diff --git a/src/crypto/internal/fips140/sha512/sha512.go b/src/crypto/internal/fips140/sha512/sha512.go
index 3e7a5e11f15198..79bd61a4e39ab6 100644
--- a/src/crypto/internal/fips140/sha512/sha512.go
+++ b/src/crypto/internal/fips140/sha512/sha512.go
@@ -31,6 +31,11 @@ const (
 	blockSize = 128
 )
 
+// The maximum number of bytes that can be passed to block(). The limit exists
+// because implementations that rely on assembly routines are not preemptible.
+const maxAsmIters = 512
+const maxAsmSize = blockSize * maxAsmIters // 64KiB
+
 const (
 	chunk     = 128
 	init0     = 0x6a09e667f3bcc908
@@ -248,6 +253,11 @@ func (d *Digest) Write(p []byte) (nn int, err error) {
 	}
 	if len(p) >= chunk {
 		n := len(p) &^ (chunk - 1)
+		for n > maxAsmSize {
+			block(d, p[:maxAsmSize])
+			p = p[maxAsmSize:]
+			n -= maxAsmSize
+		}
 		block(d, p[:n])
 		p = p[n:]
 	}
diff --git a/src/crypto/sha1/sha1.go b/src/crypto/sha1/sha1.go
index 46e47df1d32cf2..4e117201485bf3 100644
--- a/src/crypto/sha1/sha1.go
+++ b/src/crypto/sha1/sha1.go
@@ -27,6 +27,11 @@ const Size = 20
 // The blocksize of SHA-1 in bytes.
 const BlockSize = 64
 
+// The maximum number of bytes that can be passed to block(). The limit exists
+// because implementations that rely on assembly routines are not preemptible.
+const maxAsmIters = 1024
+const maxAsmSize = BlockSize * maxAsmIters // 64KiB
+
 const (
 	chunk = 64
 	init0 = 0x67452301
@@ -143,6 +148,11 @@ func (d *digest) Write(p []byte) (nn int, err error) {
 	}
 	if len(p) >= chunk {
 		n := len(p) &^ (chunk - 1)
+		for n > maxAsmSize {
+			block(d, p[:maxAsmSize])
+			p = p[maxAsmSize:]
+			n -= maxAsmSize
+		}
 		block(d, p[:n])
 		p = p[n:]
 	}
diff --git a/src/crypto/sha1/sha1_test.go b/src/crypto/sha1/sha1_test.go
index 8b4618df556271..7ab7fba078e9de 100644
--- a/src/crypto/sha1/sha1_test.go
+++ b/src/crypto/sha1/sha1_test.go
@@ -14,7 +14,9 @@ import (
 	"fmt"
 	"hash"
 	"io"
+	"runtime"
 	"testing"
+	"time"
 )
 
 type sha1Test struct {
@@ -267,16 +269,16 @@ func TestOutOfBoundsRead(t *testing.T) {
 }
 
 var bench = New()
-var buf = make([]byte, 8192)
 
