotCompiledWithCudaSupport)
     }
 
diff --git a/candle-core/src/op.rs b/candle-core/src/op.rs
index 7b0e18fe..db6ef87f 100644
--- a/candle-core/src/op.rs
+++ b/candle-core/src/op.rs
@@ -43,11 +43,8 @@ pub(crate) enum Op {
 
 pub(crate) trait UnaryOp {
     const NAME: &'static str;
-    const KERNEL_BF16: &'static str;
-    const KERNEL_F16: &'static str;
-    const KERNEL_F32: &'static str;
-    const KERNEL_F64: &'static str;
-    const KERNEL_U32: &'static str;
+    const KERNEL: &'static str;
+    const V: Self;
     fn bf16(v1: bf16) -> bf16;
     fn f16(v1: f16) -> f16;
     fn f32(v1: f32) -> f32;
@@ -57,11 +54,8 @@ pub(crate) trait UnaryOp {
 
 pub(crate) trait BinaryOp {
     const NAME: &'static str;
-    const KERNEL_BF16: &'static str;
-    const KERNEL_F16: &'static str;
-    const KERNEL_F32: &'static str;
-    const KERNEL_F64: &'static str;
-    const KERNEL_U32: &'static str;
+    const KERNEL: &'static str;
+    const V: Self;
     fn bf16(v1: bf16, v2: bf16) -> bf16;
     fn f16(v1: f16, v2: f16) -> f16;
     fn f32(v1: f32, v2: f32) -> f32;
@@ -88,11 +82,8 @@ macro_rules! bin_op {
     ($op:ident, $name: literal, $e: expr) => {
         impl BinaryOp for $op {
             const NAME: &'static str = $name;
-            const KERNEL_BF16: &'static str = concat!("b", $name, "_bf16");
-            const KERNEL_F16: &'static str = concat!("b", $name, "_f16");
-            const KERNEL_F32: &'static str = concat!("b", $name, "_f32");
-            const KERNEL_F64: &'static str = concat!("b", $name, "_f64");
-            const KERNEL_U32: &'static str = concat!("b", $name, "_u32");
+            const KERNEL: &'static str = concat!("b", $name);
+            const V: Self = $op;
             fn bf16(v1: bf16, v2: bf16) -> bf16 {
                 $e(v1, v2)
             }
@@ -121,11 +112,8 @@ macro_rules! unary_op {
     ($op: ident, $name: literal, $a: ident, $e: expr) => {
         impl UnaryOp for $op {
             const NAME: &'static str = $name;
-            const KERNEL_BF16: &'static str = concat!("u", $name, "_bf16");
-            const KERNEL_F16: &'static str = concat!("u", $name, "_f16");
-            const KERNEL_F32: &'static str = concat!("u", $name, "_f32");
-            const KERNEL_F64: &'static str = concat!("u", $name, "_f64");
-            const KERNEL_U32: &'static str = concat!("u", $name, "_u32");
+            const KERNEL: &'static str = concat!("u", $name);
+            const V: Self = $op;
             fn bf16($a: bf16) -> bf16 {
                 $e
             }
@@ -158,6 +146,7 @@ unary_op!(Sqrt, "sqrt", v, v.sqrt());
 /// <https://en.wikipedia.org/wiki/Activation_function#Comparison_of_activation_functions>
 impl UnaryOp for Gelu {
     const NAME: &'static str = "gelu";
+    const V: Self = Gelu;
     fn bf16(v: bf16) -> bf16 {
         bf16::from_f32_const(0.5)
             * v
@@ -191,20 +180,13 @@ impl UnaryOp for Gelu {
     fn u32(_: u32) -> u32 {
         0
     }
-    const KERNEL_BF16: &'static str = "ugelu_bf16";
-    const KERNEL_F16: &'static str = "ugelu_f16";
-    const KERNEL_F32: &'static str = "ugelu_f32";
-    const KERNEL_F64: &'static str = "ugelu_f64";
-    const KERNEL_U32: &'static str = "ugelu_u32";
+    const KERNEL: &'static str = "ugelu";
 }
 
 impl UnaryOp for Relu {
     const NAME: &'static str = "relu";
-    const KERNEL_BF16: &'static str = "urelu_bf16";
-    const KERNEL_F16: &'static str = "urelu_f16";
-    const KERNEL_F32: &'static str = "urelu_f32";
-    const KERNEL_F64: &'static str = "urelu_f64";
-    const KERNEL_U32: &'static str = "urelu_u32";
+    const KERNEL: &'static str = "urelu";
+    const V: Self = Relu;
     fn bf16(v: bf16) -> bf16 {
         v.max(bf16::ZERO)
     }
diff --git a/candle-core/src/storage.rs b/candle-core/src/storage.rs
index 7acf6dd0..4e630a58 100644
--- a/candle-core/src/storage.rs
+++ b/candle-core/src/storage.rs
@@ -9,11 +9,11 @@ pub enum Storage {
 }
 
 impl Storage {
-    pub fn try_clone(&self) -> Result<Self> {
+    pub fn try_clone(&self, layout: &Layout) -> Result<Self> {
         match self {
             Self::Cpu(storage) => Ok(Self::Cpu(storage.clone())),
             Self::Cuda(storage) => {
-                let storage = storage.try_clone()?;
+                let storage = storage.try_clone(layout)?;
                 Ok(Self::Cuda(storage))
             }
         }
diff --git a/candle-core/src/tensor.rs b/candle-core/src/tensor.rs
index f64bd6f2..4b9b3306 100644
--- a/candle-core/src/tensor.rs
+++ b/candle-core/src/tensor.rs
@@ -709,7 +709,7 @@ impl Tensor {
     pub fn copy(&self) -> Result<Tensor> {
         let tensor_ = Tensor_ {
             id: TensorId::new(),
-            storage: Arc::new(self.storage.try_clone()?),
+            storage: Arc::new(self.storage.try_clone(self.layout())?),
             layout: self.layout.clone(),
             op: None, // TODO
             is_variable: false,