 func benchmarkSize(b *testing.B, size int) {
+	buf := make([]byte, size)
 	sum := make([]byte, bench.Size())
 	b.Run("New", func(b *testing.B) {
 		b.ReportAllocs()
 		b.SetBytes(int64(size))
 		for i := 0; i < b.N; i++ {
 			bench.Reset()
-			bench.Write(buf[:size])
+			bench.Write(buf)
 			bench.Sum(sum[:0])
 		}
 	})
@@ -284,7 +286,7 @@ func benchmarkSize(b *testing.B, size int) {
 		b.ReportAllocs()
 		b.SetBytes(int64(size))
 		for i := 0; i < b.N; i++ {
-			Sum(buf[:size])
+			Sum(buf)
 		}
 	})
 }
@@ -304,3 +306,40 @@ func BenchmarkHash1K(b *testing.B) {
 func BenchmarkHash8K(b *testing.B) {
 	benchmarkSize(b, 8192)
 }
+
+func BenchmarkHash256K(b *testing.B) {
+	benchmarkSize(b, 256*1024)
+}
+
+func BenchmarkHash1M(b *testing.B) {
+	benchmarkSize(b, 1024*1024)
+}
+
+var sinkSTW []byte
+
+// BenchmarkSTW reports how long a garbage collection had to wait while a hash
+// ran alongside it, as gcwait-ns/op. Assembly is not preemptible, so a call
+// that covers the whole input blocks every goroutine in the process for as
+// long as it runs; bounding the call gives the collector a way in between
+// chunks. Run with GOMAXPROCS>=2 so the two actually overlap.
+func BenchmarkSTW(b *testing.B) {
+	buf := make([]byte, 64<<20)
+	var total time.Duration
+	var iters int
+	b.SetBytes(int64(len(buf)))
+	for b.Loop() {
+		done := make(chan struct{})
+		go func() {
+			defer close(done)
+			h := New()
+			h.Write(buf)
+			sinkSTW = h.Sum(nil)
+		}()
+		start := time.Now()
+		runtime.GC() // one per iteration, so the mean is well defined
+		total += time.Since(start)
+		iters++
+		<-done
+	}
+	b.ReportMetric(float64(total.Nanoseconds())/float64(iters), "gcwait-ns/op")
+}
diff --git a/src/crypto/sha512/sha512_test.go b/src/crypto/sha512/sha512_test.go
index 080bf694f03652..a222a5f3ce4d43 100644
--- a/src/crypto/sha512/sha512_test.go
+++ b/src/crypto/sha512/sha512_test.go
@@ -14,7 +14,9 @@ import (
 	"fmt"
 	"hash"
 	"io"
+	"runtime"
 	"testing"
+	"time"
 )
 
 type sha512Test struct {
@@ -998,16 +1000,16 @@ func maybeCloner(h hash.Hash) any {
 }
 
 var bench = New()
-var buf = make([]byte, 8192)
 
 func benchmarkSize(b *testing.B, size int) {
+	buf := make([]byte, size)
 	sum := make([]byte, bench.Size())
 	b.Run("New", func(b *testing.B) {
 		b.ReportAllocs()
 		b.SetBytes(int64(size))
 		for i := 0; i < b.N; i++ {
 			bench.Reset()
-			bench.Write(buf[:size])
+			bench.Write(buf)
 			bench.Sum(sum[:0])
 		}
 	})
@@ -1015,14 +1017,14 @@ func benchmarkSize(b *testing.B, size int) {
 		b.ReportAllocs()
 		b.SetBytes(int64(size))
 		for i := 0; i < b.N; i++ {
-			Sum384(buf[:size])
+			Sum384(buf)
 		}
 	})
 	b.Run("Sum512", func(b *testing.B) {
 		b.ReportAllocs()
 		b.SetBytes(int64(size))
 		for i := 0; i < b.N; i++ {
-			Sum512(buf[:size])
+			Sum512(buf)
 		}
 	})
 }
@@ -1038,3 +1040,40 @@ func BenchmarkHash1K(b *testing.B) {
 func BenchmarkHash8K(b *testing.B) {
 	benchmarkSize(b, 8192)
 }
+
+func BenchmarkHash256K(b *testing.B) {
+	benchmarkSize(b, 256*1024)
+}
+
+func BenchmarkHash1M(b *testing.B) {
+	benchmarkSize(b, 1024*1024)
+}
+
+var sinkSTW []byte
+
+// BenchmarkSTW reports how long a garbage collection had to wait while a hash
+// ran alongside it, as gcwait-ns/op. Assembly is not preemptible, so a call
+// that covers the whole input blocks every goroutine in the process for as
+// long as it runs; bounding the call gives the collector a way in between
+// chunks. Run with GOMAXPROCS>=2 so the two actually overlap.
+func BenchmarkSTW(b *testing.B) {
+	buf := make([]byte, 64<<20)
+	var total time.Duration
+	var iters int
+	b.SetBytes(int64(len(buf)))
+	for b.Loop() {
+		done := make(chan struct{})
+		go func() {
+			defer close(done)
+			h := New()
+			h.Write(buf)
+			sinkSTW = h.Sum(nil)
+		}()
+		start := time.Now()
+		runtime.GC() // one per iteration, so the mean is well defined
+		total += time.Since(start)
+		iters++
+		<-done
+	}
+	b.ReportMetric(float64(total.Nanoseconds())/float64(iters), "gcwait-ns/op")
+}